\r\n\t \r\n\tRecently in 2019, International Council on Systems Engineering (INCOSE) has released the latest version of the “Guidelines for the Utilization of ISO/IEC/IEEE 15288 in the Context of System of Systems (SoS) Engineering” to industry for review and comments. The document was developed under the Partner Standards Development Organization cooperation agreement between ISO and IEEE, as it was approved by Council Resolution 49/2007. This document provides guidance for the utilization of ISO/IEC/IEEE 15288 in the context of SoS in many domains, including healthcare, transportation, energy, defense, corporations, cities, and governments. This document treats an SoS as a system whose elements are managerially and/or operationally independent systems, and which together usually produce results that cannot be achieved by the individual systems alone. This INCOSE guide book perceives that SoS engineering demands a balance between linear procedural procedures for systematic activity and holistic nonlinear procedures due to additional complexity from SoS perspectives. \r\n\tThe objective of this book is to provide a comprehensive reference on Systems-of-Systems Engineering, Modeling, Simulation and Analysis (MS&A) for engineers and researchers in both system engineering and advanced mathematical modeling fields. \r\n\tThe book is organized in two parts, namely Part I and Part II. Part I presents an overview of SOS, SOS Engineering, SOS Enterprise Architecture (SOSEA) and SOS Enterprise (SOSE) Concept of Operations (CONOPS). Part II discusses SOSE MS&A approaches for assessing SOS Enterprise CONOPS (SOSE-CONOPS) and characterizing SOSE performance behavior. Part II focuses on advanced mathematical application concepts to address future complex space SOS challenges that require interdisciplinary research involving game theory, probability and statistics, non-linear programming and mathematical modeling components.
\r\n
\r\n\tPart I should include topics related to the following areas: \r\n\t- SOS and SOS Engineering Introduction \r\n\t- Taxonomy of SOS \r\n\t- SOS Enterprise (SOSE), SOSE CONOPS, Architecture Frameworks and Decision Support Tools
\r\n
\r\n\tPart II should address the following research areas: \r\n\t- SOS Modeling, Simulation & Analysis (SOS M&SA) Methods \r\n\t- SOS Enterprise Architecture Design Frameworks and Decision Support Tools \r\n\t- SOS Enterprise CONOPS Assessment Frameworks and Decision Support Tools.
",isbn:null,printIsbn:null,pdfIsbn:null,doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!0,hash:"677fbbd5fc2550e8be540f40c0969a62",bookSignature:"Dr. Tien Manh Nguyen",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/7772.jpg",keywords:"Autonomy of Constituents, Operational Independence, Taxonomy, Acquisition Classification, SOS Enterprise Architecture Design, Decision Support Tools, State Modeling, SOS Simulation Methods, DOD Architecture Framework, Enterprise System Engineering, SOS Enterprise CONOPS, Satellite Operations (SATOPS)",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:0,numberOfDimensionsCitations:0,numberOfTotalCitations:0,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"October 31st 2019",dateEndSecondStepPublish:"November 21st 2019",dateEndThirdStepPublish:"January 20th 2020",dateEndFourthStepPublish:"April 9th 2020",dateEndFifthStepPublish:"June 8th 2020",remainingDaysToSecondStep:"21 days",secondStepPassed:!0,currentStepOfPublishingProcess:3,editedByType:null,kuFlag:!1,editors:[{id:"210657",title:"Dr.",name:"Tien",middleName:"Manh",surname:"Nguyen",slug:"tien-nguyen",fullName:"Tien Nguyen",profilePictureURL:"https://mts.intechopen.com/storage/users/210657/images/system/210657.jpg",biography:"Dr. Tien M. Nguyen received his M.A. in Mathematics, and his Ph.D. in Applied Mathematics from the Claremont Graduate University; M.S.E.E. in Communication Systems Theory from University of California San Diego; and B.S.E. in Electronics and M.S.E. in Electromagnetic Field Theory from California State University Fullerton (CSUF). He also completed all course requirements and passed the comprehensive exam for his M.S.E.E. in Digital Signal Processing from California State University Long Beach. Dr. Nguyen is an expert in Satellite Operations (SATOPS), Satellite Communications (SATCOMs), advanced mathematical modeling for complex systems-of-systems, sensing and communication networks.\nCurrently, he serves as Adjunct Research Professor at CSUF, Mathematics Dept. Concurrently, he is also with the Aerospace Corporation, serving as a Sr. P.E. in Space System Group Program Office, Space System Architect Division, Global Partnerships Subdivision. He has more than 13-years of service at Aerospace, and prior to his current position; he has served as Sr. Engineering Specialist, Sr. Project Lead, Section Manager, Associate Director, Interim Director, and Principal Technical Staff (the highest technical level at the corporation). At Aerospace, he invented HPA linearizer, GMSK synchronizers and developed advanced optimization techniques using game theory for achieving affordable and low-risk acquisition strategy. Prior to CSUF, he had also held a Research Assistant Professor at the Catholic University of America in concurrent with The Aerospace Corporation positions. \nHe was a Engineering Fellow from Raytheon, where he had 10-year of services at Raytheon, serving as Program Area Chief Engineer, Program Chief Engineer, PI, Technical Director, Program Manager, Lead Architect and Lead System Engineer for many advanced programs and pursuits related to sensing and communication networks. At Raytheon, he invented radar-communication technology and gun barrel detector using millimeter-wave. Previous to Raytheon and Aerospace Corporation, Dr. Nguyen was with NASA/JPL for more than 11-years, where he served as the NASA delegate to the international Consultative Committee for Space Data System (CCSDS). Many of his works on RF and Modulation were adopted as the CCSDS standards for USB waveforms and space RF systems. At JPL he invented QPSK phase ambiguity resolver and developed innovative optimization technique for simultaneous range-command-telemetry operation. He built the first laser lab and automated manufacturing lab when he was with ITT Technical Services in the early ’80s. \nHe has published more than 250 technical reports and papers. His work has appeared in NASA TechBrief, textbook, Open Access Book, SIAM Publication, CCSDS Blue Book, and Wiley & Sons Encyclopedia of Electrical and Electronics Engineering. He was selected as a Vietnamese-American Role Model by KCSI-TV, Channel 18 in 2002, and Recognition Honoree at 50-Year Celebration of CSUF in 2007. He received numerous Raytheon, Aerospace and NASA awards, and Air Force commendations. He holds 16 patents. 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\n\t\t\t
1. Introduction
\n\t\t\t
This Chapter addresses the wheeled autonomous mobile robots navigation problem starting from very simple solutions which are used to solve more complex tasks. This way, it is considered a hybrid (discrete-time/continuous-time) approach, composed by several individual continuous controllers, each of them solving a particular navigation problem, but when are considered as a whole constitute a new approach for more demanding navigation challenges. The discrete part of this system is compound by a high order supervisor, which gives the logic switching. In particular, this Chapter deals with Switching Systems, which are hybrid system characterized by the fact that only a unique controller could be active at any time. This kind of control architecture presents some benefits as for example the modularity and the possibility to analyze the whole system behavior, allowing the designer to conclude stability. It also allows, conversely, decomposing a given task in simpler subtasks which could be treated separately in order to facilitate the design process.
\n\t\t\t
The interest on asymptotic stability is due to our interest on the control system analysis. For this reason, several well-known concepts such as Lyapunov stability and common Lyapunov functions (Liberzon, 2003) will be treated along this Chapter, in order to prove stability for the individual controllers as well as for the switching controller. So, it will be shown under a control point of view the design and analysis of stable switching controllers and two applications examples to wheeled robots navigation: firstly, developing a switching controller for reactive obstacle avoidance (Toibero et al., 2009); and secondly, its applications at the local navigation level in a simultaneous localization and map building (SLAM) task (Auat Cheeín, 2009).
\n\t\t\t
Robotic autonomy is directly related to the capability the robots have to perform given task without continuous human guidance. Arkin (1998) proposed a way to deal with this autonomy, by decomposing a task into individual behaviors such as e.g. move-to-goal, find-next-point, return-to-start, wander and halt. Next, these behaviors may be selected or fused according to a desired performance. Within the several available behaviours, the interest is on a key feature for robot autonomy: obstacle detection, identification and avoidance.
\n\t\t\t
In this context, there are two main approaches: path planning controllers or reactive controllers. In path planning controllers, the obstacle is to be detected and avoided by defining a new secure path. Instead of that, reactive controllers only react in response to the sensory inputs without major computational effort. In the following, a wall-following (WF) controller already designed is considered as the basis of our obstacle avoider controller. A WF task is characterized by maintaining a constant distance from the robot to a wall (or to an object) and can be properly combined with other tasks in order to obtain higher degrees of autonomy for the mobile platform, e.g. the skill Go-to-goal avoiding obstacles in (Boada et al., 2003). Typically a WF controller has to recognize the distance and orientation errors between the robot and the wall. These two control states can be measured or estimated using sonar, laser rangefinder or information extracted from a video camera. Besides, WF controllers can be easily adapted for navigation along corridors by setting a desired distance relative to the centre of the corridor. Regarding the environment surrounding the robot, a WF controller becomes useful for reactive navigation in unknown environments. In this context, it can be used as an obstacle avoider by considering the obstacle as part of a wall to be followed. Therefore, it is relevant to design controllers for walls with several kinds of contours. The inclusion of such situations leads to a new control problem: to deal with discontinuities on the wall contour. To solve this problem most of the papers in the literature use fuzzy-logic: (Braunstingl & Ezkerra, 1995), (Wang & Liu, 2004), (Ando, 1996), or switching controllers: (Fazli & Kleeman, 2005), (Borenstein & Koren, 1989), (Zhang et al., 2004). The WF problem, as an important component of current robotic research, has been widely considered. In the early work in (van Turennout & Hounderd, 1992) a WF controller was used to avoid obstacles and to follow unknown walls. Then (Ando, 1996) proposes a way to extend the capabilities of this behavior but as a path planning problem, without describing the controller. In (Braunstingl & Ezkerra, 1995) the contour following problem is treated by using a fuzzy logic controller. More recently (Bicho, 2000) has used neural networks in order to estimate the relative orientation of the robot and the wall. In (Zhang et al., 2004) a complete switching controller that allows the robot to track sharp discontinuous trajectories is presented. This last switching approach includes a stability demonstration at the switching times but the controllers need a path to be tracked and the paper does not consider obstacle avoidance while tracking the trajectory. Here, the WF problem is addressed by using a laser rangefinder and odometry in fully unknown environments. Initially, it will be assumed that the wall’s contour is smoothly varying and it is proposed an expression relating the contour variations with the saturation of control actions which is useful to design a saturation-free controller. This first part includes the simpler case of straight walls. Then, the contour-following (CF) problem is treated as an extended approach of the WF problem when considering discontinuities such as corners. For this CF controller three individual subsystems were considered, one characterizing each behavior: re-orientation, wall-following and circle-performer. The stability at the switching times is considered and discussed.
\n\t\t\t
In addition to the use of WF in move-to-goal and obstacle avoidance behaviors considered by several authors, other complementary applications of a CF controller are the mapping of interior environments (Auat Cheein, 2009), (Edlinger & von Puttkamer, 1994), (Fazli & Kleeman, 2005) in surveillance tasks and within teleoperation contexts (Wang & Liu, 2004) using a similar behavior for telecommanding a mobile robot.
\n\t\t\t
The remaining of this Chapter is organized as follows. Section 2 presents the mobile robot kinematcis. Section 3 proposes a WF controller to maintain this desired distance for straight and smooth varying walls based on laser and odometric information only. Next, in Section 4 some limitations of this approach are shown; and a switching scheme that allows the fully contour-following of the object is presented, including several experimental results in Section 5. As a final example application, in Section 6 it is shown the incorporation of this controller to a SLAM task showing also additional experimental results.
\n\t\t
\n\t\t
\n\t\t\t
2. Mobile Robot
\n\t\t\t
The unicycle-type wheeled mobile robot is to be considered in this Chapter. Let us set the specific notation, with reference to Figure 1, the global or task coordinate system is denoted by [W] and the coordinate system attached to the robot by [R]. The robot states variables are x, y and; where denotes the heading of the vehicle relative to the WX-axis of the world coordinate system. Vector \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t[\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\ty\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tθ\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t]\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tT\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tdefines the posture of the vehicle. The kinematics of the robot can be modeled by the well known kinematics model.
The robot is equipped with a laser radar sensor. As it can be seen in Figure 1, some lateral beams are used to estimate the object contour angle, whereas all beams are used to define a safety-zone, which purpose is to detect possible collisions between the robot and the object. The selection of the side of the object to follow is based on the initial conditions. Firstly the robot computes the object orientation and the distance to the object for its right side and also for its left side, then, the robot will take the nearest side to follow and will keep following this side. Each beam is identified by its angle, e.g. for the beam at 0º, the notation d000 is used to denote the distance measured by this beam. From here on, to simplify the notation, it will be assumed that the robot follows only the wall at the right side of the robot.
\n\t\t
\n\t\t
Figure 1.
Laser radar
\n\t\t
\n\t\t\t
3. Standard Wall-Following Control
\n\t\t\t
A WF controller will be referred as standard in this Chapter, when do not allow to follow discontinuous walls. It could be said that allows the robot to follow continuous (straight) and smooth varying contours. This appreciation is based on its stability proof. Two control states must be defined: the robot-to-wall angle in Section3.1; and the robot-to-wall distance in Section3.2.
\n\t\t
\n\t\t
\n\t\t\t
3.1 Wall Angle Computation
\n\t\t\t
The wall angle estimation is performed by using only two beams: one perpendicular to the heading of the robot, and the other may be selected depending on the desired robot-wall distance. In order to obtain a more reliable value, it is considered a group of beams at each side of the robot, thus resulting ten different angle values. Each value is obtained according to
These values are then fused together using a decentralized Kalman filter (Brawn & Hwang, 1997) which returns an improved estimation for the wall angle \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tθ\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\ta\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t with respect to the world coordinate system. In Toibero et al. (2009) details and derivations of this filter can be found.
\n\t\t
\n\t\t
Figure 2.
Wall angle computation. Resulting in the value \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tθ\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\t\ta\n\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t010\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tof the wall-angle related to robot posture \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\ty\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tand\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tθ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t in the world coordinate system for the beam at 10º
\n\t\t
\n\t\t\t
3.2 Robot-wall distance computation
\n\t\t\t
The wall-distance computation to a wall at the right side of the robot is obtained by
where \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tθ\n\t\t\t\t\t\t\t\t\t̃\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t is the difference between the heading angle of the robot and the wall angle. This angle is properly defined in the next paragraphs. It can be obtained a similar expression for the distance to a wall at the left side of the robot by replacing \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t000\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\twith\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t180\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t. Note that according with (3) it is assumed that the distance from the robot to the wall is considered for null orientation error.
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3.2.1 Controller description and analysis
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This controller renders a control law for wall-following based on the laser sensorial information and the odometry of the robot. The reference for this controller is the desired distance from the robot to the wall\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\t\ts\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t. As can be seen in Figure 3, the control errors are defined (Toibero et al., 2006b), as follows
Equation (4.a) states the distance error between the actual distance to the wall and the desired distance to the wall \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\t\ts\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t while equation (4.b) states the orientation error between the estimated wall angle and the heading angle of the robot in the world coordinate system [W].
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Figure 3.
Wall-following controller scheme. Distance error calculation. Note that the value for the distance error could be negative.
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The time variations of the control errors are given by
where, \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tθ\n\t\t\t\t\t\t\t\t\t\t\t˙\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\t\ta\n\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tis the derivative of the reference for the wall orientation. This derivative is null for a straight wall. Now, taking into consideration the control system analysis, the following - globally positive definite and radially unbounded - Lyapunov candidate function is proposed
where \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\t\t̃\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t̃\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t was selected as in (Kelly & Carelli, 1996) and \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tξ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tis a dumb variable:
where \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tν\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tmax\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is the desired linear velocity; \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tK\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tθ\n\t\t\t\t\t\t\t\t\t\t\t\t̃\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t≥\n\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tis a positive definite design constant, and \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tθ\n\t\t\t\t\t\t\t\t\t\t\t\t̃\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is a design constant that indicates the slope of the tanh function which can be adjusted with \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tK\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tθ\n\t\t\t\t\t\t\t\t\t\t\t\t̃\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t in order to bound the control action to its saturation values. By substituting (9) in (8) the derivative of the Lyapunov candidate function becomes
Equation (10) states that the control system is Lyapunov stable but not asymptotically stable. To prove the asymptotic stability the autonomous nature of the closed-loop system is considered. The closed-loop equations can be obtained by replacing the control actions in (5)
By applying the Krasovskii-LaSalle theorem (Vidyasagar, 1993) in the \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tΩ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tregion, with
the only invariant is\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t̃\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t. Therefore, by invoking LaSalle theorem, it can be concluded that the origin of the state space is globally uniformly asymptotically stable.
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3.2.2 Experimental results
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This controller was proved in a real office environment with a Pioneer3-DX mobile robot. The robot length is about 330millimeters. The values of the design parameters were set to:\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t0.025\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tK\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tθ\n\t\t\t\t\t\t\t\t\t\t\t\t̃\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t11.5\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tθ\n\t\t\t\t\t\t\t\t\t\t\t\t̃\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t0.3\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tand \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\t\ts\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t500\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tmillimeters. In order to show the performance of the proposed controller, three different experiments were carried out:
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The robot follows a straight wall.
The robot follows a wall with smoothly varying contour.
The robot follows an almost-circular contour.
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Figure 4.
a) Trajectory described by the robot following a wall with straight contour. The contour of the wall was reconstructed by using laser information. b) Distance between the robot and the straight wall. The linear velocity for this experiment was set to 200millimetres per second.
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Figure 5.
a) Trajectory described by the robot following a wall of variable contour. As can be seen, the wall presents variations on its contour and on its texture. b) Robot wall distance in the variable contour experiment. The error is less than 25millimetres – a small value when compared to the size of the robot.
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From Figures 4 to 6, a good performance of the proposed controller can be concluded. For all the experimental situations the errors are not significant. But it can be noted the impossibility of the controller to follow discontinuous walls‘ contours. These results inspire the development of the Contour-following controller of the next Section.
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Figure 6.
a) Robot following an almost-circular contour. The linear velocity for this experiment was set to 200millimetres per second. b) Robot wall distance in the circular path experiment. The error is less than 25millimetres.
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4. Contour-Following Controller
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A stable switching between several controllers is a proper way to improve performance or to achieve control objectives that are difficult or impossible to consider under continuous nonlinear control. The proposed switching controller is designed to follow the contour of objects which have at least a size comparable with that of the robot (Toibero et al., 2006a). The basic idea is to use the wall-following controller described in Section 2. The controller is designed within the context of stability theory for switching systems. The WF controller acting alone shows a good performance when following a wall, but there are two cases which it cannot deal with:
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Abrupt variations in the contour of the object which makes it difficult to estimate the actual object’s angle. In this case (Figure 7.a) the distance measured by the laser beams varies suddenly.
Abrupt variations in the contour due to an interior corner that causes the robot to crash against the object (Figure 7.b).
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Figure 7.
Main problems when following contours: a) the presence of an open corner and b) the presence of an interior corner.
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The first step is given by the proper detection of these situations, and fortunatelly, both can be detected by using the laser radar. For example, the first case can be detected by computing the variance of the length of the lateral beams (note that these lateral beams estimates the wall angle). So, this variance would have a value close to zero when the robot is following a wall, but it will become larger when this contour is lost. Therefore, a threshold value can be defined in order to generate a loss of wall event. On the other hand, for the second case, collisions can be detected as an invasion of the robot safety-zone. If the length of any beam lies within this predefined safety-zone, then a possible collision event is generated.
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At this point, we aggregate two new individual subsystems, one to deal with each situation, thus building a switching system.
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4.1-. Handling the case of missing the wall to follow
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In this case, the robot has lost the wall to follow. This behavior is activated when non-consistent measurements of the control states \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tθ\n\t\t\t\t\t\t\t\t\t\t̃\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t and \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t̃\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t are obtained. The proposed solution is to describe a circular path of radius R on the floor (Figure 8) until one of the following conditions is fulfilled:
\n\t\t\t\t
The wall can be followed again using the wall-following behavior provided that \n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\t\t̃\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t̃\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\t\t\to\n\t\t\t\t\t\t\t\t\t\t\t\t\ts\n\t\t\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t (Figure 8.a and Figure 8.b); being \n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t̃\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\t\t\t\to\n\t\t\t\t\t\t\t\t\t\t\t\t\ts\n\t\t\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t the last value of \n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\t\t̃\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t just before switching. This way, it could be assumed that \n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t̃\n\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\ṫ\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t considering the value of \n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\t\t̃\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t does not change at the beginning and at the end of this behavior.
A possible collision between the robot and the wall is detected (Figure 8.c.), as considered in Section 3.2.
\n\t\t\t\t
Figure 8.
Handling “loss of wall” situations.
\n\t\t\t\t
In order to be able to guarantee stability, a controller must be included, and this controller should share the same control states which the standart WF controller had. For this reason,we included a simple controller to describe a circular path of radius\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tR\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, based on the previous wall-following controller, though the distance error is not considered. Therefore, considering the following errors as in (4)
where \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tθ\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tc\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\tr\n\t\t\t\t\t\t\t\t\t\t\tc\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is the heading reference to perform the desired circular path
Here, the plus/minus sign of (14) denotes that the reference \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tθ\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tc\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\tr\n\t\t\t\t\t\t\t\t\t\t\tc\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t will generate a left or right turn. That is, the robot will turn left (right) if it is following an object at its left (right) side. Then, replacing (14) into (13) and considering its time derivative, we obtain
Finally, by replacing (18) in (17), the asymptotic stability of the control system can immediately be proved. That is, this controller guarantees that the robot will perform a circular path by acting only on the robot angular velocity.
\n\t\t\t
\n\t\t
\n\t\t
\n\t\t\t
4.2 Handling possible collisions
\n\t\t\t
This behavior is activated when an obstacle appears in front of the robot at a distance\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\tp\n\t\t\t\t\t\t\t\t\t\ta\n\t\t\t\t\t\t\t\t\t\tc\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t≤\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tf\n\t\t\t\t\t\t\t\t\t\tr\n\t\t\t\t\t\t\t\t\t\to\n\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t, being \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\tp\n\t\t\t\t\t\t\t\t\t\ta\n\t\t\t\t\t\t\t\t\t\tc\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t the smallest distance to the obstacle measured inside the robot safety-area, which is also characterized by and angle \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\tp\n\t\t\t\t\t\t\t\t\t\ta\n\t\t\t\t\t\t\t\t\t\tc\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t on the laser range finder framework. Also, \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tf\n\t\t\t\t\t\t\t\t\t\tr\n\t\t\t\t\t\t\t\t\t\to\n\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t(defined in Section2) is selected to be equal to the actual robot wall distance \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\ta\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t and\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\ta\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tf\n\t\t\t\t\t\t\t\t\t\tr\n\t\t\t\t\t\t\t\t\t\to\n\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t. The objective of this behavior is to avoid possible collisions by rotating the robot until a free-path condition (characterized by an empty safety-area) is again achieved, and\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\t̃\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t+\n\t\t\t\t\t\t\t\t\t\tT\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\t̃\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t, where \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tis the obstacle detection instant, and \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tT\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tis the time during this behavior was active until switching to the wall-following behavior. Under the above mentioned conditions, this behavior will always achieve a free- path condition satisfying \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\t̃\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t+\n\t\t\t\t\t\t\t\t\t\tT\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\t̃\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t (see Figure 9). Analogously to the behavior described in Section4.1, it could be assumed that\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\t̃\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\ṫ\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t, considering that \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t̃\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t does not change at the beginning and at the end of this behavior.
\n\t\t\t
Figure 9.
Handling possible collision situations, a) obstacle detected at instant\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t, and b) free-path condition achieved with \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\t\t\t̃\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\t\t+\n\t\t\t\t\t\t\t\t\t\t\t\tT\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t≤\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\t\t\t\t̃\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\tat instant \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t+\n\t\t\t\t\t\t\t\t\t\tT\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t
\n\t\t\t
To this aim, it is proposed a controller to allow the robot to positioning itself at a desired orientation angle\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tθ\n\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t. The orientation error between the heading angle of the robot and the desired orientation is defined as shown in Figure 10\n\t\t\t
where \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tθ\n\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tθ\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\tp\n\t\t\t\t\t\t\t\t\t\ta\n\t\t\t\t\t\t\t\t\t\tc\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t±\n\t\t\t\t\t\t\t\t90\n\t\t\t\t\t\t\t\tº\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t is a constant value that is updated so as to attain an open area.
As done in the previous section, by replacing (21.b) into (20), the asymptotic stability of this control system, that is \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tθ\n\t\t\t\t\t\t\t\t\t̃\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t→\n\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t as\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t→\n\t\t\t\t\t\t\t\t∞\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t, can easily be proved.
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5. Switching System
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Once each part was designed it is necessary to desing the supervisor logics. Figure 11 presets the final block diagram, which includes three behaviors: wall-following, orientation and rotation (circular path performer). The switching signal generated by the supervisor, takes one of three possible values: a) \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tσ\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tif the controller for object-following is active, b) \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tσ\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tif the orientation controller is active and c) \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tσ\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tif the controller to perform a circular path is active.
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Figure 11.
Block diagram of the Contour-Following controller.
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Figure 12.
Supervisor logic.
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Transitions between these discrete states are ruled by the logic described in Figure 12 (Toibero et al., 2006a). Where, as mentioned before, the “Possible crash” condition is detected as an invasion to the guard-zone shown in Figure 1.c and the “Loss of wall” condition depends on the variance of the length of the laser beams on the side of the robot. It is easy to see that these transitions do not depends on the control states values, but on data provided by the laser range finder. This a priori unpredictable data will define the value for the switching signal\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tσ\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t
\n\t\t\t
\n\t\t\t\t
5.1. Stability Analysis
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Given a family of systems, it is desired that the switched system be stable for every switching signal\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tσ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t. This is known as stability under arbitrarily switching and has been the subject of several studies (Vu & Liberzon, 2005), (Liberzon, 2003) and (Mancilla-Aguilar, 2000). In fact, common Lyapunov functions are considered in order to prove stability for arbitrary switching. Finding a common Lyapunov function could be a difficult task, but if such function is found, the restrictions over the switching signal disappear, allowing the stable switching between the involved controllers. So, a basic fact that is used in this Section is that the existence of a Common Lyapunov Function with suitable properties guarantees uniform stability, as stated in (Liberzon & Morse, 1999). Let us define a Common Lyapunov Function
Given a positive definite continuously differentiable function\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tV\n\t\t\t\t\t\t\t\t\t:\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tℝ\n\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t→\n\t\t\t\t\t\t\t\t\tℝ\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, then, it is said that \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tV\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tis a common Lyapunov function for the family of systems\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tχ\n\t\t\t\t\t\t\t\t\t\t˙\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tf\n\t\t\t\t\t\t\t\t\t\tp\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\tχ\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\tp\n\t\t\t\t\t\t\t\t\t∈\n\t\t\t\t\t\t\t\t\tP\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t,if there exists a positive definite continuous function \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tW\n\t\t\t\t\t\t\t\t\t:\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tℝ\n\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t→\n\t\t\t\t\t\t\t\t\tℝ\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tsuch that
Where \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tp\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tis some index set. Now, the following theorem can be stated
If all systems in the family \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tχ\n\t\t\t\t\t\t\t\t\t\t˙\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tf\n\t\t\t\t\t\t\t\t\t\tp\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\tχ\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\tp\n\t\t\t\t\t\t\t\t\t∈\n\t\t\t\t\t\t\t\t\tP\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tshare a radially unbounded common Lyapunov function, then the switched system \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\t˙\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tf\n\t\t\t\t\t\t\t\t\t\tσ\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is globally uniformely asymptoticaly stable (GUAS).
\n\t\t\t\t
The main point in this well-known theorem is that the rate of decrease of V along solutions, given by (22), is not affected by switching, hence asymptotic stability is uniform with respect to\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tσ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t. Now, the purpose is to find a Common Lyapunov Function for the three continuous controllers. Then, it is first necessary to show that the closed-loop systems corresponding to each controller share a common equilibrium point at the origin. From Sections 3, 4.1 and 4.2, the closed-loop equations are
It is clear that the origin is a common equilibrium point for the involved controllers. Then, from (6) and (16), a common Lyapunov function for the switching among these controllers is given by (6). Therefore, it can be concluded that the switching control system composed by the three subsystems described in the previous sections is stable for any switching signal\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tσ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, because every behavior is at least stable considering the common Lyapunov function (6). However, the proposed application is composed by an asymptotically stable main behavior (wall-following) and two complementary stable behaviors (orientation and circular-path performer). As it was shown along this paper, the complementary behaviors are active only during special situations and the system always returns to the main behavior. Therefore, the GUAS property for the overall switched system can be concluded, provided that the wall following behavior is asymptoticaly stable (AS).
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6. Experimental results
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The switching contour-follower controller described in this Chapter has been implemented in a Pioneer III mobile robot navigating through a typical office environment at 150millimetres per second. In the following figures it can be seen the trajectory described by the robot when following the interior contour of the Institute of Automatics (INAUT). As mentioned before, the office contour was reconstructed by using the laser sensorial information.
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The first experiment (Figure 13) shows a typical situation when following discontinuous contours. The robot follows the outline of a rectangular box at 400millimetres. From this picture it can be appreciated the good performance of the controller when switching between the wall-following and the circular path controller, in this specially discontinuous contour.
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Figure 13.
Robot following a rectangular contour
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\n\t\t\t\tFigure 14 depicts the performance of the control system when unknown obstacles appear in front of the robot: in this case first avoiding a human being and finally due to a block in the corridor, the robot returns to keep following the corridor the opposite side.
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Figure 14.
Robot moving along a corridor avoiding obstacles
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Figure 15.
Robot moving along a corridor avoiding obstacles
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The controller constants were set to: \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tν\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tmax\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t=150millimeters per second, \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t0.02\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t, \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tK\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tθ\n\t\t\t\t\t\t\t\t\t\t\t̃\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t0.25\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tand\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tθ\n\t\t\t\t\t\t\t\t\t\t\t̃\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t5\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t. The sample time was of 100milliseconds. The desired distance to the object was selected as 0.38meters, the selection of this value was based on the size of the doors, and larger values for \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\td\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\ta\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\tl\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t do not allow the robot to pass across them.
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7. Mobile robot SLAM algorithm combined with a stable switching controller
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Once treated the obstacle avoidance problem, its inclusion to a new system is considered in this Section. In the introductory section, some paragraph dedicated to possible applications to this algorithm mentioned mapping of unknown environments. In fact, simultaneous localization and map building (SLAM) is a challenging problem in mobile robotics that has attracted the interest of an increasing number of researchers in the last decade (Thrun et al., 2005), (Briechle & Hanebeck, 2004). Self-localization of mobile robots is obviously a fundamental issue in autonomous navigation: a mobile robot must be able to estimate its position and orientation (pose) within a map of the environment it is navigating within (Pfister et al., 2003), (Garulli et al., 2005). However, in many applications of practical relevance (like exploration tasks or operations in hostile environments), a map is not available or it is highly uncertain. Therefore, in such cases the robot must use the measurements provided by its sensory equipment to estimate a map of the environment and, at the same time, to localize itself within the map. Several techniques have been proposed to solve the SLAM problem (Thrun et al., 2005), (Durrant-Whyte & Bailey, 2006 a), (Durrant-Whyte & Bailey, 2006 b).
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The SLAM algorithm implemented in this final Section consists on a sequential Extended Kalman Filter (EKF) feature-based SLAM. Prior to the experimental results, it is necessary to devote some paragraphs to its functioning algorithms for completness. This algorithm fuses corners (convex and concave) and lines of the environment in the SLAM system state. Corners are defined in a Cartesian coordinate system whereas lines are defined in the polar system. In addition to the SLAM system state, a secondary map is maintained. This secondary map stores the information on the endpoints of each segment associated with a line of the environment (representing walls). The secondary map and the SLAM system state are updated simultaneously. Once a new feature is added to the SLAM system state, it is also added to the secondary map. The feature extraction method allows the rejection of moving agents of the environment. Equations (26) and (27) show the SLAM system state and its covariance. As it can be seen, the SLAM system state has the robot’s pose estimation (\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tχ\n\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tand the parameters that define the features of the environment. The covariance matrix has covariance of the robot’s pose estimation (\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tP\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tv\n\t\t\t\t\t\t\t\t\t\tv\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t), the covariance of the features’ parameters (\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tP\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t) and the corresponding cross correlations. The elements of the SLAM system state are attached to a global coordinate system determine at the SLAM’s first execution (Durrant-Whyte & Bailey, 2006a).
The combination of the SLAM algorithm with a strategy for exploration or navigation inside the environment is known as Active SLAM and has been a key poblem in the implementation of autonomous mobile robots. The integration of SLAM algorithms with control strategies to govern the motion of a mobile robot and the ability of selecting feasible destinations on its own will endow the vehicle with full autonomy (Liu et al., 2008), (Liu et al., 2007).
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The combination of control strategies with the SLAM algorithm has been addressed from two significantly different points of view. Whereas the first one considers how the control is used to reduce errors during the estimation process (Durrant-Whyte & Bailey, 2006 a), (Durrant-Whyte & Bailey, 2006 b) the second one concerns exploration techniques providing the best map from the reconstruction perspective (Andrade-Cetto & Sanfeliu, 2006). Despite the duality between regulation and estimation, whatever the control strategy is implemented, it will not be guaranteed that, in general, the mobile robot will follow a specific trajectory inside the environment. In many applications, the control signal is not considered as an input of the SLAM algorithm, and, instead, odometry measurements of the robot are used (Guivant & Nebot, 2001), (Durrant-Whyte & Bailey, 2006a), (Durrant-Whyte & Bailey, 2006b). Thus, most of the associated implementations focus on the low-level, basic control-reactive behavior, leaving the motion planning and control as a secondary algorithm. Thus, albeit restricted to a local reference frame attached to the robot, active exploration strategies for indoor environments are proposed in (Andrade-Cetto & Sanfeliu, 2006), (Liu et al., 2008). As an example, a boundary exploration problem is proposed in (Xi, 2008). In this case, the robot has to reach the best point determined in the boundary of its local point of view. From a global reference perspective, these implementations have a random behavior inside the environment. To solve the lack of global planning, some implementations have included algorithms for searching optimal path based on the information acquired of the environment. These algorithms usually require the map to be gridded and, accordingly, they compute a feasible path to a possible destination (closure of the loop or global boundary points) without specifying the control law implemented on the mobile robot. Despite of the advances made so far, the integration of control strategies based on the SLAM system state (map and vehicle) to guide the robot inside an unknown environment from a local and a global reference frame following a pre-established plan is not quite studied or implemented in real time.
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In this work, the robot starts at an unknown position inside an unknown environment and by an active exploration, searches for boundary points from a local reference frame attached to the robot. From now on, these boundary points will be designated by local uncertainty points. Once a local uncertainty point is determined, a trajectory connecting this point and the robot’s current pose is generated. The trajectory is continued by one resulting from the execution of a switching adaptive controller (De la Cruz et al., 2008) articulated with an avoiding obstacle algorithm to prevent the collision with moving agents. Once a neighborhood of the local uncertainty point is reached by the robot, the vehicle searches for a new boundary point. This process is repeated until no additional local uncertainty point can be determined. Once this stage is reached - mainly due to the fact that the environment is occupied with already mapped features -, the robot searches for global destination regions. The global destination regions are represented by global uncertainty points. These points are determined by using the Gaussian distribution of each random variable involved in the EKF-SLAM system state. Thus, according to the geometrical information given by the secondary map of the environment, the entire map is circumscribed by four virtual segments that determine the limits of the known environment. Then, a set of points contained inside the limits of the virtual features is generated by a Monte Carlo experiment, and those that are not navigable are rejected. The probability attached to each one of the remaining point is estimated based on the concept of sum of Gaussians, which yields an estimate of the occupational probability of each point. Those points whose probability values do not fall near zero (free space point) or near one (non-empty point) will be considered as a global uncertainty point. This kind of points can be attached to the boundary of the map - unexplored region - or to badly mapped features. Once a global uncertainty point is determined -according to the needs of the navigation purposes - a hybrid contour-following control (Toibero et al., 2007) is implemented to drive the robot to that point. Once a neighborhood of the global uncertainty point is reached, the exploration switches to the mode of searching for local uncertainty points in a local reference frame. The entire navigation system stops when no global uncertainty points are found, what will happen when the map is complete. During the entire navigation or exploration phase, the SLAM algorithm continues been executed Additional information about this topic can be found in (Auat Cheein, 2009). Figure 16 shows the general architecture of the SLAM algorithm with the non-reactive behavior controllers (the adaptive switching controller and the hybrid contour following) implemented on the mobile robot.
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Figure 16.
General SLAM - Control system architecture where the control uses SLAM system state information for planning purposes
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\n\t\t\t\tFigure 17 shows the real time experimentation of the SLAM algorithm combined with the two control strategies. The experimentation was carried out at the facilities of the Instituto de Automatica. As it can be seen, the map obtained by the SLAM was built consistently. The local controller (adaptive switching control) and the global controller (hybrid contour following) have allowed the entire navigation of the mobile robot within the Instituto de Automatica.
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Figure 17.
Map reconstruction of the Institute of Automatics
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In Figure 17, the green circles are the corners detected in the environment, the solid dark lines are the segments associated with walls whereas red crosses are the beginning and ending points of such segments; the red points are the path travelled by the mobile robot and the yellow points are raw laser data.
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8. Conclusions
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In this Chapter it has been presented a switched countour-following controller, which allows a wheeled mobile robot to follow discontinuous walls‘ contours. This controller has been developed by considering a standard (stable) wall-following controller and aggregating two complementary (also stable) controllers. One risponsible for avoid collisions between the robot and the object which is being followed, and the other responsible for find a lost contour of this same object. This new swiching controller proved to be stable with respect to its swiching signal, guaranteing that the robot will be able to stay at a desired robot-to-object distance, and with the same object orientation.
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Next, this controllers was included into a SLAM algorithm, in order to deal with the exploration and map construction of unknown environments, exposing the modularity capability of this kind of control architecture.
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In designing the control system, the asymptotic stability of the individual controllers as well the asymptotic stability at the switching times (for the switching controller) were considered and proved.
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Several experimental results in a Pioneer III mobile robot with odometry and laser radar sensor have been included; showing the good performance of the proposed control strategy in a laboratory setting, in the first attemps, and later, in a large scale setting for the SLAM experiment.
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Acknowledgments
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Authors thank to the National Council of Scientific and Technical Research of Argentina (CONICET) for partially supporting this research.
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\n',keywords:null,chapterPDFUrl:"https://cdn.intechopen.com/pdfs/10266.pdf",chapterXML:"https://mts.intechopen.com/source/xml/10266.xml",downloadPdfUrl:"/chapter/pdf-download/10266",previewPdfUrl:"/chapter/pdf-preview/10266",totalDownloads:2466,totalViews:175,totalCrossrefCites:0,totalDimensionsCites:1,hasAltmetrics:0,dateSubmitted:null,dateReviewed:null,datePrePublished:null,datePublished:"March 1st 2010",readingETA:"0",abstract:null,reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/10266",risUrl:"/chapter/ris/10266",book:{slug:"mobile-robots-navigation"},signatures:"Juan Marcos Toibero, Flavio Roberti, Fernando Auat Cheein, Carlos Soria and Ricardo Carelli",authors:null,sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Mobile Robot",level:"1"},{id:"sec_3",title:"3. Standard Wall-Following Control ",level:"1"},{id:"sec_4",title:"3.1 Wall Angle Computation",level:"1"},{id:"sec_5",title:"3.2 Robot-wall distance computation",level:"1"},{id:"sec_5_2",title:"3.2.1 Controller description and analysis",level:"2"},{id:"sec_6_2",title:"3.2.2 Experimental results",level:"2"},{id:"sec_8",title:"4. Contour-Following Controller",level:"1"},{id:"sec_8_2",title:"4.1-. Handling the case of missing the wall to follow",level:"2"},{id:"sec_10",title:"4.2 Handling possible collisions",level:"1"},{id:"sec_11",title:"5. Switching System",level:"1"},{id:"sec_11_2",title:"5.1. Stability Analysis",level:"2"},{id:"sec_13",title:"6. Experimental results",level:"1"},{id:"sec_14",title:"7. Mobile robot SLAM algorithm combined with a stable switching controller",level:"1"},{id:"sec_15",title:"8. Conclusions",level:"1"},{id:"sec_16",title:"Acknowledgments",level:"1"}],chapterReferences:[{id:"B1",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tAndo\n\t\t\t\t\t\t\tY.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tYuta\n\t\t\t\t\t\t\tS.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1996\n\t\t\t\t\tA reactive wall-following algorithm and its behaviors of an autonomous mobile robot with sonar ring.. Journal of Robotics and Mechatronics, 8 1), 33\n\t\t\t\t\t39 .\n\t\t\t'},{id:"B2",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tAndrade-Cetto\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSanfeliu\n\t\t\t\t\t\t\tA.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2006 Environment Learning for Indoors Mobile Robots, 978-3-54032-795-0 Series: Springer Tracts in Advanced Robotics, 23 Springer\n\t\t\t'},{id:"B3",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tArkin\n\t\t\t\t\t\t\tR. 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Conf. on Machine Learning and Cybernetics, 26\n\t\t\t\t\t29 , 2004\n\t\t\t'},{id:"B35",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tXi\n\t\t\t\t\t\t\tB.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tGuo\n\t\t\t\t\t\t\tR.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSun\n\t\t\t\t\t\t\tF.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tHuang\n\t\t\t\t\t\t\tY.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2008 Simulation Research for ActiveSimultaneous Localization and Mapping Based on Extended Kalman Filter, in: Proc. of the IEEE International Conference on Automation and Logistics, 2443\n\t\t\t\t\t2448 , 978-1-42442-502-0 1-3 Sept, Quingdao, China.\n\t\t\t'},{id:"B36",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tZhang\n\t\t\t\t\t\t\tZ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSarkar\n\t\t\t\t\t\t\tN.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tYun\n\t\t\t\t\t\t\tX.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2004 Supervisory control of a mobile robot for agile motion coordination, IEEE Int. Conf. on Robotics and Automation, 3\n\t\t\t\t\t2196\n\t\t\t\t\t2203\n\t\t\t\t\n\t\t\t'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Juan Marcos Toibero",address:null,affiliation:'
'}],corrections:null},book:{id:"3642",title:"Mobile Robots Navigation",subtitle:null,fullTitle:"Mobile Robots Navigation",slug:"mobile-robots-navigation",publishedDate:"March 1st 2010",bookSignature:"Alejandra Barrera",coverURL:"https://cdn.intechopen.com/books/images_new/3642.jpg",licenceType:"CC BY-NC-SA 3.0",editedByType:"Edited by",editors:[{id:"6195",title:"Prof.",name:"Alejandra",middleName:null,surname:"Barrera",slug:"alejandra-barrera",fullName:"Alejandra Barrera"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},chapters:[{id:"10262",title:"A 3D Omnidirectional Sensor For Mobile Robot Applications",slug:"a-3d-omnidirectional-sensor-for-mobile-robot-applications",totalDownloads:2368,totalCrossrefCites:1,signatures:"Remi Boutteau, Xavier Savatier, Jean-Yves Ertaud and Belahcene Mazari",authors:[null]},{id:"10245",title:"Optical Azimuth Sensor for Indoor Mobile Robot Navigation",slug:"optical-azimuth-sensor-for-indoor-mobile-robot-navigation",totalDownloads:2381,totalCrossrefCites:0,signatures:"Keita Atsuumi and Manabu Sano",authors:[null]},{id:"10258",title:"Vision Based Obstacle Detection Module for a Wheeled Mobile Robot",slug:"vision-based-obstacle-detection-module-for-a-wheeled-mobile-robot",totalDownloads:3152,totalCrossrefCites:0,signatures:"Oscar Montiel, Alfredo Gonzalez and Roberto Sepulveda",authors:[null]},{id:"10256",title:"Fast 3D Perception for Collision Avoidance and SLAM in Domestic Environments",slug:"fast-3d-perception-for-collision-avoidance-and-slam-in-domestic-environments",totalDownloads:2268,totalCrossrefCites:2,signatures:"Dirk Holz, David Droeschel, Sven Behnke, Stefan May and Hartmut Surmann",authors:[null]},{id:"10247",title:"Sensors Fusion Technique for Mobile Robot Navigation Using Fuzzy Logic Control System",slug:"sensors-fusion-technique-for-mobile-robot-navigation-using-fuzzy-logic-control-system",totalDownloads:2439,totalCrossrefCites:0,signatures:"S.Parasuraman, Bijan Shirinzadeh and V.Ganapathy",authors:[null]},{id:"10243",title:"Z˜(inf) - Monocular Localization Algorithm with Uncertainty Analysis for Outdoor Applications",slug:"z-inf-monocular-localization-algorithm-with-uncertainty-analysis-for-outdoor-applications",totalDownloads:1930,totalCrossrefCites:6,signatures:"Elmar Mair and Darius Burschka",authors:[null]},{id:"10265",title:"Parallel Projection Based Self Localization Method for Mobile Navigation Applications",slug:"parallel-projection-based-self-localization-method-for-mobile-navigation-applications",totalDownloads:1473,totalCrossrefCites:0,signatures:"Shung Han Cho, Yuntai Kyong, Yunyoung Nam and Sangjin Hong",authors:[null]},{id:"10252",title:"Vision Based SLAM for Mobile Robot Navigation Using Distributed Filters",slug:"vision-based-slam-for-mobile-robot-navigation-using-distributed-filters",totalDownloads:2884,totalCrossrefCites:0,signatures:"Young Jae Lee and Sankyung Sung",authors:[null]},{id:"10250",title:"Omnidirectional Vision Based Topological Navigation",slug:"omnidirectional-vision-based-topological-navigation",totalDownloads:2147,totalCrossrefCites:1,signatures:"Toon Goedeme and Luc Van Gool",authors:[null]},{id:"10238",title:"Neural Networks Based Navigation and Control of a Mobile Robot in a Partially Known Environment",slug:"neural-networks-based-navigation-and-control-of-a-mobile-robot-in-a-partially-known-environment",totalDownloads:2137,totalCrossrefCites:0,signatures:"Diana D. Tsankova",authors:[null]},{id:"10259",title:"Navigation Planning with Human-Like Approach",slug:"navigation-planning-with-human-like-approach",totalDownloads:1469,totalCrossrefCites:0,signatures:"Yasar Ayaz, Atsushi Konno, Khalid Munawar, Teppei Tsujita and Masaru Uchiyama",authors:[null]},{id:"10237",title:"Approaches to Door Identification for Robot Navigation",slug:"approaches-to-door-identification-for-robot-navigation",totalDownloads:1703,totalCrossrefCites:1,signatures:"E. Jauregi, E. Lazkano and B. Sierra",authors:[null]},{id:"10255",title:"Path Planning and Execution for Planetary Exploration Rovers Based on 3D Mapping",slug:"path-planning-and-execution-for-planetary-exploration-rovers-based-on-3d-mapping",totalDownloads:1686,totalCrossrefCites:0,signatures:"Andres Mora, Keiji Nagatani and Kazuya Yoshida",authors:[null]},{id:"10236",title:"A Decentralised Software Process Approach For Real Time Navigation of Service Robots",slug:"a-decentralised-software-process-approach-for-real-time-navigation-of-service-robots",totalDownloads:1563,totalCrossrefCites:0,signatures:"S. 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Gasca-Martinez, Rigoberto Lopez-Padilla and Raul E. 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Benitez-Read and Erick Rojas-Ramirez",authors:[null]}]},relatedBooks:[{type:"book",id:"178",title:"Advances in Robot Navigation",subtitle:null,isOpenForSubmission:!1,hash:"15c636fbb26b21858432449cca2d5b13",slug:"advances-in-robot-navigation",bookSignature:"Alejandra Barrera",coverURL:"https://cdn.intechopen.com/books/images_new/178.jpg",editedByType:"Edited by",editors:[{id:"6195",title:"Prof.",name:"Alejandra",surname:"Barrera",slug:"alejandra-barrera",fullName:"Alejandra Barrera"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"},chapters:[{id:"16161",title:"Conceptual Bases of Robot Navigation Modeling, Control and Applications",slug:"conceptual-bases-of-robot-navigation-modeling-control-and-applications",signatures:"Silas F. R. Alves, Joao M. Rosario, Humberto Ferasoli Filho, Liz K. A. Rincon and Rosana A. T. 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Kiruba",authors:[{id:"1451",title:"Dr.",name:"Tamil",middleName:null,surname:"Selvi",fullName:"Tamil Selvi",slug:"tamil-selvi"},{id:"40677",title:"Dr.",name:"Mercy",middleName:null,surname:"Shalinie",fullName:"Mercy Shalinie",slug:"mercy-shalinie"},{id:"40678",title:"Dr.",name:"Hariharasudan",middleName:null,surname:"M",fullName:"Hariharasudan M",slug:"hariharasudan-m"},{id:"40679",title:"Dr.",name:"Kiruba",middleName:null,surname:"Ganesh",fullName:"Kiruba Ganesh",slug:"kiruba-ganesh"}]},{id:"16167",title:"Navigation Among Humans",slug:"navigation-among-humans",signatures:"Mikael Svenstrup",authors:[{id:"23589",title:"MSc",name:"Mikael",middleName:null,surname:"Svenstrup",fullName:"Mikael Svenstrup",slug:"mikael-svenstrup"}]},{id:"16168",title:"Brain-actuated Control of Robot Navigation",slug:"brain-actuated-control-of-robot-navigation",signatures:"Francisco Sepulveda",authors:[{id:"28245",title:"Dr.",name:"Francisco",middleName:null,surname:"Sepulveda",fullName:"Francisco Sepulveda",slug:"francisco-sepulveda"}]},{id:"16169",title:"A Distributed Mobile Robot Navigation by Snake Coordinated Vision Sensors",slug:"a-distributed-mobile-robot-navigation-by-snake-coordinated-vision-sensors",signatures:"Yongqiang Cheng, Ping Jiang and Yim Fun Hu",authors:[{id:"28051",title:"Dr.",name:"Yongqiang",middleName:null,surname:"Cheng",fullName:"Yongqiang Cheng",slug:"yongqiang-cheng"},{id:"40503",title:"Dr.",name:"Ping",middleName:null,surname:"Jiang",fullName:"Ping Jiang",slug:"ping-jiang"},{id:"40504",title:"Prof.",name:"Yim Fun",middleName:null,surname:"Hu",fullName:"Yim Fun Hu",slug:"yim-fun-hu"}]},{id:"16170",title:"Knowledge Modelling in Two-Level Decision Making for Robot Navigation",slug:"knowledge-modelling-in-two-level-decision-making-for-robot-navigation",signatures:"Rafael Guirado, Ramón González, Fernando Bienvenido and Francisco Rodríguez",authors:[{id:"22922",title:"Dr.",name:"Francisco",middleName:null,surname:"Rodriguez",fullName:"Francisco Rodriguez",slug:"francisco-rodriguez"},{id:"30840",title:"MSc",name:"Rafael",middleName:null,surname:"Guirado",fullName:"Rafael Guirado",slug:"rafael-guirado"},{id:"40815",title:"Dr.",name:"Ramón",middleName:null,surname:"González",fullName:"Ramón González",slug:"ramon-gonzalez"},{id:"40816",title:"Dr.",name:"Fernando",middleName:null,surname:"Bienvenido",fullName:"Fernando Bienvenido",slug:"fernando-bienvenido"}]},{id:"16171",title:"Gait Training using Pneumatically Actuated Robot System",slug:"gait-training-using-pneumatically-actuated-robot-system",signatures:"Natasa Koceska, Saso Koceski, Pierluigi Beomonte Zobel and Francesco Durante",authors:[{id:"28428",title:"Prof.",name:"Saso",middleName:null,surname:"Koceski",fullName:"Saso Koceski",slug:"saso-koceski"},{id:"39210",title:"Prof.",name:"Natasa",middleName:null,surname:"Koceska",fullName:"Natasa Koceska",slug:"natasa-koceska"},{id:"39212",title:"Prof.",name:"Francesco",middleName:null,surname:"Durante",fullName:"Francesco Durante",slug:"francesco-durante"},{id:"162372",title:"Prof.",name:"Pierluigi",middleName:null,surname:"Beomonte Zobel",fullName:"Pierluigi Beomonte Zobel",slug:"pierluigi-beomonte-zobel"}]}]}]},onlineFirst:{chapter:{type:"chapter",id:"62277",title:"Basic Antenatal Care Approach to Antenatal Care Service Provision",doi:"10.5772/intechopen.79361",slug:"basic-antenatal-care-approach-to-antenatal-care-service-provision",body:'
1. Introduction
Antenatal care (ANC) is an umbrella term used to describe medical care and procedures that are carried out to and for the pregnant women [1]. It is the health care that is rendered to the pregnant women throughout pregnancy until the child’s birth and is aimed at detecting the already existing problems and/or problems that can develop during pregnancy, affecting the pregnant woman and/or her unborn child [2]. The care includes various screening tests, diagnostic procedures, prophylactic treatments, some of which are done routinely, and others are provided to the women based on identified problems and risk factors.
2. Importance of antenatal care
According to Pattinson [2], ANC benefits both the mother and the baby; it assists in screening, diagnosing and managing or controlling the risk factors that might adversely affect the pregnant women and/or the pregnancy outcome. Maternal and perinatal death rates remain the major challenge of health care in South Africa. During 2005–2007, triennium maternal deaths had increased by 20% when comparing them to the 2002–2004 triennium [3]. However, due to changes in the treatment programmes for HIV-positive pregnant women and the focus on reducing deaths in specific categories such as obstetric haemorrhage, a significant fall in both the numbers of maternal deaths and mortality ratios has since been reported in South Africa. An overall reduction of 24% (1152 from 2008–2010 to 2014–2016) has been achieved [4]. Nevertheless, much more still needs to be done for the country to be able to maintain this fall and to obtain an exponential fall. Several major challenges still remain mainly relating to the quality of care, inter-facility transport, and knowledge and skills of health professionals [4]. Furthermore, the majority of preventable deaths during pregnancy and childbirth have been attributed to poor ANC [5]. According to these authors, non-attendance of ANC clinics carries an approximately four times increased risk of maternal deaths compared with the general pregnant population who attend ANC clinics. The provision of adequate ANC is advocated by most authors worldwide as the cornerstone for maternal and perinatal care. The detection of high-risk pregnancies through ANC has been advocated as a good tool for reducing maternal and perinatal mortality rates [6].
The purpose of ANC is to screen, diagnose and manage or control the risk factors that might adversely affect the pregnant woman and/or the pregnancy outcome. Both Pattinson and Snyman [2, 7] attest to this by saying: ‘The quality of health care that a pregnant woman receives during ANC has an impact on the health of the woman and on the outcome of pregnancy’. Ekabua et al. [1] highlight the four major goals of ANC as being (a) promotion and maintenance of the physical and social health of the mother and the baby, (b) detection and management of complications during pregnancy, (c) development of birth preparedness and complication readiness plan and (d) preparation of the women for normal puerperium. The World Health Organisation (WHO) identifies ANC as one of the most widely used strategies to improve maternal and child health [8]. It was also one of the worldwide strategies towards the achievement of millennium development goal (MDGs numbers 4 and 5, which were to reduce child deaths by 75% and improve maternal health by 50% by 2015 [9].
Three South African reports, namely the Saving Mothers report by the National Committee on Confidential Enquiry into Causes of Maternal Deaths (NCCEMD), Saving Babies report for the Perinatal Problem Identification Programme (PPIP) and Saving Children report for the Child Health Problem Identification Programme (CHPIP), review the health care provided to the mothers, babies and children in South Africa [10]. The findings of these reports highlight avoidable causes of the deaths of mothers, babies and children and make recommendations to improve the quality of care provided to mothers, babies and children at the time when they need it most. All three committees highlight, in their triennial reports, the importance of ANC for reducing maternal, perinatal and children’s deaths. Bradshaw et al. [10] further emphasise that addressing the health challenges should involve strengthening the provision of healthcare packages within the continuum of care and recognise that the effectiveness of each package depends on whether it provides high-impact, evidence-based interventions and also on the coverage and quality of the service rendered. ANC can screen for, detect and thus prevent many maternal complications that might occur before childbirth and could significantly improve the outcomes for unborn infants [2].
The one document by the NCCEMD, which might appear old but which conveys a very important message for South Africa, is the Saving Mothers Policy and Management Guidelines for Common Causes of Maternal Deaths [11]. This policy document highlights that one of the major areas of substandard care identified in South Africa is the poor initial assessment of patients during ANC visits. The authors attribute this to the fact that the midwives are trained in the traditional method of history taking, clinical examination and special investigations when assessing patients. This might make it difficult to assimilate the multiple abnormalities found and to formulate a management plan for a patient with multiple organ disease, the very type of cases described in the maternity mortality reports [12].
South Africa has a burden of high maternal and perinatal mortality rates and therefore needs to work very hard to address this problem. The number of reported maternal mortalities had increased by 20% during the 2005–2007 triennium compared to the 2002–2004 trienniums [3]. The constant rise in maternal and perinatal mortality rates resulted in South Africa’s inclusion of the MNCWH programme as one of the priority programmes in the 10-year strategic plan for the country [12]. The majority of the provider-related preventable deaths in South Africa have been attributed to poor ANC.
South Africa can address the problem of the constantly rising maternal and perinatal mortality rates because the majority of avoidable provider-related maternal deaths can be avoided through providing proper and good-quality ANC services [13]. The Saving Mothers Report 2008–2010 indicates that a total of (16.6%, n = 713) of women who died during this triennium did not attend ANC clinics and (7.0%, n = 300) attended ANC clinics infrequently [14]. The Saving Mothers’ Report indicates that the avoidable causes of maternal deaths included a number of health provider-related issues such as poor initial assessments, problems with recognising problems, delays in referring the pregnant women to different healthcare facilities causing pregnant women to be managed at inappropriate healthcare levels, incorrect management, substandard management/care and failure to take actions when abnormalities were found [14].
3. Approaches to antenatal care
Several approaches to ANC are used in different countries including the traditional approach, goal-directed ANC, focussed ANC (FANC) and the basic ANC (BANC) approach. While some countries structure and develop their own approaches to suit their unique circumstances, other countries might simply adopt an approach existing elsewhere. This could create problems if the situations in the two countries differ. Developing countries (like South Africa, Botswana, Swaziland, Kenya and Zimbabwe) adopted ANC programmes modelled on the approaches used in developed countries [15]. These approaches use risk assessments to identify women who are likely to experience complications during their pregnancies and assume that more clinic visits imply better pregnancy outcomes. In these approaches, scarce resources of developing countries might be devoted to women with high-risk pregnancies, implying that women with low-risk pregnancies might not receive optimal care [16]. This approach has been challenged by the WHO [17]. The Maternal and Neonatal Programme [18] argues that frequent ANC visits are often logically and financially impossible for women to manage and place additional burdens on the healthcare system. Frequent ANC visits do not necessarily improve pregnancy outcomes [1]. The WHO realised that traditional ANC programmes, meant for developed countries, were poorly implemented and largely ineffective when used in developing countries [16].
The WHO designed and tested an FANC package that included only counselling, examinations and tests serving an immediate purpose and having a proven health benefit as an ideal approach to be used by developing countries [19]. In the FANC approach, the WHO recommends reducing the number of ANC visits to four, and this has not been found to pose risks to the health of mothers or babies [19]. The FANC approach recognises that every pregnant woman is at risk of experiencing complications and therefore emphasises that all pregnant women should receive the same basic care and monitoring for complications [18]. However, the WHO emphasises that once a pregnant woman has been identified to have high-risk factors, she should be referred to a higher level of care [18]. The WHO therefore advocates that after the initial assessment, pregnant women should be categorised into two groups: those who have low-risk factors who should follow the FANC reduced number of ANC visits approach and those who have high-risk factors who should be referred for hospital management of their pregnancies [19]. The Maternal, Child and Women’s Health Unit of the KwaZulu-Natal (KZN) Department of Health reviewed and revised its ANC guidelines on the basis of the WHO’s model of FANC to improve the quality of ANC provided at the clinics in the KZN province [20].
According to the MNH Programme [18], the FANC approach is one of several essential maternal and neonatal care interventions that are evidence-based and that build on global lessons learned about saving the lives of mothers and newborn babies. The FANC approach also includes a classifying form designed to assist ANC health-care providers to identify women who have conditions requiring treatment and more frequent monitoring. It also includes classifying forms needed to implement the package and instructions for its use [19].
The WHO provided key recommendations which form standards for maternal and neonatal care service delivery, providing guidance for assisting countries to improve the health and survival of women and newborn babies during pregnancy, childbirth and the postnatal period and can be modified to suit the circumstances of a specific country [21]. These WHO provisions allow each country, intending to adopt the FANC approach, to modify the guidelines to suit the circumstances of the specific country. The WHO indicates that it might be necessary, when introducing the FANC package in practice (depending on the specific country), that the country’s national clinical standards and guidelines for ANC might require updating, the pre-service training curricula in ANC and in-service training for ANC providers and their supervisors might need to be modified, and a plan for implementing changes with regard to medications, equipment and supplies to implement the package should be assessed [21].
4. Approaches to antenatal care services in South Africa
Until 2007, South Africa used the traditional approach to ANC. Historically, this traditional ANC service model was developed in the early 1900s. This model assumed that frequent ANC visit, and classifying pregnant women into low- and high-risk groups by predicting potential obstetric complications, was the best way to care for the mother and the foetus [22]. The use of the traditional ANC approach in South Africa was prescribed by the South African Nursing Council (SANC) in the scope of practice for midwives [23]. The SANC prescribed that the midwives should ensure that pregnant women attend ANC clinics once a month until 28 weeks’ gestation and thereafter every fortnight until 36 weeks’ gestation. Thereafter, a pregnant woman should continue attending the clinic at PHC level every week until her baby is born or until she reached 42 weeks’ gestation whichever comes first. Should the woman not give birth by 42 weeks’ gestation, she had to be referred for hospital management [23]. With the traditional approach, a pregnant woman could have up to 12 ANC visits conducted at a PHC clinic level during one pregnancy. This is one of the aspects that have been challenged by the WHO [24].
The traditional ANC approach was replaced by the FANC approach which is a goal-oriented ANC approach that was recommended by researchers during 2001 and adopted by the WHO in 2002 [21]. The NDoH identified BANC as the ideal approach to ensure that quality and effective ANC is provided [25]. According to the Saving Babies Report 2008–2009, improvement in access to good-quality ANC services could make a major contribution towards reducing perinatal and child deaths [26].
South Africa adopted and modified the FANC model to suit the South African circumstances and referred to it as the BANC approach [27, 28]. This followed the realisation by the NDoH that the traditional ANC approach was not working well for South Africa. Midwives, the key providers of ANC services, requested for a programme based on the principles used in the Integrated Management of Childhood Illnesses (IMCI) programme with flow diagrams and protocols [2]. In 2007, the NDoH advised that all health facilities providing ANC services had to adopt the BANC approach by the end of 2008 [29]. The BANC approach is used in the public health institutions of South Africa to provide healthcare services to pregnant women and is listed as one of the priority interventions for reducing maternal and child mortality in this country [25]. South Africa’s NDoH introduced the BANC approach in 2007 and advised that all health facilities providing antenatal care (ANC) services should have adopted this approach by the end of 2008 [29]. The NDoH provided training for the lead trainers from all the provinces and made available various documents such as a handbook, guidelines and guides for facility managers [2, 28, 29]. The lead trainers were expected to cascade the training into their respective provinces and to institute and facilitate the implementation of the BANC approach.
5. The basic antenatal care (BANC) approach
Pattinson [28] describes the BANC approach as the minimum level of ANC that every pregnant woman should receive. Every aspect of the BANC approach has been developed from the best research evidence, and the only aspects of ANC that have been shown to be effective are included in the BANC approach [28]. The BANC approach does not intend to replace any existing programme but aims to combine all resources and to facilitate their use [28]. The BANC approach was introduced as a quality improvement strategy based on the belief that good-quality ANC could reduce maternal and perinatal mortalities and improve maternal health, aiming to achieve MDGs 4 and 5 [30]. This then led to the introduction of the BANC approach in the PHC clinics. Thus, the BANC was an approach being used in South Africa to render ANC services during the time of this study.
The BANC approach has been simplified to the bare minimum so that ANC services can be provided by every PHC clinic’s midwives [28]. Because the BANC approach is a modified version of the FANC approach, it has many characteristics similar to the FANC approach. These include the approach focusing on early ANC attendance by all pregnant women and on limiting the total number of ANC visits to a minimum of four or five visits per pregnancy for low-risk women. This requires that ANC services should be provided daily at every facility frequented by pregnant women so that the first ANC visit takes place as soon as the pregnancy has been confirmed or the very first time that a pregnant woman visits a health facility [28]. If a pregnant woman is brought into the health system early, her health problems could be detected and managed or controlled early and treatment then has a greater chance of success. Pattinson [28] also states that all pregnant women with high-risk factors should be referred to the next level of care so that nurses at PHC level have sufficient time to attend to women with low-risk factors. Every site where pregnant women make contact with health services should be utilised because if all PHC clinics are providing BANC, then ANC could be started as soon as the pregnancy had been confirmed [2].
The BANC approach requires that two sets of checklists be used for recording purposes during ANC visits: one checklist to record the first visit and the other to use during subsequent follow-up visits. Pattinson [28] recommends that before commencing implementation of the BANC approach, each facility has to develop its own specific protocols for the management of obstetric conditions which must be in line with the South African National Maternity Care Guidelines and should be displayed in the facility. All the protocols should be counter-signed by the head of the obstetric unit from the hospital to which the facility refers the women with high-risk factors or complications during pregnancy. The protocols should be reviewed annually. Regular auditing of the ANC service should be an on-going process to ensure continuous improvement based on identifying and addressing potential shortcomings [2].
The BANC approach focuses on the quality rather than on the quantity of visits, with special emphasis on the fact that every visit should be goal directed [31]. The approach is included in the list of strategies provided by the NDoH to achieve MDGs 4 and 5 which are to reduce perinatal deaths and improve maternal health by 2015 [32]. A baseline audit of the ANC service and an analysis of the strengths, weaknesses, opportunities and threats (SWOT) of the facility should be conducted before commencing the implementation of the BANC approach. This enables the midwives to compile a realistic plan and process map for the implementation of the BANC approach [2]. Documents such as the handbook, guidelines and facility manager’s guides are available to be used by the midwives during the implementation of the BANC approach [2]. According to the BANC handbook, each clinic should have one or more supervisors to perform the clinical supervision and the administrative tasks [2]. The manager is responsible for providing supportive supervision to the staff members in order to ensure that the clinic’s programmes are implemented successfully [2].
6. Provision of antenatal care services according to the basic antenatal care approach
While the BANC approach is adapted from the WHO’s FANC model, it is also designed similar to the IMCI programme [2]. This decision was taken in response to the midwives’ request for an ANC programme that has flow diagrams and protocols similar to the IMCI programme. The midwives hoped that having such a programme would assist them to render safer and better quality health care to the pregnant women [2]. It is for this reason that the BANC approach is sometimes referred to as the integrated management of pregnancy and childbirth [2, 33].
The NDoH also identified BANC as an ideal approach to ensure that quality and effective ANC is provided [25]. The implementation of BANC is seen as a positive measure to improve the quality of ANC in PHC clinics [7]. Effective and quality ANC could assist South Africa to address the problem of constantly increasing maternal and perinatal mortalities. Snyman [6] stated that the BANC quality improvement package is designed to assist ANC-related clinical management and decision-making at PHC level. This author conducted a qualitative study to assess the effectiveness of the BANC package for improving the quality of ANC services rendered at PHC facilities. With the implementation of the BANC approach, the organisational changes required at the facility level for the improvement of ANC services are facilitated with tools like the integrated flow charts for pregnant women’s management, referral protocols and checklists. This could potentially have a positive impact on the outcomes of pregnancies [7].
Guidelines on how to conduct ANC visits are detailed in the Basic Antenatal Care Principles of Good Care and Guidelines [28]. These guidelines have been adapted from a guide for essential practice by the WHO titled ‘Pregnancy, Childbirth, Postpartum and Newborn Care’ [28]. According to the BANC Principles of Good Care and Guidelines, the principles of good care include communication, workplace and administrative procedures, universal precautions, and cleanliness and organisation of ANC visits [28].
It is stated in the guidelines that communication, privacy and confidentiality during examination and counselling should be ensured at each ANC visit [28]. The importance of service hours, the availability of equipment and drugs, record keeping, and infection prevention and control are highlighted as part of the workplace and administrative procedures [28]. The guidelines describe how the ANC visits should be organised, highlighting that ANC should always begin with rapid assessment and management. All pregnant women, except those with high-risk factors, should have four to five routine ANC visits.
A pregnancy status and birth plan chart, which should be used to assess the pregnant women at each of the four ANC visits, are provided [28]. The chart is used during the first ANC visit to prepare the birth and emergency plan and reviewed and modified according to the need at each subsequent ANC visit. ‘Ask, check, look listen and feel’ criteria should always be followed during assessments of pregnant women. All pregnant women should be screened for preeclampsia, anaemia, foetal growth and post-maturity at all ANC visits [28]. All women should also be screened for syphilis, Human Immunodeficiency Virus (HIV) and Rhesus factor (RH) [28]. All routine investigations, including the rapid plasma reagent (RPR) test, haemoglobin (Hb) level test, HIV and RH tests should be done using rapid test kits. The guidelines highlight the importance of responding to observed signs and/or problems reported by the pregnant women and contain a guide on how to respond to these signs [28].
Standard preventative therapy, including tetanus toxoid injections, iron preparations and calcium supplements, should be issued to all pregnant women at each ANC [28]. A guide is included on how to advise women about nutrition and self-care [28]. The guidelines highlight the importance of preparing individualised ANC and delivery plans for each woman at the first ANC visit and that the plans should be reviewed during each subsequent visit and adjusted based on the identified needs. The plan should be prepared in consultation with the woman concerned. This ensures that the woman is involved in her own care. The plans should also include transport arrangements, infant feeding options and future contraception. A description of how the first and the follow-up visits should be conducted is provided [28].
The guidelines state that the first ANC visit should take place as early in pregnancy as possible, before 12 weeks’ gestation, preferably at the confirmation of pregnancy [28]. During the first ANC visit, all women should be classified for BANC using the classifying form/first visit checklist provided. Only women with low-risk factors should follow the BANC approach. All women with risk factors should either be referred to an appropriate level of care or follow a specially prepared schedule based on the risk factors identified. Four follow-up visits should be scheduled at 20, 26, 32 and 38 weeks’ gestation. Specific times are scheduled for performing repeat routine tests such as Hb, HIV and RPR, and these times coincide with specific routine follow-up visits. It is therefore important to schedule the follow-up visits as specified by the BANC guidelines in order to ensure the correct timing of repeat tests.
Pattinson [2] suggests that each PHC clinic should have one or more people in the role of ANC supervisor to ensure clinical and administrative supervision. The clinical supervisor should be the person with most ANC skills and should check each pregnant woman’s ANC card at the first visit and again at the 32 weeks’ visit to ensure that the clinic provides adequate care [2].
All information regarding pregnancy and consultation should be recorded in an ANC card which should not be filed at the clinic but which should be kept by the pregnant woman. The woman is advised to always carry the ANC card with her, wherever she goes, and to produce the card each time she visits any health-care institution. This practice facilitates communication between the different health-care providers involved in the care of women during pregnancy and childbirth [2].
7. Discussion
Several factors have been identified to be positively influencing the implementation of the BANC approach. These include the availability and accessibility of BANC services, policies, guidelines and protocol; various means of communication; a comprehensive package of and the integration of primary healthcare services; training and in-service education; human and material resources; the support and supervision offered to the midwives by the primary health-care supervisors; supervisors’ understanding of the approach and the levels of experience of midwives involved in the implementation of the BANC approach [34] Nevertheless, evidence still shows that not all PHC clinics have been able to successfully implement and sustain the BANC approach [35]. Ngxongo [35] discovered that out of 59 Municipal PHC clinics in eThekwini District in KwaZulu-Natal, 46% (n = 27) were successfully implementing the BANC approach. Midwives face various challenges during the implementation of the BANC approach which has resulted in some PHC clinics abandoning the BANC approach and reverting to the traditional approach to ANC [35]. These challenges include shortage of staff, lack of cooperation from referral hospitals, lack of in-service training, problems with transportation of specimens to laboratories, lack of material resources, unavailability of Basic Antenatal Care programme guidelines and lack of management support [35].
Although the BANC approach emphasises quality over quantity of visits [36], reducing the number of ANC visits has posed numerous challenges in the pregnancy outcomes. According to Hofmeyr and Mentrop [37], too few visits and the long interval between routine ANC visits in late pregnancy in the BANC approach have been responsible for a number of maternal and perinatal deaths. Hofmeyr and Mentrop [37] argue that the more frequent and closely spaced ANC visits as pregnancy advances in the traditional approach assisted in early diagnosis and management of selected ANC problems such as preeclampsia, foetal growth impairment and others and that too few visits result in missed opportunities to detect and treat asymptomatic pregnancy complications. These authors recommend modification of the BANC approach into what they call ‘BANC plus’. Their proposal is that a reasonable compromise for a middle-income country such as South Africa would be to continue to implement the WHO BANC approach with reduced, goal-orientated visits up to 32 weeks’ gestation and thereafter to revert to routine visits every 2–36 or 38 weeks, followed by weekly checks.
The international evidence supports a more regular contact between healthcare workers and pregnant women. Therefore, South Africa is gradually switching to an eight-contact model (three more visits than the current five contact Basic Antenatal Care (BANC) policy) [38]. It is envisaged that this intervention will improve the pregnancy experience as well as the outcomes of pregnant women and their babies in South Africa. The BANC + continues to emphasise the importance of conducting the first visit as early as possible, with the next visit scheduled at 20 weeks and then repeat visits at 26 weeks. The adjustments include the 30 weeks and 34 weeks and then a 2-week visit until delivery. An audit of the current BANC system has shown that two important principles of good care were often missing: a plan for further antenatal care and the delivery plan (including delivery at the appropriate level of care or hospital). Therefore, appropriate planning for the pregnancy as well as for the delivery, based on information obtained and correctly interpreted at every visit, will ensure that women and their families are ready and prepared when the big day arrives. The purpose of BANC+ is not just to increase the number of visits but also an opportunity to look again at how that care is given [38].
8. Conclusion
The introduction of the BANC approach has been a positive milestone for South Africa. Studies show that many African countries such as Ghana, Kenya, Tanzania and others have seen positive results with the implementation of the WHO FANC model [1, 8, 17]. Although South Africa is still experiencing numerous challenges with the BANC approach, there is hope that this country will also achieve positive results as the country continues to adjust and improve the BANC approach to suit its circumstances.
Acknowledgments
The author would like to acknowledge the following: Prof. NS Sibiya and Prof. NS Gwele; Durban University of Technology; SANTRUST, Fundisa and NRF.
Conflict of interest
The author declares that she has no financial or personal relationship which may have inappropriately influenced her in writing this chapter.
\n',keywords:"antenatal care, approach to health care, basic antenatal care, pregnancy, pregnancy outcome, South Africa",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/62277.pdf",chapterXML:"https://mts.intechopen.com/source/xml/62277.xml",downloadPdfUrl:"/chapter/pdf-download/62277",previewPdfUrl:"/chapter/pdf-preview/62277",totalDownloads:1042,totalViews:1666,totalCrossrefCites:0,dateSubmitted:"February 1st 2018",dateReviewed:"June 7th 2018",datePrePublished:"November 5th 2018",datePublished:"February 8th 2019",readingETA:"0",abstract:"Globally, antenatal care is advocated as the cornerstone for reducing children’s deaths and improving maternal health. The basic antenatal care approach is used in the public health institutions in South Africa to provide healthcare services to the pregnant women. The basic antenatal care approach is a modified version of the focused antenatal care approach that was recommended by researchers during 2001 and adopted by the World Health Organisation in 2002 following realisation that traditional antenatal care programmes that were meant for developed countries were poorly implemented and largely ineffective when used in developing countries. The basic antenatal care approach is listed as one of the priority interventions for reducing maternal and child mortality in the country and is recommended as the minimum level of antenatal care that every pregnant woman should receive. Every site where pregnant women make contact with healthcare services should provide antenatal care services daily using this approach so that the first antenatal care visit consultation takes place as soon as the pregnancy has been confirmed or the very first time that a pregnant woman visits a health facility. The introductions of the basic antenatal care approach have been a positive milestone for South Africa.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/62277",risUrl:"/chapter/ris/62277",signatures:"Thembelihle Sylvia Patience Ngxongo",book:{id:"7259",title:"Selected Topics in Midwifery Care",subtitle:null,fullTitle:"Selected Topics in Midwifery Care",slug:"selected-topics-in-midwifery-care",publishedDate:"February 8th 2019",bookSignature:"Ana Polona Mivšek",coverURL:"https://cdn.intechopen.com/books/images_new/7259.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"85109",title:"Dr.",name:"Ana Polona",middleName:null,surname:"Mivšek",slug:"ana-polona-mivsek",fullName:"Ana Polona Mivšek"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"243711",title:"Dr.",name:"Thembelihle Sylvia Patience",middleName:null,surname:"Ngxongo",fullName:"Thembelihle Sylvia Patience Ngxongo",slug:"thembelihle-sylvia-patience-ngxongo",email:"thembelihlen@dut.ac.za",position:null,institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Importance of antenatal care",level:"1"},{id:"sec_3",title:"3. Approaches to antenatal care",level:"1"},{id:"sec_4",title:"4. Approaches to antenatal care services in South Africa",level:"1"},{id:"sec_5",title:"5. The basic antenatal care (BANC) approach",level:"1"},{id:"sec_6",title:"6. Provision of antenatal care services according to the basic antenatal care approach",level:"1"},{id:"sec_7",title:"7. Discussion",level:"1"},{id:"sec_8",title:"8. Conclusion",level:"1"},{id:"sec_9",title:"Acknowledgments",level:"1"},{id:"sec_12",title:"Conflict of interest",level:"1"}],chapterReferences:[{id:"B1",body:'Ekabua J, Ekabua K, Njoku C. Proposed framework for making focussed antenatal care services accessible: A review of the Nigerian setting. ISRN Obstetrics and Gynecology. 2011. DOI: 10.5402/2011/253964'},{id:"B2",body:'Pattinson RC. Basic Antenatal Care Handbook. 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Patterns of routine antenatal care for low-risk pregnancies: Database of systematic review [Internet]. 2007. Available from: www.who.int/rhl/reviews/langs/CD000934.pdf [Accessed: 2013-08-09]'},{id:"B16",body:'The Free Library Population brief: Focussed ANC acceptable, tricky to implement [Internet]. 2007. Available from: www.popcouncil.org/uploads/pdfs/…/RH_FocussedAntenatalCare_A4.pdf [Accessed: 2013-02-02]'},{id:"B17",body:'Mathole T, Lindmark G, Ahlberg BM. Dilemmas and paradoxes in providing and changing antenatal care. Health Policy and Planning. 2005;20(6):385-393. DOI: 10.1093/heapol/czi046'},{id:"B18",body:'Maternal and Neonatal Health Programme. Focused antenatal care: Planning and providing care during pregnancy. [Internet]. 2004. Available from: www.mnh.jhpiego.org [Accessed: 2004-09-21]'},{id:"B19",body:'World Health Organization. WHO Programme to Map Best Reproductive Health Practices—WHO Antenatal Care Randomized Trial: Manual for Implementation of the New Model. Geneva: WHO; 2002'},{id:"B20",body:'Population Council. Adapting focussed antenatal lessons from three African countries. Program Brief No. 11. July 2008. [Internet]. 2008. Available from: www.popcouncil.org/uploads/pdfs/frontiers/pbriefs/PB11.pdf [Accessed: 2013-08-28]'},{id:"B21",body:'World Health Organization. Standards for maternal and neonatal care: Making pregnancy safer [Internet]. 2007. Available from: www.who.int/reproductivehealth/publications/maternal…health/…/en/ [Accessed: 2014-07-09]'},{id:"B22",body:'Ethiopia Health Education and Training (HEAT) Module. Antenatal Care Ethiopia HEAT Module [Internet]. 2004. Available from: www.open.edu/openlearnworks/mod/oucontent/view.php?id=28 [Accessed: 2014-10-19]'},{id:"B23",body:'South African Nursing Council. R2598. Regulations relating to the scope of practice of persons who are registered or enrolled [Internet]. 1991. 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Guidelines for Maternity Care in South Africa. A Manual for Clinics, Community Health Care Centres and District Hospitals. 3rd ed. Pretoria: Government Printer; 2007'},{id:"B33",body:'Mhlanga E. Maternal, Newborn and Child Health: 30 Years on. [Internet]. 2012. Available from: www.hst.org.za/uploads/files/chap8 08.pdf [Accessed: 2013-07-08]'},{id:"B34",body:'Ngxongo TSP. Factors influencing successful implementation of basic antenatal care in eThekwini district [thesis M. Tech dissertation]. Durban: Durban University of Technology; 2011'},{id:"B35",body:'Ngxongo TSP, Sibiya MN. Challenges regarding the implementation of basic antenatal care in eThekwini district, KwaZulu-Natal. Journal of Nursing. 2013;22(7):906-913'},{id:"B36",body:'Kinze B, Gomez P. Basic Maternal and Newborn Car: A Guide for Skilled Providers. Baltimore, MD: JHPIEGO/MNH Program; 2004'},{id:"B37",body:'Hofmeyr GJ, Mentrop L. Time for ‘basic antenatal care plus’ in South Africa? South African Medical Journal. 2015;105(11):902-903. DOI: 10.7196/SAMJ.2015.v105i11.10186'},{id:"B38",body:'World Health Organization. What’s new? Decreasing deaths during pregnancy in South Africa by improving antenatal care [Internet]. 2018. Available from: www.who.int [Accessed: 2018-02-11]'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Thembelihle Sylvia Patience Ngxongo",address:"thembelihlen@dut.ac.za",affiliation:'
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