Perspective Chapter: Fabulous Design Speed Industrial Robotic Arm

Abstract

This chapter focuses on the design of a handling 5 Degree of freedom (DOF) robot arm model for industrial application. Optimal trajectory planning of industrial robots in the assembly line is a key topic to boost productivity in a variety of manufacturing activities. The aim is to improve the speed performance using multi techniques starting from estimating the transfer function of each manipulated joint, then designing the controller for each DOF reached to modeling arm motion. The designed model has been developed the structural design and testing motion characteristics by using SolidWorks and Simscape toolbox. To enhance the speed performance, it is proposed a High-Speed Proportional Integral Derivative controller (HSPID) based on an improved GA. The comparison response time between uncontrolled and controlled systems proves that the proposed controller produced extreme reduction responses to be measured within the Microsecond unit. Based on trajectory motion, the efficiency of the proposed method is assured by case study motions. The innovative design offers the best solution to rise accurate performance and productivity.

1. Introduction

For decades, polymorphic robots are one of the most widely used mechatronic systems in the industry, which has generated the need to constantly create industrial robots with more power, speed, and precision for a wide variety of tasks to improve automation systems precisely offering lower-cost production [1, 2, 3, 4]. The manufacturing sector is moving towards industry 4.0 and demands high-end automation in the process [5]. Due to their great usefulness in the industry, industrial robot arms are widely used to move material, parts, and tools as well as the welding and painting of parts [6], offers a powerful performance in terms speed, repetitive and seemingly intelligent decisions [7, 8, 9, 10]. Structurally, a robot arm is constructed from several parts such as manipulator links, actuators, controller, and sensors where the controller acts as the brain to manipulate the mechanical parts [11, 12, 13]. A robot arm manipulator is constructed from links and joints to control the robot’s trajectory. The links of such a manipulator are connected by joints allowing either rotational motion such as in an articulated robot or translational (linear) displacement. Usually, the end effector is attached to the end joint of the structure [14, 15, 16, 17]. Precise control at each DOF of a robotic arm is considered a competitive key to improving performance through the implementation of industrial robotic arms [18, 19]. The most remarkable controller’s strategies are impedance control, force control, motion control, and hybrid motion-force control [20]. On the one side, optimizing the estimation TF model is the most important criterion to enhance controller’s design [21]. On the other side, the basis for developing a control system for a robot manipulator is a feedback loop. Therefore, it is necessary to define input signals such as torque and drive input voltage to achieve the desired operation [22, 23]. For several decades, the Proportional Integral Derivative (PID) algorithm is one of the most widely used in the industry for controlling closed-loop feedback systems, because of the less complexity with the ability to meet desired controller’s functions for wide scope plant models [24, 25, 26]. It stands for three proportional gains: proportional (Kp), integral (Ki), and derivative (Kd), where they should be jointly tuned to get better performance [27, 28]. Despite having only three parameters, the classical PID controller has been unable to meet the sophisticated requirements [29, 30, 31]. The problem with PID has been identified as poor tuning, which means that most of the controllers currently in operation have been poorly tuned. This results in a biased judgment against the PID controllers themselves [32]. The controller tuning greatly affects the control system properties, such as robustness to disturbances and noise [33].

Over 50 years, massive tuning strategies have been suggested to realize satisfied response time characteristics in terms of peak overshoot (Pos), rise time(tr), and settling time (ts). Optimizing PID controller performance can be achieved by considering systematic proportional gain adjustments, otherwise, the tuning will be inadequate and the process testing will take longer [34]. Tuning and optimizing PID gains improves the convergence speed and the global optimization by reduces the overshooting and transition time of the plant system [35]. In fact, an evolutionary algorithm (EA) presents the best solution to optimize PID gains by adapting to the system’s nonlinearity [36]. GAs are the first-class category of EA that is commonly used to generate high-quality solutions to optimize PID parameters, by relying on bio-inspired operators such as mutation, crossover, and selection [37, 38]. Usually, GA is applied to optimize a function called fitness function (FF). The FF assists GA algorithms in measuring the quality of the solution of the problem under study and how effective the solution of the problem [39]. In designing the controller, it is related to performance indices such as settling time, integral error, and so on, and might be addressed as a multiobjective function to improve the controller’s response [40].

GAs are satisfied in solving multi-objective optimization problems. A possible solution to a problem is considered individual. A group of individuals is called a population. The current population produces a new generation, eventually ceases when it reaches an individual who represents the optimal solution to the problem [41, 42]. A conventional GA requires two variables to be determined, a FF composed of a performance index ($P\mathit{\text{indices}}$) and a genetic representation of the solution domain. To formulate the performance index for PID controllers, several related researchers use the following equations to formulate cost functions such as:

integral squared error(ISE); integral absolute error (IAE); integral time squared error (ITSE); integral time absolute error (ITAE); and mean squared error(MSE) as illustrated from Eq. (1) to (5) respectively. Besides that, as it is needed to reduce the error, the FF equation is taken as an inverse of the performance indices as Eq. (6).

$$\mathit{ISE}={\int }_0^T{\left|e\left(t\right)\right|}^2.d\left(t\right)$$E1

$$\mathit{IAE}={\int }_0^T\left|e\left(t\right)\right|.d\left(t\right)$$E2

$$\mathit{\text{ITSE}}={\int }_0^{T}t{\left|e\left(t\right)\right|}^2.d\left(t\right)$$E3

$$\mathit{\text{ITAE}}={\int }_0^{T}t\left|e\left(t\right)\right|.d\left(t\right)$$E4

$$\mathit{MSE}=\frac{1}{t}{\int }_0^T{\left(e\left(t\right)\right)}^2.d\left(t\right)$$E5

$$\mathit{FF}=\frac{1}{P\mathit{\text{indices}}}$$E6

Basically, GA problems rely on three operators: selection, mutation, and crossover [43, 44, 45, 46, 47, 48]. In fact, traditional GA generates random population that might produce poor fitness and low-quality of individuals, leading to consume more time to converge through optimized solutions. Therefore, the quality of an initial population of individuals reflected considerably on the GA’s performance to produce an optimal solution. Most previous techniques concentrate on the quality of the initial population seeding, such as random initialization, nearest neighbor, and K-means clustering [49, 50, 51]. Some researchers used GA to optimize PID, for instance, Guan and Jau [52], Swati K. et al. [53], Tanvir ert et al. [54], Gun B. S. [55], and Apriaskar et al. [56]. On the other side, PSO is one of the EA’s that was developed by James Kennedy and Russell Eberhart in 1995, for solving practical issues related to optimization, inspired by the behavior of living things. It has several benefits such as being simple implementation, featuring a simple concept, efficacious computation, and more cost-effective, flexible, and balanced mechanism to improve a global and local exploration abilities [57, 58, 59, 60]. Recently, several studies using PSO to optimize PID controllers such as M. I. M. Zakki et al. [61], V. Bagyaveereswaran et al. [62], Y. Xie and J. Meng [63], B. A. Arain et al. [64], S. Howimanporn et al. [65].

Regarding previous works for optimizing PID controllers, the PSO is faster than GA when looking closely at idealistic solutions in case of does not require a detailed mathematical description of the process for formulating the Objective Function (OF) to optimize proportional gains, where the drawbacks of PSO are the lack of certainty that an optimal solution will be found and even the high computational costs associated with FF [66, 67, 68]. Consequently, standard PSOs often fail to solve these complex problems because they easily get stuck in local optima and converge slowly [69]. One of the main differences between PSO and GA is the mechanism of perturbing the solution from the old population to create a new population. These different mechanisms generate a population of solutions with different balances of enrichment and diversification. For GA, the solutions are arranged based on their fitness values [70]. Based on survey, classical GA is not the best solution with respect to PSO. A serious downside of GA comes from the way new generations are computed after the first. It contains a random component that causes generated values to be corrupted during the early stages of global search. Where proposed methods for initial seeding of populations are limited. The limited number of this approach motivates this study because there is room for improvement and finding a better starting population. To improve GA’s performance, it was proposed to apply a new technique to GA to raise precise searching constraints by introducing a new Modified Initialization Fitness Function (MIFF) technique. The proposed was applied to optimize the PID controller for each manipulated joint to enhance velocity performance. Model-Based Design Approach (MBDA) is an advanced simulation technique that is widely used to improve system design, providing explicit models to define activities in the product design and development lifecycle [71]. Additionally, rapid technology using computer-aided design (CAD) enables free-form fabrication of parts with complex geometries directly from CAD models on CNC machines without the need for special fixtures as in the material removal process, provides the best tools for developing products, faster, lower cost and more Competitive Global Market [72, 73]. The collaboration between MathWorks and SolidWorks is one of the best solutions for designing and simulating robot motion, optimizing system parameters, analyzing results in the Simulink environment, analyzing forces due to torque on mechanical joints, provides a nice tool for plotting acceleration due to displacement of arbitrary parts, visualize the motion of CAD assemblies and simplify the physics of mechanical systems without the need to derive equations of motion [74]. The concept and design of robotic arms is not a new concept but still, much work and development are required to enable robots to perform complex tasks. The challenge for robotic technology is to make it compatible with human tasks and hand movements, such as grabbing, swapping, and completing critical tasks. In this way, when we were able to precisely control the movement of the robot, we succeeded in developing the robot arm [75, 76]. In reality, the precise control of each degree of freedom of a robotic arm is a great challenge in implementing industrial work [77]. The robot simulation is used to know the robot torque that will improve and optimize the movement of the arm robot so the robot can help the industry to produce effectively and efficiently [78]. Nowadays, the modeling and control of mechatronic and robotic systems is an open and challenging field of investigation in both industry and academia. The mathematical model of a mechanical system is indeed fundamental for the development of experimental prototypes [79]. On the other side, optimal trajectory planning of industrial robots in the assembly line is a key topic to boost productivity in a variety of manufacturing tasks [80]. The main focus of this work is the design of a 5-DOF industrial robotic arm that further enhanced speed performance and optimized trajectory planning by modeling an HSPID controller based on improved GA (IGA). The GA is implemented based on MIFF as demonstrated in [81]. This provides an opportunity to maximize significantly response time.

The goal is to achieve high-speed performance in designs composed through motion components, which can be concluded as follows: 1) easily create geometric robot parts to assemble; 2) modeling and simulation of the robot arm; 3) Minimize the response time characteristics in terms of tr, ts, and PoS. This can increase the speed of moving the arm from the initial state point to the final state point and significantly reduce the cycle time. SolidWorks was used to design the mechanical structure of the robotic arm. Then perform plugin-based model integration to design controller models within Simscape compatible models, leads to export (XML) files including the part’s structure of each component for the base, shoulder, upper and lower arm, and wrist end effector. All the parts are assembled and a HSPID controller is implemented in each DOF of the robot using the Simscape blockset to construct the whole system. Finally, each manipulated joint was examined for in terms of tr, ts, and PoS. This chapter is organized as follows: Section 2 presents the design methodology, including modeling the Simscape configuration, estimating TFs of each manipulated joint, designing the HSPID controller, and a motion detection strategy. Section 3 presents the simulation results approach for estimating TFs, the response time of the designed model with and without a controller, and the simulation results approach for estimating motion based on three different trajectory signals. Section 4 discusses of the results. Section 5 summarizes the results and provides recommendations for future research.

2. Procedure design methodology

This section describes process design techniques including modeling, simulation, and HSPID controllers. Basically, a robotic arm consists of 5 limbs and 5 joints. To verify system-level design and simulation models, we need to define the structure of the system and its behavior. In this work, models related to Solidworks and Simscape were semantically defined using plugin-based model integration to obtain compatible structural and simulatable models leads to export of the models in XML file. The organizational charting procedure design methodology shown in Figure 1 includes various blocks as shown in the following diagram.

• Mechanical configuration and assembly components.

• Modeling Simscape.

• Estimation TFs of the manipulator’s joints.

• Designing HSPID controller for joint’s manipulators.

• Mimic trajectory planning.

• Analyze response time characteristics and motion results.

Figure 1.

Scheme of design procedure.

2.1 3D CAD component design and assembly

It is possible to simulate the mechanical behavior of the robot components using axis material during the motion study of the robot, by using SolidWorks in conjunction with Matlab to design high-quality control systems, providing the ability to transform all the component’s parameters into XML files, to be imported a dynamic parameter of the physical structure into MATLAB environment, including the inertia matrix calculations for each manipulated joint [82], offers an amazing solution that could be allowed to perform the drawing of a mechanical model to be applied in as a real geometric and mass measurements. In this study, the components (rigid bodies) are built individually and assembled links serially. Figure 2 presents all the designed rigid bodies of the robotic arm labeled from base to tip: base, shoulder, lower arm, upper arm, connector, Wrist, and end effector. First, we need to attach the base to the robot frame, connect the shoulders to the forearms, connect the upper arms to the forearms via connectors, and connect the wrists to two rigid upper arm bodies. Also, the end effector must be attached to the object for manipulation. In addition to determining the size parameters of the system such as body, height, and weight, the rotation of the rotary joints should be installed. A motion analysis is then presented to verify the effectiveness of the model configuration in terms of velocity and distance. Consequently, different parameters with different settings will lead to various results. Figure 3 shows the whole system constructed based on 5 joints and 5 links.

Figure 2.

Three-dimensional solid rigid parts, (a) lower arm, (b) upper arm, (c) connector, (d) shoulder, (e) wrist, (f) end effector, (g) base.

Figure 3.

Designed robot model.

2.2 Modeling Simscape

The Simscape Multibody is used to perform the simulation of links, joints, and dynamic analysis motion. The 3D solid model contains the robot body and a manipulated joint is being used for assembling the whole system. Further, employ SimMechanics tools to produce the XML file for each rigid body. The floor blockset was used as a world frame reference for rigid transformation to set the gravitational force direction. To investigate the motion parameters and response time characteristics, it was used a scope simulator for this purpose. Figure 4 illustrates the Simscape model of the whole system, representing the joint revolutions and rigid parts as follows; base, shoulder, lower arm, connector, upper arm, wrist, and the end effector.

Figure 4.

Simscape model of the whole system.

2.3 Estimate TF of the manipulator’s joint

To design a motion controller, we need to estimate the TF for each manipulator joint. This is considered a significant problem in most previous studies, where poor estimation accuracy leads to poor controller design [83]. In this subsection, we present the procedure of estimation TF form utilizing the linear analysis tool for each manipulator’s joint, which represented a nonlinearity plant system. Nine steps were performed in the estimation as follows:

• Open the Model Linearization Tool from a Simscape model.

• Set Actuation to Motion Selection on the joint rotation, and set Sensing on Velocity to make a connection with revolution joint system, then highlight the signals as an analysis point.

• Select Linearization Manager from the Simulink Apps gallery, to assign the portion of the model to linearize.

• Choose the Signal in the model to specify an analysis point for the injected signal. Then select the type of analysis point from the Insert Analysis Points gallery on the Linearization tab.

• Specifying an additive input to a signal by configuring the revolution block’s input signal as an Input Perturbation.

• Setting the revolution block’s output signal to be an open-loop output to take the measurement from the injected signal.

• At this point, the software adds annotations to the model that describe the type of linear analysis point after the analysis points are finished, and identify the type of analysis point for the Simscape model for each linear analysis point.

• Select the linear model (transfer function) in the Linear Analysis Workspace, then choose Result Viewer from the Plots and Results Viewer to see the linearized model equations.

• To be defined the TF of the other revolution components, repeat steps 2 and 3 for all signals.

2.4 Proposed IGA

The most important feature of the GA is how it transforms the system output into a fitness value to depress the errors in the reference trajectories of the plant model-based PID controller. Therefore, the chosen IAE evolution or FF should be used to compute the total error between the reference and the system output for each set of generated PID gains. By proposing two techniques the GA could be significantly improved. Firstly, using optimization-based tune (OBT) to find the best optimal solution as explained in [31]. Secondly, initialized FF based on the best optimal constraints to initialize the constraints of GA chromosomes as demonstrated in [73], to modify initialization FF (MIFF) based on the best optimal constraints using CHR tuning method to improve constraint’s level of GA chromosomes. This method represented as a $\mathit{CH}{R}_{\mathit{OBT}}$, where the proportional gains which resulted by $\mathit{CH}{R}_{\mathit{OBT}}$ are $\left(K{p}_{\mathit{CH}{R}_{\mathit{OBT}}}\right)$,$\left(K{i}_{\mathit{CH}{R}_{\mathit{OBT}}}\right)$ and $\left(K{d}_{\mathit{CH}{R}_{\mathit{OBT}}}\right)$. The mathematical expression of the cost function can be formulated as in Eq. (7).

$$\mathit{\text{Cost Function}}=\sum _{n=1}^m\frac{\mid \mathit{rn}-\mathit{yn}\mid }{m}$$E7

The initial controller gains $\mathit{Kp}\left(i,j\right)$, $\mathit{Ki}\left(i,j\right)$, $\mathit{Kd}\left(i,j\right)$ based on the results of $\mathit{CH}{R}_{\mathit{OBT}}$ can be modified regarding to generated constraints, which are represented as the following equations:

$$K{p}_{\mathit{\text{MIFF}}}\left(i,j\right)=x1\left(0\right)+K{p_{\mathit{CHR}}}_{\mathit{OBT}}$$E8

$$K{i}_{\mathit{\text{MIFF}}}\left(i,j\right)=x2\left(0\right)+K{i_{\mathit{CHR}}}_{\mathit{OBT}}$$E9

$$K{d}_{\mathit{\text{MIFF}}}\left(i,j\right)=x3\left(0\right)+K{i_{\mathit{CHR}}}_{\mathit{OBT}}$$E10

The population in each generation is represented by a 100 x 4 population (P) matrix as expressed in Eq. (11), to produce chromosomes number in the population. Each row represents one chromosome-based MIFF that compromise $K{p}_{\mathit{\text{MIFF}}}\left(i,j\right)$, $K{i}_{\mathit{\text{MIFF}}}\left(i,j\right)$, $K{\mathit{id}}_{\mathit{\text{MIFF}}}\left(i,j\right)$ and fitness values $F{F}_{\mathit{\text{MIFF}}}\left(i,j\right)$ of the corresponding chromosomes.

$$\text{P}\_\mathit{\text{MIFF}}=\left|\begin{array}{cccc}\mathit{\text{Kp}}{\left(\mathrm{1},\mathrm{1}\right)}_{\mathit{\text{MIFF}}}& \mathit{Ki}{\left(1,2\right)}_{\mathit{\text{MIFF}}}& \mathit{Kd}{\left(1,3\right)}_{\mathit{\text{MIFF}}}& F{\left(1,4\right)}_{\mathit{\text{MIFF}}}\\ \mathit{Kp}{\left(2,1\right)}_{\mathit{\text{MIFF}}}& K{i\left(2,2\right)}_{\mathit{\text{MIFF}}}& K{d\left(2,3\right)}_{\mathit{\text{MIFF}}}& F{\left(2,4\right)}_{\mathit{\text{MIFF}}}\\ \dots .& \dots .& \dots .& \dots .\\ \dots .& \dots .& \dots .& \dots \\ \mathit{Kp}{\left(i,j\right)}_{\mathit{\text{MIFF}}}& \mathit{Ki}{\left(i,j\right)}_{\mathit{\text{MIFF}}}& \mathit{Kd}{\left(i,j\right)}_{\mathit{\text{MIFF}}}& F{\left(i,j\right)}_{\mathit{\text{MIFF}}}\end{array}\right|$$E11

The cost function has been minimized subjected to $\mathit{Kp}\left(i,j\right),\mathit{Ki}\left(i,j\right),\mathit{Kd}\left(i,j\right)$ as Eq. (12), Eq. (13), Eq. (14), respectively:

$$\mathit{Kp}{min}_{\mathit{\text{MIFF}}}\le \mathit{Kp}\left(i,j\right)\le \mathit{Kp}{\mathit{max}}_{\mathit{\text{MIFF}}}$$E12

$$\mathit{Ki}{min}_{\mathit{\text{MIFF}}}\le \mathit{Ki}\left(i,j\right)\le \mathit{Ki}{\mathit{max}}_{\mathit{\text{MIFF}}}$$E13

$$\mathit{Kd}{min}_{\mathit{\text{MIFF}}}\le \mathit{Kd}\left(i,j\right)\le \mathit{Kd}{\mathit{max}}_{\mathit{\text{MIFF}}}$$E14

Where $\mathit{Kp}\left(i,j\right)$, $\mathit{Ki}\left(I,j\right),$ and$\mathit{Kd}\left(i,j\right)$ are the optimized proportional gains in the $j$^th area. The error ($e_{\mathit{\text{MIFF}}}$) and the modified cost function-based MIFF might be formulated as in Eq. (15) and Eq. (16), respectively.

$$e_{\mathit{\text{MIFF}}}=1-\frac{\mathit{Gp}\left(s\right)\ast C\left(s\right)}{1+\mathit{Gp}\left(s\right)\ast C\left(s\right)}$$E15

$$\mathit{\text{Cost functio}}{n}_{\mathit{\text{MIFF}}}=\sum _1^n\frac{\mid e_{\mathit{\text{MIFF}}\left(n\right)}\mid }{m}$$E16

$\mathit{\text{Where}}$:

(n) is the order of data depending on sampling time.

(m) is the total number of data.

The cost function was written in m-code for each estimated TF, prepared to be imported into GA toolbox, to be run the GA-based MIFF ($G{A}_{\mathit{\text{MIFF}}}$). The boundaries setting (parameters and operators) were settled as the following:

Iteration: 100; Mutation rate: 0.1; Population size: 100; Arithmetic Crossover; FF: IAE.

2.5 Designing HSPID controller for joint’s manipulators

The control topology relies on the injected signals and the feedback position of the end-effector for the demands of the robot application. Figure 5 shows the Simscape model of the robot arm based on the designed HSPID controller which is constructed from five controllers that are connected with each manipulator’s joint, allowing the joints to reach the required angles. It was modeled HSPID controllers regarding each revolution joint IGA to maximize responses with minimal loop interaction and sufficient. The HSPID controller was linked with each revolution joint through motion input with sample time(Ts) of 0.1 s. The proposed HSPID controller model ($C{\left(s\right)}_{\mathit{\text{MIFF}}}$) and the plant model ($\mathit{Gp})$ can be represented in s -domain as Eq. (17) and Eq. (18), respectively.

Figure 5.

The proposed HSPID controller based on the whole system.

$$\mathit{Gp}\left(s\right)=\frac{{\sum }_{i=0}^m\mathit{bi}{S}^i}{{\sum }_{j=0}^n{S}^j+\mathit{aj}}=\frac{b0S^m+b1S^{m-1}+\dots +\mathit{bm}-1S^m}{\mathit{ao}{S}^n+a1S^{n-1}+\dots +\mathit{\text{an}}-1S^n+\mathit{\text{an}}}$$E17

$$C{\left(s\right)}_{\mathit{\text{MIFF}}}=K{p}_{\mathit{\text{MIFF}}}+\frac{K{i}_{\mathit{\text{MIFF}}}}{s}+K{d}_{\mathit{\text{MIFF}}}\ast s$$E18

2.6 Mimic trajectory planning

The purpose of the robot controller is to send control signals to the joints so that the robot follows a particular path [84]. A trajectory is the robot’s position as a function of time, and a path is a geometric description of the motion. Simulation software can be used to examine the motion of the arm robot and confirm that the robot follows the path [10, 85]. A trajectory planning of a robot allows us to determine the continuous position paths that will guide the end-effector of the robot [86]. The robot arm is designed for various applications, among which are those where the end-effector to reduce risks industrial risks, in which case a position control is required. The position control of the robot can be approached in two ways, one referring to the joint space and the other to the task space. To verify the trajectory planning, it was utilized Simscape model to simulate the motion while it is in operation bypassing the exact rigid parameters of the whole system into Matlab environment, besides building the trajectory block signals containing a position for five different signals, that the robot arm should follow during the motion time. All of the above signals use one of three motion types: Point-To-Point (PTP), in which the robot positions of the trajectory move between them, or Continuous Path (CP), in which the signals move the manipulator tip along a given trajectory and the robot then accurately reproduces it. For displacements, the joint varies from −90° to 90°, and the displacement speed is modified by manipulating the angular frequency at 1 (rad/s).

As shown in Figure 6, we prepare three trajectory signals to execute three motion cases over a 12-second time trial to evaluate the maximum admissible torque at the end effector joint (joint 5), beginning from the initial state to the final state as presented in Figure 7a–c. The trajectory planning is inspected through multi-shape signals including straight lines, circles, and parabolic curves, according to the robot’s sequence to simulate its movement. Therefore, we will run the Simscape model to simulate the model’s angular trajectory based on the HSPID and display a 3D animation. Where the joint angles start in a fully extended vertical position at 0 degrees except the shoulder joint angle is fixed at 90 degrees. Finally, the end configuration was determined by the angular positions: shoulder = 60 deg., lower arm = 80 deg., upper arm = 60 deg., Wrist = 90 deg., end effector = 90 deg.

Figure 6.

Trajectory signals under three cases, (a) case1, (b) case 2, (c) case 3.

Figure 7.

Robot arm motion simulation-based HSPID controller under three case studies, (a)case 1, (b) case 2, (c) case 3.

3. Simulation results

In robot simulation, system analysis needs to be done [87]. The simulation results covered four subsections: manipulator joint estimation TF, optimization controller gain, motion results, and response time comparison between proposed controller and without controller.

3.1 Estimation TF of the manipulator joint

Figure 8 illustrates the best estimation TFs for the manipulator’s joints for the following components: shoulder, lower arm, upper arm, wrist, and end effector, which was created by a Linear Analysis application. It was noticed that all resulted TFs form has estimated in the fourth order system.

Figure 8.

Resulted estimation TFs of each revolution joint compnents, (a) shoulder, (b) lower arm, (c) upper arm, (d) wrist, (e) end effector.

3.2 Response time without controller

The response time curves of the uncontrolled system are presented in Figure 9. As shown in Table 1, it was noticed that the response time parameters measured in the second unit, that mean the system is very poor responses.

Figure 9.

Response time without controller for each joint components, (a) shoulder, (b) lower arm, (c) upper arm, (d) wrist.

Manipulator Joints	tr(s)	ts(s)	Amplitude
Lower arm	1	1	0.01
Shoulder	0.1	0.1	0.01
Upper arm	1	1	0.01
Wrist	1	1	0.01

Table 1.

Uncontrolled system responses for each joint component.

3.3 Optimization proportional-based HSPID

Figure 10 shows the best objectives achieved by IGA. These convergence results reflected positively to optimize PID gains significantly as illustrated in Table 2, to be applied on each HSPID controller individually for each manipulator’s joint.

Figure 10.

The effectivness of the IGA on FF for each revolution joint, (a) shoulder, (b) lower arm, (c) upper arm, (d) wrist, (e) end effector.

Manipulator joint	Kp(E8)	Ki (E11)	Kd (E4)	N (E6)	FF(E9)
Shoulder	3.3	7.3	3.3	3.9	5.1
Lower arm	2.4	4.5	3.2	3.8	3.1
Upper arm	3.1	5.9	4	4.7	3.1
Wrist	1.7	2.6	2.6	3	2.9
End effector	4.1	9.4	3.2	3.9	2.9

Table 2.

The optimized proportional gains and FF-based IGA for each revolution joint.

3.4 Responses based on the proposed controller

Figure 11 shows the response time results based on each common component HSPID controller with a step signal. The results show a series of system responses to the robot components’ orientation angle at a set point. The HSPID controller is a clear reduction response time, but there is some overshoot as illustrated in Table 3. The tuned linear responses look satisfactory regarding PID gains based on IGA.

Figure 11.

Case 1 response time reduction based HSPID controller for each revolution joint component.

Joint part	tr ($\mu$s)	ts ($\mu$s)	Pos
Shoulder	56.2	1352	1.047
Lower arm	58.1	1422	1.044
Upper arm	48.5	1221	1.040
Wrist	73	1130	1.041
End effector	48.1	965.7	1.114

Table 3.

Case 1 response time reduction based HSPID controller for each revolution joint.

3.5 Trajectory planning results

As shown in Figure 12, three different trajectory signals were injected into the five joint angles to investigate motion case study in x-y plane. The input values to the joints are assorted and the angle motion results were obtained. With the orientation and position vectors as input, the joint angles are obtained as output. A simulated position of the end effector is introduced to be measured the maximum torque for each case on scope simulator. The recorded cases 1,2,3 are 0.06,0.038,0.042 N.m, respectively, as shown in Figure 13. Based on the results, it is proven that changing the angle of any joint would result in a different end-effector position, and the 3D animation confirms that the arm moves quickly and precisely to the desired configuration.

Figure 12.

Trajectory motions of each joint in X-Y plane for three cases, (a) case 1, (b) case 2, (c) case 3.

Figure 13.

The torque results of the end effector joint for three case, (a) case 1, (b) case 2, (c) case 3.

4. Discussion

To demonstrate the validity of the HSPID controller, we compare the response time characteristics of controlled and uncontrolled systems. The first response comparison includes a robot arm model without a controller, and the second one includes the model-based proposed HSPID controller simulation results illustrate that the use of HSPID provides significant reduction. Table 4 refers to the improved reduction response time ratio (IRRTR) for the tr and ts of the joint manipulators. It can be seen that the maximum IRRTR for the tr occurs at the upper arm and the lowest at the shoulder. The ts results show that the greatest IRRTR occurs at the wrist and lowest at the shoulder. For comparison, the controller can efficiently compensate for orientation errors and quickly settle to an acceptable target value, providing advantages to augmenting the precision of the robot arm. In contrast, researchers can manipulate other parameters in the system to get more analytical results.

Joint components	IRRTR
	tr (%)	ts (%)
Lower arm	17,280	755
Upper arm	20,701	879
Wrist	13,753	950
Shoulder	1850	121

Table 4.

Improved reduction response time ratio (IRRTR).

5. Conclusion

In this chapter, the innovation 5 DOF robot arm has been designed by the application of SolidWorks side by side with and MATLAB Simscape toolbox for motion analysis and measuring the dynamics of the proposed model. The organigram of the design procedure is divided into five steps:(1) Mechanical configuration and assembly components, (2) Modeling Simscape, (3) Estimation TFs of the manipulator’s joints, (4) Designing HSPID controller for joint manipulators (5), Mimic trajectory planning, then analyze response time characteristics and motion result. It is proposed a novel HSPID controller based on IGA offers a best solution to optimize trajectory planning and significant effectiveness of joint’s torque.

The motion of the joint angle combinations through various angles and coordinates is controlled by applying three trajectory signals to manipulate the whole system and to compare the paths-based proposed controller with uncontrolled in terms of response time characteristics. For the 12 s trial-tested period, three case studies are and measure the distance, investigate the dynamic motion simulations, and confirm the efficiency of the design. It is observed that the HSPID enhanced the IRRTR significantly for the shoulder, lower arm, upper arm, and wrist in terms of tr by 1850%, 17,280%, 20,701%, and 13,753% respectively, and ts by121%, 755%, 879%, 950%. Thus, the efficiency of the robot arm is confirmed by the case studies, which is relating to trajectory planning. It is observed that the robot arm utilizes torque more effectively. Remarkably, the tr simulation results show that the lowest IRRTR appears into shoulder and the highest into upper arm, where the simulation ts results illustrate that the maximum IRRTR obtains in the wrist and the lowest in the shoulder. The main added value of the study is the elaboration and implementation of the new design method, which offers flexible design and higher-speed motion with less consuming energy. Finally, future manufacturing arm could be greatly improved by applying the proposed innovative design offering the best solution to increase accuracy, speed performance, and boost productivity for wide range of a various tasks.

Conflict of interest

The authors declare that there is no conflict of interest.