Autonomous Underwater Vehicle Motion Control during Investigation of Bottom Objects and Hard-to-Reach Areas

1. Introduction

Modern Autonomous Underwater Vehicles (AUVs) can solve different tasks on sea bosom research, objects search and investigation on the seabed, mapping, water area protection, and environment monitoring. In order to solve problems of bottom objects survey AUV has to move among the obstacles in a small distance from the seabed. Such motion is connected with active manoeuvring, changes in speed and direction of the movement, switch and adaptive correction of modes and control parameters. This can be exemplified by using AUV for geologic exploration and raw materials reserves estimation in the area of seamounts, which are guyots with rugged topography. Such problems arise during vehicle manoeuvring near artificial underwater point or extended objects (for example, dock stations or underwater communications). The problems of ocean physical fields’ survey are of a particular interest. These are the problems of bathymetry and seabed mapping as well as signature areas of search objects.

To perform these tasks AUV must be equipped with the systems that can define the positions of the vehicle body against the obstacles and search objects. As a rule, acoustic distance-measuring systems (multibeam and scanning sonars, and also groups of sonars with the fixed directional diagram) and other vision systems are used for these purposes. AUV path planning is carried out with the use of current sensory data due to the lack of a priori information. On the basis of measured distances the current environment model and the position of the vehicle are defined. Then taking into account vehicle dynamic features the direction of probable movement and usable motion modes are evaluated. At each control phase a motion replanning is carried out taking into account new data received from sensors and changed surrounding.

The paper presents the results of research and working outs based on the many years of experience of the Institute of Marine Technology Problems (IMTP) FEB RAS (Ageev et al., 2005). It also gives examples of realization of the offered solutions in the structure and algorithms of motion control of certain autonomous underwater vehicles-robots.

2. Control system peculiarities of AUV capable to work at severe environment

The use of AUV to perform different operations under conditions of difficult informative uncertain or extreme surrounding requires a developed complex of positioning, control, and computer vision systems onboard the vehicle. In the overall structure of control system one can mark such basic systems providing AUV functioning as an equipment carrier, and information and searching functions.

The basis of control system is a local area network composed of several computers. It provides motion control and emergency and search functions. To organize AUV’s local area network high speed channels (Ethernet) and quite slow exchange serial channels are used. To form the control navigation and sensors’ data are used. Emergency sensors are used for AUV safety. Remote change of AUV mission can be carried out with the help of acoustic link. Positioning system plays an important role. Positioning accuracy is acquired by using on-board autonomous navigation system including inertial positioning system, angular and position measuring devices, and acoustic Doppler log. An accumulating dead-reckoning error can be decreased by means of integration of hydroacoustic and stand-alone data by operating AUV with hydroacoustic navigation facilities with long or ultra-short base.

Search systems incorporated computer vision systems differ on physical principles and methods of data acquisition. Acoustic systems include high-frequency and low-frequency side-scan and sector-scan sonars as well as subbottom profiler. Current-conducting objects can be found with the use of electromagnetic locator (EML). A video system carries out imaging and object recognition. It includes photo and video cameras.

The information from sensors and measuring systems are usually stored for the following mapping of researched area (ecological, geophysical, etc.) If necessary, this information can be used in real time, for example, for contouring the areas with abnormal characteristics of measured fields.

System architecture of programmed control has hierarchic three-level organization (strategic, tactic and executive levels). Program-task (mission) for the vehicle is programmed on the highest level and in general it contains the description of desired motion path and operation modes of onboard equipment. Tactic level contains a set of vehicle behavior models (function library) and a scheduler that coordinates their work. The lowest level carries out tactical commands. To do this it contains a set of servocontrollers. Control algorithms providing “reflex” motion among the obstacles work on the lowest level.

The propulsion system is used for spatial motion, positioning, and obstacle avoiding. It provides free motion modes (motion in wide speed range, hovering, and free trim motion). There are stern and bow propulsion sections. Control forces and moments are created with the help of four stern mid-flight and several stern and fore lateral thrusting propulsions. Multi-beam echoranging system (ERS) with the range up to 75 meters is used for working out corresponding controls and obstacles detection. ERS sonars are oriented on the front aspect under different angles to vehicle fore-and-aft axis (forward, down, sideway, up).

3. Motion modes and AUV dynamics peculiarities

Trajectories of arbitrary forms are required for bottom objects survey, constructions inspection, docking with mooring facilities or homing beacons. Not only basic motion modes but more difficult modes of dynamic positioning at variable speed and circular change of thrust vector direction (start-stop, reverse, transversal, etc.) must be performed. Among typical practical tasks of this class are:

• maneuvering in specified area near the target at variable speed and heading correction, pointing to the target (signal source), approaching to the target and point positioning,

• lengthy objects search and survey,

• path selection in the rugged bottom relief.

In many cases the said missions are interconnected and can correspond to different phases of a particular vehicle mission. So we shall consider them as components of single scenery for rather complex missions’ performance.

Figure 1.

A system of coordinates and flow pattern of force in trimetric projection.

Let’s equate the model of AUV spatial motion as (fig. 1):

$$\begin{array}{l}{m}_x\dot{\upsilon }=-R_x+P\cdot \sin \vartheta +T_x\cdot \cos \alpha \cdot \cos \beta -T_y\cdot \cos \alpha -T_z\cdot \sin \beta \\ m_y\upsilon \dot{\vartheta }=R_y+P\cdot \cos \vartheta +T_x\cdot \cos \alpha +T_y\cdot \cos \alpha \\ J_z\ddot{\psi }=M_z+M_0\cdot \sin \psi +M_z^{ctrl}\\ J_y\ddot{\phi }=M_y+M_y^{ctrl}\\ \dot{X}=\upsilon \cdot \cos \vartheta \cdot \cos \phi +{\upsilon }_{Tx}\\ \dot{Y}=\upsilon \cdot \sin \vartheta +{\upsilon }_{Ty}\\ \dot{Z}=\upsilon \cdot \sin \phi \cdot \text{}\cos \vartheta +{\upsilon }_{Tz}\\ m_x=M+{\lambda }_{11}{m}_y=M+{\lambda }_{22}{m}_z=M+{\lambda }_{33}{I}_y=I_{yy}+{\lambda }_{55}{I}_z=I_{zz}+{\lambda }_{66}\end{array}$$ E1

where λ₁₁, λ₂₂, λ₃₃, λ₅₅, λ₆₆– added masses and liquid inertia moment, T_x1, T_y1, T_z1, M_y ^ctrl, M_z ^ctrl – projection of control forces and moments in a system of coordinates dependent on the vehicle, υ - speed against the flow, φ, ψ – heading and vehicle pitch correspondingly, ϑ, χ – angles of ascent and motion swing, R_x, R_y, R_z, M_y, M_z – hydrodynamic forces and moments, M₀ – moment of stability, υ_Tx, υ_Ty, υ_Tz – current velocity vector components which have constant, variable or random character, P – variable buoyancy depending, in particular, on the depth of the vehicle descent.

According to the general formulation area survey is performed with the help of maneuvering piecewise-constant speed and path program near the target (object) and start-stop control mode at point dynamic positioning or along the contour.

Horizontal motion area (X, Z) can be defined by one of the following methods:

• coordinates of the target point {X_T, Z_T}, local area radius r_T and distance to the target d_T, distance d_B to the signal source (transponder) and bearings ϑ_B,

• optional close circuit g(X,Z)=0, against which the vehicle displacement d_i is defined in directions dependent of the vehicle,

• linear zone |aX+bZ+c| ≤ Δ_l width Δ_l against extended object and relative linear {ΔX_l,ΔZ_l} and angular Δφ_l vehicle motions.

Control responses created by the stern and bow propulsions in the trimetric projection connected with the vehicle are given by (Ageev et al., 2005; Kiselev & Medvedev, 2009):

$$\begin{array}{l}{T}_x=(T_{SU}+T_{SR}+T_{SB}+T_{SL})\cdot \cos \delta \\ T_y=(T_{SU}-T_{SB})\cdot \sin \delta +T_{BH}=T_y^S+T_{BV}\\ T_z=(T_{SR}-T_{SL})\cdot \sin \delta +T_{BV}=T_z^S+T_{BH}\\ M_z^{ctrl}=(T_{SU}-T_{SB})(x_{TS}\sin \delta +y_{TS}\cos \delta )+T_{BV}\cdot x_{TB}=T_y^S\cdot d+T_{BV}\cdot x_{TB}\\ M_y^{ctrl}=(T_{SR}-T_{SL})(x_{TS}\sin \delta +z_{TS}\cos \delta )+T_{BH}\cdot x_{TB}=T_z^S\cdot d+T_{BH}\cdot x_{TB}\\ d=(x_{TS}\cdot \sin \delta +y_{TS}\cdot \cos \delta )/\sin \delta =x_{TS}+y_{TS}\cdot ctg\delta \\ T_S=T_S^{\max }\cdot sat\left(\frac{U_T^S}{T_S^{\max }}\right)T_B=T_B^{\max }\cdot sat\left(\frac{U_T^B}{T_B^{\max }}\right)\end{array}$$ E2

where Т_SU, Т_SB – vertical channel stern mid-flight propulsions thrusts (upper and bottom correspondingly), Т_SR, Т_SL - horizontal channel stern mid-flight propulsions thrusts (right and left correspondingly), Т_BH, Т_BV - horizontal and vertical bow maneuvering thrusts, х_TS, у_TS, δ - coordinates and pitch angle of stern mid-flight propulsions, х_TB - axial coordinate of bow maneuvering propulsion, U^S _T, U^B _T - control functions for stern and bow propulsion sections.

As is clear from set of equations one and the same control responses can be created by means of applying different work patterns of stern and bow propulsions. A practical application has the following modes:

• cruising motion;

• low speed motion.

The first mode is characterized by the fact that vehicle spatial motion is carried out by means of changing of attack angle with the help of variables T_x, M_Y ^CTRL, M_Z ^CTRL. At the same time only stern mid-flight propulsions form the mentioned forces and moments. This mode is used for vehicle control only at cruising speed.

In the second mode all propulsion sections are used to form vehicle motion, and control is performed according to five degrees of freedom with the help of variables T_x, T_Y, T_Z, M_Y ^CTRL, M_Z ^CTRL. This mode is used for vehicle control at low speed and during hovering.

Complex AUV motions are carried out by means of combination of these two modes. Let’s analyze several possible control methods. They differ by the logic of program algorithm and by system dynamics in performing complex spatial motions.

4. Motion control in the rugged bottom relief

AUV usage for seabed layer survey is connected with the organization of equidistant motion (motion at equally distance from the seabed) and bypassing or bending around the obstacles. Equidistant motion control assumes the formation of an equidistant model on the basis of echoranging data and data on vehicle relative motion. In this case control can be organized as an adjusted program that can forecast spatial equidistant path and direct the vehicle along it. In a plane case the task is simplified and consists in stabilization of positioning and angular error formed with the help of several range sensors. Such control method was implemented in different versions of the majority of the vehicles designed by IPMT FEB RAS (Ageev et al., 2005).

Characteristic features of the task can be illustrated on the example of control organization during seamounts (guyots) survey. They are distinguished by sharp changeable microrelief and different obstacle along the motion path (Ageev et al., 2000; Smoot, 1989). AUV use for seamounts survey is mainly connected with the geologic exploration and raw materials reserves estimation (for example, the resources of ferro-manganese nodules in the Pacific Ocean created on the guyots tilted areas). Common characteristics of the guyot macrorelief are:

• cone form with side angle up to 30 - 40 near the top;

• flat top covered with the fall-outs, the edge can have barriers;

• nodules are created in the guyot upper vein systems;

• sides and top can have picks and gorges;

• side can have terraces (width up to several kilometers), edges can have peaks and barriers.

The main objective of the survey is the estimation of amount of minerals in the given area and the conditions for the following exploitation. The second task in using AUV is reduced to SSS survey. The first task can be partly solved by using photo and TV survey. It is a rather complicated task because it is quite difficult due to the necessity to approach to the surface up to 3-5 meters.

Let’s consider potential obstacles in more detail.

Peaks are rather large underwater mounts with pike. The vehicle must pass such obstacles sideways.

Barriers and peaks can be found on terrace edges and guyot top edge. Fault ridge height can be up to dozen of meters. Bypassing of low barrier is rather simple. Peak bypassing during moving from below is a more complicated task. In this case the vehicle has to stop forward motion and emerge staying at an allowable distance from the obstacle.

Breaks and gorges are not the survey objects and the vehicle must go above them. The major problem is to recognize this land shape.

Let’s consider several motion peculiarities in typical mode taking into account dynamic features of the vehicle and power requirements. Broadly speaking, the selection of motion modes is rather optional. The following variants are possible:

• motion along the side with zero pitch or with the pitch that corresponds the side angle;

• obstacle bending “without a pause” at permanent or variable speed;

• deceleration or back motion with transfer to hovering when the obstacle that cannot be bypassed “without a pause” is found;

• body scanning without forward motion for obstacle heighting and maximal visual angle;

• complex obstacle avoiding (peak, high hurdle) with the use of backward motion at big pitch and attack angle.

It is necessary to choose the most energetically efficient motion modes. So the modes with absolute minimum resistance are more preferable. It is connected with providing an “optimal” angle of attack that corresponds preset current speed. Not all of the abovementioned modes meet this requirement. So, moving along the side with zero pitch cannot be considered appropriate as the basic mode, as in this case there can be high angles of attack, and energy consumption can be reduced only at the expense of speed decreasing. In just the same way it is difficult to provide energetically efficient mode at complicated maneuvering near the obstacle as vehicle security prioritizes. As a consequence there appears additional energy consumption for motion performing. One more peculiarity is incomplete, unreliable, fuzzy information about the bottom configuration. It leads to the suitability of construction of hybrid control structure with fuzzy-logic elements (Ageev et al., 2000; Kiselev & Medvedev, 2009). Let us cite as an example the results of motion modeling in vertical plane for such typical control modes as obstacle bending “without a pause” at equidistant curve with regard to relief, bending around high and rapid obstacles, maneuvers on tracking another more complicated bottom forms.

For descriptive reasons sonar beams are depicted at several points of motion path. The length of each beam corresponds to ERS radius of action. In most cases complicated obstacles bending is carried out with the use of deceleration and back motion modes. In all considered cases control system keeps equidistant motion at preset distance of 3 meters. When the obstacle is found it performs maneuver on its avoiding. The use of fuzzy-logic elements with failures in ERS work allows leveling equidistant motion path, especially at unreliable information intensification.

4.1. Motion along the side with preset pitch

The mostly widespread case during guyots’ research is moving along the smooth slope. Creation of control forces and moments with the help of four stern and one bow propulsions gives a chance for free selection of propulsion thrust values betweenness. In particular, if vertical force Т_Y and moment М_z are defined, then it is possible to find the equations for all thrust components at presence of all additional kinematical connections from static equations. At the same time with the purpose of energy minimization it’s possible to let that depth stabilization and motion along smooth lope is carried out at cruising mode (with the use of mid-flight propulsions), and during maneuvering and moving along steep slope stern and fore propulsions work simultaneously.

Actual angle of attack is defined by correlation of vertical thrust components, buoyancy, and uplift hydrodynamic force. As the last one nonlinearly depends on speed and angle of attack, it is obvious that power spent for motion is also in nonlinear dependence of angle of attack. This can be approximately evaluated on the basis of empirical data.

4.2. Various obstacle bending

For single obstacles avoiding such as “bench”, “hurdle”, “den”, “cutting”, and so on, typical control based on the echoranging data can be used.

When the obstacle is found a pitch that is corresponding its height is created. Vehicle dynamic features and control character are analogous to the previous case. Besides, safety distance is under control. It allows obstacle bending “without a pause” and without deceleration as well as bow propulsion switching on.

The motion mode is chosen depending on slope gradient Δ calculated on the basis of ERS data at each points of motion path.

Let d_i (i = 1...4) – is rangers’ distances directed correspondingly down, at an angle, forward, and at an angle upward; α_i, - angle between i and i +1 ranger, i φ_i – angle between vehicle fore-and-aft axis and i- th ranger, ψ - pitch. Then slope gradient is calculated as follows:

$$\Delta =\psi +\underset{i=1}{\overset{3}{\max }}\left({\phi }_i-arctg\left(\frac{d_{i+1}\cdot \sin {\alpha }_i}{d_i-d_{i+1}\cdot \sin {\alpha }_i}\right)\right){\phi }_i=({90}^o-{\alpha }_i)+{\displaystyle \sum _{k=1}^i{\alpha }_k}$$ E3

Median filtering is used to eliminate influence of rangers’ noise on calculated slope.

Let δ₁ and δ₂ are slope gradient threshold values at which the switch from cruising motion mode to the deceleration or stern propulsion mode takes place. At small slope gradient (|Δ|<δ₁) a cruising motion mode at the speed of υ ≈1 m/s is used. This mode is provided by the work of vehicle stern propulsions.

Figure 2.

Obstacle bending: “without a pause” (left) and high “hurdle” (right).

To form control М_z positional error dY=Y_T – min(d₁, d₂ соsα) (here Y_T – preset height over the bottom), program pitch in the shape of calculated surface steep Δ, angular speed on pitch ψ′, and safety distance on the front ranger d₃ are used:

$$M_z=K_1\cdot dY+K_2\cdot (\Delta -\psi )+K_3\cdot \dot{\psi }+K_4\cdot \left(1/d_3\right)$$ E4

At the same time small obstacles are bended “without a pause”. Fig. 2 (left) shows the example of obstacle bending when its height is compared with the height of vehicle motion. It depicts motion path and positions of the casing at every 20 seconds of simulation time. The width of coordinate grid square side is 10 m.

At large slope gradient (δ₁<|Δ|<δ₂) vehicle speed reduces up to 0.5 m/s. To create control moments the collaboration of stern and fore propulsions is used. It allows creating much larger trim angles.

To avoid high and rapid obstacles (|Δ|>δ₂) vehicle stops its forward motion and keeps allowable distance to the obstacle. Upon that the distance to the obstacle is controlled according to the upper and front rangers. Simultaneously upward motion on the slope with pitch stabilization takes place. Fig. 2 (right) shows the example of “hurdle” obstacle bending.

Control thrusts and moments are formed as follows:

$$\begin{array}{l}{T}_z=K_1\cdot \left(\min (d_3{d}_4)-D\right)+K_2\cdot \dot{x}\\ T_y=\{\begin{array}{l}{T}_{y\max }\Delta \le {90}^o\\ K_1\cdot (d_4-2Y_T)+K_2\cdot \dot{\psi }\Delta {90}^o\end{array}D=\{\begin{array}{l}2Y_T\Delta \le {90}^o\\ 30\Delta {90}^o\end{array}\\ M_z=K_1\cdot ({\psi }_T-\psi )+K_2\cdot \stackrel{}{\psi }\end{array}$$ E5

where К₁, К₂ – are control parameters, ψ_T – target pitch.

As distinct from previous case AUV cannot perform bending of such an obstacle “without a pause” due to its great height.

At point “A” vehicle decelerates and starts stabilizing preset distance to the obstacle. This distance is in proportion to preset motion height. Vehicle deceleration is performed smoothly due to timely obstacle detection.

4.3. Complicated obstacles avoiding

A slope with gradient of 90 and more is considered to be “peak” or “cave” obstacle. The stabilized distance to the obstacle increases up to 3040 m. It brings to backward motion under the “peak”, or to the fact that the vehicle doesn’t enter the “cave”. Fig. 3 shows the example of vehicle motion in the area of such an obstacle. The size of the obstacle is so that it is fully in the field of ERS vision. On the basis of this data vehicle emerges without entering into the “cave”.

Figure 3.

“Cave” obstacle bending (left figure) and “peak” obstacle bending (right figure).

Obstacle bending of such type is characterized by the use of deceleration and backward motion modes. The angle of attack can vary up to 180 . Fig. 3 (right) shows the example of vehicle motion under the “peak”. This case is similar to the one described above. The only difference is that AUV cannot beforehand estimate the character of the obstacle due to its great size. As a result only at point “A” a vehicle can define that it is under the “peak” and starts backward motion.

This motion algorithm allows avoiding getting into the “gorges” if their width is compared to the ERS radius of action.

The example of AUV upward motion on the slope with rather rugged relief is depicted in fig. 4.

Figure 4.

Rugged relief motion.

The whole motion path consists of several areas. Each area has its own motion mode. AUV preset motion height over the bottom is 3 m. Areas 1,2,4,5 are represented as the motion modes along the slope that has both positive and negative steep from 70 to -65 . At area 3 the vehicle performs “peak” bending. Motion at great distance from the slope at this area is explained by the fact that “peak” in the motion direction was found beforehand. At area 6 the vehicle performs exit from under the “peak” of a greater size in the same way as it was described earlier.

5. Extended objects search and tracking

Characteristic feature of the task is in organization of extended line search according to the AUV systems signals for the following object tracking in the given survey zone (Ageev et al., 2005; Inzartsev & Pavin, 2009). Practical approaches to perform such task with the use of echosounder (Inzartsev & Pavin, 2006; Pavin, 2006), magnetometric, electromagnetic (Kukarskih & Pavin, 2008) and video (Scherbatyuk et al., 2000) systems are known. Such decisions were used in AUVs “AE-2”, “XP-21”, and “R-1”. Motion control is formed by means of choosing general direction and its correction according to the contact with the object. In fuzzy situations search motions are performed in limited area.

When the object is found vehicle linear and angular motion parameters with regard to extended line are defined. These parameters are an input data for AUV control system. The task is to make so that the AUV trajectory “in average” to be as close to the tracked object as possible in the presence of positioning and dynamic errors.

If location of extended object is defined beforehand with preciseness enough for coming of the vehicle into the point of contact establishing with the detecting devices, then the vehicle mission includes:

• arrival to the object area and contact search with the object;

• maneuvering near the object and detecting of extended line orientation;

• extended line tracking at given “zone” that corresponds the area of steady state contact;

• return to the search program at occasional loss of contact with the object.

Acquisition system can include different devices that allow finding the object according to the short-range signals and identify it against the background of false signals. To solve this problem the computer video system must include high-resolution survey sonars, video system and magnetometric or electromagnetic detecting devices.

Let’s illustrate general provisions on the example of underwater cable inspection with the use of video system and electromagnetic locator designed by IPMT FEB RAS. Fig. 5 shows the layout of devices used by AUV.

Figure 5.

AUV coordinates and devices layout.

When the object is found with the help of video system at the output of recognition system for each frame the following set of values is pointed out:

• direction of recognized extended object with regard to image fore-and-aft axis;

• distance from the center of the frame to the linear object;

• length of visible part of the object.

Received parameters are used to define the position of the object in inertial system of coordinates.

In the mode of object tracking the control data is formed as:

$$\begin{array}{l}{\phi }_{tag}={\phi }_{AUV}+\Delta {\phi }_{line}\\ {\alpha }_{tag}=\Delta {\phi }_{line}\cdot sat\left(K_p\cdot \Delta d_Y+K_d\cdot {\dot{d}}_Y\right)\\ v_{tag}=f(h_{tag}{t}_{VIC})+K_v\cdot |\sin ({\alpha }_{tag})|\end{array}$$ E6

Where:

Δφ_line - object orientation in the system of coordinates connected to the camera;

K_p, K_d - amplification constants for positional and differential components;

K_ν - constant of proportionality;

α_tag- target attack angel;

Δd_Y- preset position stabilization error in diametral plane,

d^• _Y - AUV motion speed in cross direction;

f(h_tag,t_VIC) - function evaluating dependence of preset AUV speed from the motion height and operational period of video image processing system.

Extended object position according to the data of electromagnetic detecting system is defined at the moment of maximum potentials on receiving electrodes.

Figure 6.

Cable tracking with the use of on EML (upper figure), EML and video system (central figure), only video system (lower figure).

Estimated probability of the search object existence is defined on the basis of the values of potential and speed of its increasing for the period of time preceding the maximum. Particular dependence is chosen empirically on the basis of device characteristics, AUV velocity (and height), and inspected object characteristics (electromagnetic characteristics, diameter, shell thickness and so on).

At coprocessing of video, electromagnetic and navigation signals the control of the contacts with the object is performed, and the data for AUV control system is worked out (Inzartsev & Pavin, 2008). Fig. 6 shows the graphs illustrating the process of cable tracking at separate and joint use of electromagnetic locator and video system.

6. Guiding to the given target in the action of disturbances

Let’s analyze the task of AUV motion control in conditions of incomplete or unreliable information about environment and action of shift current. To be more specific let’s dwell upon the analysis of vehicle motion in guiding to the given target from random starting position. This task can be considered as a component of the closing-in scenario and coupling with underwater target.

In this case it is necessary to provide approach and hovering of the vehicle above the object (at the target) in the dynamic positioning mode. Guiding algorithm can use information received from navigation-piloting sensors and positioning system data on the vehicle coordinates, pointing to the target and distance to it. AUV motion control is conducted by transformation of control forces and moments into the thrusts, its calculated by the program and created by thrust-steering complex.

In general the algorithm must provide:

• classification of incalculable attack moments to work out adequate behavior;

• current vector autodetection with sufficient accuracy to compensate crabbing in stabilization tasks;

• behavior shaping based on the history of AUV and control algorithm conditions.

Let’s call R₁ – area radius where guiding to the target is performed, R₀ – maneuvering area radius, R – distance from vehicle to target.

Under conditions of constant current the following mode of vehicle approaching to the target is logical:

• motion on bearings (azimuth) of the target on preset constant speed at R>R₁,

• speed reduction at signing on the area R₀≤R≤R₁ and turn into the direction corresponding to the bearings sign (or value),

• position stabilization at R<R₀.

While moving into given small area program algorithm logic forms speed change mode, relative bearing φ_k and turn directions:

$$\begin{array}{l}{\phi }_{k+1}=\{\begin{array}{l}{\phi }_k{r}_k\le r_g\\ {\phi }_k+\Delta {\phi }_k\cdot sign({\epsilon }_k)r_k{r}_g\end{array}\\ {\epsilon }_k={\phi }_k-arctg(Z_k-Z_g)/(X_k-X_g)\end{array}$$ E7

It’s obvious that current influence leads to shifting of the program path against the accepted coordinate system, and to solve the problem it’s necessary to form the control possessing with “robustness” property to external resistance.

At coordinate path points definition this task resolves into choosing control providing minimum “miss” Δ in guiding to the target coordinates and path length minimum S, preassigned by points of intersection P_k ={X_k,Z_k}:

$$\begin{array}{l}\Delta ={{\displaystyle \sum \left[{(X(t_k)-X_k)}^2+{(Z(t_k)-Z_k)}^2\right]}}^{1/2}\\ S={{\displaystyle \sum \left[{(X(t_k)-X(t_{k-1}))}^2+{(Z(t_k)-Z(t_{k-1}))}^2\right]}}^{1/2}\end{array}$$ E8

where t_k – is path discrete intervals.

At the final stage of the area path investigation the task of approaching to the target and target positioning is being solved. Control possessing (U_x, U_z) provides approaching to the target and positioning near it in the basis of PID control. It’s possible at known relative position of the vehicle and target. PID-control with limitations for the value of control responses is described:

$$\begin{array}{l}{U}_x=K_1\cdot \Delta X+K_2\cdot \dot{X}+K_3\cdot {\displaystyle {\int }_{t_0}^t\Delta Xdt}{U}_z=K_1\cdot \Delta Z+K_2\cdot \dot{Z}+K_3\cdot {\displaystyle {\int }_{t_0}^t\Delta Zdt}\\ T_{x_1}=U_x\cdot \cos \phi +U_z\cdot \sin \phi T_{z_1}=-U_x\cdot \sin \phi +U_z\cdot \cos \phi \\ \sqrt{(T_{x1}^2+T_{z1}^2)}{T}_{\max }\end{array}$$ E9

In many cases positioning data required for control, has imprecise or failure character and it leads to the conclusion that a fuzzy logic vehicle can be used. The advantages of such an approach are:

• description of the vehicle behavior on the formalized language;

• availability of a priori information about the system for improvement of adjustment quality;

• “robustness” with regard to changeable conditions;

• a priori adjustment of membership function (MF) parameters to reduce the time required for identification of these parameters;

• possibility to perform nonlinear transfer between motion modes.

In program algorithm based on fuzzy regulator a standard scheme is used: fuzzification (making fuzzy) – production deduction rules- defuzzification (making logic). MF are represented as piecewise-linear forms. Such a choice provides simplicity of software implementation and computation speed.

Parameters of input and output variables of the regulator are adjusted for every certain AUV model in accordance with its hydrodynamic features.

Let’s consider input linguistic variable as an example: “Distance-to-go to the target” (fig. 7). Each variable term (near- R₀, middle - R₁, far - R₂ guiding zone) has its own velocity mode. Parameter values of MF are chosen in accordance with spatial restrictions at defined velocity mode. The restrictions are known from calculating hydrodynamic studies.

For output variables: output consists of thrusts/moments corresponding certain discrete velocity.

Figure 7.

Linguistic variable “Distance to the target” with three terms (range of values in meters).

From here the reactions of vehicle motion system on possible situations come. Situation is one of probable positions of vehicle casing against the target. In fuzzy version the situation looks as follows: “target to the right” and “vehicle in the near radius R₀”, “target behind” and “the target is far from R₂” and so on. Response to the situation can be described as follows: “if a situation is”, then “speed-up”, “no sideway motion” and “turn to the right”. Deduction rules are represented in the form of fuzzy association map (FAM) (fig. 8).

Figure 8.

Fuzzy controller deduction rules for motion to the target.

Fig. 9 shows the example of motion paths derived in algorithm modeling. The example illustrates the process of vehicle guiding to the target in two cases: in constant and variable currents. Change of current vector projection for the second case is preassigned by periodic function: V_Tx = V_Ty = Asin(ωt), where А = 0.5 m/s; ω = 0.008 Hz.

The motion is built from three linked modes: guiding along the distance at preset velocity in far zone, approaching to the target at variable velocity on entering into specified area, dynamic positioning with holding the vehicle head to stream near the target.

Two parameters are used in controlling: target direction in relation to vehicle motion direction and distance to the target.

At known current course, vehicle and target coordinates the distance D and direction φ_t.

Figure 9.

The results of modeling, a) – motion path and parameters at constant current, b) - motion path and parameters at variable current (time in seconds).

The use of fuzzy regulator brings to implicit switching of motion modes, so switching zonal boundaries (fig. 8) conditionally divide the underwater space into the zones. That zones correspond different conditions at given motion modes.

Under conditions of constant current the vehicle approaches the target and hover near it positioning itself head to stream. Under conditions of shifting current the vehicle positions close to the target, hauls and changes the speed so that to stay at the mean near the target.

Another way of solving analogous task is connected with the control organization in the case of motion to guiding sonar transponder, and to approach it discrete distance measurement R and direction (bearing) measurements θ are used. At that the task is to provide decreasing of d_m upon the average, keeping d_m = 0 and vehicle angle orientation on target bearing.

7. AUV motion control during investigation of ocean physical fields

The tasks of AUV motion control are usually connected with bottom survey, object search, and inspection in near-bottom space as well as physical fields’ measurements (Ageev et al., 2005; Kiselev & Medvedev, 2009). Manifold AUV uses for search-inspection tasks, seabed survey, bottom mapping, and aquatic medium monitoring can be considered on common grounds at the root of which the idea of ocean physical fields lies. So, for example, the task of route selection in the rugged bottom topography is a special case of a more common task of bottom path investigation and navigation according to the bathymetric map. More generally similar task arises in organization of any physical field path investigation. Spatial structure of such physical fields possesses the following features: changeability, abnormal level, and correlation in field geometry, etc.

In hands-on experience physical fields measurements in water columns and near the bottom are based on creation of survey network bound to base points, horizons or bottom points. According to the whole ocean scale observations held in different periods of time and in different places, the scientists receive average information about structure of sudden (random) fields. Though, as a rule, they are considered to be static, homogeneous, and isotropic. Small-scale phenomena research is carried out by means of establishing stations on the oceanographic grounds with the following machine processing of received information. Depth and area measurement network creates a system of transverse sections characterizing spatial structure of the field. Data received in the result of substitution of continuous field by network of point measurements is used in future for field mapping, i.e., for its reconstruction in any point by means of basis measurements profiling in network node. Nowadays along with traditional methods of oceanographic measurements the methods of path measurements with the help of autonomous, remotely operated, and towed vehicles are used. So the use of AUV has a number of advantages, especially during complex measurements at great depth and in extreme surrounding.

Fig. 10 shows the examples of bathymetric mapping and temperature field mapping with the help of data received by AUV “Klavesin” during Lomonosov Ridge research in polar expedition “Arctic Zone-2007”. During this experiment bathymetric, hydrographical, and other measurements were conducted while following along a programmed path near the bottom by geographical referencing the measurements with preciseness that AUV navigation facilities can provide.

Field mapping according to the measurement data is a common task, though rather labor-intensive. In simplified version one can confine to building separate field realization, isolines or other sections in particular. Two interconnected tasks have an independent meaning: navigation according to known map elements and motion organization according to field isolines (sections).

Let’s dwell upon probable variants of problem description.

Let ξ(X,Z) be a variable characterizing flat field section that can be defined as isoline map ξ(X,Z)=const. Field measuring device during path motion {X(t), Z(t)} gives field measurement ξ (X(t), Z(t)) with an accidental error. Let’s suppose that vehicle (measuring device) geographical coordinates and speed are defined by on-board navigation system with errors {ΔX_a, ΔZ_a}, {Δv_x, Δv_z}.

Figure 10.

Fragments of bathymetric mapping (upper) and temperature field mapping (bottom) during research over Lomonosov Ridge in Arctic zone with the help of AUV “Klavesin”.

Let’s define field variability along trajectory by field gradient value |Δξ| or change Δξ =|∇ξ|vΔt on time interval Δt.

Control U(v, X, Z, ξ, Δξ) must be organized so that:

1. ξ(X(t), Z(t)) =ξ⁰=const or v∇ξ = 0;

2. trajectory goes through all points {X_k, Z_k}, fulfilling condition ξ=ξ_max or ξ = ξ_min;

3. trajectory goes through all points fulfilling condition |∇ξ (X(t),Z(t))))|=|∇ξ|max or |Δξ (X(t), Z(t))| = |Δξ|max.

The first case corresponds to motion along preset isoline; the second one is edging of an area according to the points with extreme values of field level. This can be of interest during edging of signatures created by search objects. The last case corresponds to motion along the point with maximum rating of field gradient (change).

In all three control variants vehicle coordinates must be known. Though in some cases (for example, during isoline tracking “at the mean”) it is enough to orient velocity vector in accordance with flection of reproduced trajectory.

During integrated performing of control task and state vector evaluating knowledge of field map and its elements with preciseness better than accuracy dead reckoning allows clarifying the position of the vehicle. In this case common problem description consists in construction of computational procedure which algorithm depends on estimation covariance matrix, measured field values, gradient, and spectrum patterns of sensors noises. An alternative variant of the task performing is given below.

7.1. Path control with field isolines search and tracking

Isoline motion joins the tasks of field mapping and motion control along isoline paths, motion along which contains constant value. Program algorithm in this case must contain conditions controlling ordered transfer from one curve to another as well as angular motion control law that displays isoline flection. To choose correctly the direction of transfer between field isolines it is necessary to gain information about direction of gradient vector. This information can be gained by means of measuring gradient components with the help of differential sensors or scheme imitating gradient calculation in search motions. In this case parameters of search trajectory and radius of isoline flection as well as period of search motions and time of data updating must be coordinated.

The use of data on field for motion control is equal to inclusion of field parameter ξ(X,Z) into extended vector of system condition (1) with additional equation:

$$\xi =\nabla {\xi }_x(XZ)\cdot V\cos \chi +\nabla {\xi }_z(XZ)\cdot V\sin \chi$$ E10

where path angle is χ, drift angle and route are connected by the equation χ = φ - β.

During motion along isoline ξ(X,Z) = ξ⁰ = const velocity vector v_x=vcosχ, v_z=vsinχ must obey “at the mean” to kinematic condition:

$$\nabla {\xi }_x{V}_x+\nabla {\xi }_z{V}_z=0$$ E11

which can be expressed in terms of gradient projection on axis connected with vehicle: β= arctg(∇ξ_x1/∇ξ_z1)or in the form:

$$tg\phi =(\nabla {\xi }_{x_1}{V}_x+\nabla {\xi }_{z_1}{V}_z)/(\nabla {\xi }_{x_1}{V}_z-\nabla {\xi }_{z_1}{V}_x)$$ E12

Equation (12) gives values for programmed course if another motion parameters are known.

Let’s consider the task of motion control during search and tracking of given isoline ξ = ξ_0, considering that control vector consists of two components – one of them for position control, the other one for orientation control.

Let’s define “distance” D_ξ from point with current field value to preset isoline by equation

$$D_{\xi }=\left|\xi -{\xi }_0\right|/\left|\nabla \xi \right|$$ E13

and projection of gradient vector on motion direction as

$$p=p_v\nabla \xi =\left|\nabla \xi \right|\cos \gamma \gamma =\beta +arctg(\nabla {\xi }_{z_1}/\nabla {\xi }_{x_1})$$ E14

The choice of motion direction at yield of isoline in accordance with gradient direction must obey condition: (ξ - ξ₀) p < 0. If not, it’s necessary to perform search motion that properly orients velocity vector.

Let’s motion control to the point with coordinates

$$X_{\xi }=D_{\xi }\cdot \cos {\phi }_s{Z}_{\xi }=D_{\xi }\cdot \sin {\phi }_s$$ E15

define as:

$$\begin{array}{l}{U}_x=K_1(X-X_{\xi })+K_2\cdot \dot{X}+K_3\cdot {\displaystyle {\int }_0^t(X-X_{\xi }})dt\\ U_z=K_1(Z-Z_{\xi })+K_2\cdot \dot{Z}+K_3\cdot {\displaystyle {\int }_0^t(Z-Z_{\xi }})dt\\ \dot{X}=\nu \cdot \cos \phi \dot{Z}=\nu \cdot \sin \phi \end{array}$$ E16

where K₁, K₂, K₃ are control parameters.

In projections on vehicle axis we’ll receive:

$$\begin{array}{l}{U}_{x_1}=U_x\cdot \cos \phi +U_z\cdot \sin \phi \\ U_{z_1}=-U_x\cdot \sin \phi +U_z\cdot \cos \phi \end{array}$$ E17

where above-mentioned restrictions on a control take place.

Generally control law (24, 25) providing yield of isoline and motion in a given vicinity Δ₀ can be written as:

$$U_{\phi \xi }=\{\begin{array}{l}(U_x{U}_z)\left|\Delta \xi \right|{\Delta }_0\\ U_{\phi }=K_{\phi }(\phi -{\phi }_s)+K_{\dot{\phi }}\dot{\phi }+K_{\xi }{D}_{\xi }sign(p{\Delta }_{\xi })\left|\Delta \xi \right|\le {\Delta }_0\end{array}$$ E18

Let’s consider an example where several features of the task are evident.

Let’s define field ξ(X,Z) by isoline class approximated by cubic parabolas like Z = aX³+bX²+cX+d.

Let’s define values for control and orientation:

$$\begin{array}{l}{\nabla }_{\xi }=(3a{X}^2+2bX+c\mathrm{,1})\left|{\nabla }_{\xi }\right|={\left[1+{(3a{X}^2+2bX+c)}^2\right]}^{1/2}б\\ D_{\xi }=\left|Z-(a{X}^3+b{X}^2+cX+d)\right|/\left|{\nabla }_{\xi }\right|{\phi }_s=arctg(3a{X}^2+2bX+c)\\ X_{\xi }=D_{\xi }(3a{X}^2+2bX+c)Z_{\xi }=1\cdot D_{\xi }\end{array}$$ E19

Motion modeling results for three isoline tracking variants are represented in fig. 11.

Figure 11.

An example of isoline tracking defined by cubic parabolas in vicinity Δ₀=25 (1. a = 0.01, b=0, c=-5, d=200; 2. a = 0.005, b=0, c=-2, d=50; 3. a = 0.005, b=0.04, c=0, d=-150).

Expanded scale on X-coordinate is chosen to show greater clearness of process dynamics during isoline tracking.

In this example the most characteristic fact is that in points with greatest isoline flection the switch of control takes place depending on value of given vicinity of isoline tracking, and, consequently radius of vehicle circulation on curved trajectory.

8. Conclusion

The results of the research on development of flexible AUV control systems presented in the paper are based on practical experience of the IMTP FEB RAS. Relevance of the problems addressed in the paper stems mainly from the need for performing new complex tasks under conditions of uncertain and extreme surrounding when the AUV autonomous operation time is extended. It is crucial to develop control systems with integrated processing of search and navigation information. Control and navigation systems developed by IMTP FEB RAS enable performance of many search-and-survey operations in the sea. Navigation-control facilities are the basis for generating complex AUV behavior missions and for performing “intelligent” control scenarios. This is particularly true for inspection of underwater objects and structures, bottom relief and physical fields. The report presents the results of the major collective work, so the authors would like to thank the following colleagues whose materials were used during preparation of the paper: N.I. Rylov, Yu.V. Matvienko, O.Yu. Lvov, Yu.V. Vaulin, A.A. Boreyko, A.K. Kukarskih.