An artificial neural network based dynamic controller for a robot in a multi-agent system
Introduction
A multi-agent robot soccer system is considered as a benchmark problem for imparting human like intelligence [24]. In the Micro-Robot Soccer Tournament (MiroSot) team configuration, the agents are wheeled mobile robots [36] which constitute a class of mechanical systems called nonholonomic systems [2], [3], [42]. These systems are characterized by kinematic constraints that are not integrable and cannot be eliminated from the model equations [2], [3]. Nonholonomic behaviour in the robotic systems implies that the mechanism can be completely controlled with reduced number of actuators [8], [16]. The tools for analyzing and controlling nonholonomic mechanical systems based on known mathematical models have been discussed in [2], [11], [12]. Using Lagrange formulation and differential geometry, a general dynamical model can be derived for the mobile robots with nonholonomic constraints [2], [3]. Wheeled mobile robots can have different wheel and axle configurations and depending upon the degrees of freedom (DOF) these are divided into two groups such as a 2-DOF or a 3-DOF robot. A 2-DOF mobile robot is a three wheeled vehicle with two drive wheels and one caster wheel, and a 3-DOF mobile robot is a three wheeled vehicle with two drive wheels and one steering wheel or four omni-directional wheels [42]. A general kinematics and dynamics model of the various types of mobile robots along with the nonholonomic constraints are available in the literature [3], [42]. The tools for analyzing and controlling nonholonomic mechanical systems are based on these known mathematical models [26].
The navigation controls of the mobile robot are divided into three basic problems such as tracking a reference trajectory, following a path, and point stabilization [11], [12], [25], [29]. In the trajectory tracking problem, a wheeled mobile robot is to follow a pre-specified trajectory. The nonholonomic tracking problems were over-simplified in the initial periods of their development by neglecting the vehicle dynamics and thus considering only the steering system [22]. In such cases, the vehicle control inputs were calculated by assuming that there is ‘perfect velocity tracking’ [12]. In perfect velocity tracking it is assumed that complete kinematics and dynamics of the robot is known and the dynamics of the robot is not included in the controller design. It is also assumed that the robot follows the required trajectory without any velocity error. Control algorithms developed in the later stages for the trajectory tracking of nonholonomic mobile robots can be grouped into two categories. Algorithms belonging to the first category have a kinematic controller [22], [23] in the outer loop, which is integrated to a computed torque controller in the inner loop. The computed torque controller of the inner loop is formulated through various techniques such as sliding mode controllers [14], [21], [41], back stepping controllers [11], neural network controllers [12], [13], [15], and adaptive controllers [9], [27], [33]. Algorithms belonging to the second category do not have a kinematic controller [22], and are based on techniques such as fuzzy logic controllers [1], [5], [34], behaviour based controllers [10] and neuro-fuzzy controllers [40]. The use of the vision sensor in feedback control and trajectory tracking has gained increased attention among the researchers of the robotic vision and control [28], [41]. The design and synthesis of the controllers in the presence of uncertainties and inaccuracies of the sensor data and external noise were the challenging tasks [6].
The poor performance of the closed-loop controller using perfect velocity tracking indicates the need of a more elaborate control system which can provide a velocity tracking inner loop [12], [22]. In the artificial neural network (ANN) based control approach proposed in this paper takes into accounts this omission, and thus provides a rigorous method of using the specific vehicle dynamics to convert a steering system command into control inputs for the actual vehicle. The paper is organized as follows: the nonholonomic control problem of a robot in a robot soccer environment is discussed in Section 2. Section 3 presents the formulation of the dynamics of the MiroSot mobile robot in terms of the wheel velocities. The formulation of the control algorithm for the trajectory tracking is discussed in Section 4. The description of the learning algorithm based on the Lyapunov stability criterion and the structure of the ANN controller is given in Section 5. Section 6 describes the modelling and simulation of the MiroSot mobile robot and the controller. Simulation results of the proposed controller are given in Sections 7 followed by conclusion in Section 8.
Section snippets
Problem formulation
As shown in Fig. 1, MiroSot small league is a robot soccer game played between two teams each consisting of three players and an orange coloured golf ball. One of the three robots is act as a goalkeeper. At any instant during the game, the robots of a team have an arbitrary position and orientation with respect to the ball. Similar to the case of human players in which the one who is nearer to the ball moves to the ball, the robot which is nearer to the ball has to approach the ball
Dynamics of a wheeled mobile robot
Model of a nonholonomic mobile robot shown in Fig. 2a, consists of a vehicle with two driving wheels mounted on the same axis and a passive self-adjusted supporting wheel, for stabilizing the mechanical structure. The driving wheels are independently driven by separate DC motors and they are separated by a distance 2R. It is assumed that the mobile robot is made up of a rigid frame equipped with non-deformable wheels and that they move in a horizontal plane. Centre of mass of the robot is
Robot control scheme
In the proposed control scheme represented in Fig. 3, the angular velocity of the wheel is selected as the control variable. It is more realistic than the conventional approaches based on the heading velocity and the orientation angular velocity because the torque applied by the actuators directly connected to the wheel velocities. The heading velocity and the orientation angular velocity of the mobile robot are related to the wheel velocities through Eq. (3). In this case the controller design
Learning algorithm
As shown in Fig. 3, the actual wheel velocities are sensed through the encoder and the transformation Te given in Eq. (12) calculates the position error. The velocities in the generalized coordinates can be evaluated from the known wheel velocities using the Jacobian given in Eq. (2). The learning algorithm for the ANN controller given in Eq. (17) has to be developed by considering the system stability, so that both the position and the velocity tracking errors are converged to zero.
SIMULINK model of the robot controller
The body of a MiroSot mobile robot developed at the mechatronics laboratory of the National Institute of Technology, Calicut is shown in Fig. 5. The nominal values of the kinematic and dynamic parameters of this robot and its inertia properties are given in Table 1. Based on the dynamics of the MiroSot mobile robot represented in Eq. (8), a control algorithm is proposed and modelled using SIMULINK. Nominal values of the various parameters given in Table 1 are used in the SIMULINK model of the
Results and discussion
Trajectory tracking ability of the proposed model of the MiroSot mobile robot is established through the simulation of the robot for tracking a circular trajectory, as shown in Fig. 11. Fig. 12 shows the circular reference trajectory which is used to test the performance of the model of the proposed controller. The trajectory tracked by the robot is also shown in the same figure. In this figure, the robot is started from the location (1.5, 0) and it traverses the trajectory twice. In the first
Conclusion
The dynamics and kinematics of a nonholonomic mobile robot has been extended to the application of a MiroSot Soccer robot. The equations are formulated by considering the wheel velocities as the generalized coordinates along with the orientation angular velocity of the robot. The robot regressor dynamics formulation transforms the nonlinear robot dynamics into a linear form. An ANN based adaptive algorithm which has the capability to learn the robot dynamics on-line has been proposed for the
K.G. Jolly is working as the assistant professor in the department of Mechanical Engineering, NSS College of Engineering Palakkad, Kerala, India. He did his B.Tech from NSS College of Engineering, Palakkad, M.Tech from Indian Institute of Technology Kharagpur in Machine Dynamics and the Ph.D. degree from the National Institute of Technology Calicut in robotics. His area of interest includes mechanical vibrations, system dynamics, robotics, multi-agent system and artificial intelligence.
References (42)
- et al.
A fuzzy-based reactive controller for a nonholonomic mobile robot
Robotics and Autonomous Systems
(2004) - et al.
Simple neuron-based adaptive controller for a nonholonomic mobile robot including actuator dynamics
Neurocomputing
(2006) - et al.
A hybrid control approach to action coordination for mobile robots
Automatica
(2002) - et al.
Neural predictive control for a car like mobile robot
Robotics and Autonomous Systems
(2002) - et al.
Strategy-based decision making of a soccer robot system using a real-time self-organizing fuzzy decision tree
Fuzzy Sets and Systems
(2002) - et al.
Intelligent decision making in multi-agent robot soccer system through compounded artificial neural networks
Robotics and Autonomous Systems
(2007) - et al.
A Bezier curve based path planning in a multi-agent robot soccer system without violating the acceleration limits
Robotics and Autonomous Systems
(2009) - et al.
Designing a robust adaptive dynamic controller for nonholonomic mobile robots under modeling uncertainty and disturbances
Mechatronics
(2003) - et al.
A higher level path tracking controller for a four-wheel differentially steered mobile robot
Robotics and Autonomous Systems
(2006) - et al.
Modular Q-learning based multi-agent cooperation for robot soccer
Robotics and Autonomous Systems
(2001)
Adaptive control of dynamic mobile robots with nonholonomic constraints
Computers and Electrical Engineering
A new fuzzy robust dynamic controller for autonomous vehicles with nonholonomic constraints
Robotics and Autonomous Systems
Real-time object tracking for soccer-robots without color information
Robotics and Autonomous Systems
Evolution of fuzzy behaviours for multi-robotic system
Robotics and Autonomous Systems
Analytical Dynamics
Fuzzy control of robot manipulators-some issues on design and rule base size reduction
Engineering Applications of Artificial Intelligence
Path following control of mobile robots in presence of uncertainties
IEEE Transactions on Robotics and Automation
Introduction to Robotics–Mechanics and Control
Robust adaptive control of nonholonomic mobile robot with parameter and non-parameter uncertainties
IEEE Transactions on Robotics and Automation
Cited by (20)
Quasi-synchronization of heterogeneous nonlinear multi-agent systems subject to DOS attacks with impulsive effects
2019, NeurocomputingCitation Excerpt :The past few decades have witnessed increasing attention on the multi-agent systems due to wide applications of many fields, such as team robots, formation control of vehicles, unmanned aerial and so on [1–8].
Genetically evolved action selection mechanism in a behavior-based system for target tracking
2014, NeurocomputingCitation Excerpt :Instead of having to go through lengthy mathematical analysis, complex functions can be approximated by an artificial neural network through some pattern recognition mechanisms on a given set of data. Neural networks have been successfully applied to various area of robot control [26–28]. Tracking control is one of the most attractive applications [29–32].
Analysis of strategy in robot soccer game
2013, NeurocomputingIndirect adaptive tracking control of a nonholonomic mobile robot via neural networks
2012, NeurocomputingCitation Excerpt :The motivation of this work has been to take advantage of attractive properties of ANN to address the problem of trajectory tracking control of mobile robot systems. Other researchers have already made contributions in both areas of kinematic and dynamic tracking [32–40]. In the kinematic level, controllers that combine the backstepping scheme with neural networks and GA techniques to improve its overall performance are proposed in [33,41].
An Optimal Robust Trajectory Tracking Control Strategy for the Wheeled Mobile Robot
2024, International Journal of Control, Automation and Systems
K.G. Jolly is working as the assistant professor in the department of Mechanical Engineering, NSS College of Engineering Palakkad, Kerala, India. He did his B.Tech from NSS College of Engineering, Palakkad, M.Tech from Indian Institute of Technology Kharagpur in Machine Dynamics and the Ph.D. degree from the National Institute of Technology Calicut in robotics. His area of interest includes mechanical vibrations, system dynamics, robotics, multi-agent system and artificial intelligence.
R. Sreerama Kumar is working as professor in the department of Electrical Engineering, National Institute of Technology Calicut, Kerala, India. He did his B.Tech from NSS College of Engineering Palakkad, M.Tech from Indian Institute of Technology Madras and Ph.D. from Indian Institute of Science Bangalore. Dr. Sreerama Kumar is the recipient of the prestigious national award, constituted by the Indian Society for Technical Education, for Promising Engineering Teacher for the year 2003 for creative work done in technical education. He is fellow of the Institution of Engineers (India) and Senior Member of The Institution of Electrical and Electronics Engineers (USA). He has authored five books, and has more than 60 technical publications in reputed journals and conferences. His field of interest includes soft computation, robotics and system dynamics.
R. Vijayakumar is working as professor in the department of Mechanical Engineering, National Institute of Technology Calicut, Kerala, India. He did his B.Sc. (Engineering) degree in Mechanical Engineering from University of Kerala, and M.Tech degree in Mechanical Engineering from Indian institute of technology Kanpur and Ph.D. degree in Mechanical Engineering from the University of Calicut in 2004.