An artificial neural network based dynamic controller for a robot in a multi-agent system

Abstract

This paper proposes the modelling and simulation of an artificial neural network based computed torque controller for the trajectory planning of a robot in a multi-agent robot soccer system. The controller is designed for the tracking of the soccer robot along a dynamic Bezier path. Dynamics of the robot is formulated directly in terms of the motor torque which is more realistic than the conventional methods that are based on heading velocities. The primary feedback loop of the proposed scheme includes a kinematic controller, which generates an appropriate heading velocity command. A dynamic controller included in the inner feedforward path generates a control torque for minimizing the tracking velocity error. Another artificial neural network controller, included in a separate feedforward path, compensates for the deficiencies in the control torque due to the unknown robot dynamics. The on-line learning rules are formulated by ensuring the stability of the entire system using the Lyapunov criterion.

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.