Attraction Domains in the Control Problem of a Wheeled Robot Following a Curvilinear Path over an Uneven Surface

Abstract

The problem of motion control of a wheeled robot is considered. The robot is supposed to be moving without lateral slippage along an arbitrary, sufficiently smooth three-dimensional surface. The target path of the robot is defined by a curve with constrained curvature on a given surface. The rear wheels are assumed to be driving while the front wheels are responsible for the rotation of the robot’s platform. A control law is synthesized based on the feedback linearization approach [5]. The purpose of the paper is to construct an estimate of the invariant attraction domain in the space “cross-track - angular deviation taking into account the constraints on the maximum steering angle. This problem has received much attention in connection with precision farming applications [14]. The control goal is to drive the specified target point, taken as a middle of the rear axle, to the target path and to stabilize its motion. The system is presented in the so called Lurie form [1, 15] and embedded in the class of systems with nonlinearities constrained by the sector condition. The method of attraction domain estimation in the state space of the system is proposed. The negativity condition for the derivative of the Lyapunov function with respect to the system’s dynamics under sector conditions is formulated in terms of solvability of the linear matrix inequality (LMI) [2]. The LMI, the left side of which depends on the matrix of the quadratic form, gives the constraints of the considered optimization problem. The cost function of the optimization problem is the trace of the matrix. Such a cost function is widely used in control theory to optimize the volume of invariant sets [2]. Numerical results are presented.