Estimation of Attraction Domains in Wheeled Robot Control Using Absolute Stability Approach

Abstract

Considered is the control synthesis problem for planar motion of a wheeled robot. The mathematical model of the robot is based on kinematic relationships between the velocity of a given point of a robot platform, referred to as the target point, orientation of the platform, and control. It is supposed that all four wheels move without a lateral slippage. The front wheels are responsible for steering. The control goal is to drive the target point to the prespecified trajectory and to stabilize the motion of the target point along the prespecified trajectory. The trajectory consists of line segments and circular arcs. The current curvature of the trajectory of the target point is taken as control; it is related to the steering angle of the front wheels by a simple algebraic expression. The control is subject to two-sided constraints due to limitations on the steering angle of the front wheels. For the control law proposed, the attraction domain in the space “distance to the trajectory - orientation” is analyzed. For the initial conditions from this domain, the system is guaranteed to hit a trajectory with given exponent of stability. The numerical method based on LMIs approach is proposed to approximate the attraction domain.