Discontinuous steering control for nonholonomic systems with drift

This paper presents a simple method for the construction of steering control law for nonholonomic systems with drift and its effectiveness is tested on three different nonholonomic control systems such as a system with six state variables and three inputs, knife-edge example, and a rigid body with two torque actuators. This method does not necessitate conversion of the system models into “chained form” and does not rely on any special transformation techniques. The feedback controls are piecewise constant, states dependent and the method is based on the construction of a cost function V which is the sum of two semi-positive definite functions V1 and V2, where V1 is the function of the first m state variables which can be steered along the given vector fields and V2 is the function of the remaining n-m state variables which can be steered along the missing Lie brackets. The values of the functions V1 and V2 allow in determining a desired direction of system motion and permit to construct a sequence of controls such that the sum of these functions decreases in an average sense.