Set point stabilizing control for a mobile robot with trailer

A novel method for the construction of state-dependent set point stabilizing control for a class of nonholonomic systems is applied to a model of a car-like robot with trailer-a typical representative of this class. This method does not necessitate conversion of the system model into a "chained form", and thus does not rely on any special transformation techniques. The feedback control are piecewise constant and the method is based on the introduction of a novel concept of guiding functions. The guiding functions are not Lyapunov functions, however, a comparison of their values allows one to determine a desired direction of system motion and to construct a sequence of controls such that the sum of the guiding functions decreases in an average sense.