Learning control for uncertain nonholonomic mechanical systems

This paper considers the problem of controlling uncertain nonholonomic mechanical systems performing repetitive motions. It is proposed that a simple and effective solution to this problem can be obtained by first using a reduction procedure to obtain a lower dimensional system which retains the mechanical system structure of the original system, and then controlling: the reduced system using a learning algorithm in such a way that the complete system evolves in the desired manner. This approach ensures convergence of the actual system motion to the desired motion despite considerable uncertainty regarding the system dynamic model. The efficacy of the proposed learning controller is illustrated through computer simulations with nonholonomic mechanical systems arising from both explicit kinematic constraints and from symmetries of the system dynamics.