Control of uncertain nonholonomic mechanical systems using reduction and adaptation

This paper considers the problem of controlling nonholonomic mechanical systems in the presence of incomplete information concerning the system model and state. 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 adaptively controlling the reduced system in such a way that the complete system is driven to the goal configuration. This approach is shown to ensure accurate motion control without knowledge of the system dynamic model or rate measurements. The efficacy of the proposed control strategy is illustrated through preliminary laboratory experiments with a symmetric nonholonomic mechanical system.