Adaptive stabilization of uncertain nonholonomic mechanical systems

This paper presents a new adaptive controller as a solution to the problem of stabilizing nonholonomic mechanical systems in the presence of incomplete information concerning the system dynamic model. The proposed control system consists of two subsystems: a slightly modified version of the kinematic stabilization strategy of M'Closkey and Murray(1) which generates a desired velocity trajectory for the nonholonomic system, and an adaptive control scheme which ensures that this velocity trajectory is accurately tracked. This approach is shown to provide arbitrarily accurate stabilization to any desired configuration and can be implemented with no knowledge of the system dynamic model. The efficacy of the proposed stabilization strategy is illustrated through extensive computer simulations with nonholonomic mechanical systems arising from explicit constraints on the system kinematics and from symmetries of the system dynamics.