ADAPTIVE STABILIZATION OF UNCERTAIN NONHOLONOMIC MECHANICAL SYSTEMS

This paper presents a new adaptive controller as a solution to the pro blem of stabilizing nonholonomic mechanical systems in the presence of incomplete information concerning the system dynamic model. The propo sed control system consists of two subsystems: a slightly modified ver sion of the kinematic stabilization strategy of M'Closkey and Murray(1 ) which generates a desired velocity trajectory for the nonholonomic s ystem, and an adaptive control scheme which ensures that this velocity trajectory is accurately tracked. This approach is shown to provide a rbitrarily accurate stabilization to any desired configuration and can be implemented with no knowledge of the system dynamic model. The eff icacy of the proposed stabilization strategy is illustrated through ex tensive computer simulations with nonholonomic mechanical systems aris ing from explicit constraints on the system kinematics and from symmet ries of the system dynamics.