Submitted to the 1995 IEEE Conference on Decision and Controls

This paper presents initial results on the control of mechanical systems for which group symmetries exist (i.e., the dynamics are invariant under the action of a Lie group) and are not fully annihilated by the addition of nonholonomic constraints. These types of systems are characterized by the persistence of momentum-like drift terms which are not directly controllable via the inputs to the system. We show that for systems with nonholonomic constraints (in direct contrast with unconstrained systems or systems with holonomic constraints) there exists the possibility for controlling these momentum terms. The snakeboard is used as a motivating example, and some comment is given as to the utility of these equations for robotic locomotion, as well as to more general problems which can be treated using this framework.