Control of mechanical systems with symmetries and nonholonomic constraints

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) that 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 with symmetries 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 general robotic locomotion.