Towards automated gait generation for dynamic systems with non-holonomic constraints

In this paper we generate gaits for dynamics systems that are subject to non-holonomic velocity constraints. These systems are referred to as mixed non-holonomic systems. The motion of such systems is governed by both the non-holonomic constraints acting on the system and a system of differential equations constraining the evolution of generalized momentum. We propose a method that utilizes both governing motions, that is, satisfying all the constraints and instantaneously conserving momentum along un-restricted directions, to generate gaits for systems like the snakeboard, which belongs to the family of mixed non-holonomic systems. We accomplish this by defining a new scaled momentum variable. This scaled momentum allows us to easily explore the design of gaits that causes momentum to evolve such that a desired non-trivial motion results