Motion Planning for Dynamic Variable Inertia Mechanical Systems with Non-holonomic Constraints

In this paper, we address a particular flavor of the motion planning problem, that is, the gait generation problem for underactuated variable inertia mechanical systems. Additionally, we analyze a rather general type of mechanical systems which we refer to as mixed systems. What is unique about this type of mechanical system is that both non-holonomic velocity constraints as well as instantaneous conservation of the generalized momentum variables defined along the allowable motion direction completely specify the systems velocity.

By analyzing this general type of mechanical systems, we lay the grounds for a general and intuitive analysis of the gait generation problem. Through our approach, we provide a novel framework not only for classifying different types of mechanical systems, but also for identifying a partition on the space of allowable gaits.

By applying our techniques to mixed systems which according to our classification are the most general type of mechanical systems, we verify the generality and applicability of our approach. Moreover, mixed systems yield the richest family of allowable gaits, hence, superseding the gait generation problem for other simpler types of mechanical systems. Finally, we apply our analysis to a novel mechanical system, the variable inertia snakeboard, which is a generalization of the original snakeboard that was previously studied in the literature.