Original manuscript: 2019/06/08

In this report we study the modelling of simple mechanical systems evolving on trivial principal bundles, specifically locomotion systems with nonholonomic constraints.

We show how we can model motion via group actions on configuration manifolds and assess the relationship between the constraints (and constrained variables) and the variables that physically induce motion on the vehicle by studying principal bundles.

With knowledge of the controllability (using the Lie algebra rank condition) of this formulation of a constrained simple mechanical system, we proceed to outlining a methodology to design a universal control algorithm for constrained mechanical systems using the method of virtual surfaces (or potential functions).

Lastly, we design a set of virtual surfaces to make a rolling disk (arguably the simplest practical nonholonomic system) stabilise to a point, track a path, and avoid a sequence of obstacles in the plane.

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Last Updated: Fri Mar 15 08:14:05 2024