Geometry and control of the nonholonomic integrator: An electrodynamics analogy

TL;DR

This paper explores generalized nonholonomic integrators using geometric methods, establishing controllability conditions and linking optimal trajectories to electromagnetic analogies.

Contribution

It introduces a geometric framework for controllability analysis and connects optimal control trajectories to electrodynamics analogies.

Findings

Controllability characterized via Stokes' theorem and complex analysis.

Optimal trajectories resemble charged particle motion in electromagnetic fields.

Provides necessary and sufficient conditions for controllability.

Abstract

We consider some generalizations of the classical nonholonomic integrator and give a geometric approach to characterize controllability for these systems. We use Stokes' theorem and results from complex analysis to obtain necessary and sufficient conditions for controllability. Furthermore, we show that optimal trajectories of certain minimum energy optimal control problems defined on these systems can be identified with the trajectory of a charged particle in an electromagnetic field.