Characterization of accessibility for affine connection control systems at some points with nonzero velocity

TL;DR

This paper extends the understanding of accessibility in affine connection control systems to points with nonzero velocity, broadening the scope of controllability analysis for various mechanical systems.

Contribution

It generalizes the accessibility algebra description for systems at nonzero velocities under certain geometric restrictions, building on prior zero-velocity results.

Findings

Provides a new characterization of accessibility algebra at nonzero velocities

Applies the results to various mechanical control systems

Enhances the theoretical framework for controllability analysis

Abstract

Affine connection control systems are mechanical control systems that model a wide range of real systems such as robotic legs, hovercrafts, planar rigid bodies, rolling pennies, snakeboards and so on. In 1997 the accessibility and a particular notion of controllability was intrinsically described by A. D. Lewis and R. Murray at points of zero velocity. Here, we present a novel generalization of the description of accessibility algebra for those systems at some points with nonzero velocity as long as the affine connection restricts to the distribution given by the symmetric closure. The results are used to describe the accessibility algebra of different mechanical control systems.