Global Controllability Criteria and Motion Planning of Regular Affine Systems With Drifts

TL;DR

This paper establishes criteria for the global controllability of affine nonlinear control systems with drifts and explores motion planning solutions, including lift existence proofs for certain systems.

Contribution

It provides necessary and sufficient controllability conditions for affine systems with drifts and introduces a homotopy continuation method for motion planning.

Findings

Controllability criteria are established for codimension-1 and 2 cases.

Global existence of control curve lifts is proven for specific drifted systems.

The homotopy continuation method is effective for motion planning in these systems.

Abstract

In this article, we give a condition for the global controllability of affine nonlinear control systems with drifts on Euclidean spaces. Under regularity assumptions, the condition is necessary and sufficient in the codimension-1 and codimension-2 cases, and holds for systems of higher codimensions under mild restrictions. We then investigate motion planning problems for codimension-1 affine systems, and give proof of the global existence of the lift to control curves for certain drifted systems using the homotopy continuation method.