On the Motion Planning and Feedback Stabilization of Nonlinear Systems with Drift

Abstract

View Video Presentation: https://doi.org/10.2514/6.2021-1959.vid The motion planning problem (MPP) is the problem of finding a control input that steers a control system between two arbitrarily given points. Several algorithms have been developed for the motion planning of nonlinear driftless systems over the 1990's using \textit{differential geometric control} tools. However, little is known about MPP of nonlinear systems with drift. With the contemporary research flurry on motion planning in the robotics community, mostly using optimal control and machine learning techniques, we aim in this paper to demonstrate the capabilities of differential geometric control theory in solving the MPP for nonlinear systems with drift and also in designing feedback stabilization using Lie brackets for systems that fail Brockett's necessary condition for stabilization using smooth feedback.