Bounded and Finite-time-reaching Switched Feedback Control of First-order Nonholonomic Systems

Abstract

This paper is concerned with stabilizing feedback control for a class of nonholonomic driftless systems, whose controllability Lie algebra rank condition is satisfied by up to first-order Lie brackets. We propose a switched feedback law which drives all the initial states to the origin with bounded control inputs (as opposed to unbounded, division-by-zero-type discontinuous control). The discontinuity of the feedback law takes place on a subspace defined by the ‘parallelism’ condition for the base and the fiber vectors in R³ (or simply q×→=0). We also show that the complement set of this discontinuity region is homotopic to SO (3) which is isomorphic to an SO (2)-bundle on S². The proposed control law is examined by numerical simulations.