Switched Feedback Control for a class of First-order Nonholonomic Driftless 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 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 ℝ 3 (or simply q × ϕ = 0). We also show that the complement of this discontinuity region is homotopic to SO (3) which is also isomorphic to S 2 × S . The proposed control law is examined by numerical simulations.