Exponential stabilization of mobile robots with nonholonomic constraints

Abstract

This paper presents an exponentially stable controller for a two degrees of freedom robot with nonholonomic constraznts. Although this type of system is open loop controllable, this system has been shown to be nonstabilizable via pure smooth feedback [2], 171. I n this paper, a particular class of piecewise continuous controllers is shown to stabilize the system exponentially. This controller has the feature that it does not require infinitely fast switching, as required, for example, by sliding controllers.

Application of transverse functions to control differentially driven wheeled robots using velocity fields

“…The transverse function for this system can be found based on the following exponential map (6) and (8). Recalling basis X given by (25) and computing A from (9) one obtains…”

“…Later on it is assumed that ε 1 is defined by the following formula (6) and (8). The constructive method of computation of a transverse function has been proposed in [11].…”

“…We not hence function f evolves o Assume that f = [ f x f y f θ satisfying (6) and (8). Rec computing A from (9) one o…”

“…election of a transverse function for the given driftless e system is not unique. Basically, such a function should sfy quite general conditions covered by (6) and (8). The structive method of computation of a transverse function been proposed in [11].…”

“…In order to cover a more complicated case when linear controllability is lost one needs to use nonlinear techniques based on discontinuous or time-varying feedbacks, cf. [6][7][8][9]. However, both approaches have significant drawbacks that hinder achieving asymptotic stabilization at a point with an acceptable performance and robustness to unmodelled dynamics.…”