Chapter 7
MODELING AND CONTROL OF
NONHOLONOMIC MECHANICAL SYSTEMS
Alessandro De Luca and Giuseppe Oriolo
Dipartimento di Informatica e Sistemistica
Universit`
a degli Studi di Roma “La Sapienza”
Via Eudossiana 18, 00184 Roma, ITALY
{
deluca,oriolo
}
@dis.uniroma1.it
Abstract
The goal of this chapter is to provide tools for analyzing and controlling nonholonomic
mechanical systems.
This classical subject has received renewed attention because
nonholonomic constraints arise in many advanced robotic structures, such as mobile
robots, space manipulators, and multifingered robot hands. Nonholonomic behavior
in robotic systems is particularly interesting, because it implies that the mechanism
can be completely controlled with a reduced number of actuators. On the other hand,
both planning and control are much more diﬃcult than in conventional holonomic sys
tems, and require special techniques. We show first that the nonholonomy of kinematic
constraints in mechanical systems is equivalent to the controllability of an associated
control system, so that integrability conditions may be sought by exploiting concepts
from nonlinear control theory. Basic tools for the analysis and stabilization of nonlinear
control systems are reviewed and used to obtain conditions for partial or complete non
holonomy, so as to devise a classification of nonholonomic systems. Several kinematic
models of nonholonomic systems are presented, including examples of wheeled mobile
robots, freeﬂoating space structures and redundant manipulators. We introduce then
the dynamics of nonholonomic systems and a procedure for partial linearization of the
corresponding control system via feedback. These points are illustrated by deriving
the dynamical models of two previously considered systems. Finally, we discuss some
general issues of the control problem for nonholonomic systems and present openloop
and feedback control techniques, illustrated also by numerical simulations.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
7.1
Introduction
Consider a mechanical system whose configuration can be described by a vector of
generalized coordinates
q
∈ Q
. The configuration space
Q
is an
n
dimensional smooth
manifold, locally diffeomorphic to an open subset of
IR
n
. Given a trajectory
q
(
t
)
∈ Q
,
the
generalized velocity
at a configuration
q
is the vector ˙
q
belonging to the tangent
space
T
q
(
Q
).
In many interesting cases, the system motion is subject to constraints that may arise
from the structure itself of the mechanism, or from the way in which it is actuated and
controlled. Various classifications of such constraints can be devised. For example,
constraints may be expressed as equalities or inequalities (respectively,
bilateral
or
unilateral
constraints) and they may explicitly depend on time or not (
rheonomic
or
scleronomic
constraints).
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '10
 DanielNassrallah
 Control Engineering, Differential topology, Holonomic, NONHOLONOMIC MECHANICAL SYSTEMS

Click to edit the document details