Chap7-Modelling_ControlOfNonholonomicMechanicalSystems

Chap7-Modelling_ControlOfNonholonomicMechanicalSystems -...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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 multiFngered 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 Frst 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 classiFcation of nonholonomic systems. Several kinematic models of nonholonomic systems are presented, including examples of wheeled mobile robots, free-floating 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. ±inally, we discuss some general issues of the control problem for nonholonomic systems and present open-loop and feedback control techniques, illustrated also by numerical simulations.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
7.1 Introduction Consider a mechanical system whose confguration can be described by a vector oF generalized coordinates q ∈Q . The confguration space Q is an n -dimensional smooth maniFold, locally di±eomorphic to an open subset oF IR n . Given a trajectory q ( t ) , the generalized velocity at a confguration 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 classifcations oF such constraints can be devised. ²or 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).
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/07/2011 for the course MECH 646 taught by Professor Danielnassrallah during the Fall '10 term at American University of Beirut.

Page1 / 57

Chap7-Modelling_ControlOfNonholonomicMechanicalSystems -...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online