Journal ArticleDOI
Control and stabilization of nonholonomic dynamic systems
TLDR
In this article, a class of inherently nonlinear control problems arising directly from physical assumptions about constraints on the motion of a mechanical system is identified and a general procedure for constructing a piecewise analytic state feedback which achieves the desired result is suggested.Abstract:
A class of inherently nonlinear control problems has been identified, the nonlinear features arising directly from physical assumptions about constraints on the motion of a mechanical system. Models are presented for mechanical systems with nonholonomic constraints represented both by differential-algebraic equations and by reduced state equations. Control issues for this class of systems are studied and a number of fundamental results are derived. Although a single equilibrium solution cannot be asymptotically stabilized using continuous state feedback, a general procedure for constructing a piecewise analytic state feedback which achieves the desired result is suggested. >read more
Citations
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Book
A Mathematical Introduction to Robotic Manipulation
TL;DR: In this paper, the authors present a detailed overview of the history of multifingered hands and dextrous manipulation, and present a mathematical model for steerable and non-driveable hands.
Journal ArticleDOI
Developments in nonholonomic control problems
Ilya Kolmanovsky,N.H. McClamroch +1 more
TL;DR: Nonholonomic control systems as discussed by the authors provide a good introduction to the subject for nonspecialists in the field, while perhaps providing specialists with a better perspective of the field as a whole.
Journal ArticleDOI
Control of chained systems application to path following and time-varying point-stabilization of mobile robots
TL;DR: Application to the control of nonholonomic wheeled mobile robots is described by considering the case of a car pulling trailers, and globally stabilizing time-varying feedbacks are derived.
Journal ArticleDOI
Structural properties and classification of kinematic and dynamic models of wheeled mobile robots
TL;DR: The structure of the kinematic and dynamic models of wheeled mobile robots is analyzed and it is shown that, for a large class of possible configurations, they can be classified into five types, characterized by generic structures of the model equations.
Book
Geometric control of mechanical systems
Francesco Bullo,Andrew D. Lewis +1 more
TL;DR: In this article, a comprehensive set of modeling, analysis and design techniques for a class of simple mechanical control systems is presented, that is, systems whose Lagrangian is kinetic energy minus potential energy.
References
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Mathematical aspects of classical and celestial mechanics
TL;DR: The main purpose of the book as discussed by the authors is to acquaint mathematicians, physicists and engineers with classical mechanics as a whole, in both its traditional and its contemporary aspects As such, it describes the fundamental principles, problems, and methods of classical mechanics, with the emphasis firmly laid on the working apparatus, rather than the physical foundations or applications.
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Geometric Phases In Physics
Frank Wilczek,Alfred D. Shapere +1 more
TL;DR: In the last few years, considerable interest has been focused on the phase that waves accumulate when the equations governing the waves vary slowly as discussed by the authors, which is known as the Berry's phase.
Journal ArticleDOI
Controllability of nonlinear systems
TL;DR: In this article, the controllability of nonlinear systems described by the equation dx/dt - F(x,u) was discussed and it was shown that strong accessibility implies strong accessibility for a large class of manifolds including Euclidean spaces.
Journal ArticleDOI
Feedback stabilization and tracking of constrained robots
N.H. McClamroch,Danwei Wang +1 more
TL;DR: In this paper, the effects of constraint force required to maintain satisfaction of the constraints are considered, and conditions for stabilization and tracking using feedback are developed using mathematical models for constrained robot dynamics.
Journal ArticleDOI
A general theorem on local controllability
TL;DR: In this article, a general sufficient condition for local controllability of a nonlinear system at an equilibrium point is given. And a number of new necessary and sufficient conditions are obtained.