In this paper, we describe a constrained Lagrangian and Hamiltonian formalism for the optimal control of nonholonomic mechanical systems. In particular, we aim to minimize a cost functional, given initial and final conditions where the controlled dynamics are given by a nonholonomic mechanical system. In our paper, the controlled equations are derived using a basis of vector fields adapted to t...

A new passive wheel type leg-wheeled hybrid mobile robot based on surface motion principle was introduced. To produce the propulsion force, a passive wheel was installed at the end of the parallel mechanism structured leg connecting with the frame-body to make the wheel vertical to the ground at any time. With the inertia framework, the robot framework and some assumptions, two forms of Maggie ...

This paper addresses the feedback control design for a class of nonholonomic systems which are subject to inequality stateconstraints defining a constrained (viability) set K. Based on concepts from viability theory, the necessary conditions forselecting viable controls for a nonholonomic system are given, so that system trajectories starting in K always remain inK. Furthermore, a c...

320 NOTICES OF THE AMS VOLUME 52, NUMBER 3 Introduction Nonholonomic systems are, roughly speaking, mechanical systems with constraints on their velocity that are not derivable from position constraints. They arise, for instance, in mechanical systems that have rolling contact (for example, the rolling of wheels without slipping) or certain kinds of sliding contact (such as the sliding of skate...

In the first part of the paper we present a new point of view on the geometry of nonholonomic mechanical systems with linear and affine constraints. The main geometric object of the paper is the nonholonomic connection on the distribution of constraints. By using this connection we obtain the Newton forms of Lagrange–d’Alembert equations for nonholonomic mechanical systems with linear and affin...

The extended nonholonomic double integrator (ENDI) cannot be asymptotically stabilized by a continuous and time-invariant feedback controller since it violates the Brockett’s condition. In this paper, a new continuous control scheme is proposed to stabilize the ENDI system without drift. The dynamics of an ENDI system is enlarged to a higher dimensional space where a continuous but time-varying...

Linearization of nonholonomic systems at equilibrium positions has been plagued from the very beginning by mistakes and misunderstandings. Bottema [3] corrected Whittaker’s originary procedure [8]; and Naimark and Fufaev [7] developed Bottema’s idea, deriving a scheme which is the currently accepted one. Something nagging however remains about the derivation of the characteristic equation for a...

(ABSTRACT) In this thesis we study the methods for motion planning for nonholonomic systems. These systems are characterized by nonholonomic constraints on their generalized velocities. The motion planning problem with constraints on the velocities is transformed into a control problem having fewer control inputs than the degrees of freedom. The main focus of the thesis is on the study of motio...

This document is a brief overview of the Hamilton-Jacobi theory of Chaplygin systems based on [1]. In this paper, after reducing Chaplygin systems, Ohsawa et al. use a technique that they call Chaplygin Hamiltonization to turn the reduced Chaplygin systems into Hamiltonian systems. This method was first introduced in a paper by Chaplygin in 1911 where he reduced some nonholonomic systems by the...