We prove the following nonholonomic version of the classical Moser theorem: given a bracket-generating distribution on a connected compact manifold (possibly with boundary), two volume forms of equal total volume can be isotoped by the flow of a vector field tangent to this distribution. We describe formal solutions of the corresponding nonholonomic mass transport problem and present the Hamilt...

This thesis develops a hybrid decentralized formation control framework to coordinate multiple mobile robots with nonholonomic constraints. The proposed approach deploys a control theoretic bottom-up approach where, some low level behavior based controllers are coordinated by a discrete event system with supervisory control. The robots are required to navigate in an unstructured environment wit...

In this paper we discuss stabilization of a nonholonomic system consisting of a unicycle with rider. We show in particular that one can achieve stability of slow steady vertical motions by imposing a feedback control force on the rider’s limb.

In this paper we discuss asymptotic stability in energy-preserving systems which have an almost Poisson structure. In particular we consider a class of Poisson systems which includes the Toda lattice. In standard Hamiltonian systems one of course does not expect asymptotic stability. The key here is the structure of the phase space of the Poisson or almost Poisson systems and the nature of the ...

Nonholonomic mechanical systems naturally occur when there are rolling constraints [4] or Lagrangian symmetries leading to momentum constraints [1]. Examples include kinematic wheeled vehicles, free floating satellites with appendages, and simplified models of biomimetic locomotion. This work considers the local motion planning problem for a specific class of nonholonomic systems— those whose c...

When multiple arms are used to manipulate a large object, it is necessary to maintain and control contacts between the object and effector(s) on one or more arms. The contacts are characterized by holonolnic as well as nonholonomic constraints. This paper addresses the control of rnechaaical systems subject to nonholonomic constraints, rolling constraints in particular. It has been shown that s...

We introduce a discretization of the Lagrange-d’Alembert principle for Lagrangian systems with nonholonomic constraints, which allows us to construct numerical integrators that approximate the continuous flow. We study the geometric invariance properties of the discrete flow which provide an explanation for the good performance of the proposed method. This is tested on two examples: a nonholono...

We show that the contact dynamics obtained from Herglotz variational principle can be described as a constrained nonholonomic or vakonomic ordinary Lagrangian system depending on dissipative variable with an adequate choice of one constraint. As consequence we obtain and systems calculus constraints variable. The variation energy other quantities are also giving usual results.

Nonholonomic mechanical systems encompass a large class of practically interesting robotic structures, such as wheeled mobile robots, space manipulators, and multi-fingered robot hands. However, few results exist on the cooperative control in generic, distributed approach. In this work we extend recently developed Interconnection Damping Assignment Passivity-Based Control (IDA-PBC) method to sy...