We show that the Suslov nonholonomic rigid body problem studied in [10, 13, 26] can be regarded almost everywhere as a generalized Chaplygin system. Furthermore, this provides a new example of a multidimensional nonholonomic system which can be reduced to a Hamiltonian form by means of Chaplygin reducing multiplier. Since we deal with Chaplygin systems in the local sense, the invariant manifold...

In this paper, we propose a novel approach to reactive obstacle avoidance for nonholonomic systems. The method is based on the deformation of an initial trajectory computed by a motion planner. The deformation we perform keeps the nonholonomic constraints of the system satisfied. The deformation algorithm is based on a potential field generated by obstacles. We applied this approach to the mobi...

|A nonholonomic motion planner for mobile manipulators moving in cluttered environments is presented. The approach is based on a discontinous feedback law under the infuence of a special potential eld. Convergence is shown via Lyapunov's direct method. Utilizing redundancy, the methodology allows the system to perform secondary, connguration dependent, objectives such as singularity avoidance. ...

Several aspects of Dirac reduction are compared and formulated from the same geometric point of view. A link with nonholonomic reduction is found. The theory of optimal momentum maps and reduction is extended from the category of Poisson manifolds to that of closed Dirac manifolds. An optimal reduction method for a class of nonholonomic systems is formulated. Several examples are studied in det...

Many important problems in multibody dynamics, the dynamics of wheeled vehicles and motion generation, involve nonholonomic mechanics. Many of these systems have symmetry, such as the group of Euclidean motions in the plane or in space and this symmetry plays an important role in the theory. Despite considerable advances on both Hamiltonian and Lagrangian sides of the theory, there remains much...

We consider a class of dynamical systems on a Lie group G with a leftinvariant metric and right-invariant nonholonomic constraints (so called LR systems) and show that, under a generic condition on the constraints, such systems can be regarded as generalized Chaplygin systems on the principle bundle G → Q = G/H , H being a Lie subgroup. In contrast to generic Chaplygin systems, the reductions o...

Lagrangian systems with ideal nonholonomic constraints can be expressed as implicit index 2 differential-algebraic equations (DAEs) and can be derived from the Lagrange-d’Alembert principle. We define a new nonholonomically constrained discrete Lagrange-d’Alembert principle based on a discrete Lagrange-d’Alembert principle for forced Lagrangian systems. Nonholonomic constraints are considered a...

This paper investigates the problem of global stabilization by state feedback for a class of uncertain nonholonomic systems in chained form with partial inputs saturation. By using input-state-scaling technique and backstepping recursive approach, a state feedback control strategy is presented. With the help of a switching control strategy, the designed controller renders that the states of clo...

We recall the notion of a nonholonomic system by means of an example of classical mechanics, namely the vertical rolling disk. For a general mechanical system with nonholonomic constraints, we present a Lagrangian formulation of the nonholonomic and vakonomic dynamics using the method of anholonomic frames. We use this approach to deal with the issue of when a nonholonomic system can be interpr...

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...