Motion planning for coupled rigid bodies in a horizontal plane is investigated. The rigid bodies are serially connected by passive revolute joints. The dynamic constraints on the system are second-order nonholonomic constraints. We attempted to control those n coupled rigid bodies by the translational acceleration inputs at the first joint. If each rigid body is hinged at the center of percussi...

This paper presents several classical mechanical systems with nonholonomic constraints from the point of view of sub-Riemannian geometry. For those systems that satisfy the bracket generating condition the system can move continuously between any two given states. However, the paper provides a counterexample to show that the bracket generating condition is not also a sufficient condition for co...

This paper deals with coordinated tasks for mobile nonholonomic manip-ulators. The systems are composed of a nonholonomic mobile platform and a simple kinematic chain holonomic arm. First, concepts such that redundancy and singular conngurations are deened. Then, reduced diierential models are introduced. It is then possible to work with a set of independant task coordinates. Applications follo...

This paper is concerned with the stabilization of nonholonomic systems in port-controlled Hamiltonian formulae via generalized canonical transformations. A special class of timevarying generalized canonical transformations are introduced which preserves the passivity property. Utilizing this transformation timevarying asymptotically stabilizing controllers for the nonholonomic Hamiltonian syste...

The paper presents a new method of performing integrator backstepping in systems that are discontinuous, either due to their inherent structure or because of the applied control input. The proposed technique is applied to the stabilization problem of the dynamic system of a nonholonomic mobile robot. Simulation studies indicate that the methodology can also help alleviate the problem of chatter...

This paper presents a theoretical framework for linearization and stabilization of second-order nonholonomic chained systems. By giving a new criterion for the problem of nonsmooth nonregular feedback linearization, it is proved that second-order chained systems are nonregular static state feedback linearizable. A discontinuous control law is obtained based on linear system theory and the inver...

This paper presents a theoretical framework for nonregular feedback linearization and stabilization of second-order nonholonomic chained systems. By giving a new criterion for the problem of nonsmooth nonregular feedback linearization, it is proved that second-order chained systems are nonregular static state feedback linearizable. A discontinuous control law is obtained based on linear system ...

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...

We consider kinematic chains evolving on a nite{ dimensional Lie group G under nonholonomic constraints, where snake{like global motion is induced by shape variations of the system. In particular, we consider the case when the evolution of the system is restricted to a subspace h of the corresponding Lie algebra G; where h is not a subalgebra of G and it generates the whole algebra under Lie br...