This paper presents the dynamic modeling of a nonholonomic mobile robot and the dynamic stabilization problem. The dynamic model is based on the kinematic one including nonholonomic constraints. The proposed control strategy allows to solve the control problem using linear controllers and only requires the robot localization coordinates. This strategy was tested by simulation using Matlab-Simul...

This paper presents procedural guidelines for the construction of discontinuous state feedback controllers for driftless, kinematic nonholonomic systems, with extensions to a class of dynamic nonholonomic systems with drift. Given an ndimensional kinematic nonholonomic system subject to κ Pfaffian constraints, system states are partitioned into “leafwise” and “transverse,” based on the structur...

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...

Invariant manifolds of equations governing the dynamics of conservative nonholonomic systems are investigated. These manifolds are assumed to be uniquely projected onto configuration space. The invariance conditions are represented in the form of generalized Lamb’s equations. Conditions are found under which the solutions to these equations admit a hydrodynamical description typical of Hamilton...

An optimal motion planning scheme using genetic algorithm with wavelet approximation is proposed for nonholonomic systems. The motion planning of nonholonomic systems can be formulated as an optimal control of a driftfree system. A cost function is introduced to incorporate the control energy and the final state errors. The control inputs are determined to minimize the cost functional. By using...

The problem of controlling nonholonomic systems via dynamic state feedback and its structural aspects are analyzed. Advantages and drawbacks with respect to the use of static state feedback laws are discussed. In particular, nonholonomic constraints are shown to yield possible singularities in the dynamic extension process. Nevertheless, these singularities can be avoided by the proper design o...

The nonholonomic motion planning problem is considered for a novel class of modular mobile manipulators, where each module is implemented as a planar parallel manipulator with idler wheels. This assembly is actuated by shape changes of its modules, which, under the in uence of the nonholonomic constraints on the wheels, induce a global snake{like motion of the assembly. The kinematics for a 2{ ...

We discuss an extension of the Hamilton–Jacobi theory to nonholonomic mechanics with a particular interest in its application to exactly integrating the equations of motion. We give an intrinsic proof of a nonholonomic analogue of the Hamilton–Jacobi theorem. Our intrinsic proof clarifies the difference from the conventional Hamilton–Jacobi theory for unconstrained systems. The proof also helps...