The goal of this chapter is to provide tools for analyzing and controlling nonholonomic mechanical systems. This classical subject has received renewed attention because nonholonomic constraints arise in many advanced robotic structures, such as mobile robots, space manipulators, and multifingered robot hands. Nonholonomic behavior in robotic systems is particularly interesting, because it impl...

Abstract Nonholonomic mechanics describes the motion of systems constrained by nonintegrable constraints. One its most remarkable properties is that derivation nonholonomic equations not variational in nature. However, this paper, we prove (Theorem 1.1) for kinetic systems, solutions starting from a fixed point q are true geodesics family Riemannian metrics on image submanifold $${{\mathcal {M}...

This paper presents a motion planner and nonholonomic controller for a mobile robot, with global collision avoidance and convergence properties. This closed loop approach combines appropriately designed (dipolar) potential fields with discontinuous feedback and is suitable for real time implementation. It makes use of a novel kind of Lyapunov functions which are useful for nonholonomic navigati...

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 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 ...

Trajectory planning is one of the fundamental problems in mobile robotics. A wide variety of approaches have been proposed over the years to deal with the various issues of this problem. This thesis presents an original and complete solution to tackle the motion planning problem for nonholonomic mobile robots in two-dimensional space. Given a set of obstacles, an initial and a goal con guration...

The paper considers the brachistochronic motion of a variable mass nonholonomic mechanical system [3] in a horizontal plane, between two specified positions. Variable mass particles are interconnected by a lightweight mechanism of the ‘pitchfork’ type. The law of the time-rate of mass variation of the particles, as well as relative velocities of the expelled particles, as a function of time, ar...