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...

Non-holonomic systems may appear in several forms, including combinations between holonomic and nonholonomic constraints for vehicle formations. Examples of the latter are non-holonomic formation constraints with holonomic vehicles or holonomic formation constraints with non-holonomic vehicles. In this paper the problem of non-holonomic systems with holonomic or non-holonomic constraints is add...

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 ...

This paper presents a geometric description of Lagrangian and Hamiltonian systems on Lie affgebroids subject to affine nonholonomic constraints. We define the notion of nonholonomically constrained system, and characterize regularity conditions that guarantee that the dynamics of the system can be obtained as a suitable projection of the unconstrained dynamics. It is shown that one can define a...

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...

We address the problem of motion planning for nonholonomic cooperating mobile robots manipulating and transporting objects while holding them in a stable grasp. We present a general approach based on the calculus of variations that allows us to obtain optimal trajectories and actuator forces/torques for any maneuver in the presence of obstacles. In addition, geometric constraints such as joint ...

We present a new and complete multi-level approach for solving path planning problems for nonholonomic robots. At the rst level a path is found that disrespects (some of) the nonholonomic constraints. At each next level a new path is generated, by transformation of the path generated at the previous level. The transformation is such that more nonholonomic constraints are respected than at the p...