This paper provides a method for a controllable nonholonomic mechanical system. By use of the nonholonomy of the disk’s rolling constraint in the plane and the condition of chained form conversion, a multi-joint nonholonomic manipulator, which uses only two actuators and can be converted into chained form and achieves control simplicity, is presented. The Frobenius and Chow theorems prove that ...

We extend Hamilton–Jacobi theory to Lagrange–Dirac (or implicit Lagrangian) systems, a generalized formulation of Lagrangian mechanics that can incorporate degenerate Lagrangians as well as holonomic and nonholonomic constraints. We refer to the generalized Hamilton–Jacobi equation as the Dirac–Hamilton–Jacobi equation. For non-degenerate Lagrangian systems with nonholonomic constraints, the th...

Exploiting unique features of nonholonomic systems, innovative and advantageous mechanisms can be designed. We have proposed a nonholonomic manipulator which is a controllable n joint manipulator with only two actuators. In order to create its nonholonomic constraint, a special type of velocity transmission, called the nonholonomic gear, was developed. There are many possible alternatives for d...

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...

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...

This paper presents a new fuzzy Lyapunov controller for nonholonomic mobile vehicles. A symbiosis between classical backstepping techniques and fuzzy logic was realized. The control system ensures a good robustness with respect to outside perturbations. These perturbations can interact with the vehicle. They are sources of uncertainty for the system model and can perturb the validity of the non...

In nonholonomic dynamics, symmetries do not always lead to conservation laws. In this paper we study conditions for a nonholonomic system with symmetry to have conservation laws linear in momentum.

A method is presented for planning obstacle-avoiding paths for a system which exhibits nonholonomic constraints. The method is based on the use of harmonic functions. Linear constraints on the velocity of a nonholonomic system can be directly expressed as Neumann boundary conditions for a harmonic function. Such boundary conditions are easily represented in a resistive network. The resulting po...

Virtual constraints are relations imposed in a control system that become invariant via feedback instead of real physical acting on the system. Nonholonomic systems mechanical with non-integrable velocities. In this work, we introduce notion virtual nonholonomic geometric framework. More precisely, it is controlled distribution associated an affine connection We show existence and uniqueness la...

based on dynamic modeling, robust trajectory tracking control of attitude and position of a spherical mobile robot is proposed. in this paper, the spherical robot is composed of a spherical shell and three independent rotors which act as the inner driver mechanism. owing to rolling without slipping assumption, the robot is subjected to two nonholonomic constraints. the state space representatio...