In the first part of the paper we present a new point of view on the geometry of nonholonomic mechanical systems with linear and affine constraints. The main geometric object of the paper is the nonholonomic connection on the distribution of constraints. By using this connection we obtain the Newton forms of Lagrange–d’Alembert equations for nonholonomic mechanical systems with linear and affin...

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...

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...

A geometrically exact model of a Cosserat rod with nonholonomic constraints is outlined. The constraint forces are derived from the framework of nonholonomic mechanics by using arguments from Cauchy analysis, and a thorough discussion is given concerning the nature of these constraints. By making an additional assumption on the magnitude of the deflections, a simplified model similar to the Eul...

This paper develops an automatic parking algorithm based on a fuzzy logic controller with the vehicle pose for the input and the steering angle for the output. In this way some feasible reference trajectory path have been introduced according to geometric and kinematic constraints and nonholonomic constraints to simulate motion path of car. Also a novel method is used for parking space detec...