320 NOTICES OF THE AMS VOLUME 52, NUMBER 3 Introduction Nonholonomic systems are, roughly speaking, mechanical systems with constraints on their velocity that are not derivable from position constraints. They arise, for instance, in mechanical systems that have rolling contact (for example, the rolling of wheels without slipping) or certain kinds of sliding contact (such as the sliding of skate...

This paper deals with twisting motion of a falling cat robot by two torque inputs around her waist. The cat robot consists of two rigid columns and has internally two actuators at the joint to generate torque inputs around the normal coordinates. This system is a nonholonomic system whose angular momentum is conserved. W e obtain the Lagrange’s equation of motion with nonholonomic constraint an...

In this survey paper some issues concerning a singularity concept in robotics are addressed. Singularities analyzed the scope of inverse kinematics for serial manipulator, motion planning task nonholonomic systems and optimal control covering large area practical robotic systems. An attempt has been made to define term singularity, which is independent on specific task. A few classifications si...

The theory of mechanical systems with nonholonomic constraints has a long history in classical mechanics; see e.g. the books by Neimark & Fufaev [14], Edelen [6], Rosenberg [16], Arnold [l] and the references quoted in there. In this literature, nonholonomic mechanical systems are described within the variational framework by Euler-Lagrange equations with extra terms corresponding to the constr...

A correction to the previously published article “New Form of Kane’s Equations of Motion for Constrained Systems”1 is presented. Misuse of the transformation matrix between time rates of change of the generalized coordinates and generalized speeds (sometimes called motion variables) resulted in a false conclusion concerning the symmetry of the generalized inertia matrix. The generalized inertia...

This paper addresses a problem of autonomous parking a nonholonomic (car-like) vehicle. This research work is carried out within the framework of the PRAXITELE project which aims to develop a future-oriented urban transportation system based on a eet of electric computer-driven vehicles. At the present stage of the project, the designed vehicles have been equiped for the computer-driven motion ...

This paper describes the problem of designing control laws for path following robots, including two types of nonholonomic mobile manipulators. Due to a cascade structure of the motion equation, a backstepping procedure is used to achieve motion along a desired path. The control algorithm consists of two simultaneously working controllers: the kinematic controller, solving motion constraints, an...

Abstract In this work we establish the relation between Jacobi last multiplier, which is a geometrical tool in solution of problems mechanics and that provides Lagrangian descriptions constants motion for second-order ordinary differential equations, nonholonomic where dynamics determined by Hamel’s equations.