This paper studies local configuration controllability of multibody systems with nonholonomic constraints. As a nontrivial example of the theory, we consider the dynamics and control of a multibody spherical robot. Internal rotors and sliders are used as the mechanisms for control. Our model is based on equations developed by the second author for certain mechanical systems with nonholonomic co...

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}...

Plenty of approaches to stabilize chained nonholonomic systems have been proposed in the literature. However, the stabilization with constrained inputs is seldom addressed. This problem has practical importance since all physical nonholonomic systems have actuator limitations. In this article, a novel switching control design is proposed. The design strategy is inspired by the structural simila...

Plenty of approaches to stabilize chained nonholonomic systems have been proposed in the literature. However, the stabilization with constrained inputs is seldom addressed. This problem has practical importance since all physical nonholonomic systems have actuator limitations. In this article, a novel switching control design is proposed. The design strategy is inspired by the structural simila...

solvable by means of a simple hybrid control law, i.e., it is possible to achieve global exponential stability of the zero equilibrium in the presence of (small) perturbations vanishing at the origin. The control law retains the basic properties of the discontinuous control laws proposed in [1], namely exponential convergence rate and lack of oscillatory behavior. The results presented in this ...

This paper is concerned with the stabilization of nonholonomic systems in port-controlled Hamiltonian formulae via generalized canonical transformations. A special class of timevarying generalized canonical transformations are introduced which preserves the passivity property. Utilizing this transformation timevarying asymptotically stabilizing controllers for the nonholonomic Hamiltonian syste...

We report on new applications of the Poincaré and Sundman timetransformations to the simulation of nonholonomic systems. These transformations are here applied to nonholonomic mechanical systems known to be Hamiltonizable (briefly, nonholonomic systems whose constrained mechanics are Hamiltonian after a suitable time reparameterization). We show how such an application permits the usage of vari...

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...

Nonlinear H∞ control is considered for uncertain nonholonomic systems with external disturbances in their chained form kinematic models. State feedback controllers are explicitly constructed to guarantee an L2 gain performance from the disturbance to the system output. Without the presence of the disturbance, the system states are regulated to the origin. Recent results in robust and adaptive c...

We propose a systematic modelling of the nonholonomic mobile manipulators built from a robotic arm mounted on a wheeled mobile platform. It extends the fundamental notions of nonholonomy, mobility and manœuvrability to the case of these hybrid holonomic/nonholonomic systems. It offers unambiguous definitions and models to the designer of kinematic control laws.