The problem of controlling nonholonomic systems via dynamic state feedback and its structural aspects are analyzed. Advantages and drawbacks with respect to the use of static state feedback laws are discussed. In particular, nonholonomic constraints are shown to yield possible singularities in the dynamic extension process. Nevertheless, these singularities can be avoided by the proper design o...

Planning trajectories for nonholonomic systems is difficult and computationally expensive. When facing unexpected events, it may therefore be preferable to deform in some way the initially planned trajectory rather than to re-plan entirely a new one. We suggest here a method based on affine transformations to make such deformations. This method is exact and fast: the deformations and the result...

This paper presents a method of path optimization for nonholonomic systems. This method consists in iteratively modifying a given feasible path in order to make a cost related to the path decrease. The paper presents two main applications of this method: the first one is an algorithm that solves the problem of path planning for complex kinematic systems (i. e. trucks with two trailers) in extre...

This paper investigates the problem of global stabilization by state-feedback for a class of high-order nonholonomic systems in power chained form with time-varying delays. By using input-state-scaling, and adding a power integrator techniques, and choosing an appropriate Lyapunov-Krasoviskii functional, a state-feedback controller is constructed. Based on switching strategy to eliminate the ph...

Robust hybrid controller design is presented in this paper for motion/force control of mechanical systems subjected to a set of holonomic or classical nonholonomic constraints and in the presence of uncertainties about plant parameters. A uni ed and systematic procedure is employed to derive the controllers for both holonomic and nonholonomic constrained mechanical systems, respectively. The pr...

Formation control is an important problem in multi-agent systems. In this paper, it is assumed that a target is moving with a disturbed dynamics, and then, a k-coverage formation control is designed for every nonholonomic agent to improve tracking qualities. A virtual agent approach is adopted in the formation control design. The stability of the tracking error system is analyzed. Finally, some...

This paper considers the position control problem of nonholonomic mobile robots with plant uncertainties and external disturbances. A robust passivity-based controller using fuzzy logic is proposed based on the reduced-form dynamic model of nonholonomic systems. The fuzzy logic system, whose parameters are tuned on-line, is introduced to learn the unknown (uncertain) plant dynamics due to the u...

Nonrelativistic Newton and Schrödinger equations remain correct not only under holonomic but also under nonholonomic transformations of the spacetime coordinates. Here we study the properties of transformations which are holonomic in the space coordinates while additionally tranforming the time in a path-dependent way. This makes them nonholonomic in spacetime. The resulting transformation form...

This paper is concerned with control of nonholonomic systems in the presence of parametric modeling uncertainty. The specific problem considered is that of parking a wheeled mobile robot of unicycle type with unknown parameters, whose kinematics can be described by Brockett’s nonholonomic integrator after an appropriate state and control coordinate transformation. We employ the techniques of su...

We consider nonholonomic systems with elastic collisions and propose a concept of generalised solutions to Lagrange-d’Alembert equations. In the light of this concept we describe dynamics of the collisions. Several applications have been investigated. 1. The Description of the Problem Let us start from the following model example. There is a solid ball B of radius r and of mass m and let its ce...