We recall the notion of a nonholonomic system by means of an example of classical mechanics, namely the vertical rolling disk. For a general mechanical system with nonholonomic constraints, we present a Lagrangian formulation of the nonholonomic and vakonomic dynamics using the method of anholonomic frames. We use this approach to deal with the issue of when a nonholonomic system can be interpr...

We consider a simple motivating example of non-Hamiltonian dynamical system with time-dependent constraints obtained by imposing rheonomic non-integrable Bilimovich’s constraint on freely rotating rigid body. Dynamics this low-dimensional nonlinear nonautonomous dynamic involves different kinds stable and unstable attractors, quasi strange compact noncompact invariant attractive curves, etc. To...

This paper studies the construction of geometric integrators for nonholonomic systems. We derive the nonholonomic discrete Euler-Lagrange equations in a setting which permits to deduce geometric integrators for continuous nonholonomic systems (reduced or not). The formalism is given in terms of Lie groupoids, specifying a discrete Lagrangian and a constraint submanifold on it. Additionally, it ...

The purpose of this paper is to study the modeling method for nonholonomic systems with friction by linear complementary problem (LCP). Firstly, the dynamic equation with multipliers for the nonholonomic system with friction is given. Secondly, a standard linear complementary model is established, which describes the normal and tangential characteristics for a nonholonomic system. Thirdly, by u...

When the generalized velocity of a mechanical system satis es an equality condition that cannot be written as an equivalent condition on the generalized position, the system is called a nonholonomic system [1, 2]. Nonholonomic condition may arise from constraints such as pure rolling of a wheel or from physical conservation laws such as the conservation of angular momentum of a free oating body...

a mobile manipulator robot is known as a complex system due to some properties such as coupling between the manipulator and mobile chassis, holonomic and nonholonomic constraints, multivariable and nonlinear dynamics. the control of robot faces the external disturbance, parametric uncertainty and unmodeled dynamics. therefore, the use of an adaptive fuzzy system is suggested for its capability ...

In the paper we present new control algorithms for a special class of mobile manipulators, namely for nonholonomic mobile manipulators. A mobile manipulator is defined as a robotic system composed of a mobile platform and a manipulator mounted on the platform equipped with non-deformable wheels. Such a combined system is able to perform manipulation tasks in a much larger workspace than a fixed...

In this paper, we consider a hybrid control strategy for stabilization of nonholonomic systems. In particular, we deal with a typical nonholonomic system, namely a two-wheeled vehicle. We first rewrite the system in a chained form, and then transform it into a nonholonomic integrator (NHI) system. Finally, we apply and modify the hybrid control method for the NHI system, so that the entire syst...

Abstract In this paper a dexterity measure is proposed for driftless nonholonomic systems. Admissible motions at a given state of a nonholonomic system are described by the controllability (Lie) algebra of the system. The algebra is completely described by Lie monomials (vector fields) produced by the Lie bracketing of vector fields associated with the system. At a given state, the nonholonomic...