We consider nonholonomic geodesic flows of left-invariant metrics and left-invariant nonintegrable distributions on compact connected Lie groups. The equations of geodesic flows are reduced to the Euler–Poincaré–Suslov equations on the corresponding Lie algebras. The Poisson and symplectic structures give raise to various algebraic constructions of the integrable Hamiltonian systems. On the oth...

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...

In this paper, we derive the augmented Birkhoff equation of linear contraints nonholonomic systems firstly. Base on a conserved quantity or a combination of some conserved quantities, we study the stability of linear contraints nonholonomic systems. Finally, a numerical example is provided to demonstrate the potential and effectiveness of the method.

We introduce a discretization of the Lagrange-d’Alembert principle for Lagrangian systems with nonholonomic constraints, which allows us to construct numerical integrators that approximate the continuous flow. We study the geometric invariance properties of the discrete flow which provide an explanation for the good performance of the proposed method. This is tested on two examples: a nonholono...

This paper presents procedural guidelines for the construction of discontinuous state feedback controllers for driftless, kinematic nonholonomic systems, with extensions to a class of dynamic nonholonomic systems with drift. Given an ndimensional kinematic nonholonomic system subject to κ Pfaffian constraints, system states are partitioned into “leafwise” and “transverse,” based on the structur...

The geometry of constrained Lagrangian systems is developed using the Lagrange-d’Alembert principle, extending the variational approach of Marsden, Shkoller, and Patrick, Comm. Math. Phys. 199:351–395 from holonomic to nonholonomic systems. It emerges that the instrinsic geometry of nonholonomic systems corresponds to the geometry of the distributional Hamiltonian systems of Sniatycki, Rep. Mat...

Title of Dissertation: Motion Control for Nonholonomic Systems on Matrix Lie Groups Herbert Karl Struemper, Doctor of Philosophy, 1997 Dissertation directed by: Professor P. S. Krishnaprasad Department of Electrical Engineering In this dissertation we study the control of nonholonomic systems defined by invariant vector fields on matrix Lie groups. We make use of canonical constructions of coor...

An optimal motion planning scheme using genetic algorithm with wavelet approximation is proposed for nonholonomic systems. The motion planning of nonholonomic systems can be formulated as an optimal control of a driftfree system. A cost function is introduced to incorporate the control energy and the final state errors. The control inputs are determined to minimize the cost functional. By using...