A Riemannian Geometric Approach to Output Tracking for Nonholonomic Systems

摘要

The problem of designing coordinate-invariant output tracking control laws for nonholonomic mechanical systems is addressed. The velocity constrained Euler-Lagrange equations of motion are expressed through a constrained affine connection which is compatible with the kinetic energy Riemannian metric. This formalism is used in designing an output tracking control law via backstepping, which is shown to guarantee exponential stability when the initial distance between the output and reference trajectory is within injectivity radius of the output manifold. In particular this enables almost-global tracking when the output manifold is a rank-1 symmetric space. The control law is intrinsic to the Riemannian structure, and is explicitly constructed. The control law is applied to the problem of tracking the reduced attitude of a rigid body with a nonholonomic velocity constraint. Numerical simulations illustrating the tracking performance are presented.