Smooth, Time-invariant Regulation of Nonholonomic Systems via Energy Pumping-and-Damping

TL;DR

This paper introduces a smooth, time-invariant energy pumping-and-damping control method for nonholonomic systems, ensuring asymptotic regulation with almost global solutions for integrators and local stability for chained systems.

Contribution

It develops a novel energy-based control approach using interconnection and damping assignment for nonholonomic systems, with almost global regulation solutions for integrators.

Findings

Almost global regulation for nonholonomic integrators

Local stability for chained systems

Simulation results show improved performance

Abstract

In this paper we propose an energy pumping-and-damping technique to regulate nonholonomic systems described by kinematic models. The controller design follows the widely popular interconnection and damping assignment passivity-based methodology, with the free matrices partially structured. Two asymptotic regulation objectives are considered: drive to zero the state or drive the systems total energy to a desired constant value. In both cases, the control laws are smooth, time-invariant, state-feedbacks. For the nonholonomic integrator we give an almost global solution for both problems, with the objectives ensured for all system initial conditions starting outside a set that has zero Lebesgue measure and is nowhere dense. For the general case of higher-order nonholonomic systems in chained form, a local stability result is given. Simulation results comparing the performance of the proposed controller with other existing designs are also provided.