New high order sufficient conditions for configuration tracking

TL;DR

This paper introduces new high-order sufficient conditions for mechanical control systems to accurately track any desired configuration curve, expanding the theoretical framework for control design.

Contribution

It generalizes existing tracking conditions for affine connection control systems using averaging and kinematic reduction techniques.

Findings

New conditions guarantee trajectory tracking for a broad class of systems.

The results extend previous tracking conditions to higher-order scenarios.

The approach combines averaging with kinematic reduction for proof.

Abstract

In this paper, we propose new conditions guaranteeing that the trajectories of a mechanical control system can track any curve on the configuration manifold. We focus on systems that can be represented as forced affine connection control systems and we generalize the sufficient conditions for tracking known in the literature. The new results are proved by a combination of averaging procedures by highly oscillating controls with the notion of kinematic reduction.