Some applications of quasi-velocities in optimal control

TL;DR

This paper explores the use of quasi-velocities in formulating and solving optimal control problems for nonholonomic systems on Lie algebroids, including both kinematic and dynamic cases, with illustrative examples.

Contribution

It introduces a Lie algebroid-based framework for optimal control problems using quasi-velocities, extending recent results and providing detailed examples.

Findings

Unified framework for kinematic and dynamic control problems

Application of Lie algebroids to nonholonomic systems

Illustrative examples demonstrating the approach

Abstract

In this paper we study optimal control problems for nonholonomic systems defined on Lie algebroids by using quasi-velocities. We consider both kinematic, i.e. systems whose cost functional depends only on position and velocities, and dynamic optimal control problems, i.e. systems whose cost functional depends also on accelerations. The formulation of the problem directly at the level of Lie algebroids turns out to be the correct framework to explain in detail similar results appeared recently (Maruskin and Bloch, 2007). We also provide several examples to illustrate our construction.