Covariant formulation for the optimal control of jointed arm robots: an alternative to Pontryagin's principle

TL;DR

This paper introduces a covariant formulation for optimal control of jointed arm robots, utilizing Hermite finite elements and conjugate gradient algorithms to improve efficiency and convergence in actuator command optimization.

Contribution

It presents a novel covariant approach combined with Hermite finite elements for more efficient and accurate optimal control of articulated robots.

Findings

Demonstrates super convergence of Hermite's technique

Shows effectiveness of conjugate gradient in control optimization

Provides a generic example illustrating method performance

Abstract

We elaborate algorithms able to efficiently command the actuators of an articulated robot. Our time discretization method is based on cubic and quintic Hermite Finite Elements. The suggested control optimization consists in minimizing directly the selected criterium by a conjugate gradient type algorithm. A generic example illustrates the super convergence of the Hermite's technique.