Geometric Control of a Robot's Tool

TL;DR

This paper introduces a rigorous geometric approach to controlling a robot's tool using Riemannian PD-regulators, employing invariance principles and Lyapunov stability, with simulations demonstrating effectiveness.

Contribution

It presents novel intrinsic formulations for robot tool control using Riemannian geometry and invariance principles, including methods for singularity-free control and constraints.

Findings

Effective control of robot tool position demonstrated in simulations.

New geometric control methods handle constraints and singularities.

Stability and convergence validated through Lyapunov analysis.

Abstract

The goal of this paper is to present a rigorous and intrinsic formulation of a Riemannian PD-regulator of the robot's tool, The first one is based upon the Lasalle's invariance principle, we use it to control the tool's position in the workspace under the assumption of absence of singularities in configuration space, The second method deals with geometrical constraints on the trajectory of the robot's tool with the same assumption, we construct a unique orthogonal force that is viewed as a gravitational force that keeps the tool constrained, We also present a variation of the first method in the case of double pendulum based on the Lyapunov stability theorem. With this modification, we control the tool and the difference between the two angles, we did simulations on a two-link manipulator that shows the efficiency of the presented methods.