A family of virtual contraction based controllers for tracking of flexible-joints port-Hamiltonian robots: theory and experiments

TL;DR

This paper introduces a novel control design method called virtual contraction based control (v-CBC) for flexible-joint robots within the port-Hamiltonian framework, ensuring exponential trajectory tracking and preserving system properties.

Contribution

It develops a constructive v-CBC method that guarantees exponential convergence and preserves system structure for flexible-joint robots in the port-Hamiltonian setting.

Findings

Closed-loop virtual system is contractive under potential energy matching.

Exponential convergence to desired trajectories is achieved.

System properties like structure preservation and differential passivity are maintained.

Abstract

In this work we present a constructive method to design a family of virtual contraction based controllers that solve the standard trajectory tracking problem of flexible-joint robots (FJRs) in the port-Hamiltonian (pH) framework. The proposed design method, called virtual contraction based control (v-CBC), combines the concepts of virtual control systems and contraction analysis. It is shown that under potential energy matching conditions, the closed-loop virtual system is contractive and exponential convergence to a predefined trajectory is guaranteed. Moreover, the closed-loop virtual system exhibits properties such as structure preservation, differential passivity and the existence of (incrementally) passive maps.