Desired Impedance Allocation for Robotic Systems

TL;DR

This paper extends Virtual Decomposition Control to include second-order impedance behavior, incorporating inertia for improved contact and trajectory tracking in robotic systems, validated through experiments on a haptic exoskeleton.

Contribution

It introduces a novel second-order impedance control method within the VDC framework, enabling inertia realization while maintaining modularity and stability.

Findings

Enhanced contact stability with stiffer environments by 70%

Superior tracking performance over first-order methods

Validated robustness through stability analysis

Abstract

Virtual Decomposition Control (VDC) has emerged as a powerful modular framework for real-world robotic control, particularly in contact-rich tasks. Despite its widespread use, VDC has been fundamentally limited to first-order impedance allocation, inherently neglecting the desired inertia due to the mathematical complexity of second-order behavior allocation. However, inertia is crucial, not only for shaping dynamic responses during contact phases, but also for enabling smooth acceleration and deceleration in trajectory tracking. Motivated by the growing demand for high-fidelity interaction control, this work introduces, for the first time in the VDC framework, a method to realize second-order impedance behavior. By redefining the required end-effector velocity and introducing a required acceleration and a pseudo-impedance term, we achieve second-order impedance control while preserving the modularity of VDC. Rigorous stability analysis confirms the robustness of the proposed controller. Experimental validation on a 7-degree-of-freedom haptic exoskeleton demonstrates superior tracking and contact performance compared to first-order methods. Notably, incorporating inertia enables stable interaction with environments up to 70% stiffer, highlighting the effectiveness of the approach in real-world contact-rich scenarios.