Leveraging Port-Hamiltonian Theory for Impedance Control Benchmarking

TL;DR

Impedance control benchmarking across diverse robots is challenging; this work motivates physics-based, standardized benchmarks and introduces Port-Hamiltonian (PH) metrics to enable application-agnostic assessment of impedance performance. It develops a causal PH impedance model in Cartesian space, derives a differentiable n-DoF passivity condition, and defines an impedance fidelity measure based on step-response power, all validated in Gazebo simulations. The key contributions are a PH Cartesian impedance formulation, a time-varying-reference passivity criterion independent of force-torque sensing, and a fidelity metric demonstrated on a 6-DoF arm and a 3-DoF quadruped leg. The framework offers application-agnostic benchmarking tools that enhance reproducibility and cross-architecture comparisons for impedance controllers.

Abstract

This work proposes PH-based metrics for benchmarking impedance control. A causality-consistent PH model is introduced for mass-spring-damper impedance in Cartesian space. Based on this model, a differentiable, force-torque sensing-independent, n-DoF passivity condition is derived, valid for time-varying references. An impedance fidelity metric is also defined from step-response power in free motion, capturing dynamic decoupling. The proposed metrics are validated in Gazebo simulations with a six-DoF manipulator and a quadruped leg. Results demonstrate the suitability of the PH framework for standardized impedance control benchmarking.

Figures (4)

• Figure 1: Step power characterization of a 6-DoF robotic arm with (top) and without (bottom) inertia shaping (IS). Dashed lines are the step reference power. With IS the root mean square error of \ref{['eq:step_power_equivalence']} was 13.114W, and without IS was 18.016W, both over the 0.25s interval shown. Tuning to achieve a stable step response without IS was more difficult than with IS. Then, the Cartesian power without IS displayed some spikes (solid red line).
• Figure 2: Passivity characterization of the 3-DoF quadruped leg following a CPG trajectory. The integrated command power (solid blue) is non-monotonic but shows an increasing average over time, while the Hamiltonian gap (dot-dashed black) confirms the controller’s growing passivity.
• Figure 3: Jumping demonstration of the 3-DoF quadruped leg. Foot vertical reference (dashed black) and state (solid blue) are relative to the robot trunk, or the leg support in this case. In solid orange is the trunk absolute height.
• Figure 4: Passivity characterization of the 3-DoF quadruped leg performing jumps. The integrated command power (blue) increases over time. The Hamiltonian gap (black) remains below the integrated command power, satisfying the passivity condition, and the valleys show the jump demand.