# Impedance control of a cable-driven SEA with mixed $H_2/H_\infty$ synthesis

## TL;DR

This paper introduces a novel impedance control method for cable-driven series elastic actuators using mixed H2/H-infinity synthesis with relaxed passivity, enhancing stability and performance in human-robot interaction.

## Contribution

It develops a less conservative impedance control approach by relaxing passivity constraints and applying mixed H2/H-infinity synthesis for improved physical human-robot interaction.

## Key findings

- Effective tracking of desired torque in simulations and experiments
- Control input maintained below motor velocity limits
- Guaranteed relaxed passivity at low frequencies

## Abstract

Purpose: This paper presents an impedance control method with mixed $H_2/H_\infty$ synthesis and relaxed passivity for a cable-driven series elastic actuator to be applied for physical human-robot interaction. Design/methodology/approach: To shape the system's impedance to match a desired dynamic model, the impedance control problem was reformulated into an impedance matching structure. The desired competing performance requirements as well as constraints from the physical system can be characterized with weighting functions for respective signals. Considering the frequency properties of human movements, the passivity constraint for stable human-robot interaction, which is required on the entire frequency spectrum and may bring conservative solutions, has been relaxed in such a way that it only restrains the low frequency band. Thus, impedance control became a mixed $H_2/H_\infty$ synthesis problem, and a dynamic output feedback controller can be obtained. Findings: The proposed impedance control strategy has been tested for various desired impedance with both simulation and experiments on the cable-driven series elastic actuator platform. The actual interaction torque tracked well the desired torque within the desired norm bounds, and the control input was regulated below the motor velocity limit. The closed loop system can guarantee relaxed passivity at low frequency. Both simulation and experimental results have validated the feasibility and efficacy of the proposed method. Originality/value: This impedance control strategy with mixed $H_2/H_\infty$ synthesis and relaxed passivity provides a novel, effective and less conservative method for physical human-robot interaction control.