# Passivity guaranteed stiffness control with multiple frequency band specifications for a cable-driven series elastic actuator

## TL;DR

This paper presents a novel $H_
fty$ synthesis approach for passivity-guaranteed stiffness control in cable-driven series elastic actuators, optimizing performance across multiple frequency bands for improved human-robot interaction safety and robustness.

## Contribution

It introduces a structured $H_
fty$ synthesis method that enhances stiffness control performance across specific frequency ranges while ensuring passivity, outperforming traditional PID approaches.

## Key findings

- Achieved improved stiffness rendering accuracy and robustness.
- Validated controller effectiveness through simulations and experiments.
- Guaranteed passivity across all designed frequency bands.

## Abstract

Impedance control and specifically stiffness control are widely applied for physical human-robot interaction. The series elastic actuator (SEA) provides inherent compliance, safety and further benefits. This paper aims to improve the stiffness control performance of a cable-driven SEA. Existing impedance controllers were designed within the full frequency domain, though human-robot interaction commonly falls in the low frequency range. We enhance the stiffness rendering performance under formulated constraints of passivity, actuator limitation, disturbance attenuation, noise rejection at their specific frequency ranges. Firstly, we reformulate this multiple frequency-band optimization problem into the $H_\infty$ synthesis framework. Then, the performance goals are quantitatively characterized by respective restricted frequency-domain specifications as norm bounds. Further, a structured controller is directly synthesized to satisfy all the competing performance requirements. Both simulation and experimental results showed that the produced controller enabled good interaction performance for each desired stiffness varying from 0 to 1 times of the physical spring constant. Compared with the passivity-based PID method, the proposed $H_\infty$ synthesis method achieved more accurate and robust stiffness control performance with guaranteed passivity.