# Sensitivity of Legged Balance Control to Uncertainties and Sampling Period

## TL;DR

This paper investigates how sensor and actuator uncertainties affect legged robot balance control, revealing that sampling periods up to 200 ms do not impair stability, supported by simulations and experiments with a humanoid robot.

## Contribution

It introduces a robust control framework that accounts for uncertainties and demonstrates that longer sampling periods do not compromise balance, validated through robot experiments.

## Key findings

- Sampling periods up to 200 ms do not affect maximum tracking error.
- Robust control approach effectively manages uncertainties in legged robots.
- Experimental validation confirms theoretical predictions.

## Abstract

We propose to quantify the effect of sensor and actuator uncertainties on the control of the center of mass and center of pressure in legged robots, since this is central for maintaining their balance with a limited support polygon. Our approach is based on robust control theory, considering uncertainties that can take any value between specified bounds. This provides a principled approach to deciding optimal feedback gains. Surprisingly, our main observation is that the sampling period can be as long as 200 ms with literally no impact on maximum tracking error and, as a result, on the guarantee that balance can be maintained safely. Our findings are validated in simulations and experiments with the torque-controlled humanoid robot Toro developed at DLR. The proposed mathematical derivations and results apply nevertheless equally to biped and quadruped robots.