# Feedback MPC for Torque-Controlled Legged Robots

## TL;DR

This paper introduces a feedback MPC approach using DDP with barrier functions and frequency-dependent costs to enable stable torque control in legged robots at practical update rates.

## Contribution

It proposes a novel DDP-based MPC method with barrier functions and frequency-dependent costs for torque-controlled legged robots, addressing update rate limitations.

## Key findings

- Achieves stable locomotion in simulation and hardware
- Effectively handles inequality constraints with barrier functions
- Reduces sensitivity to high-frequency errors

## Abstract

The computational power of mobile robots is currently insufficient to achieve torque level whole-body Model Predictive Control (MPC) at the update rates required for complex dynamic systems such as legged robots. This problem is commonly circumvented by using a fast tracking controller to compensate for model errors between updates. In this work, we show that the feedback policy from a Differential Dynamic Programming (DDP) based MPC algorithm is a viable alternative to bridge the gap between the low MPC update rate and the actuation command rate. We propose to augment the DDP approach with a relaxed barrier function to address inequality constraints arising from the friction cone. A frequency-dependent cost function is used to reduce the sensitivity to high-frequency model errors and actuator bandwidth limits. We demonstrate that our approach can find stable locomotion policies for the torque-controlled quadruped, ANYmal, both in simulation and on hardware.