An MPC Walking Framework With External Contact Forces

TL;DR

This paper introduces an advanced MPC-based walking control framework that plans external contact forces for robots, enabling improved disturbance rejection through a two-step optimization process involving MIQP and QP solutions.

Contribution

It extends linear MPC for walking robots by incorporating external contact force planning using a two-step optimization with MIQP and QP, allowing real-time multi-contact force computation.

Findings

Can withstand 2-3x larger disturbances with external contact forces.

Achieves real-time optimization at 100-300 Hz for MIQP and <1kHz for QP.

Demonstrates effectiveness through simulations with external contacts.

Abstract

In this work, we present an extension to a linear Model Predictive Control (MPC) scheme that plans external contact forces for the robot when given multiple contact locations and their corresponding friction cone. To this end, we set up a two-step optimization problem. In the first optimization, we compute the Center of Mass (CoM) trajectory, foot step locations, and introduce slack variables to account for violating the imposed constraints on the Zero Moment Point (ZMP). We then use the slack variables to trigger the second optimization, in which we calculate the optimal external force that compensates for the ZMP tracking error. This optimization considers multiple contacts positions within the environment by formulating the problem as a Mixed Integer Quadratic Program (MIQP) that can be solved at a speed between 100-300 Hz. Once contact is created, the MIQP reduces to a single Quadratic Program (QP) that can be solved in real-time ($<$ 1kHz). Simulations show that the presented walking control scheme can withstand disturbances 2-3x larger with the additional force provided by a hand contact.