Bilevel Optimization for Real-Time Control with Application to Locomotion Gait Generation

TL;DR

This paper introduces a bilevel optimization framework for real-time control, enhancing MPC for legged robots by optimizing contact schedules to improve stability and gait quality.

Contribution

It extends real-time iteration methods to a bilevel control setting, enabling high-level parameter optimization alongside low-level MPC in real-time.

Findings

Improved disturbance rejection in quadrupedal robot control.

Generation of qualitatively new gaits.

Enhanced stability and optimality in control performance.

Abstract

Model Predictive Control (MPC) is a common tool for the control of nonlinear, real-world systems, such as legged robots. However, solving MPC quickly enough to enable its use in real-time is often challenging. One common solution is given by real-time iterations, which does not solve the MPC problem to convergence, but rather close enough to give an approximate solution. In this paper, we extend this idea to a bilevel control framework where a "high-level" optimization program modifies a controller parameter of a "low-level" MPC problem which generates the control inputs and desired state trajectory. We propose an algorithm to iterate on this bilevel program in real-time and provide conditions for its convergence and improvements in stability. We then demonstrate the efficacy of this algorithm by applying it to a quadrupedal robot where the high-level problem optimizes a contact schedule in real-time. We show through simulation that the algorithm can yield improvements in disturbance rejection and optimality, while creating qualitatively new gaits.