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


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.

Structure of the bilevel optimization. The MPC uses parameters from the high-level optimization and outputs the control inputs and state trajectory. When applied to the quadruped, the high-level parameter is the contact schedule. The green dots indicate contact with the ground and show how the contact schedule changes over time.

Additional Info

Authors: Zachary Olkin, Aaron Ames

Location: Amber Lab, Caltech

Date: October 2023 - April 2024

Paper (Link coming soon)