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

arXiv: https://arxiv.org/abs/2409.12366 · HTML: https://mlsanity.com/paper/2409.12366/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2024.

## Built on by (most cited first, 1 of 1)

- [Sequential QCQP for Bilevel Optimization with Line Search](https://mlsanity.com/paper/2505.14647/) (2025)

## Abstract (arXiv)

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.