Differentiable Robust Model Predictive Control

TL;DR

This paper introduces a differentiable optimization framework for robust model predictive control that enables automatic, real-time tuning of controllers to handle uncertainties and disturbances in autonomous systems.

Contribution

It presents a unifying perspective on differentiable control using the implicit function theorem and integrates it with tube-based MPC for improved robustness and tunability.

Findings

Effective in real-time tuning of robust controllers.

Demonstrated on multiple nonlinear robotic systems.

Validated through simulations and hardware experiments.

Abstract

Deterministic model predictive control (MPC), while powerful, is often insufficient for effectively controlling autonomous systems in the real-world. Factors such as environmental noise and model error can cause deviations from the expected nominal performance. Robust MPC algorithms aim to bridge this gap between deterministic and uncertain control. However, these methods are often excessively difficult to tune for robustness due to the nonlinear and non-intuitive effects that controller parameters have on performance. To address this challenge, we first present a unifying perspective on differentiable optimization for control using the implicit function theorem (IFT), from which existing state-of-the art methods can be derived. Drawing parallels with differential dynamic programming, the IFT enables the derivation of an efficient differentiable optimal control framework. The derived scheme is subsequently paired with a tube-based MPC architecture to facilitate the automatic and real-time tuning of robust controllers in the presence of large uncertainties and disturbances. The proposed algorithm is benchmarked on multiple nonlinear robotic systems, including two systems in the MuJoCo simulator environment and one hardware experiment on the Robotarium testbed, to demonstrate its efficacy.