COAt-MPC: Performance-driven Constrained Optimal Auto-Tuner for MPC

Albert Gassol Puigjaner, Manish Prajapat, Andrea Carron, Andreas Krause, Melanie N. Zeilinger
ETH Zurich
IEEE RA-L 2025
Paper Code arXiv

COAt-MPC explores the space of MPC cost function parameters and builds a belief about the a-priori unknown performance function through data, utilizing tools from Gaussian processes. COAt-MPC incorporates safe exploration ideas and recursively recommends sufficiently informative parameters that ensure exploration while satisfying the performance constraint. We establish convergence guarantees to the optimal tuning parameters in a finite number of samples while ensuring performance constraint satisfaction with an arbitrarily high probability. For finite time convergence, we present a sample complexity bound and demonstrate its applicability with discrete set operators required for discrete domains. In particular, our sample complexity result removes an explicit dependence on the discretization step size and thus significantly improves prior safe exploration results in discrete domains. Additionally, we demonstrate the effectiveness of COAt-MPC in the application of autonomous racing. We tune a Model Predictive Contouring Control formulation with the objective of optimizing the lap time while avoiding undesirable effects such as halting. Our evaluation includes a comprehensive analysis in both simulation and in experiments on a 1:28 scale RC racecar.

Abstract

A key challenge in tuning Model Predictive Control (MPC) cost function parameters is to ensure that the system performance stays consistently above a certain threshold. To address this challenge, we propose a novel method, COAt-MPC, Constrained Optimal Auto-Tuner for MPC. With every tuning iteration, COAt-MPC gathers performance data and learns by updating its posterior belief. It explores the tuning parameters' domain towards optimistic parameters in a goal-directed fashion, which is key to its sample efficiency. We theoretically analyze COAt-MPC, showing that it satisfies performance constraints with arbitrarily high probability at all times and provably converges to the optimum performance within finite time. Through comprehensive simulations and comparative analyses with a hardware platform, we demonstrate the effectiveness of COAt-MPC in comparison to classical Bayesian Optimization (BO) and other state-of-the-art methods. When applied to autonomous racing, our approach outperforms baselines in terms of constraint violations and cumulative regret over time.

Method

Our approach leverages the assumption of Lipschitz continuity in the objective function to construct pessimistic and optimistic constraint sets. We use the optimistic set to define a goal location at each iteration, while we restrict our recommendations to be within the pessimistic set. We present a theoretical analysis of our method, conclusively demonstrating its ability to achieve optimal tuning parameters in finite time while guaranteeing the satisfaction of the performance constraint with arbitrarily high probability. Our algorithm’s goal is (i) to ensure the performance constraint satisfaction while (ii) converging to the optimal cost function weights with few tuning iterations. For the former part (i), we sample weights from the constructed pessimistic set, which guarantees satisfying the constraint with high probability. To ensure the later part (ii), we set a goal in the constructed optimistic set, outside of which the weights do not satisfy the constraint. Additionally, to converge to the optimal weights with fewer tuning iterations, we employ a goal-directed approach and use an expansion method towards this goal.

Results

We present an extensive evaluation of COAt-MPC in an autonomous racing application. Our evaluation is conducted using an autonomous racing simulation and a RC platform. Our method outperforms baselines in terms of performance constraint violations while converging to the optimal parameters in much less iterations.

RC racecar results

COAt-MPC demo on a small scalle RC race car.

BibTeX


@article{puigjaner2015coatmpc,
    title={COAt-MPC: Performance-driven Constrained Optimal Auto-Tuner for MPC},
    author={Gassol Puigjaner, Albert and Prajapat, Manish and Carron, Andrea and Krause, Andreas and Zeilinger, Melanie N},
    journal={IEEE Robotics and Automation Letters},
    year={2025}
}