[Paper Review] Gaussian Process-based Stochastic Model Predictive Control for Overtaking in Autonomous Racing

Tim Brüdigam, Alexandre Capone+3 more|arXiv (Cornell University)|May 25, 2021

Advanced Control Systems OptimizationEngineering21 citations

TL;DR

This paper proposes a Gaussian Process-based Stochastic Model Predictive Control (GP-SMPC) framework for autonomous overtaking in racing, where a trailing vehicle learns the leading car's behavior via Gaussian process regression and uses stochastic MPC to plan safe, optimistic overtaking trajectories under uncertainty. The method enables active overtaking by leveraging predictive modeling of the leader's motion and probabilistic constraint handling, validated in a simulation scenario with successful trajectory planning on a straight track.

ABSTRACT

A fundamental aspect of racing is overtaking other race cars. Whereas previous research on autonomous racing has majorly focused on lap-time optimization, here, we propose a method to plan overtaking maneuvers in autonomous racing. A Gaussian process is used to learn the behavior of the leading vehicle. Based on the outputs of the Gaussian process, a stochastic Model Predictive Control algorithm plans optimistic trajectories, such that the controlled autonomous race car is able to overtake the leading vehicle. The proposed method is tested in a simple simulation scenario.

Motivation & Objective

• To address the lack of active overtaking strategies in autonomous racing, which has largely focused on lap-time optimization.
• To enable the trailing autonomous vehicle to proactively overtake a leading vehicle by predicting its behavior and planning safe, optimistic maneuvers.
• To integrate Gaussian process regression for modeling uncertainty in the leading vehicle's motion with stochastic model predictive control for robust trajectory planning.
• To develop a framework that allows the autonomous vehicle to identify and exploit weaknesses in the leading vehicle's driving pattern during overtaking.

Proposed method

• A Gaussian process (GP) is trained on historical data of the leading vehicle's motion to predict its future trajectory and quantify model uncertainty.
• The GP predictions are used to generate probabilistic constraints for a stochastic Model Predictive Control (SMPC) framework, ensuring safety under uncertainty.
• Constraint tightening is applied using chi-squared distributed random variables to transform probabilistic constraints into deterministic equivalents.
• The SMPC problem is formulated as a quadratic program with state and control input constraints, minimizing deviation from a reference trajectory while respecting safety margins.
• The method uses a linearized, discretized model of the ego vehicle for prediction and applies the optimized control inputs to a nonlinear continuous-time model in simulation.
• Infeasible SMPC problems are handled by retaining the previous solution, ensuring robustness during real-time execution.

Experimental results

Research questions

• RQ1 How can an autonomous racing vehicle actively overtake a leading vehicle when overtaking is not passively enabled by the leader?
• RQ2 Can Gaussian process regression effectively model the behavior of a leading race car to inform overtaking decisions?
• RQ3 How can stochastic model predictive control be used to plan optimistic yet safe overtaking trajectories under uncertainty in the leader’s motion?
• RQ4 What is the impact of probabilistic constraint handling on the feasibility and safety of overtaking maneuvers in autonomous racing?
• RQ5 Can the integration of GP-based prediction and SMPC enable the ego vehicle to identify and exploit favorable overtaking opportunities?

Key findings

• The GP-SMPC framework successfully generated feasible overtaking trajectories in a simulated straight-track scenario, demonstrating the ability to plan optimistic yet safe maneuvers.
• The method enabled the ego vehicle to overtake the leading vehicle by identifying and exploiting a temporary gap in the leader’s motion, as predicted by the GP.
• The use of probabilistic constraints via chi-squared distributed variables ensured that collision probability remained below a predefined threshold, enhancing safety.
• The SMPC formulation with constraint tightening maintained feasibility even under model uncertainty, with infeasible cases handled by retaining prior control inputs.
• The simulation results confirmed that the integration of GP-based behavior modeling and SMPC enables active overtaking, a capability largely absent in prior autonomous racing research focused on lap-time optimization.