Dynamic games can be an effective approach for modeling interactive behavior between multiple competitive agents in autonomous racing and they provide a theoretical framework for simultaneous prediction and control in such scenarios. In this work, we propose DG-SQP, a numerical method for the solution of local generalized Nash equilibria (GNE) for open-loop general-sum dynamic games for agents with nonlinear dynamics and constraints. In particular, we formulate a sequential quadratic programming (SQP) approach which requires only the solution of a single convex quadratic program at each iteration. The three key elements of the method are a non-monotonic line search for solving the associated KKT equations, a merit function to handle zero sum costs, and a decaying regularization scheme for SQP step selection. We show that our method achieves linear convergence in the neighborhood of local GNE and demonstrate the effectiveness of the approach in the context of head-to-head car racing, where we show significant improvement in solver success rate when comparing against the state-of-the-art PATH solver for dynamic games.

In head-to-head racing, an accurate model of interactive behavior of the opposing target vehicle (TV) is required to perform tightly constrained, but highly rewarding maneuvers such as overtaking. However, such information is not typically made available in competitive scenarios, we therefore propose to construct a prediction and uncertainty model given data of the TV from previous races. In particular, a one-step Gaussian process (GP) model is trained on closed-loop interaction data to learn the behavior of a TV driven by an unknown policy. Predictions of the nominal trajectory and associated uncertainty are rolled out via a sampling-based approach and are used in a model predictive control (MPC) policy for the ego vehicle in order to intelligently trade-off between safety and performance when attempting overtaking maneuvers against a TV. We demonstrate the GP-based predictor in closed loop with the MPC policy in simulation races and compare its performance against several predictors from literature. In a Monte Carlo study, we observe that the GP-based predictor achieves similar win rates while maintaining safety in up to 3x more races. We finally demonstrate the prediction and control framework in real-time in a experimental study on a 1/10th scale racecar platform operating at speeds of around 2.8 m/s, and show a significant level of improvement when using the GP-based predictor over a baseline MPC predictor. Videos of the hardware experiments can be found at https://youtu.be/KMSs4ofDfIs.

The blue car successfully overtakes the green car with predictions from the GP opponent model (red)

The blue car is unable to overtake, but stays safe with predictions from the GP opponent model (red)

The blue car is unable to overtake and collides with the green car with predictions from an optimal control opponent model (red)