Game Theoretic Motion Planning for Multi-robot Racing

  • Zijian WangEmail author
  • Riccardo Spica
  • Mac Schwager
Conference paper
Part of the Springer Proceedings in Advanced Robotics book series (SPAR, volume 9)


This paper presents a real-time game theoretic planning algorithm for a robotic vehicle (e.g. a drone or a car) to race competitively against multiple opponents on a racecourse. Our algorithm plans receding horizon trajectories to maximally advance the robot along the racecourse, while taking into account the opponents’ intentions and responses. We build on our previous work (Spica et al Theoretic approach to autonomous two-player drone racing, 2018 [1]), which only considered racing with two robots. Our algorithm uses an iterative best response scheme with a new sensitivity term to find approximate Nash equilibria in the space of the multiple robots’ trajectories. The sensitivity term seeks Nash equilibria that are advantageous to the ego robot. We demonstrate our approach through extensive multi-player racing simulations, where our planner exhibits rich behaviors such as blocking, overtaking, nudging or threatening, similar to what we observe from racing with human participants. Statistics also reveal that our game theoretic planner largely outperforms a baseline model predictive controller that does not consider the opponents’ responses. Experiments are conducted with four quadrotor aerial robots to validate our approach in real time and with physical robot hardware.



This work was supported by the Toyota Research Institute (TRI). This article solely reflects the opinions and conclusions of its authors and not TRI or any other Toyota entity. The authors are grateful for this support.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Aeronautics and AstronauticsStanford UniversityStanfordUSA

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