A Real-Time Game Theoretic Planner for Autonomous Two-Player Drone Racing

• Published in: IEEE transactions on robotics 2020-10, Vol.36 (5), p.1389-1403
• Main Authors: Spica, Riccardo, Cristofalo, Eric, Wang, Zijian, Montijano, Eduardo, Schwager, Mac
• Format: Article
• Language: English
• Subjects: Aerial robotics; Algorithms; Collision avoidance; Computer simulation; drone racing; Drones; Game theory; Games; Iterative methods; motion and path planning; Nash equilibrium; path planning for multiple mobile robot systems; Prediction algorithms; Predictive control; Racetracks; Racing; Robots; Sensitivity; Sensitivity enhancement; Trajectory; vision-based pose estimation
• ISSN: 1552-3098; 1941-0468
• DOI: 10.1109/TRO.2020.2994881

In this article, we propose an online 3-D planning algorithm for a drone to race competitively against a single adversary drone. The algorithm computes an approximation of the Nash equilibrium in the joint space of trajectories of the two drones at each time step, and proceeds in a receding horizon fashion. The algorithm uses a novel sensitivity term, within an iterative best response computational scheme, to approximate the amount by which the adversary will yield to the ego drone to avoid a collision. This leads to racing trajectories that are more competitive than without the sensitivity term. We prove that the fixed point of this sensitivity enhanced iterative best response satisfies the first-order optimality conditions of a Nash equilibrium. We present results of a simulation study of races with 2-D and 3-D race courses, showing that our game theoretic planner significantly outperforms a model predictive control (MPC) racing algorithm. We also present results of multiple drone racing experiments on a 3-D track in which drones sense each others' relative position with onboard vision. The proposed game theoretic planner again outperforms the MPC opponent in these experiments where drones reach speeds up to {1.25\,}\mathrm{{m}}/\mathrm{{s}}.