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

arXiv: https://arxiv.org/abs/1801.02302 · HTML: https://mlsanity.com/paper/1801.02302/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jan 2018.

## Built on by (most cited first, 21 of 21)

- [Semantics for Robotic Mapping, Perception and Interaction: A Survey](https://mlsanity.com/paper/2101.00443/) (2021)
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- [Deep Latent Competition: Learning to Race Using Visual Control Policies in Latent Space](https://mlsanity.com/paper/2102.09812/) (2021)
- [OIL: Observational Imitation Learning](https://mlsanity.com/paper/1803.01129/) (2018)
- [Blending Data-Driven Priors in Dynamic Games](https://mlsanity.com/paper/2402.14174/) (2024)
- [Agile Flight Emerges from Multi-Agent Competitive Racing](https://mlsanity.com/paper/2512.11781/) (2025)
- [Auto-Encoding Bayesian Inverse Games](https://mlsanity.com/paper/2402.08902/) (2024)
- [Optimization-Guided Diffusion for Interactive Scene Generation](https://mlsanity.com/paper/2512.07661/) (2025)
- [Decision-Making Among Bounded Rational Agents](https://mlsanity.com/paper/2210.08672/) (2022)
- [DiffFP: Learning Behaviors from Scratch via Diffusion-based Fictitious Play](https://mlsanity.com/paper/2511.13186/) (2025)
- [Superhuman Safe and Agile Racing through Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2605.22748/) (2026)
- [Crazyflow: An Accurate, GPU-Accelerated, Differentiable Drone Simulator in JAX](https://mlsanity.com/paper/2606.01478/) (2026)
- [Game-theoretic Objective Space Planning](https://mlsanity.com/paper/2209.07758/) (2022)
- [Measuring Sociality in Driving Interaction](https://mlsanity.com/paper/2306.13992/) (2023)
- [Decoupled SGDA for Games with Intermittent Strategy Communication](https://mlsanity.com/paper/2501.14652/) (2025)
- [Self-Supervised Learning to Fly using Efficient Semantic Segmentation and Metric Depth Estimation for Low-Cost Autonomous UAVs](https://mlsanity.com/paper/2510.16624/) (2025)
- [SPIRAL: Self-Play Incremental Racing Algorithm for Learning in Multi-Drone Competitions](https://mlsanity.com/paper/2510.22568/) (2025)
- [Curriculum-Based Iterative Self-Play for Scalable Multi-Drone Racing](https://mlsanity.com/paper/2510.22570/) (2025)
- [Real-Time Learning of Predictive Dynamic Obstacle Models for Robotic Motion Planning](https://mlsanity.com/paper/2511.00814/) (2025)
- [Bayesian Inverse Games with High-Dimensional Multi-Modal Observations](https://mlsanity.com/paper/2601.00696/) (2026)

## Abstract (arXiv)

To be successful in multi-player drone racing, a player must not only follow the race track in an optimal way, but also compete with other drones through strategic blocking, faking, and opportunistic passing while avoiding collisions. Since unveiling one's own strategy to the adversaries is not desirable, this requires each player to independently predict the other players' future actions. Nash equilibria are a powerful tool to model this and similar multi-agent coordination problems in which the absence of communication impedes full coordination between the agents. In this paper, we propose a novel receding horizon planning algorithm that, exploiting sensitivity analysis within an iterated best response computational scheme, can approximate Nash equilibria in real time. We also describe a vision-based pipeline that allows each player to estimate its opponent's relative position. We demonstrate that our solution effectively competes against alternative strategies in a large number of drone racing simulations. Hardware experiments with onboard vision sensing prove the practicality of our strategy.