Strategizing at Speed: A Learned Model Predictive Game for Multi-Agent Drone Racing

Andrei-Carlo Papuc1 Lasse Peters1 Sihao Sun1 Laura Ferranti1 Javier Alonso-Mora1
1TU Delft
Paper Code

Abstract

Autonomous drone racing pushes the boundaries of high-speed motion planning and multi-agent strategic decision-making. Success in this domain requires drones not only to navigate at their limits but also to anticipate and counteract competitors' actions. In this letter, we study a fundamental question that arises in this domain: how deeply should an agent strategize before taking an action? To this end, we compare two planning paradigms: the Model Predictive Game (MPG), which finds interaction-aware strategies at the expense of longer computation times, and contouring Model Predictive Control (MPC), which computes strategies rapidly but does not reason about interactions. We perform extensive experiments to study this trade-off, revealing that MPG outperforms MPC at moderate velocities but loses its advantage at higher speeds due to latency. To address this shortcoming, we propose a Learned Model Predictive Game (LMPG) approach that amortizes model predictive gameplay to reduce latency. In both simulation and hardware experiments, we benchmark our approach against MPG and MPC in head-to-head races, finding that LMPG outperforms both baselines.

Learned Model Predictive Game (LMPG)

To get the strategic benefits of game-theoretic planning without paying its latency cost online, we introduce LMPG. LMPG amortizes the computation of receding-horizon Nash equilibria by training a neural network, for each player, that directly predicts the Nash strategy from the current race state. A differentiable trajectory-optimization layer sits on top of the network to guarantee that predicted strategies remain dynamically feasible, and the whole pipeline is trained end-to-end via simultaneous gradient play, differentiating through the KKT conditions of the underlying game.

The result is a policy that runs in about 3.5 ms — a 14× speedup over solving the game online — while retaining (and in our experiments, even exceeding) the quality of the non-amortized MPG solutions it was trained to imitate.

LMPG pipeline: observation encoding, neural network with differentiable trajectory optimization layer, and hierarchical low-level control

(A) Composition of the observations used by the neural network employed by LMPG. (B) Pipeline overview of LMPG: observations are fed into a neural network that embeds differentiable trajectory optimization as a final layer to predict a receding-horizon strategy. (C) A linear MPC tracks the reference strategy via feedback linearization. In simulation, the output of this controller is directly fed into the simulated dynamics. (D) Hierarchical control scheme employed in hardware experiments: using the Agilicious framework, the drone tracks the receding-horizon strategy by combining a geometric controller with incremental nonlinear dynamic inversion (INDI).

Results

We benchmark LMPG against MPG and two predict-then-plan MPC variants (constant-velocity and strategy-optimal opponent prediction) in round-robin tournaments across four race tracks, under both idealized (synchronous) and realistic (asynchronous, latency-exposed) execution modes, in simulation and on physical quadrotors.

  1. With computation time removed from the equation, MPG wins every race against contouring MPC — game-theoretic reasoning is decisively better when it's free.
  2. Once solver latency is allowed to affect the race, MPG's edge shrinks at high speed and disappears at high speed: its solve time can spike past 2 s in interactive scenarios, causing off-track drifts.
  3. LMPG matches the solve time of the cheapest MPC baseline while reliably beating all baselines — MPC (cvel), MPC (sopt), and MPG — in the challenging high-speed, asynchronous setting.
  4. A single LMPG policy trained across four tracks generalizes zero-shot to unseen tracks, still outperforming the strategy-optimal MPC baseline.
  5. These trends transfer from simulation to real hardware: in real flight tournaments, LMPG dominates head-to-head races against MPG and MPC, including zero-shot on an unseen track.
Head-to-head win-rate results across simulation and real-world flight tournaments, plus latency comparison

Head-to-head racing results in simulation and real-life. (A), (B) Win rates for MPC (cvel) vs. MPG in a simulated tournament with synchronous (A) and asynchronous (B) execution modes. (D), (E) Win rates for LMPG vs. MPC/MPG in a simulated tournament with synchronous (D) and asynchronous (E) execution modes. (G), (H) Zero-shot win rates for LMPG-GEN vs. MPC (sopt) in a simulated tournament with synchronous (G) and asynchronous (H) execution modes. (C), (F) Win rates for the real-world flight tournament on the lemniscate track. (I) Zero-shot win rates for the real-world flight tournament on the trefoil track. (J) Trajectory planning time distributions for all methods. (K) Low level system latencies distributions encountered during real-life experiments. (L) Vizualization of a single real-life lap of LMPG-GEN deployed zero-shot vs MPC (sopt) on the trefoil track.

Acknowledgments

This work was supported by the Office of Naval Research Global under Grant N62909-25-12027 (Project SECURE) and by the Dutch Research Council (NWO) under Grant no. 20256 (Project Accurate Aerial Manipulation).

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The driving behavior of autonomous vehicles is typically governed by the cost function of their motion planner, which encodes objectives such as speed tracking, smoothness, lane keeping, and collision avoidance. However, tuning the parameters that shape this cost function is a challenging task that requires technical expertise, limiting the vehicle's ability to adapt to evolving traffic scenarios or end-user preferences. This work presents a language-driven framework for adaptive cost design in autonomous driving. A Large Language Model (LLM) interprets structured scenario descriptions and natural language user queries to generate the parameters applied to a risk-aware Model Predictive Path Integral (MPPI) controller. The system incorporates a human-in-the-loop validation stage in which the proposed behavioral changes are described in non-technical language and confirmed prior to deployment. Users may additionally provide feedback either before or after deployment, enabling iterative refinement of the vehicle's motion behavior. The framework is evaluated across multiple queries in realistic driving scenarios to assess its effectiveness. Simulation results demonstrate that our method successfully induces behavioral changes that align with the intended requirements in an intuitive manner, thereby bridging the gap between intelligent vehicle control systems and end users.
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pdf IEEE web
Control Barrier Functions (CBFs) have proven to be an effective tool for performing safe control synthesis for nonlinear systems. However, guaranteeing safety in the presence of disturbances and input constraints for high relative degree systems is a difficult problem. In this work, we propose the Robust Policy CBF (RPCBF), a practical approach for constructing robust CBF approximations online via the estimation of a value function. We establish conditions under which the approximation qualifies as a valid CBF and demonstrate the effectiveness of the RPCBF-safety filter in simulation on a variety of high relative degree input-constrained systems. Finally, we demonstrate the benefits of our method in compensating for model errors on a hardware quadcopter platform by treating the model errors as disturbances.
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