Learning to Play Trajectory Games Against Opponents with Unknown Objectives

Research output: Contribution to journalArticleScientificpeer-review

2 Downloads (Pure)


Many autonomous agents, such as intelligent vehicles, are inherently required to interact with one another. Game theory provides a natural mathematical tool for robot motion planning in such interactive settings. However, tractable algorithms for such problems usually rely on a strong assumption, namely that the objectives of all players in the scene are known. To make such tools applicable for ego-centric planning with only local information, we propose an adaptive model-predictive game solver, which jointly infers other players' objectives online and computes a corresponding generalized Nash equilibrium (GNE) strategy. The adaptivity of our approach is enabled by a differentiable trajectory game solver whose gradient signal is used for maximum likelihood estimation (MLE) of opponents' objectives. This differentiability of our pipeline facilitates direct integration with other differentiable elements, such as neural networks (NNs). Furthermore, in contrast to existing solvers for cost inference in games, our method handles not only partial state observations but also general inequality constraints. In two simulated traffic scenarios, we find superior performance of our approach over both existing game-theoretic methods and non-game-theoretic model-predictive control (MPC) approaches. We also demonstrate our approach's real-time planning capabilities and robustness in two-player hardware experiments.

Original languageEnglish
Pages (from-to)4139-4146
JournalIEEE Robotics and Automation Letters
Issue number7
Publication statusPublished - 2023

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • Collision avoidance
  • Games
  • human-aware motion planning
  • integrated planning and learning
  • Maximum likelihood estimation
  • multi-robot systems
  • Optimization
  • Planning
  • Robots
  • Trajectory
  • Trajectory games


Dive into the research topics of 'Learning to Play Trajectory Games Against Opponents with Unknown Objectives'. Together they form a unique fingerprint.

Cite this