Potential iLQR: A Potential-Minimizing Controller for Planning Multi-Agent Interactive Trajectories

Talha Kavuncu, Ayberk Yaraneri, Negar Mehr

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Many robotic applications involve interactions between multiple agents where an agent’s decisions affect the behavior of other agents. Such behaviors can be captured by the equilibria of differential games which provide an expressive framework for modeling the agents’ mutual influence. However, finding the equilibria of differential games is in general challenging as it involves solving a set of coupled optimal control problems. In this work, we propose to leverage the special structure of multi-agent interactions to generate interactive trajectories by simply solving a single optimal control problem, namely, the optimal control problem associated with minimizing the potential function of the differential game. Our key insight is that for a certain class of multi-agent interactions, the underlying differential game is indeed a potential differential game for which equilibria can be found by solving a single optimal control problem. We introduce such an optimal control problem and build on single-agent trajectory optimization methods to develop a computationally tractable and scalable algorithm for planning multi-agent interactive trajectories. We will demonstrate the performance of our algorithm in simulation and show that our algorithm outperforms the state-of-the-art game solvers. To further show the real-time capabilities of our algorithm, we will demonstrate the application of our proposed algorithm in a set of experiments involving interactive trajectories for two quadcopters.

Original languageEnglish (US)
Title of host publicationRobotics
Subtitle of host publicationScience and Systems XVII
EditorsDylan A. Shell, Marc Toussaint, M. Ani Hsieh
PublisherMIT Press Journals
ISBN (Print)9780992374778
StatePublished - 2021
Externally publishedYes
Event17th Robotics: Science and Systems, RSS 2021 - Virtual, Online
Duration: Jul 12 2021Jul 16 2021

Publication series

NameRobotics: Science and Systems
ISSN (Electronic)2330-765X


Conference17th Robotics: Science and Systems, RSS 2021
CityVirtual, Online

ASJC Scopus subject areas

  • Artificial Intelligence
  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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