Potential iLQR: A Potential-Minimizing Controller for Planning Multi-Agent Interactive Trajectories
This addresses the problem of scalable and efficient trajectory planning for multi-agent robotic systems, offering a computationally tractable solution for interactive scenarios.
The paper tackles the challenge of planning multi-agent interactive trajectories by proposing a potential-minimizing controller that solves a single optimal control problem instead of coupled ones, demonstrating performance gains over state-of-the-art game solvers in simulations and real-time quadcopter experiments.
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.