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

Abstract

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.

Efficient Constrained Multi-Agent Interactive Planning using Constrained Dynamic Potential Games

“…, N T }. (27) In order to compute the KKT conditions for the multivariate constrained optimal control, we write the Lagrangian of (10) as L P (x k , u k , ξ k , δ k ) = R(x N T , N T ) + δ N T g(x N T , N T )…”

“…Remark 1: It should be noted that Theorem-2 will hold even in the cases when agents' costs depends on other agents states and actions provided that pair of agents treat each other symmetrically, i.e, the dependence of agent i's cost on the state and action of agent j is similar to the dependence of agent j's cost on the state and action of agent i. Please refer to [27] for more details. Note that (11) captures all scenarios where agents have individual costs such as tracking costs, goal-reaching costs, and energy consumption costs subject to both joint and individual constraints.…”

“…Their simplicity and tractability have warranted their implementation across various applications such as resource allocation, cooperative control, power networks, and communication networks [22], [23], [24], [25], [26]. Recently, potential games were used in [27] for interactive planning. However, no constraints were considered in [27].…”

“…Recently, potential games were used in [27] for interactive planning. However, no constraints were considered in [27]. Moreover, the agents had to penalize for collisions only symmetrically in order for the method to be applicable.…”