Strategic Decision-Making in Multi-Agent Domains: A Weighted Constrained Potential Dynamic Game Approach

TL;DR

This work tackles scalable strategic decision-making in multi-agent domains by recasting interactive planning problems as weighted constrained potential dynamic games (WCPDGs). By proving that many practical cost structures yield a potential function whose weighted differences reproduce individual incentives, the authors reduce the equilibrium computation to a single constrained optimal control problem, enabling real-time capable planning without centralized coordination. The approach is validated through dyadic and multi-agent simulations and a hardware experiment with quadrotors and humans, showing substantial solve-time improvements over state-of-the-art solvers and intuitive, collision-free trajectories. The results highlight the practical impact of constrained potential dynamics for fast, principled multi-agent motion planning in environments with hard state and input constraints and asymmetric inter-agent interactions.

Abstract

In interactive multi-agent settings, decision-making and planning are challenging mainly due to the agents' interconnected objectives. Dynamic game theory offers a formal framework for analyzing such intricacies. Yet, solving constrained dynamic games and determining the interaction outcome in the form of generalized Nash Equilibria (GNE) pose computational challenges due to the need for solving constrained coupled optimal control problems. In this paper, we address this challenge by proposing to leverage the special structure of many real-world multi-agent interactions. More specifically, our key idea is to leverage constrained dynamic potential games, which are games for which GNE can be found by solving a single constrained optimal control problem associated with minimizing the potential function. We argue that constrained dynamic potential games can effectively facilitate interactive decision-making in many multi-agent interactions. We will identify structures in realistic multi-agent interactive scenarios that can be transformed into weighted constrained potential dynamic games (WCPDGs). We will show that the GNE of the resulting WCPDG can be obtained by solving a single constrained optimal control problem. We will demonstrate the effectiveness of the proposed method through various simulation studies and show that we achieve significant improvements in solve time compared to state-of-the-art game solvers. We further provide experimental validation of our proposed method in a navigation setup involving two quadrotors carrying a rigid object while avoiding collisions with two humans.

Figures (8)

• Figure 1: Visualizations and the corresponding snapshots of the hardware experiment. The two quadrotors and two humans need to reach their designated goal positions while avoiding collision with others. The two quadrotors are carrying a rod. In this case, each quadrotor needs to account for the motions of humans as well as the other quadrotor, as they share the constraint imposed by the rod. As shown in the figure, with our algorithm, the two quadrotors are able to avoid nearby humans by changing their orientations elegantly while carrying the rod. (Refer to Appendix \ref{['sec: exempt']} for the approval details for conducting experiments with human subjects.) We have also included a supplementary video of the experiment which will be available at http://ieeexplore.ieee.org.
• Figure 2: The snapshots of the trajectories found by our algorithm when three unicycle agents interact with each other and exchange their positions diagonally over a time interval of 5s. The cost functions are highly asymmetric, and Agent 1 incurs more costs for getting close to other agents. Agents move from their start positions to their respective goal positions. Dashed lines represent the nominal path for each agent. Because of the asymmetric nature of the interaction, Agent 1 yields to other agents and deviates more from its nominal path to move towards its goal.
• Figure 3: Schematic of the cost function dependencies for a running example with three agents interacting with one another.
• Figure 4: Schematic of an interaction where each agent in the environment treats all the other agents in a similar fashion. In such scenarios, the underlying dynamic game becomes a weighted potential dynamic game. Note that in this figure, the edges with the same color indicate the same value of the cost coefficient.
• Figure 5: Schematic of interactions where each agent in the environment is treated by all the other agents in a similar fashion. In such scenarios, the underlying dynamic game becomes a weighted potential dynamic game. It should be noted that edges with the same color indicate the same value of the cost coefficient.

Theorems & Definitions (7)

• proof
• proof
• proof
• proof
• proof
• proof
• proof