PACT: Potential Differential Game-Based Multi-Agent Coordination for Time-Critical Missions

Increased interest in utilizing low-altitude airspace has sparked the deployment of multi-agent unmanned aerial vehicles (UAVs) to perform a wide range of tasks. Time-critical coordination (TCC) tasks, such as surveillance, environmental monitoring, perimeter defense, entertainment, light shows, and flying ad-hoc networks, represent key emerging uses of low-altitude airspace. Successful execution of such complex missions hinges on tightly synchronized execution, making efficient multi-agent UAV cooperation essential. In this work, we formulate the TCC problem for a fixed set of N UAVs as a potential differential game, enabling all agents' objectives to be unified through a single potential function. By decoupling spatial motion from temporal evolution, the TCC formulation reduces the coordination task to a one-dimensional time-synchronization problem. Leveraging this structure, we construct a potential function that captures the coordination goal, characterize conditions under which equilibria exist for the resulting N-agent potential game, and show that computing the equilibrium reduces to solving a single optimal control problem. Finally, we develop an iterative receding-horizon algorithm to compute the solution of potential game efficiently and demonstrate its effectiveness through simulation results.