Stackelberg-Nash Game-Theoretic Formation Path Planning for Multi-Agent Interactions

As technologies advance, multi-agent systems have been used in various domains. In a multi-agent formation path planning system, a number of aspects including formation maintenance, collision avoidance, control consumption, reaching the destination and the interactions among agents need to be considered together. To solve this, we model multi-agent formation path planning in the Stackelberg-Nash game (SNG) framework to address the mentioned issues. In the SNG, the leader can adopt a global perspective and make multi-step predictions to plan a formation path that avoids obstacles. However, the followers can only perform myopic planning due to their limited capabilities. We introduce the natural logarithm barrier functions penalizing the collision constraints and we utilize the first-order condition to approximate the optimality condition, serving as a consideration term for all followers' potential reactions. We employ the receding horizon algorithm (RHA) to plan the formation path for the leader and followers. Case studies in an environment with obstacles demonstrate the superior performance of our SNG framework. Compared with the Nash-game and Non-game frameworks, our framework outperforms in maintaining standard formation and effective control consumption. This work contributes to the discourse on agent-based coordination and offers scalable, efficient strategies in complex environments.