Weighted Buffered Voronoi Cells for Distributed Semi-Cooperative Behavior

This paper introduces the Weighted Buffered Voronoi tessellation, which allows us to define distributed, semicooperative multi-agent navigation policies with guarantees on collision avoidance. We generate the Voronoi cells with dynamic weights that bias the boundary towards the agent with the lower relative weight while always maintaining a buffered distance between two agents. By incorporating agent weights, we can encode selfish or prioritized behavior among agents, where a more selfish agent will have a larger relative cell over less selfish agents. We consider this semi-cooperative since agents do not cooperate in symmetric ways. Furthermore, when all agents start in a collision-free configuration and plan their control actions within their cells, we prove that no agents will collide. Simulations demonstrate the performance of our algorithm for agents navigating to goal locations in a position-swapping game. We observe that agents with more egoistic weights consistently travel shorter paths to their goal than more altruistic agents.