How to Beat Speed with Quantity: A Many-to-One Multi-Vehicle Racing Framework

In this work, we propose a hierarchical motion planning framework for a swarm of collective vehicles with a lower maximum speed to race against a single adversary with a higher maximum speed, where the swarm gains a competitive advantage by collaborating. The proposed path planner framework consists of two planning layers: the decision layer and the execution layer. The racing strategy of the swarm is planned in the decision layer, which determines the discrete path and changes the formation of the cooperative vehicles according to the game's progress. A Gestalt Nash Game (GNG) framework is designed to depict the racing game and determine the strategy of each swarm member: cooperative block or all-full sprint. Then, an interaction-enhanced iterated best response algorithm is introduced to solve each vehicle's optimal trajectory and infer the adversary's planning path, searching the Nash equilibrium solution for this multi-vehicle racing. Furthermore, the execution layer employs the discrete trajectories obtained in the decision layer as the B-spline control points and considers the kinematic constraints to get smooth and feasible trajectories. We also combine the MPC method with the simplified Pacejka tire model to drive the vehicle motion. Illustrative simulation examples with different initial conditions are presented, showing that the slower group can beat the faster adversary with a higher probability using the proposed hierarchical path planner.