Limiting Computation Levels in Prioritized Trajectory Planning with Safety Guarantees

In prioritized planning for vehicles, vehicles plan trajectories in parallel or in sequence. Parallel prioritized planning offers approximately consistent computation time regardless of the number of vehicles but struggles to guarantee collision-free trajectories. Conversely, sequential prioritized planning can guarantee collision-freeness but results in increased computation time as the number of sequentially computing vehicles, which we term computation levels, grows. This number is determined by the directed coupling graph resulted from the coupling and prioritization of vehicles. In this work, we guarantee safe trajectories in parallel planning through reachability analysis. Although these trajectories are collision-free, they tend to be conservative. We address this by planning with a subset of vehicles in sequence. We formulate the problem of selecting this subset as a graph partitioning problem that allows us to independently set computation levels. Our simulations demonstrate a reduction in computation levels by approximately 64% compared to sequential prioritized planning while maintaining the solution quality.