Limiting Computation Levels in Prioritized Trajectory Planning with Safety Guarantees

TL;DR

This work guarantees safe trajectories in parallel planning through reachability analysis and addresses this conservativeness by planning with a subset of vehicles in sequence as a graph partitioning problem, which limits the size of the resulting subgraphs.

Abstract

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.

Figures (4)

• Figure 1: Example of prioritized trajectory planning with prediction inconsistency in a dynamic environment. Vehicle 2 has lower priority. Arrows indicate predictions. Gradient fills indicate predicted occupied areas.
• Figure 2: Distributed planning framework overview, illustrated for vehicle $i$. $\glslink{sym:stateAgent}{^{(i)}}$: measured states; $\glslink{sym:setReachable}{\mathcal{R}}$: reachable sets; $/$: undirected/directed coupling graph; $\varGamma$: graph partition; $\glslink{sym:prediction}{ \glslink{sym:prediction}{ \tilde{\bm{x}} }^{(i)} }$: predicted trajectory. Time argument omitted.
• Figure 3: Parallel trajectory planning with pdmpc. Parallel coupling constraints are on the left time-shifted previous trajectorieskuwata2007distributedshen2023reinforcement, on the right reachable sets (our approach). Occupancies are inflated to account for uncertainty.
• Figure 4: Effect of computation level limit on solution quality. $\bar{v}$: normalized average speed. Computation level limit of 1: purely parallel computation, computation level limit of $\infty$: purely sequential computationalrifaee2016coordinated.

Theorems & Definitions (1)

• remark thmcounterremark