Hierarchical Time-Optimal Planning for Multi-Vehicle Racing

TL;DR

The paper tackles time-optimal trajectory planning in multi-vehicle racing where opponents move dynamically. It proposes a two-stage hierarchical planner that couples discrete high-level behavior selection, via a spatio-temporal visibility-graph-based planning, with a continuous time-optimal control problem (OCP) constrained by maneuver envelopes and soft slack terms. Key contributions include progress-variant behavioral planning, maneuver-envelope generation to encode overtaking decisions, and a single-core OCP implementation that achieves comparable performance to parallel optimization while offering superior scalability. Empirical results on randomized Modena-track scenarios show overtaking times comparable to a pseudo-parallel approach and demonstrate favorable computation-time scaling with the number of opponents, highlighting real-time feasibility on limited hardware. Overall, the method enables robust, near-global-optimal racing decisions on a single core, with practical implications for real-time autonomous racing and related high-speed planning tasks.

Abstract

This paper presents a hierarchical planning algorithm for racing with multiple opponents. The two-stage approach consists of a high-level behavioral planning step and a low-level optimization step. By combining discrete and continuous planning methods, our algorithm encourages global time optimality without being limited by coarse discretization. In the behavioral planning step, the fastest behavior is determined with a low-resolution spatio-temporal visibility graph. Based on the selected behavior, we calculate maneuver envelopes that are subsequently applied as constraints in a time-optimal control problem. The performance of our method is comparable to a parallel approach that selects the fastest trajectory from multiple optimizations with different behavior classes. However, our algorithm can be executed on a single core. This significantly reduces computational requirements, especially when multiple opponents are involved. Therefore, the proposed method is an efficient and practical solution for real-time multi-vehicle racing scenarios.

Figures (8)

• Figure 1: Overview of the hierarchical planning approach.
• Figure 2: 3D track with road frame $\mathcal{R}$ and velocity frame $\mathcal{V}$.
• Figure 3: Overview of the behavioral planning algorithm.
• Figure 4: Behavioral planning for an example maneuver with a single opponent. The top figure shows the generation of progress variants, while the middle and bottom figures depict the visibility graphs for the variants (1.1,1) and (0.9,1).
• Figure 5: Generation of maneuver envelopes.