Sampling-Based Motion Planning with Online Racing Line Generation for Autonomous Driving on Three-Dimensional Race Tracks

TL;DR

This work tackles trajectory planning for autonomous racing on complex 3D tracks by introducing a sampling-based local planner that explicitly accounts for three-dimensional track effects. The method combines a 3D track representation with a racing-line framework, sampling in curvilinear coordinates, and a trajectory generation scheme that produces relative (to the racing line) jerk-optimal curves while optionally switching to traditional jerk-optimal longitudinal curves to maintain feasibility, all mapped into Cartesian space via a velocity-aligned frame. Feasibility is ensured through three soft checks using track boundaries, minimum turning radius, and 3D gg-diagrams that incorporate vertical acceleration $ ilde g$, with an elliptical prediction term to manage opposing vehicles in the cost function. A key contribution is online racing-line generation, which recalculates a time-optimal line for a finite spatial horizon and, when combined with the local planner, reduces lap times in multi-vehicle scenarios on complex circuits, while preserving racing-line adherence in solo runs. The results demonstrate improved lap times and more effective utilization of dynamic limits on 3D tracks such as LVMS and MPCB, highlighting the practical potential for real-time, online racing-line-aware planning in autonomous racing systems.

Abstract

Existing approaches to trajectory planning for autonomous racing employ sampling-based methods, generating numerous jerk-optimal trajectories and selecting the most favorable feasible trajectory based on a cost function penalizing deviations from an offline-calculated racing line. While successful on oval tracks, these methods face limitations on complex circuits due to the simplistic geometry of jerk-optimal edges failing to capture the complexity of the racing line. Additionally, they only consider two-dimensional tracks, potentially neglecting or surpassing the actual dynamic potential. In this paper, we present a sampling-based local trajectory planning approach for autonomous racing that can maintain the lap time of the racing line even on complex race tracks and consider the race track's three-dimensional effects. In simulative experiments, we demonstrate that our approach achieves lower lap times and improved utilization of dynamic limits compared to existing approaches. We also investigate the impact of online racing line generation, in which the time-optimal solution is planned from the current vehicle state for a limited spatial horizon, in contrast to a closed racing line calculated offline. We show that combining the sampling-based planner with the online racing line generation can significantly reduce lap times in multi-vehicle scenarios.

Figures (8)

• Figure 1: The race cars of the TUM Autonomous Motorsport (right) and Cavalier (left) teams in a banked turn on the LVMS.
• Figure 2: Structure of our local planning approach with all needed inputs.
• Figure 3: Representation of a closed, counterclockwise orientated 3D race track with negative banking ($\varphi<0$) and without slope ($\mu=0$).
• Figure 4: Comparison of jerk-optimal and relative trajectory generation with $\dot{s}_{\mathrm{0}} = 53m\per s$, $\ddot{s}_{\mathrm{0}} = 2m\per s\squared$, $N_{\mathrm{\dot{s}}} = 6.0$, and $T = 4s$.
• Figure 5: Elliptical shaped prediction costs with $k_\mathrm{s}=0.015$ and $k_\mathrm{n}=0.5$ of an opposing vehicle located at $s_{\mathrm{pr},m}(t)=n_{\mathrm{pr},m}(t)=0$.