Online Time-Optimal Trajectory Planning on Three-Dimensional Race Tracks

TL;DR

This paper presents an online method for generating time-optimal trajectories on 3D race tracks, accounting for vehicle dynamics, track geometry, and race rules, enabling real-time racing strategies and overtaking maneuvers.

Contribution

It introduces an efficient online planning framework that solves optimal control problems in real-time for racing, incorporating 3D track effects and rule-based speed constraints.

Findings

Reproduces offline lap times during single vehicle racing.

Finds new time-optimal trajectories during overtaking.

Handles speed limit violations with a slack variable.

Abstract

We propose an online planning approach for racing that generates the time-optimal trajectory for the upcoming track section. The resulting trajectory takes the current vehicle state, effects caused by \acl{3D} track geometries, and speed limits dictated by the race rules into account. In each planning step, an optimal control problem is solved, making a quasi-steady-state assumption with a point mass model constrained by gg-diagrams. For its online applicability, we propose an efficient representation of the gg-diagrams and identify negligible terms to reduce the computational effort. We demonstrate that the online planning approach can reproduce the lap times of an offline-generated racing line during single vehicle racing. Moreover, it finds a new time-optimal solution when a deviation from the original racing line is necessary, e.g., during an overtaking maneuver. Motivated by the application in a rule-based race, we also consider the scenario of a speed limit lower than the current vehicle velocity. We introduce an initializable slack variable to generate feasible trajectories despite the constraint violation while reducing the velocity to comply with the rules.