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

Matthias Rowold, Levent Ogretmen, Ulf Kasolowsky, Boris Lohmann

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations


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 three-dimensional 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.

Original languageEnglish
Title of host publicationIV 2023 - IEEE Intelligent Vehicles Symposium, Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9798350346916
StatePublished - 2023
Event34th IEEE Intelligent Vehicles Symposium, IV 2023 - Anchorage, United States
Duration: 4 Jun 20237 Jun 2023

Publication series

NameIEEE Intelligent Vehicles Symposium, Proceedings


Conference34th IEEE Intelligent Vehicles Symposium, IV 2023
Country/TerritoryUnited States


  • autonomous racing
  • racing line
  • three-dimensional planning
  • time-optimal
  • trajectory planning


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