Finding the Racing Line

Over the last couple of weeks, I’ve been tinkering with various ways of visualising rally stage route data downloaded as KML files. The nature of the routes is such that the linestring can often describe quite a ragged route, made up of it is as a series of concatenated straight line segments.

Whilst looking for ways of smoothing routes — a recommended approach appears to be to use a Savitzky-Golay smoothing filter (?!) — I stumbled across various papers and code repositories relating to racing line optimisation.

One handy repo, TUMFTM/laptime-simulation, included a Python code utility for smoothing a circuit given the track centerline retrieved from OpenStreetMap. If you give it a non-closed route as the input linestring, it currently closes it with a staight line connecting the two ends, but it would be useful to try to tweak it to work with non-closed routes (I opened a related issue).

For a general review of approaches to lap time simulation, see Lap time simulation: Comparison of steady state, quasi-static and transient racing car cornering strategies, Blake Siegler, Andrew Deakin & David Crolla, University of Leeds, SAE TECHNICAL paper series, 2000-01-3563. See also Blake Siegler’s PhD thesis, 2002, from the University of Leeds, Lap Time Simulation for Racing Car Design.

Whilst many of the raceline optimisation papers are a bit beyond me (?!), skimming through them and looking at the pictures may provide further ideas about what sorts of thing may be of interest in terms of rally stage route profiles. Where papers have related code repositories, this could also serve as a useful "for real" tutorial guide in how to convert differential equations as described in a paper into differential equations modeled in code.

I’ve added various papers to my reading list, and for want of anywhere else to keep a record of them, thought I’d post them here.

But first, an introduction to corners….

And to racing lines…

For a more detailed look at smoothing trajectories and finding racing lines, albeit in circuit racing, see for example:

• Heilmeier, A., Wischnewski, A., Hermansdorfer, L., Betz, J., Lienkamp, M. and Lohmann, B., 2019. Minimum curvature trajectory planning and control for an autonomous race car. Vehicle System Dynamics. DOI: 10.1080/00423114.2019.1631455 and the related Python code repositories TUMFTM/global_racetrajectory_optimization and TUMFTM/trajectory_planning_helpers. This group is also responsible for the aforementioned laptime simulation package, TUMFTM/laptime-simulation.
• Trajectory Planning and Control for an Autonomous Race Vehicle, Nitin R. Kapania, PhD. thesis, 2016, Stanford University.
• Computing the racing line using Bayesian optimization, A Jain & M Morari, preprint, 2020 [code repository: jainachin/bayesrace]
• On minimum time vehicle manoeuvring: The theoretical optimal lap Casanova, D., 2000. PhD thesis, Cranfield University.
• Lap time optimisation of a racing go-kart, Lot, R. and Dal Bianco, N., 2016. Vehicle System Dynamics, 54(2), pp.210-230.
• Racing Line Optimisation for Autonomous Vehicles, Joe Davison, BSc project, University of Bath, 2019-20.

It would be interesting to know how circuit racing lines and rally racing lines might differ in terms of optimisation strategy and physics models.

For example, here’s a take on rally racing lines:

And here’s a tutorial on some of the maths (along with a related blog post and PDF):

The associated article also refers to a couple of PhD theses:

• Measurement and analysis of rally car dynamics at high attitude angle, Michael Croft-White, Cranfield University, 2006
• Dynamics and Control of Drifting in Automobiles Rami Hindiyeh, Rami Hindiyeh, Stanford University, 2013

Readings wise, this looks like it could be relevant to that: Minimum time vs maximum exit velocity path optimization during cornering, Velenis, E. and Tsiotras, P., 2005 In 2005 IEEE international symposium on industrial electronics (pp. 355-360).

Surface type and surface evolution (i.e. road order effect) as well as weather may also have a significant effect. For example:

• Minimum Time Cornering: The Effect of Road Surface and Car Transmission Layout, Tavernini, D., Massaro, M., Velenis, E., Katzourakis, D.I. and Lot, R. (2013) Vehicle System Dynamics, 51 (10), 1533-1547. (doi:10.1080/00423114.2013.813557).
• Modeling aggressive maneuvers on loose surfaces: The cases of trail-braking and pendulum-turn Velenis, E., Tsiotras, P. and Lu, J., 2007. In 2007 European Control Conference (ECC) (pp. 1233-1240).

Other rally related papers include:

• Trail-braking driver input parameterization for general corner geometry Velenis, E., Tsiotras, P. and Lu, J., 2008. (No. 2008-01-2986). SAE Technical Paper.
• High-Speed Cornering for Autonomous Off-Road Rally Racing, You, C. and Tsiotras, P., 2019. IEEE Transactions on Control Systems Technology.
• Hybrid Hierarchical Rally Driver Model for Autonomous Vehicle Agile Maneuvering on Loose Surfaces, Acosta, M., Kanarachos, S. and Fitzpatrick, M.E., 2017, July. 14th International Conference on Informatics in Control, Automation and Robotics (ICINCO) (pp. 216-225)
• Real-time trail-braking maneuver generation for off-road vehicle racing You, C. and Tsiotras, P., 2018, June. In 2018 Annual American Control Conference (ACC) (pp. 4751-4756).

For general techniques for analysing race car open telemetry data:

• Insights into vehicle trajectories at the handling limits: analysing open data from race car drivers Kegelman, J.C., Harbott, L.K. and Gerdes, J.C., 2017. Vehicle system dynamics, 55(2), pp.191-207.

PS in passing, an interesting looking blog on WRC aero: wrcwings.tech.

PPS Although slightly off topic, fascinating nonetheless, from the Honda R&D website, register and check out their F1 technical review https://www.hondarandd.jp/summary.php?sid=23&lang=en