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Trajectory Planning Using Tire Thermodynamics for Automated Drifting

Takao Kobayashi, Trey P. Weber, J. Christian Gerdes

TL;DR

This work addresses the impact of tire temperature on tire-road friction and its effect on autonomous trajectory planning. It introduces a simple tire thermodynamics model that links rear-tire temperature to friction and integrates it into both steady-state and dynamic drifting trajectory planning, with an LQR tracker whose gains adapt to temperature changes. The approach yields dynamically feasible trajectories and improved tracking in experiments on a full-size drifting platform, Takumi, outperforming constant-friction baselines, and demonstrates robustness of the closed-loop behavior to friction changes. The study highlights the practical value of incorporating tire thermodynamics into vehicle control, with potential extensions to more advanced optimization and data-driven heat-transfer modeling for broader driving conditions.

Abstract

Automated vehicles need to estimate tire-road friction information, as it plays a key role in safe trajectory planning and vehicle dynamics control. Notably, friction is not solely dependent on road surface conditions, but also varies significantly depending on the tire temperature. However, tire parameters such as the friction coefficient have been conventionally treated as constant values in automated vehicle motion planning. This paper develops a simple thermodynamic model that captures tire friction temperature variation. To verify the model, it is implemented into trajectory planning for automated drifting - a challenging application that requires leveraging an unstable, drifting equilibrium at the friction limits. The proposed method which captures the hidden tire dynamics provides a dynamically feasible trajectory, leading to more precise tracking during experiments with an LQR (Linear Quadratic Regulator) controller.

Trajectory Planning Using Tire Thermodynamics for Automated Drifting

TL;DR

This work addresses the impact of tire temperature on tire-road friction and its effect on autonomous trajectory planning. It introduces a simple tire thermodynamics model that links rear-tire temperature to friction and integrates it into both steady-state and dynamic drifting trajectory planning, with an LQR tracker whose gains adapt to temperature changes. The approach yields dynamically feasible trajectories and improved tracking in experiments on a full-size drifting platform, Takumi, outperforming constant-friction baselines, and demonstrates robustness of the closed-loop behavior to friction changes. The study highlights the practical value of incorporating tire thermodynamics into vehicle control, with potential extensions to more advanced optimization and data-driven heat-transfer modeling for broader driving conditions.

Abstract

Automated vehicles need to estimate tire-road friction information, as it plays a key role in safe trajectory planning and vehicle dynamics control. Notably, friction is not solely dependent on road surface conditions, but also varies significantly depending on the tire temperature. However, tire parameters such as the friction coefficient have been conventionally treated as constant values in automated vehicle motion planning. This paper develops a simple thermodynamic model that captures tire friction temperature variation. To verify the model, it is implemented into trajectory planning for automated drifting - a challenging application that requires leveraging an unstable, drifting equilibrium at the friction limits. The proposed method which captures the hidden tire dynamics provides a dynamically feasible trajectory, leading to more precise tracking during experiments with an LQR (Linear Quadratic Regulator) controller.
Paper Structure (16 sections, 31 equations, 12 figures, 2 tables)

This paper contains 16 sections, 31 equations, 12 figures, 2 tables.

Table of Contents

  1. INTRODUCTION
  2. Vehicle Modeling
  3. Path Tracking Model
  4. Single Track Model
  5. Tire Force Model
  6. Tire Thermal Model
  7. Trajectory Planning and Control
  8. Steady state drifting trajectory
  9. Dynamic drifting trajectory
  10. Controller
  11. Experimental Validation
  12. Test Platform
  13. Steady state drifting
  14. Dynamic drifting
  15. Discussion
  16. ...and 1 more sections

Figures (12)

  • Figure 1: "Takumi": An automated drifting platform
  • Figure 2: Single track model with reference path
  • Figure 3: Tire friction map using tread temperature: the friction coefficient is estimated using an observerb4 and the parameters are identified from 30 deg.C, where the real tires are totally in the slip region. The points around 25 deg.C means the rear tires still have the margin from the friction limit, therefore it is impossible to estimate the friction parameters.
  • Figure 4: Tire thermodynamic model: Whereas the front tire temperature remains same, the rear tire temperature rises dramatically while drifting.
  • Figure 5: Flowchart to compute a set of drifting equilibria using the tire thermodynamics model
  • ...and 7 more figures