IP Library Granted Patent US 12,479,439
Granted Patent B2
US 12,479,439 · App. 18/182,474 · Granted Nov 25, 2025

Systems and methods for neural-EXPTANH learned tire models

Inventors: Yan Ming Jonathan Goh (Palo Alto, CA); Franck Djeumou (Palo Alto, CA)
Assignees: Toyota Research Institute, Inc.; Toyota Jidosha Kabushiki Kaisha
B60W30/18172B60W40/101G05B13/027G05B13/048B60W2520/10B60W2520/14B60W2520/20B60W2520/28B60W2720/26
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Quick Facts
Patent No.
US 12,479,439
App. No.
18/182,474
Granted
Nov 25, 2025
Kind
B2
Abstract

System, methods, and other embodiments described herein relate to tire models based on neural-ExpTanh parameterization. In one embodiment, a method includes operating a vehicle with a control framework incorporating an ExpTanh function; calculating prior slip data based on measurements obtained by the control framework; selecting a confidence parameter; using a first predictive model to determine ExpTanh parameters based upon the prior slip data, the measurements, and the confidence parameter; and inputting a slip parameter and the ExpTanh parameters into the ExpTanh function to estimate a tire force.

Claims (19)

1 . A method comprising: operating a vehicle with a control framework incorporating an ExpTanh function; calculating prior slip data based on measurements obtained by the control framework; using a first Neural Network predictive model to determine ExpTanh parameters based upon the prior slip data and the measurements; and inputting a slip parameter and the ExpTanh parameters into the ExpTanh function to estimate a tire force, wherein the ExpTanh function has multiple inflection points based on the ExpTanh parameters; and adjusting a vehicle control input based on the tire force estimate.

2 . The method of claim 1 , wherein using the first Neural Network predictive model to determine the ExpTanh parameters is further based on scaling parameters; and the method further comprises: using, in parallel with the first Neural Network predictive model, a second Neural Network predictive model to determine the scaling parameters based on the prior slip data.

3 . The method of claim 2 , wherein the method further comprises: adjusting the tire force by the scaling parameters to estimate a pair of lateral and longitudinal tire forces.

4 . The method of claim 3 , wherein using the first or second Neural Network predictive models includes using a stochastic gradient descent algorithm to obtain the ExpTanh parameters.

5 . The method of claim 4 , wherein the prior slip data contains slip angle data and longitudinal slip ratio data; and the slip parameter is a current total slip.

6 . The method of claim 2 , further comprising selecting a confidence parameter and wherein using the first Neural Network predictive model to determine the ExpTanh parameters is further based upon the confidence parameter.

7 . The method of claim 6 , wherein the measurements include at least one of yaw rate data, velocity data, sideslip angle data, front axle wheel speed data, or rear axle wheel speed data.

8 . The method of claim 7 , wherein one or more parameters of the ExpTanh parameters is passed through a function to ensure the one or more parameters of the ExpTanh parameters have a nonnegative value.

9 . A system comprising: a processor; and a memory storing instructions that, when executed by the processor, cause the processor to: operate a vehicle with a control framework incorporating an ExpTanh function; calculate prior slip data based on measurements obtained by the control framework; use a first Neural Network predictive model to determine ExpTanh parameters based upon the prior slip data and the measurements; and input a slip parameter and the ExpTanh parameters into the ExpTanh function to estimate a tire force, wherein the ExpTanh function has multiple inflection points based on the ExpTanh parameters; and adjust a vehicle control input based on the tire force estimate.

10 . The system of claim 9 , wherein the instruction to use the first predictive model to determine the ExpTanh parameters is further based on scaling parameters; and the system further includes instructions to: use, in parallel with the first Neural Network predictive model, a second Neural Network predictive model to determine the scaling parameters based on the prior slip data.

11 . The system of claim 10 , wherein the system further includes instructions to: adjust the tire force by the scaling parameters to estimate a pair of lateral and longitudinal tire forces.

12 . The system of claim 11 , wherein the use of the first or second Neural Network predictive models includes the use of a stochastic gradient descent algorithm to obtain the ExpTanh parameters.

13 . The system of claim 12 , wherein the prior slip data contains slip angle data and longitudinal slip ratio data; and the slip parameter is a current total slip.

14 . The system of claim 9 , wherein the system further includes the instruction to select a confidence parameter and wherein the instruction to use the first Neural Network predictive model to determine the ExpTanh parameters is further based upon the confidence parameter.

15 . The system of claim 14 , wherein the measurements include at least one of yaw rate data, velocity data, sideslip angle data, front axle wheel speed data, or rear axle wheel speed data.

16 . The system of claim 15 , wherein the system further includes instructions to pass one or more parameters of the ExpTanh parameters through a function to ensure the one or more parameters of the ExpTanh parameters have a nonnegative value.

17 . A non-transitory computer-readable medium including instructions that when executed by one or more processors cause the one or more processors to: operate a vehicle with a control framework incorporating an ExpTanh function; calculate prior slip data based on measurements obtained by the control framework; use a first Neural Network predictive model to determine ExpTanh parameters based upon the prior slip data and the measurements; and input a slip parameter and the ExpTanh parameters into the ExpTanh function to estimate a tire force, wherein the ExpTanh function has multiple inflection points based on the ExpTanh parameters; and adjust a vehicle control input based on the tire force estimate.

18 . The non-transitory computer-readable medium of claim 17 , wherein the instructions further include to apply scaling parameters to estimate a lateral tire force estimate or a longitudinal tire force estimate from the tire force estimate.

19 . The non-transitory computer-readable medium of claim 18 , wherein the instructions further include to adjust the vehicle control input based on the lateral tire force estimate, or the longitudinal tire force estimate.

Assignments (2)
ASSIGNMENT OF ASSIGNOR'S INTEREST Recorded Jan 13, 2026
From: TOYOTA RESEARCH INSTITUTE, INC.
To: TOYOTA JIDOSHA KABUSHIKI KAISHA
Reel/Frame 073451/0799 →
ASSIGNMENT OF ASSIGNOR'S INTEREST Recorded Apr 12, 2023
From: GOH, YAN MING JONATHAN; DJEUMOU, FRANCK
To: TOYOTA RESEARCH INSTITUTE, INC.; TOYOTA JIDOSHA KABUSHIKI KAISHA
Reel/Frame 063301/0838 →
Continuity (1)
Related Publication 20240308522A1 · Sep 19, 2024
References Cited (70)
US 6550320B1 · Giustino · 2003 [cited by examiner]
US 7069135B2 · Bertrand · 2006 [cited by examiner]
US 7225072B2 · Fangeat · 2007 [cited by examiner]
US 7426431B2 · Fangeat · 2008 [cited by examiner]
US 7945429B2 · Miyashita · 2011 [cited by examiner]
US 8844346B1 · Singh et al. · 2014 [cited by applicant]
US 8886395B2 · Singh et al. · 2014 [cited by applicant]
US 8983749B1 · Singh · 2015 [cited by examiner]
US 9222854B2 · Singh et al. · 2015 [cited by applicant]
US 9340211B1 · Singh · 2016 [cited by examiner]
US 9358846B2 · Singh et al. · 2016 [cited by applicant]
US 9428013B2 · Singh · 2016 [cited by applicant]
US 9434409B2 · Singh · 2016 [cited by applicant]
US 9442045B2 · Singh · 2016 [cited by applicant]
US 9636955B2 · Singh et al. · 2017 [cited by applicant]
US 9663115B2 · Singh · 2017 [cited by examiner]
US 9739689B2 · Singh · 2017 [cited by applicant]
US 9751533B2 · Singh · 2017 [cited by applicant]
US 9752962B2 · Singh · 2017 [cited by examiner]
US 9821611B2 · Singh · 2017 [cited by applicant]
US 9873293B2 · Singh et al. · 2018 [cited by applicant]
US 9874496B2 · Singh · 2018 [cited by applicant]
US 9995654B2 · Singh · 2018 [cited by applicant]
US 10093321B1 · Berntorp et al. · 2018 [cited by applicant]
US 10124809B2 · Thor et al. · 2018 [cited by applicant]
US 10632978B2 · Gustafsson et al. · 2020 [cited by applicant]
US 11067431B2 · Cyllik et al. · 2021 [cited by applicant]
US 11491995B2 · Ishigami · 2022 [cited by examiner]
US 12039812B2 · Sakakibara · 2024 [cited by examiner]
US 20030164036A1 · Giustino · 2003 [cited by examiner]
US 20160159365A1 · Singh · 2016 [cited by examiner]
US 20200250899A1 · Sakakibara · 2020 [cited by examiner]
US 20220274452A1 · Hasegawa · 2022 [cited by examiner]
US 20220402498A1 · Jonasson · 2022 [cited by examiner]
CN 111708977A · 2020 [cited by examiner]
CN 112784355B · 2021 [cited by applicant]
CN 111891131B · 2021 [cited by applicant]
CN 113978470A · 2022 [cited by applicant]
EP 4029745A1 · 2022 [cited by applicant]
JP 2022115315A · 2022 [cited by applicant]
WO 2021079004A1 · 2021 [cited by applicant]
Rahman et al. “Neural Ordinary Differential Equations for Nonlinear System Identification”, arXiv:2203.00120v2 [cs.LG]. Mar. 15, 2022. [cited by applicant]
Koch et al. “Physics-informed Machine Learning of Parameterized Fundamental Diagrams”, arXiv:2208.00880v1 [cs.LG]. Aug. 1, 2022. [cited by applicant]
Quaglino et al. “SNODE: Spectral Discretization of Neural ODEs for System Identification”, arXiv:1906.07038v2 [cs.NE]. Jan. 17, 2020. [cited by applicant]
Alvarez et al. “DyNODE: Neural Ordinary Differential Equations for Dynamics Modeling in Continuous Control”, arXiv:2009.04278v1 [cs.LG]. Sep. 9, 2020. [cited by applicant]
Zhong et al. “Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control”, arXiv:1909.12077v4 [cs.LG]. Apr. 30, 2020. [cited by applicant]
Zhong et al. “A Differentiable Contact Model to Extend Lagrangian and Hamiltonian Neural Networks for Modeling Hybrid Dynamics”, arXiv:2102.06794v3 [cs.RO]. Nov. 12, 2021. [cited by applicant]
Gäfvert et al. “Novel Semi Empirical Tire Models for Combined Braking and Cornering”, Department of Automatic Control, Lund Institute of Technology. Apr. 2003. [cited by applicant]
Svendius, Jacob. “Tire Modeling and Friction Estimation”, PhD thesis, Lund University, 2007. [cited by applicant]
Acosta et al. “Tire lateral force estimation and grip potential identification using Neural Networks, Extended Kalman Filter, and Recursive Least Squares”, Neural Computing and Applications, vol. 30, pp. 3445-3465, 2017. [cited by applicant]
Guarneri et al. “A Neural-Network-Based Model for the Dynamic Simulation of the Tire/Suspension System While Traversing Road Irregularities”, IEEE Transactions on Neural Networks, vol. 19, pp. 1549-1563, 2008. [cited by applicant]
Xu et al. “Tire Force Estimation in Intelligent Tires Using Machine Learning”, IEEE Transactions on Intelligent Transportation Systems, vol. 23, pp. 3565-3574, 2022. [cited by applicant]
Paden et al. “A Survey of Motion Planning and Control Techniques for Self-driving Urban Vehicles”, IEEE Transactions on Intelligent Vehicles, vol. 1, pp. 33-55, 2016. [cited by applicant]
Falcone et al. “Predictive Active Steering Control for Autonomous Vehicle Systems,” IEEE Transactions on Control Systems Technology, vol. 15, pp. 566-580, 2007. [cited by applicant]
Kong et al. “Kinematic and dynamic vehicle models for autonomous driving control design”, 2015 IEEE Intelligent Vehicles Symposium (IV), pp. 1094-1099, 2015. [cited by applicant]
Polack et al. “The kinematic bicycle model: A consistent model for planning feasible trajectories for autonomous vehicles?”, 2017 IEEE Intelligent Vehicles Symposium (IV), pp. 812-818, 2017. [cited by applicant]
Goh et al. “Toward Automated Vehicle Control Beyond the Stability Limits: Drifting Along a General Path”, Journal of Dynamic Systems Measurement and Control-transactions of the Asme, vol. 142, 2019. [cited by applicant]
Balachandran et al. “Human-Centric Intelligent Driving: Collaborating with the Driver to Improve Safety”, Automated Road Transportation Symposium, pp. 85-109, Springer, 2023. [cited by applicant]
Subosits et al. “Impacts of Model Fidelity on Trajectory Optimization for Autonomous Vehicles in Extreme Maneuvers”, IEEE Transactions on Intelligent Vehicles, vol. 6, pp. 546-558, 2021. [cited by applicant]
Chen et al. “Neural Ordinary Differential Equations”, NeurIPS, 2018. [cited by applicant]
Djeumou et al. “Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modeling”, 4th Annual Conference on Learning for Dynamics and Control, 2022. [cited by applicant]
Djeumou et al. “Taylor-Lagrange Neural Ordinary Differential Equations: Toward Fast Training and Evaluation of Neural ODEs”, IJCAI, 2022. [cited by applicant]
Goh et al. “Nonlinear Model Predictive Control for Highly Transient Autonomous Drifting”, 15th International Symposium on Advanced Vehicle Control, 2022. [cited by applicant]
Kingma et al. “Adam: A Method For Stochastic Optimization” arXiv preprint arXiv:1412.6980, 2014. [cited by applicant]
Matuško et al. “Neural network based tire/road friction force estimation”, Engineering Applications of Artificial Intelligence 21, pp. 442-456, 2008. [cited by applicant]
Hindiyeh et al. “A Controller Framework for Autonomous Drifting: Design, Stability, and Experimental Validation”, Journal of Dynamic Systems Measurement and Control-transactions of the Asme, vol. 136, p. 051015, 2011. [cited by applicant]
Goh et al. “Simultaneous Stabilization and Tracking of Basic Automobile Drifting Trajectories”, 2016 IEEE Intelligent Vehicles Symposium (IV), pp. 597-602, 2016. [cited by applicant]
Spielberg et al. “Neural network vehicle models for high-performance automated driving”, Science Robotics, vol. 4, 2019. [cited by applicant]
Pacejka, Hans B. “Tyre and Vehicle Dynamics”, Butterworth-Heinemann, second edition. p. 184-191. 2006. [cited by applicant]
Goh, Jonathan Yan Ming. “Automated Vehicle Control Beyond the Stability Limits”, Stanford University, p. 17-48. 2019. [cited by applicant]