Estimation of tire–road friction for road vehicles: a time delay neural network approach

  • Alexandre M. RibeiroEmail author
  • Alexandra Moutinho
  • André R. Fioravanti
  • Ely C. de Paiva
Technical Paper


The performance of vehicle active safety systems is dependent on the friction force arising from the contact of tires and the road surface. Therefore, an adequate knowledge of the tire–road friction coefficient is of great importance to achieve a good performance of different vehicle control systems. This paper deals with the tire–road friction coefficient estimation problem through the knowledge of lateral tire force. A time delay neural network (TDNN) is adopted for the proposed estimation design. The TDNN aims at detecting road friction coefficient under lateral force excitations avoiding the use of standard mathematical tire models, which may provide a more efficient method with robust results. Moreover, the approach is able to estimate the road friction at each wheel independently, instead of using lumped axle models simplifications. Simulations based on a realistic vehicle model are carried out on different road surfaces and driving maneuvers to verify the effectiveness of the proposed estimation method. The results are compared with a classical approach, a model-based method modeled as a nonlinear regression.


Road friction estimation Artificial neural networks Recursive least squares Vehicle safety Road vehicles 



This work was supported by FCT, Portugal, through IDMEC under projects LAETA (UID/EMS/ 50022/2019). The mobility of A. Ribeiro has been possible with the Erasmus Mundus SMART2 support (Project Reference: 552042-EM-1-2014-1-FR-ERA MUNDUS-EMA2) coordinated by CENTRALESUPELEC. The authors also acknowledge the support of FAPESP through Regular project AutoVERDE N. 2018/04905-1, Ph.D. FAPESP 2018/05712-2 and CNPq Grant 305600/2017-6.


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Department of Computational MechanicsSchool of Mechanical EngineeringCampinasBrazil
  2. 2.Institute of Mechanical Engineering - IDMEC, LAETA, Instituto Superior TécnicoUniversidade de LisboaLisbonPortugal
  3. 3.Department of Integrated SystemsSchool of Mechanical EngineeringCampinasBrazil

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