Journal of the Brazilian Society of Mechanical Sciences and Engineering manuscript No. (will be inserted by the editor) Estimation of Tire-Road Friction for Road Vehicles: a Time Delay Neural Network Approach Alexandre M. Ribeiro · Alexandra Moutinho · Andr´eR. Fioravanti · Ely C. de Paiva Received: date / Accepted: date Abstract The performance of vehicle active safety sys- different road surfaces and driving maneuvers to verify tems is dependent on the friction force arising from the effectiveness of the proposed estimation method. the contact of tires and the road surface. Therefore, an The results are compared with a classical approach, a adequate knowledge of the tire-road friction coefficient model-based method modeled as a nonlinear regression. is of great importance to achieve a good performance Keywords Road friction estimation Artificial neural of different vehicle control systems. This paper deals · networks Recursive least squares Vehicle safety with the tire-road friction coefficient estimation prob- · · · Road vehicles lem through the knowledge of lateral tire force. A time delay neural network (TDNN) is adopted for the pro- posed estimation design. The TDNN aims at detecting 1 Introduction road friction coefficient under lateral force excitations avoiding the use of standard mathematical tire models, One of the primary challenges of vehicle control is that which may provide a more efficient method with robust the source of force generation is strongly limited by the results. Moreover, the approach is able to estimate the available friction between the tire tread elements and road friction at each wheel independently, instead of the road. In order to better understand vehicle handling using lumped axle models simplifications. Simulations due to force generation mechanisms, several research based on a realistic vehicle model are carried out on activities related to vehicle dynamics and control fields are oriented towards estimation of all components of Alexandre M. Ribeiro the tire-ground contact. Department of Computational Mechanics, School of Mechan- The knowledge of specific tire-road contact opera- ical Engineering, Mendeleyev Street 200, 13083-860 Camp- tion points, such as the saturation point where the tire inas, Brazil generates the maximum force available from friction, E-mail: [email protected] could lead to a new range of applications in vehicle con- Alexandra Moutinho trol. Moreover, current commercial vehicle safety sys- arXiv:1908.00452v2 [cs.NE] 14 Nov 2019 Institute of Mechanical Engineering - IDMEC, LAETA, Insti- tuto Superior T´ecnico,Universidade de Lisboa, Av. Rovisco tems, such as Anti-lock Brake Systems (ABS), Traction Pais, 1049-001 Lisbon, Portugal Control Systems (TCS) and Electronic Stability Con- E-mail: [email protected] trol (ESC) could have a significant improvement in per- Andr´eR. Fioravanti formance by the knowledge of the full vehicle states and Department of Computational Mechanics, School of Mechan- operating conditions that are still limited by the lack of ical Engineering, Mendeleyev Street 200, 13083-860 Camp- information [1]. Therefore, to reach this full potential inas, Brazil E-mail: fi[email protected] the recognition of the tire's limit handling is indispens- able. With this is mind, we emphasize the importance Ely C. de Paiva Department of Integrated Systems, School of Mechanical of estimating the vehicle road conditions, specifically Engineering, Mendeleyev Street 200, 13083-860 Campinas, the Tire Road Friction Coefficient (TRFC). Brazil Friction estimation often relies on a model-based es- E-mail: [email protected] timator using a well-defined and interpretable mathe- 2 Alexandre M. Ribeiro et al. matical model for the purpose of capturing the inherent feedforward neural network with linear output is used friction effects under the tire dynamics (forces and mo- with the vehicle longitudinal dynamics. The proposed ments). The most common model-based approaches use estimator is validated through a noiseless signal data. the steering system model [2,3], quarter-car model [4], four-wheel vehicle dynamic model [5], powertrain and In [25] and [26] a feedforward neural network is syn- wheel dynamics model [6]. thesized using the vehicle response to both longitudinal For the estimation problem, in [7] the correlation be- and lateral excitations. Therefore, the estimation is in- tween the self-aligning moment of the steering wheels vestigated under acceleration or brake maneuver while and road friction was firstly examined. Lately, [8,9, cornering. 5,10] explored the use of a nonlinear Recursive Least Squares method employed as a mean for identification Among the model-based methods that implement of tire-road friction through an observed data composed TRFC estimation using neural networks, some prior by the self-aligning moment and also expanded for a works also estimate friction through road conditions. lateral dynamic force analysis. It is the case of vision-based works used to estimate The wheel dynamic model can also be utilized with the road conditions ahead of the vehicle, where the a tire model to estimate the friction. In [11,12,13] the task becomes a classification problem. In [27], an im- wheel rolling motion is used to detect the longitudinal age dataset was used to train three machine learning force and longitudinal friction adopting the powertrain models including logistic regression, support vector ma- configuration and wheel drive engine. The estimator is chine, and neural networks to predict the friction class. built primarily exploring the force-slip ratio plane and In a similar form [28] proposes a convolutional neu- its relationship with the road friction coefficient. ral network model to learn region-specific features for road surface condition classification and how to infer Another model-based approach discussed in liter- the friction coefficient. Other works also implemented ature is a slip-slope algorithm. This method is based the classification by analyzing the road texture [29,30]. on the assumption that the low slip-plane zone (lin- ear region of the force-slip plane, characterizing normal In this study, the presented estimation process fo- driving conditions) can be used to estimate the tire- cuses on the dynamic characteristics of a rear-motorized- road friction. Distinct studies [14,15,16] have shown wheels electric vehicle to achieve the tire road friction this methodology. estimation and contributes in the following aspect: the Despite the majority of model-based methods, a num- estimator is developed by means of a time delay neural ber of algorithms have been studied based on differ- network (TDNN) as a way to identify the TRFC based ent concepts to estimate the surface condition. In [17, exclusively on the lateral force information and the es- 18], an optical sensor is used as a tire sensor that can timates are compared with a nonlinear least squares measure the road ahead and the tire carcass deflections (NLS) estimator based on a moving data window. which may be exploited in the estimation of friction potential. Cameras are also used to identify different Although TDNN have been used for diverse pur- surfaces. The detection is based on the light polariza- pose such as speech recognition [31], movement behav- tion changing when reflected from road surface [19]. ior [32], joint angle estimation [33] and nonlinear behav- Also, [20] proposed a method that merges weather data ior prediction of a time series [34], no other work has and road images taken by a camera on the vehicle. studied the TDNN as a reliable procedure to estimate More recently, based on the hypothesis that the fric- or measure the effect of TRFC on a vehicle dynamic. tion coefficient affects the natural frequency of the ve- Our main motivation for using TDNN is that the time- hicle systems, such as in-wheel motor drive system or delay arrangement structure enables the network to ef- steering system, the road-friction is estimated through fectively capture the temporal vehicle response due to frequency analysis [21,22]. a change in road friction. In the field of Machine Learning and Artificial Intel- ligence the work presented in [23] primarily designed a This paper is organized as follows: Section 2 presents feedforward neural network optimizing its topology by a vehicle theory development with mathematical mod- means of Genetic Algorithms to determine the actual els for the tire force models which are used in the es- tire forces from the measured signals. The estimated timation method. Section 3 details the least squares values were shown to have potential of exploring the regression method. In Section 4, the TDNN estimation nuances about TRFC. algorithm proposed is described. Simulation results are In [24], friction force estimation is presented in a shown and analyzed in Section 5. Finally, this paper is stricted accelerating/decelerating maneuver. A two-layer concluded in Section 6. Estimation of Tire-Road Friction for Road Vehicles: a Time Delay Neural Network Approach 3 2 Tire-Ground Contact Model wheelbase distance. δi stand for tire steering angles and the subscripts fl, fr, rl and rr denote quantities corre- When sufficient excitations exist in the lateral direc- sponding respectively to the front left, front right, rear tion, vehicle lateral dynamics can be used as the basis left and rear right wheels. In the vehicle model sign con- of the TRFC estimation. The most common tire fric- vention, the steering angle is negative for left turns and tion models used in the literature are those of algebraic positive for right turns. tire slip angle and force relationships. Although many approaches to the tire-road friction modeling can be found, for this work we selected three analytical mod- 2.1 Mathematical Formulation els. These models were chosen for their clear and simple formulation. They have fewer tunning parameters and Tire models express the relationship between tire forces have a good representation of the tire forces nonlinear- and moments with slip ratio and slip angle. ities.