METHOD AND SYSTEM FOR ESTIMATE A TIRE-ROAD FRICTION COEFFICIENT

Abstract

A method for estimating a tire-road friction coefficient comprises: determining a derivative of a slip ratio based on a wheel rotational speed and at least one acceleration signal; determining a standard deviation of the slip ratio derivative; calculating a circle with a radius based on the standard deviation of the slip ratio derivative; and mapping the radius of the circle to points of a given dataset to determine an estimate of the tire-road friction coefficient. The at least one acceleration signal may include a longitudinal acceleration of the vehicle. The slip ratio derivative may also be calculated based on a wheel angular velocity, a derivative of the wheel angular velocity, an effective tire radius, and the longitudinal acceleration.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This PCT international patent application claims priority to U.S. Provisional Patent Application Serial No. 63 / 334,712, filed April 26, 2022, entitled “Method And System For Tire-Road Friction Coefficient Estimation,” the entire disclosure of which is incorporated herein by reference. TECHNICAL FIELD

[0002] The present disclosure generally relates to predicting a tire-road friction coefficient by utilizing system statistical characteristics such as their means, variances, and distributions. BACKGROUND

[0003] Automotive control technologies play a significant role in the sustainable development of the automotive industry. Many researchers have long dedicated themselves to the field of advanced automotive control systems. Thus, several classic approaches for controlling engines, powertrains, and vehicles have been developed and implemented. With the gradual increase in machine learning and intelligent algorithms, along with the year-by-year improvement in microcontroller technologies, a data-driven methodology has the potential to replace or enhance the performance of existing control and estimation algorithms. From a vehicle perspective, vehicle dynamics has received considerable research attention since the appearance of the first car.Continuous progress has been made to improve vehicle handling performance with control applications such as anti-lock brake control, traction control, stability control, trajectory tracking, and so on. Today, autonomous vehicles have even higher demands regarding vehicle safety, stability, and control. It is worth noting that the control efforts (forces) applied to a vehicle play a crucial role in determining vehicle dynamics.

[0004] Drive torque is transferred from the power source to the wheels. The delivered torque depends on tire traction forces resulting from tire-road interactions, which is one of the most important aspects for modern ground vehicles such as internal combustion engine (IC)-powered vehicles, electric vehicles (EVs), and hybrid vehicles. Tire-road interaction forces are the only forces a vehicle receives from the ground and are therefore critical to vehicle maneuverability and chassis stability. The dominant forces acting on a vehicle are generated by tire-road interactions. It is intuitive that tire properties (such as tire material and texture, inflation pressure, and temperature) and road conditions (dry, wet, snowy, and icy) affect force generation.For a given vehicle with all available information, an accurate estimation of the road conditions interacting with the vehicle is essential for vehicle control to achieve optimized performance. At the same time, vehicle skidding can be prevented and its stability improved.

[0005] Many previous publications have described methods for estimating friction coefficients, particularly with applications to vehicle dynamics. Research in this area can be divided into two categories: cause-based and effect-based.

[0006] The cause-based approach generally uses special sensors to measure friction-related parameters and attempts to develop the correlation between these parameters and tire-road friction, which can be regarded as a supervised training process. These friction-related parameters mainly reflect the cause of friction, such as tire deformation, road light absorption capacity, road texture, and tire vibration, among others. This approach is also defined as the experimentally based method without the need for a dynamic model. It can provide an estimate of road conditions even when the vehicle is traveling at a constant speed, but often fails under exceptional circumstances not covered by the training datasets.Meanwhile, the required sensors, such as optical sensors, radar, or cameras, are generally expensive and are not installed in most production vehicles. Sensor reliability and robustness determine the accuracy of estimates.

[0007] The action-based approach generally focuses on effects or consequences due to tire-road friction, which is why excitation is often required to generate such effects. Typically, a simplified mathematical model is assumed; this is therefore also called a model-based approach. Studies related to this approach can be further divided into three groups: wheel and vehicle dynamics-based, tire model-based, and slip-gradient-based approaches. For the wheel and vehicle dynamics-based approach, vehicle motion is used to estimate the friction coefficient. Typically, a two-wheel model, a quarter-wheel model, and a four-wheel vehicle model are used.Some vehicle conditions can be directly detected by sensors, while some can only be estimated using different estimation algorithms, such as recursive least squares and extended Kalman filter. There are also several tire models, such as the magic formula, brush model, and Dugoff model. In these tire models, multiple parameters can be used to specify characteristics of a specific type of tire. Based on the measured / estimated tire force, the maximum tire-road friction coefficient can be derived, which is one of the parameters used in the tire model. The final slip-slope method is based on the hypothesis that the relationship between the friction coefficient and the slip ratio is linear at small slip. The approximate slope corresponds to different road conditions or maximum friction coefficients.However, if the slip is too small, the model may fail due to the undetected slope. All of these models require the vehicle speed to calculate the slip ratio. During the calibration or testing process, additional GPS or other sensors may be installed to accurately measure vehicle speed, but speed is often inferred from other sensors on production vehicles. The estimation error in vehicle speed is always present, resulting in a deviation of the calculated slip ratio and the estimated friction coefficient from their true values. The deviation can be even worse, especially under normal circumstances, where the actual difference between wheel speed and vehicle speed may be smaller than the speed estimation error or system noise.

[0008] Several different approaches for real-time estimation of the tire-road friction coefficient have been proposed in the literature. Cause-based approaches can be cost-sensitive due to the requirement of additional sensors, whereas the effect-based approach based on a dynamic model may be more attractive for use in an actual production vehicle. In model-based algorithms, researchers typically use measurements of vehicle motion to obtain the expected estimate. Two types of vehicle dynamics models are typically considered, including longitudinal and lateral vehicle dynamics. SUMMARY

[0009] The present disclosure provides a method for estimating a tire-road friction coefficient in a vehicle. The method includes: determining a derivative of a slip ratio based on a wheel speed and at least one acceleration signal; determining a standard deviation of the derivative of the slip ratio; calculating a circle with a radius based on the standard deviation of the derivative of the slip ratio; and mapping a radius of the circle to points of a given data set to determine an estimate of the tire-road friction coefficient.

[0010] The present disclosure also provides a system for estimating a tire-road friction coefficient in a vehicle. The system comprises a processor and memory including instructions. The instructions, when executed by the processor, cause the processor to: determine a derivative of a slip ratio based on a wheel speed and at least one acceleration signal; determine a standard deviation of the derivative of the slip ratio; calculate a circle having a radius based on the standard deviation of the derivative of the slip ratio; and determine a mapping between a radius of the circle and points of a given data set to determine an estimate of the tire-road friction coefficient. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Further details, features and advantages of embodiments of the invention will become apparent from the following description of embodiments with reference to the accompanying drawings. Fig. Figure 1 shows a graph comprising friction coefficient curves for various different surfaces; Fig. 2 shows a plan view of a schematic vehicle model comprising four tires; Fig. 3 shows a side view of a schematic model of a tire of a vehicle; Fig. 4 shows a block diagram of a sequential EKF algorithm for determining a friction coefficient and tire slip; Fig. 5 shows a speed estimation graph of vehicle speed as a function of time; Fig. 6 shows an acceleration estimation graph of longitudinal acceleration as a function of time; Fig. Figure 7 shows a graph of estimated longitudinal force as a function of time; Fig. Figure 8 shows a graph of longitudinal acceleration profiles for wet, dry and icy road conditions; Fig. Figure 9 shows a graph of friction coefficient as a function of slip for wet, dry and icy road conditions; Fig. Figure 10 shows a graph of friction coefficient as a function of slip with plots showing gradient approximations and tire models for wet, dry, and icy road conditions; Fig. Figure 11 shows values ​​of friction coefficients as a function of gradient for wet, dry and icy road conditions; Fig. 12 shows a graph of a derivative of the slip ratio as a function of the slip ratio with plots showing the derivative of the slip ratio with and without a slip term overlaid with a friction coefficient curve showing the friction coefficient as a function of the slip ratio; Fig. Figure 13 shows a graph of a derivative of the slip ratio as a function of the slip ratio with plots for roads with different friction coefficients; Fig. 14 shows a graph of a derivative of the slip ratio as a function of the derivative of the slip ratio with plots showing statistical circles of an evaluation index for roads with different friction coefficients; Fig. 15 shows a block diagram of a compensation system in accordance with an aspect of the present disclosure; and Fig. 16 shows a block diagram of a system for estimating a tire-road friction coefficient in a vehicle, in accordance with one aspect of the present disclosure. DETAILED DESCRIPTION

[0012] With reference to the drawings, the present invention will be described in detail with respect to the following embodiments. The present disclosure provides a method for estimating a slip ratio and a tire-road friction coefficient.

[0013] The present disclosure relates to predicting a tire-road friction coefficient by utilizing system statistical characteristics, such as their means, variances, and distributions, integrated with other algorithms. Leveraging these statistical features provides a new perspective for estimating a tire-road friction coefficient in terms of accuracy, efficiency, and feasibility. The statistical information behind the data can support existing classical methods to improve system performance. Accurate estimation of a tire-road friction coefficient can provide precise control for the tire to improve vehicle performance. Several cause-based and effect-based methods have been proposed, each with its own limitations.The data-driven method proposed in this application aims to utilize statistical information from data obtained from production vehicle sensors, allowing a computationally inexpensive black-box model to be approximated and integrated into the existing algorithm. A sequential EKF (extended Kalman filter) model, integrated with a gradient method, is selected as the baseline algorithm. A new evaluation index linked to the slip ratio is proposed. I. INTRODUCTION

[0014] The road condition is linked to the normalized traction force that a tire can provide, also called the traction coefficient, and is defined as a ratio between a longitudinal force and a normal force acting on the wheel when only the vehicle's longitudinal dynamics are considered. ρ=FxFz where Fx and Fz are the longitudinal and normal forces, respectively.

[0015] Advanced and accurate traction force control may require a maximum value of the normalized traction force and must be estimated in real time. This maximum value, or more accurately the tire-road friction coefficient (μ) of the force, is an index that represents the road surface characteristics, such as icy, snowy, wet, and dry. Accordingly, its value varies between zero and one for different road conditions. It is important to have a better understanding of the road friction coefficient so that both active and passive vehicle safety related to traction performance can be further improved. For example, a correct real-time estimation of the tire-road friction coefficient would enable the anti-lock braking system to initiate braking with the optimal brake pressure, which is an efficient way to stop the vehicle after a short distance.Additionally, it would be helpful to control the torque profile of the engine and / or motor to deliver the maximum available torque for best track performance. Profiles of the friction coefficient µ on different road surfaces as a function of tire slip ratio are shown in . Fig. 1 is recorded as an example. It should be noted that the longitudinal slip ratio λ is usually defined by the following equation (2). λ={1−Re⋅ωVx, if Vx ⩾ Re⋅ω,⋅Vx≠01−VxRe⋅ω, if Vx <Re⋅ω,ω≠0 where R e is the effective tire radius; ω is the wheel angular velocity; and V x is the vehicle's longitudinal speed.

[0016] Fig. Figure 1 shows a graph comprising friction coefficient curves 20, 22, 24 for dry, wet, and snowy roads, respectively. The relative heights of the peaks of curves 20, 22, 24 from Fig. 1 correspond to the roughness of the road surfaces, such as dry or wet roads; therefore, the peak value represents the road friction coefficient µ. The corresponding slip ratio is also called the optimal slip. For a specific road, Fig. 1, that there is a linear region at low values ​​of the slip ratio (stable region). Within this region, the friction coefficient is a monotonically increasing function of the slip ratio until it reaches its optimal value. In this linear low-slip region, a gradient rate K can be approximated using the equation ρ = Kλ to identify the road condition. This equation is defined based on the assumption of proportional relationships between the normalized friction coefficient and the slip ratio. However, if the slip ratio is too small (e.g., < 0.005) at very low excitation due to low acceleration or deceleration during normal driving, only a small difference can be detected. On the other hand, at a high slip ratio, it is relatively easy to determine the road condition due to the obvious deviation among individual curves.Beyond the optimal slip ratio, the normalized traction force gradually saturates and slowly decreases.

[0017] A longitudinal motion-based method can provide a more general approach to normal vehicle acceleration or deceleration. The vehicle model states can be obtained either through direct measurements or estimations using recursive least squares or developed observers. Once these states are obtained, the relationship between the actual friction coefficient and the slip ratio can be found. Based on this relationship, an algorithm based on a conventional model can be used to provide the maximum available friction coefficient.To obtain the actual friction coefficient, both the longitudinal force and the vertical force should first be calculated; and the slip ratio can be calculated using equation (2) based on the estimated (or measured) vehicle speed, the measured wheel speed, and the effective tire radius. The present disclosure provides an extended Kalman filter (EKF) based on a vehicle dynamics model and can be used as a model-based algorithm. This model can be verified using one or more simulations; however, it has certain problems with real test data. A new evaluation criterion based on data mining and kriging is provided to compensate for the problems with this conventional algorithm.

[0018] The remainder of the present disclosure is organized as follows: Section II provides a brief introduction to the vehicle and wheel dynamics model used in the following sequential EKF or S-EKF structure. The S-EKF structure is validated using simulations and test data from different road conditions. Then, in Section III, a detailed deduction process for the proposed new evaluation criterion is described. The potential of this criterion is also demonstrated using simulation data. II. DYNAMIC MODEL AND EXTENDED KALMAN FILTER

[0019] This section describes a used mathematical vehicle model and the structure of sequential EKF models for state estimation. A. Vehicle and wheel model

[0020] A four-wheel vehicle dynamics model is in Fig. 2, and a free body schematic diagram of a tire is shown in Fig. 3. The longitudinal x and lateral y directions are defined using a right-handed orthogonal axis system. Note that neither pitch nor roll motions are considered. The corresponding dynamic equations defining the longitudinal, lateral, and yaw motions are as follows in equations (3) to (5): M(v˙x−vyφ˙)Fxflcosδl−Fyflsinδl+Fxfrcosδr−Fyfrsinδr+Fxrl+Fxrr−Fxa M(v˙y+vxφ˙)=Fyflcosδl+Fxflsinδl+Fyfrcosδr+Fxfrsinδr+Fyrl+Fyrr Lzφ¨=Fyflcosδllf+Fxflsinδllf+Fyfrcosδrlf+Fxfrsin −Fyrrlr−Fyrllr−12Fxflcosδlbf+12Fyflsinδlbf +12Fxfrcosδrbf−12Fyfrsinδrbf−12Fxrlbr+12F where M is the vehicle mass; v x and v y are the vehicle's longitudinal and lateral velocities; φ is the yaw angle; δ is the steering angle; Fxa is the air resistance force; and Fxij and Fyij represent the longitudinal and lateral forces of each wheel, where i stands for the front and rear axles and j stands for the left and right wheels.

[0021] The tire behavior is described in equation (6) below: lr⋅w˙=Tt−Tb−Mr−Fx⋅R where I r is the moment of inertia of the wheel; w is the wheel speed; T t and T b the traction or braking torque; M r is the rolling resistance related to tire pressure and wheel speed; and R is the tire radius. B. Structure of sequential extended Kalman filters

[0022] During the experiment, vehicle speed can be obtained with a certain level of accuracy using an accelerometer, GPS, or sensor fusion. However, direct integration of the acceleration signal results in signal drift due to sensor bias, and high-accuracy GPS is not available for production vehicles. The wheel speed sensor can be used to calculate vehicle speed, but this is not useful because both wheel speed and vehicle speed are required in equation (2), and they cannot both come from the same source. Furthermore, tire forces are not available for all production vehicles. This is needed to accurately estimate these unknown conditions.

[0023] A Kalman filter is an algorithm that estimates the system state from measured data. It was developed by the engineer Rudolf Kalman in 1960. The Kalman filter uses a two-stage process. The first stage predicts the system states, and the second stage uses noisy measurements to correct the estimated system states. A sequential extended Kalman filter (EKF) can be used for state estimation using the equations of the vehicle and tire dynamics model. Fig. 4 shows a block diagram comprising the signal flow of a sequential EKF algorithm 50 for determining a friction coefficient uxij and a tire slip λ.

[0024] The sequential EKF algorithm 50, which is used in Fig. 4, comprises a first Kalman filter 52 designed to determine a vehicle speed v x , v y, a predicted rotation speed φ̇ e and a predicted acceleration axe,aye.

[0025] In the first Kalman filter 52, the following dynamic equations can be used: vx(t)=vx(t−1)+Δt⋅(ax(t−1)+vy(t−1)⋅φ˙(t−1))vy(t)=vy(t−1)+Δt⋅(a y(t−1)−vx(t−1)⋅φ˙(t−1))φ˙(t)=φ˙(t−1)ax(t)=ax(t−1)ay(t)=ay(t−1)

[0026] The system state vector can be written as xs = [v x , v y , a x , a y , φ̇] T and the system input vector as u = [a x , a y , φ̇] T . System outputs are all conditions under which the longitudinal and lateral velocities are estimated and the acceleration signals and yaw rates are filtered as part of the inputs to the second EKF. The sequential EKF algorithm 50, which is described in Fig. 4, also includes a second Kalman filter 54 designed to determine the force vectors Fxij,Fyij. In the second Kalman filter 54, a random walk model is used for each discrete period, Fxij(t)=Fxij(t−1), used for the force dynamics, assuming that the first derivative is zero. The second Kalman filter 54 accepts an output from the first EKF block 52 along with the wheel speed ω i and the steering angle δ. The force vector of all wheels [Fxfr,Fxfl,Fyl,Fxrr,Fxrl,Fyr]T is defined as states and system outputs. The sequential EKF algorithm 50, which is Fig. 4, also includes an output calculator 56 designed to calculate the friction coefficient uxij and tire slip λ based on wheel speed ω i , the vehicle speed v x , v yfrom the first Kalman filter 52 and the force vectors Fxij,Fyij from the second Kalman filter 54.

[0027] The sequential EKF structure is developed based on the vehicle and wheel dynamics. A simulation is used to verify the developed vehicle and wheel dynamics. The road condition can be defined in the simulation software, and an acceleration event along a straight line is simulated. Fig. 5 shows a speed estimation graph of vehicle speed as a function of time, comprising a first plot 60 of test data from the simulation and a second plot 62 of estimated values ​​of speed as a function of time. Fig. 6 shows an acceleration estimation graph of longitudinal acceleration as a function of time, comprising a first plot 64 of test data from the simulation and a second plot 66 of estimated values ​​of longitudinal acceleration as a function of time. Fig. Figure 7 shows a graph of estimated longitudinal force as a function of time, comprising a first plot 68 of test data from the simulation and a second plot 70 of estimated values ​​of the longitudinal force as a function of time.

[0028] As in Fig. As shown in Figures 5-7, the vehicle speed, longitudinal acceleration, and forces are well estimated. Accordingly, the relationship between the friction coefficient and the calculated slip ratio can be plotted, with the peak value being the estimated friction coefficient. Two observations from the simulation results are highlighted below: 1) The simulation environment assumes an ideal situation without any noise. White measurement noise can be added to the measurements, but in practice, no fixed noise pattern exists. Further verification using test data with system and measurement noise would be beneficial; and 2) Vehicle simulation is capable of generating enough data to calculate the slip ratio, even when the vehicle is operating in an unstable region. Therefore, a nice non-linear friction curve can be obtained. For actual applications, the vehicle is likely to have very low slip and remain within the stable region. Therefore, a gradient method is a practical approach for the real test data. Based on these considerations, three sets of acceleration test data under different road conditions are selected to verify the sequential EKF algorithm. The acceleration profile of each test data set is shown in Fig. 8, which includes three plots 72, 74, 76 of longitudinal acceleration as a function of time and for different conditions. Fig. 8 includes a first plot 72 showing longitudinal acceleration for wet conditions, a second plot 74 showing longitudinal acceleration for dry conditions, and a third plot 76 showing longitudinal acceleration for icy conditions.

[0029] It should be noted that a linear slope is approximated according to the estimates. Using the sequential EKF algorithm, these states of interest can be estimated. A pre-calibrated tire model is used to construct a projection mapping between the slope and the friction coefficient, as shown in Fig. 9-10 shown. Fig. Figure 9 shows a graph of a friction coefficient as a function of slip for different conditions; Fig. 9 includes a first plot 78 showing a friction coefficient fit curve for wet road conditions, a second plot 80 showing a friction coefficient fit curve for dry road conditions, and a third plot 82 showing a friction coefficient fit curve for icy road conditions. Fig. Figure 10 shows a graph of a friction coefficient as a function of slip with plots showing gradient approximations and tire models for different road conditions; Fig. 10 includes a first plot 84 showing a friction coefficient fit curve for wet road conditions, a second plot 86 showing a friction coefficient fit curve for dry road conditions, and a third plot 88 showing a friction coefficient fit curve for icy road conditions. Fig. Figure 10 also shows plots 90, 91, 92, 93, 94, 95 of the friction coefficient as a function of time and for different values ​​of µ. Plot 90 shows the friction coefficient as a function of slip for µ = 0.1; plot 91 shows the friction coefficient as a function of slip for µ = 0.25; plot 92 shows the friction coefficient as a function of slip for µ = 0.45; plot 93 shows the friction coefficient as a function of slip for µ = 0.65; plot 94 shows the friction coefficient as a function of slip for µ = 0.85; and plot 95 shows the friction coefficient as a function of slip for µ = 1.0.

[0030] Fig. Figure 11 shows a plot showing estimated values ​​of the friction coefficient as a function of slope and for different conditions. Fig. 11 includes a first point 96 showing the estimated value of the friction coefficient for wet conditions, a second point 97 showing the estimated value of the friction coefficient for dry conditions, and a third point 98 showing the estimated value of the friction coefficient for icy conditions.

[0031] In the Fig. 8-11 shows that the slip ratio becomes negative even under acceleration. Small errors can mislead the slip ratio calculations. These errors can arise mainly from two sources: a) there is no directly measured vehicle speed, and its estimation errors are an inherent property; and b) the EKF model cannot guarantee estimation accuracy with a unique set of parameters for all road conditions, and tuning the estimation model to fit all road conditions can be difficult. Another disadvantage is that the selection range of data points affects the gradient approximation, which affects the final estimated friction coefficient. III. NEW EVALUATION CRITERION AND PROPOSED PROCEDURE

[0032] Both the EKF algorithm and the vehicle model are technically very mature and offer little room for improvement. Based on all these observations, a new evaluation criterion, combined with the friction coefficient, is proposed to compensate for the existing algorithms. A. New evaluation criterion and its validation using CarSim data

[0033] It is logical to consider modifying the slip ratio, as the slip ratio is directly related to the vehicle's driving on different roads. Referring again to equation (2) for the slip ratio, it is assumed that the radius for a specific tire is constant, and the wheel speed can be accurately measured from the sensors installed for the ABS system; only the vehicle speed needs to be accurately estimated. If this estimation can be avoided, the entire calculation process would be simplified. The derivation of the slip ratio is shown in the following equation (8): λ'=Re2ω'Vx−ReωVx'(Reω)2=Re2ω'ω(1−λ)−ReωVx'(Reω)2

[0034] In equation (8), all variables can be obtained from the installed sensors (wheel speed and vehicle acceleration), except for the slip ratio λ itself. If this term can be ignored, calculations can be completed using only available sensors. Since we already know this, in practical application scenarios, the vehicle is always controlled in the stable region with a small slip ratio, which indicates that λ can be neglected in the numerator. The derivative of the slip ratio is simplified into the following format after ignoring the λ term: λ'=Re2ω'ω−ReωVx'(Reω)2

[0035] The difference between before and after neglecting the λ term is recorded using the simulation data as shown in Fig. 12, which includes: a first plot 100 showing the friction coefficient as a function of the slip ratio λ, a second plot 102 showing the derivative of the slip ratio λ' as a function of the slip ratio λ, as calculated without using the slip term (e.g., using equation (9)), and a third plot 104 showing the derivative of the slip ratio λ' as a function of the slip ratio λ, as calculated using the slip term (e.g., using equation (8)). When the slip ratio λ is small, the second and third plots 102, 104 are almost the same, with a slight difference, which validates the assumptions for equation (9). The deviation becomes more obvious when the slip ratio λ is large. Another observation of the derivation of the slip ratio is that there is an inflection point, similar to the relationship between friction coefficient and slip ratio.After neglecting the λ term, the absolute amplitude definitely deviates from the true value, but the overall trend does not change significantly. This encourages the use of the derivative of the slip ratio as a new criterion and the development of a new methodology to reveal the relationship between the new criterion and the friction coefficient.

[0036] Fig. Figure 13 shows a graph comprising plots 110, 112, 114 showing simulation results of the derivative of the slip ratio as a function of the slip ratio and for roads with different friction coefficients. Fig. 13 includes a first plot 110 showing the derivative of the slip ratio for a road friction coefficient of 0.25, a second plot 112 showing the derivative of the slip ratio for a road friction coefficient of 0.50, and a third plot 114 showing the derivative of the slip ratio for a road friction coefficient of 0.85.

[0037] Statistical districts are in Fig. 14, where progressively larger circles correspond to smaller values ​​of the road friction coefficient µ, and where the center of each circle is the mean value of the new criterion and the radius is three times its standard deviation. Fig. Figure 14 includes a first plot 120 for µ = 0.15, a second plot 122 for µ = 0.25, a third plot 124 for µ = 0.50, a fourth plot 126 for µ = 0.75, a fifth plot 128 for µ = 0.85, and a sixth plot 130 for µ = 1.0. Each of the respective circles shown in plots 120, 122, 124, 126, and 128 delegates the statistical information for deriving the slip ratio under different road conditions. The size of each circle corresponds to a road surface condition. This phenomenon can be explained using the relationship between the longitudinal force F and the slip ratio λ. For a small tire slip ratio, the longitudinal force F can be approximated by the following equation (10): F=Cλ where C is the longitudinal stiffness of the tire. Assume that a tire running on a road with a low coefficient of friction has relatively low stiffness. Therefore, applying the same longitudinal force to the tire running on a low-friction road will produce a high slip ratio, which corresponds to a large slip ratio change. The rate of change of the slip ratio is the magnitude of the derivative of the slip ratio. This explains why there are more oscillations (or a larger magnitude) of the derivative of the slip ratio for the data obtained for a low-friction road surface. B. Proposed structure

[0038] The phenomenon observed based on simulation data provides useful information about using a simplified evaluation criterion using only off-the-shelf sensors to estimate the tire-road friction coefficient. Fig. Figure 15 shows a block diagram of a compensation system 200 in accordance with one aspect of the present disclosure. In the top row, a slope-based friction coefficient calculator 202 is used using the sequential EKF and the slope method to calculate an EKF-estimated friction coefficient mu EKF (or µ EKF). The slope method-based friction coefficient calculator 202 also includes determining a first confidence coefficient w1 based on a range of the slip ratio. In the lower row, a proposed method 204 is provided for calculating a friction coefficient mu estimated based on the derivative of the slip ratio. ds (or µ ds ). The proposed method 204 may also be called the slip ratio derivation (DS) method.

[0039] The slope method-based friction coefficient calculator 202 includes a sequential EKF 210 designed to determine a speed v and a longitudinal force F xbased on one or more acceleration signals, wheel speed, and engine torque. The gradient-based friction coefficient calculator 202 also includes a gradient calculator 212 configured to determine a gradient of µ as a function of slip based on the speed v, the longitudinal force F x and based on a normal force F z . The slope method-based friction coefficient calculator 202 also includes a first friction coefficient calculator 214 configured to determine the EKF-estimated friction coefficient µ EKF by mapping the slope data from the slope calculator 212 to a given data set 215. The slope method-based friction coefficient calculator 202 also includes a first confidence estimator 216 configured to determine the first confidence coefficient w1 based on a range of slip ratios.

[0040] The compensation system 200 includes one or more on-board sensors 230, such as cameras or other sensors located within an ego vehicle that can detect the road surface or other objects. The on-board sensors 230 may, for example, include cameras that detect light in the visible spectrum and / or non-visible light, such as infrared, radar, and / or lidar sensors.

[0041] The compensation system 200 includes a weighting function 206 which determines a final friction coefficient µ F as a weighted average of the EKF-estimated friction coefficient µ EKF from the friction coefficient calculator 202 based on a gradient method, the friction coefficient µ estimated based on the derivative of the slip ratio dsfrom the proposed method 204, and / or data from the one or more on-board sensors 230. In some embodiments, the weighting function 206 may determine a final confidence value w F which provides a confidence for the final friction coefficient µ F In some embodiments, the weighting function 206 may determine the final friction coefficient µ F based on the EKF-estimated friction coefficient µ EKF from the friction coefficient calculator 202 based on a gradient method, the friction coefficient µ estimated based on the derivative of the slip ratio dsfrom the proposed method 204, and / or on data from the one or more on-board sensors 230 and proportional to relative values ​​of the corresponding confidence coefficients w1, w2. In some embodiments, the weighting function 206 may employ a rule-based approach, also called fuzzy logic, to determine the final friction coefficient µ F and / or the final confidence value w F to determine.

[0042] The proposed method 204 includes a slip ratio derivative calculator 220 configured to calculate the derivative of the slip ratio λ' based on a wheel speed and based on one or more vehicle acceleration signals. The slip ratio derivative calculator 220 may use equation (9) to determine the derivative of the slip ratio λ'. The proposed method 204 also includes a circle calculator 222 configured to calculate a mean and a standard deviation σ of the derivative of the slip ratio λ' and to form circles with a radius = 3 σ. The proposed method 204 also includes a second friction coefficient calculator 224 configured to determine the friction coefficient estimate mu ds (or µ ds ) by mapping a radius of the circle to points of a given data set 215.

[0043] The proposed method 204 also includes a second confidence estimator 226 configured to compare an acceleration value, such as a value of the longitudinal acceleration and Vx' with a predetermined acceleration threshold, to determine the second confidence coefficient w2 based on the comparison between the acceleration value and the predetermined acceleration threshold. For example, the second confidence estimator 226 may set the second confidence coefficient w2 equal to zero unless the acceleration value exceeds the predetermined acceleration threshold, and then set the second confidence coefficient w2 to a non-zero value. The second confidence estimator 226 may therefore selectively use the friction coefficient estimate mu ds (or µ ds ) when determining the final friction coefficient µ F activate based on the acceleration value.

[0044] In some embodiments, the proposed method 204 may use a Kriging model to determine a relationship between the derivative of the slip ratio λ' and the friction coefficient mu ds to represent.

[0045] Fig.16 shows a block diagram of a system 300 for estimating a tire-road friction coefficient in a vehicle, in accordance with one aspect of the present disclosure. The system 300 includes a wheel speed sensor 302, an acceleration sensor 304, and a controller 310 operatively coupled to each of the sensors 302, 304. The controller 310 may be programmed or otherwise configured to perform one or more functions and / or method steps of the present disclosure, including one or more steps of the compensation system 200. In some embodiments, the controller 310 is programmed or otherwise configured to implement one or more of the gradient-based friction coefficient calculator 202, the proposed method 204, and / or the weighting function 206.

[0046] The controller 310 may control one or more functions and / or components within the vehicle. Additionally or alternatively, the controller 310 may be configured to communicate one or more signals, such as signals based on the final friction coefficient µ F and / or the final confidence value w F , to one or more controllers, such as a powertrain control module (PCM), a traction control module, a steering controller, and / or a braking controller.

[0047] One or more controls may be designed to adjust based on the final friction coefficient µ F and / or the final confidence value w F, of one or more operating characteristics, such as functions and / or parameters that affect the function of the vehicle. Examples of such operating characteristics may include signals for controlling steering, braking, and / or generating and controlling drive torque to propel the vehicle. For example, the drive torque, braking force, and / or steering forces may be limited to a value that can be effectively transferred by the tires to the road surface.

[0048] The controller 310 includes a processor 312 coupled to a storage memory 314. The storage memory 314 includes an instruction memory 316 that stores instructions, such as program code, for execution by the processor 312. The storage memory 314 also includes a data memory 316 for holding data for use by the processor 312. The data memory 316 may, for example, record the result of functions calculated by the processor 312 and / or values ​​of parameters measured by one or more sensors, such as the wheel speed sensor 302, an acceleration sensor 304.

[0049] The system, methods, and / or processes described above, as well as steps thereof, may be implemented in hardware, software, or any combination of hardware and software suitable for a particular application. The hardware may include a general-purpose computer and / or a dedicated computing device or specific computing device, or a particular aspect or component of a specific computing device. The processes may be implemented in one or more microprocessors, microcontrollers, embedded microcontrollers, programmable digital signal processors, or other programmable devices, together with internal and / or external memory.The processes may also, or alternatively, be implemented in an application-specific integrated circuit, a programmable gate array, programmable array logic, or any other device or combination of devices configured to process electronic signals. It is further understood that one or more of the processes may be implemented as computer-executable code executable on a machine-readable medium.

[0050] The computer-executable code may be generated using a structured programming language such as C, an object-oriented programming language such as C++, or any other high-level or low-level programming language (including assembly languages, hardware description languages, and database programming languages ​​and technologies) that can be stored, compiled, or interpreted to run on any of the above devices, as well as heterogeneous combinations of processors, processor architectures, or combinations of different hardware and software, or any other machine capable of executing program instructions.

[0051] Thus, in one aspect, each of the above-described methods and combinations thereof may be embodied in computer-executable code that, when executed on one or more computing devices, performs the steps thereof. In another aspect, the methods may be embodied in systems that perform the steps thereof and may be distributed across devices in a number of ways, or all functionality may be integrated into a dedicated, stand-alone device or other hardware. In another aspect, the means for performing the steps associated with the above-described processes may include any of the above-described hardware and / or software. All such permutations and combinations are intended to be within the scope of the present disclosure.As used herein, "a," "an," and "the" refer to both singular and plural references unless the context clearly indicates otherwise. For example, a "processor" programmed to perform various functions refers to one processor programmed to perform each function individually, or to more than one processor collectively programmed to perform the various functions.

[0052] The foregoing description is not intended to be exhaustive or limiting of the disclosure. Individual elements or features of a particular embodiment are generally not limited to that particular embodiment, but are interchangeable and may be used in a selected embodiment, even if not specifically shown or described. The same may also be varied in various ways. Such variations are not to be regarded as a departure from the disclosure, and all such modifications are intended to be included within the scope of the disclosure. QUOTES CONTAINED IN THE DESCRIPTION

[0000] This list of documents submitted by the applicant was generated automatically and is included solely for the convenience of the reader. This list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions. Cited patent literature

[0000] US 63 / 334,712

[0001]

Claims

[1] A method for estimating a tire-road friction coefficient in a vehicle, comprising: Determining a derivative of a slip ratio based on a wheel speed and at least one acceleration signal; Determining a standard deviation of the derivative of the slip ratio; calculating a circle with a radius based on the standard deviation of the derivative of the slip ratio; and Mapping the radius of the circle to points of a given data set to determine an estimate of the tire-road friction coefficient. [2] The method of claim 1, further comprising: adjusting, based on the estimate of the tire-road friction coefficient, an operating characteristic of at least one of a steering function, a braking function, and a drive torque generation function. [3] The method of claim 1, wherein the radius of the circle is equal to three times the standard deviation of the derivative of the slip ratio. [4] The method of claim 1, wherein the at least one acceleration signal comprises a longitudinal acceleration of the vehicle. [5] The method of claim 4, wherein determining the derivative of the slip ratio based on the wheel speed and at least one acceleration signal comprises calculating the derivative of the slip ratio λ' as: λ'=Re2ω'ω−ReωVx'(Reω)2 where ω is a wheel angular velocity, ω' is a derivative of the wheel angular velocity, R e is an effective tire radius and Vx' is the longitudinal acceleration. [6] The method of claim 1, wherein a kriging model is used to represent a relationship between the derivative of the slip ratio and the estimate of the tire-road friction coefficient. [7] The method of claim 1, further comprising: Determining an EKF-estimated friction coefficient using a sequential EKF and a slope method for determining; and Determine a final friction coefficient based on the tire-road friction coefficient estimate and the EKF-estimated friction coefficient. [8] The method of claim 7, wherein determining the final friction coefficient comprises calculating a weighted average of the tire-road friction coefficient estimate and the EKF-estimated friction coefficient. [9] The method of claim 8, wherein calculating the weighted average is based on a ratio of a first confidence coefficient and a second confidence coefficient. [10] The method of claim 9, further comprising determining the first confidence coefficient based on a range of a slip ratio. [11] The method of claim 9, further comprising determining the second confidence coefficient based on comparing the at least one acceleration signal with an acceleration threshold. [12] A system for estimating a tire-road friction coefficient in a vehicle, comprising: a processor and a memory comprising instructions that, when executed by the processor, cause the processor to: Determining a derivative of a slip ratio based on a wheel speed and at least one acceleration signal; Determining a standard deviation of the derivative of the slip ratio; Calculating a circle with a radius based on the standard deviation of the derivative of the slip ratio; and Determining a mapping between the radius of the circle and points of a given data set to determine an estimate of the tire-road friction coefficient. [13] The system of claim 12, wherein the instructions further cause the processor to adjust, based on the estimate of the tire-road friction coefficient, an operating characteristic of at least one of a steering function, a braking function, and a drive torque generation function. [14] The system of claim 12, wherein the radius of the circle is equal to three times the standard deviation of the derivative of the slip ratio. [15] The system of claim 12, wherein the at least one acceleration signal comprises a longitudinal acceleration of the vehicle.

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