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Accuracy requirements for the road friction coefficient estimation of a friction-adaptive automatic emergency steer assist (ESA)

Accuracy requirements for the road friction coefficient estimation of a friction-adaptive... The number of traffic accidents resulting in personal injury and property damage is increasingly being reduced by effective advanced driver assistance systems (ADAS). Nevertheless, many traffic accidents still cannot be prevented today because they are due to wet, snow- and ice-covered roads. For this reason, the Institute of Automotive Engineering (IAE) of the Techni- cal University of Braunschweig is investigating the road friction coefficient sensitivity and adaptation of advanced driver assistance systems (ADAS) currently in series production from 2018 to 2021 as part of the ‘Road Condition Cloud’ research project funded by the German Research Foundation (DFG) to increase driving safety, particularly on wet, snow- and ice- covered roads. In this article, the road friction coefficient sensitivity and adaptation of an automatic emergency steer assist is simulatively investigated. This assist overrides the driver to automatically execute an evasive maneuver. The driving maneuver used is a standardized obstacle-avoidance maneuver that is simulatively repeated on a dry, wet, snow- and ice-covered road. The road friction coefficient sensitivity shows that this test is already failed on a wet road because the simulated vehicle does not pass the second lane without errors. Subsequently, a road friction coefficient adaptation of the emergency steer assist is investigated. This adaptation varies the maximum lateral acceleration of the evasive trajectory depending on an estimated value of the road friction coefficient in order not to exceed the maximum adhesion coefficient of the wheels during the evasive maneuver. Ideally, the estimated value matches the true road friction coefficient so that the second lane is passed without errors even on a wet, snow- and ice-covered road. In contrast, an existing difference determines whether the second lane is reached. Finally, the necessary accuracy requirements of the road friction coefficient estimation are determined in an novel estimation error diagram. A road friction coefficient adaptation increases the driving safety of driver advanced assistance systems (ADAS) that are in series production today and future highly automated driving functions (HAF) and is necessary for automated driving because the driver is not present as a fallback level. The described results were presented before in [1]. Keywords Road friction coefficient · Road friction coefficient sensitivity · Road friction coefficient adaption · Automatic emergency steer assist · Friction-adaptive advanced driver assistance systems (ADAS) 1 Introduction The number of traffic accidents resulting in personal injury and property damage is increasingly being reduced by effec- tive advanced driver assistance systems (ADAS). Neverthe- less, many traffic accidents still cannot be prevented today * Tim Ahrenhold because they are due to wet, snow- and ice-covered roads t.ahrenhold@tu-bs.de [2]. For this reason, the road friction coefficient in particular Jannes Iatropoulos determines driving safety in road traffic. j.iatropoulos@tu-bs.de For legal reasons, automatic emergency brake assists Roman Henze (AEB) currently in series production only become active r.henze@tu-bs.de when it is no longer possible to take evasive action and the Institute of Automotive Engineering (IAE), Technical remaining relative distance falls below the last point to steer University Braunschweig, Hans-Sommer-Straße 4, distance. Because the collision-avoiding braking distance Braunschweig 38106, Niedersachsen, Germany Vol.:(0123456789) 1 3 Automotive and Engine Technology exceeds the last point to steer distance at high driving involving a sudden lane change are examined and it is speeds, automatic emergency brake assists cannot always described that many drivers often recognize an impending avoid a collision, but only at low driving speeds. collision too late. In [35] it is explained that the average In contrast, emergency steer assists (ESA) in series pro- driver often notices other road users too late to avoid a duction today become active when rapid steering by the collision. driver is detected at low relative distances. These assists Already in [36] it is recognized in the context of driving superimpose an additional torque on the driver’s steering tests with a suddenly appearing obstacle that only experi- wheel torque, which supports the driver in taking evasive enced drivers stabilize the vehicle during an evasive maneu- action [3, pp. 755-758]. As a result, a possible collision can ver. Inexperienced drivers are often unable to do so, control- always be avoided if the driver begins to steer before the last ling the vehicle response that occurs during evasive action. point to steer distance is reached. In [37], a user study recognizes that the average driver often Currently in series production, the last point to brake and reacts too late to avoid an impending collision by taking steer distance is calculated by the constant road friction coef- evasive action. The results of this study indicate that only c fi ient of a dry road, so that collisions on wet, snow- and ice- an automatic emergency steer assist that overrides the driver covered roads are not prevented. For this reason, a friction- can avoid an impending collision, especially on wet, snow- adaptive emergency steer assist (ESA) that automatically and ice-covered roads. execute an evasive maneuver has high potential to increase In [11, 14, 28, 38, 39], driving simulator studies are driving safety even on wet, snow- and ice-covered roads. described that superimpose an additional torque on the This friction-adaptive assist can be implemented through driver’s steering wheel torque during evasive action when technical advances in the development of sensors for reliable rapid driver steering is detected. The driving simulator study clearance detection, since all other sensors and actuators are in [38] illustrates that an emergency steering assist improves already available in series production [3, pp. 553–577] [4, driver behavior when a collision is imminent. The study pp. 1021–1040] [5]. in [39] examines the vehicle dynamics during an evasive For example, active lane keeping assist (LKA) systems in maneuver and highlights that driving stability is increased series production today use one or more cameras to reliably because the emergency steering assist reduces the overshoot determine the vehicle position within the lane. This position of the yaw rate. In [28], over 70 % of users favorite an auto- determines the additional torque that is superimposed on the matic emergency steering assist that overrides the driver in driver’s steering wheel torque [6–8]. emergency situations. The study in [14] illustrates that an Today, a difference is made between two groups of emer - emergency steering assist reduces the number of collisions gency steer assists. The assists of the first group superim- and decreases the humans reaction time by at least 100 ms. pose an additional torque on the driver’s steering wheel In [11], two studies with a sudden lane change are torque, which assists the driver in taking evasive action. described. In the first study, the driver’s steering wheel These assists are described in [9–15] and use as actuator, for torque is superimposed by an additional torque. To increase example, the electric motor of an electromechanical steering driving stability, the steering wheel angle is superimposed system (EPS). Because the assists in this group cooperate in the second study by an additional angle. The first study with the driver, driver models are required that represent emphasizes that an additional torque is not always sufficient human driving behavior, especially in emergency situations to prevent the vehicle from leaving the lane during a sudden such as an evasive maneuver. These models are described, lane change. In contrast, the second lane are almost always for example, in [16–20]. Further, in [21–25] different evasive traversed without error when the driver is supported by an trajectories are compared with the human driving behavior. additional angle in the second study. The assists of the second group superimpose an addi- In [40], an emergency steer assist investigated in real traf- tional angle on the steering wheel angle of the driver, which fic is described. This is activated during lane changes with cannot be overridden by the driver. These assistants are a high probability of leading to a critical driving situation studied in [26–31], among others, and use, for example, a to stabilize the driving situation or prevent a collision. This superposition transmission as actuator. Because the assists assist is able to override the driver. in this group do not interact with the driver, driver models More advanced approaches in [41–43] investigate the are not required. combination of an emergency brake assist with an emer- Critical driving situations occur when the driver fails gency steer assist that is in series production today. The to steer appropriately in an emergency situation such as an trade-off between braking and evasion is described in [9 ] evasive maneuver or a sudden lane change. In [32], traffic as a function of relative speed and road friction coefficient. accidents are studied and recognized that over 70 % of In [27, 31, 44] approaches are described that determine the deadly collisions occur on the shoulder or median strip last point to steer distance as a function of the road friction when the driver leaves his lane. In [33, 34], accidents coefficient in order not to exceed the maximum adhesion 1 3 Automotive and Engine Technology Table 1 Representative road friction coefficients Road condition class Dry Wet Snow Ice Road friction coefficient 1.0 0.6 0.3 0.15 Fig. 1 Methods Fig. 3 Input and output parameters of the used trajectory calculation 3 Function The trajectory used by the emergency steer assist is calcu- lated by an optimizer. This optimizer minimizes the evasive trajectory length x depending on two input parameters. These two input parameter are the lateral offset y to be achieved and the predefined maximum lateral acceleration a of the evasive trajectory (Fig. 3). y,max The y-coordinate y(x) of the evasion trajectory are calcu- Fig. 2 Value ranges of the road condition classes lated by a seventh degree polynomial, the lateral offset y to be achieved, and the trajectory length x . 7 6 coefficient of the wheels, especially on wet, snow- and ice- x x y(x) = y − 20 + 70 covered roads. x x e e (1) 5 4 In [42], a steer assist is described that additionally brakes x x − 84 + 35 individual wheels as desired in order not to exceed the maxi- x x e e mum adhesion coefficient of the inside and outside wheels of the curve. This additionally increases the yaw rate and The curvature (s) of the evasive trajectory is determined by shortens the length of the calculated evasive trajectories. the first and second derivatives of the coordinates x and y(x) In this paper, the road friction coefficient sensitivity and with respect to the arc length s. adaption of an automatic emergency steer assist is simula- ẋ (s)y ̈(s) − x ̈(s)ẏ (s) tively investigated using a validated dual track model. This 𝜅 (s) = (2) 3∕2 2 2 assist overrides the driver to automatically execute an eva- ẋ (s) + ẏ (s) sive maneuver along a calculated evasive trajectories. The For this, the differential quotient ds of the arc length s is driving maneuver used is the obstacle-avoidance maneuver standardized in ISO 3888-2, which is transferred to the sim- calculated by the differential quotients dx and dy of the coor - dinates x and y(x). ulation and repeated on a dry, wet, snow- and ice-covered roadway [45]. √ 2 2 ds = (dx) +(dy) (3) The yaw angle  (s) of the evasive trajectory is calculated by integrating the curvature (s) . This is used for the yaw 2 Method angle control of the emergency steer assist and described in Sect. 5. The method used takes into account the true road friction coefficient  and an estimated value  of the true road R E (s) = (s) ds (4) friction coefficient (Fig.  1). In this article, the road friction coefficient sensitivity and adaptation for the four classes of a dry, wet, snow-covered The yaw rate (s) of the evasive trajectory is calculated by and ice-covered road are investigated (Fig. 2) and representa- the curvature (s) and initial driving speed v and a side slip tive road friction coefficients are assigned to them (Table  1). angle  is neglected. 1 3 ̇𝜓 Automotive and Engine Technology (s) = 𝜅 (s) ⋅ v (5) The lateral acceleration a (s) of the used evasive trajectory is calculated like the yaw rate (s) by the curvature (s) and initial vehicle speed v . a (s) = (s) ⋅ v (6) y,max The maximum curvature  of the evasive trajectory is max determined by the maximum lateral acceleration a and y,max is not exceeded by this optimizer. −2 = a ⋅ v (7) max y,max Fig. 4 Obstacle avoidance track in the simulation The maximum lateral acceleration a of the evasive tra- y,max jectory is calculated in series production today by the accel- The evasive trajectory from Fig. 4 is calculated by Eq. 1 eration of gravity g and in particular the constant road fric- tion coefficient  of a dry road. The factor k describes the to Eq. 8 from Sect. 3 and the representative road friction coefficient  of the dry road (Table 1) from Sect. 2 (Fig. 5a). ellipse of kamm’s circle and takes values between 1.0 and 0.8 for current summer and winter tires [3, pp. 899–904]. Figure 5b shows the lateral acceleration a (x) of the eva- sive trajectory calculated by Eq. 7. This is limited by Eq. 8 a =  ⋅ g ⋅ k y,max R (8) and an assumed factor k of 0.9 [47]. Figure 6a shows the yaw angle  (x) of the evasive trajec- tory calculated by Eq. 4. This is determined by integrating the curvature (s). 4 Driving maneuver The road friction coefficient sensitivity and adaption are investigated simulatively with a validated dual track model as part of the obstacle-avoidance maneuver of ISO 3888-2. The test parameters and dimensions of this driving maneuver are described in [45]. The dual track model used includes a validated Magic Formula tire model of version 5.2 according to [46] with the individual parameters of a current winter tire. This test is used to subjectively evaluate the vehicle dynamics during an evasive maneuver. An initial lane is driven through at a constant driving speed and then changed to a second lateral offset lane. This test is passed if the lane markings are not overrun. The lengths of the initial and offset lanes are constant. The widths are determined depending on the individual vehi- cle width (Table 2). In this paper, a vehicle width of 2 m is used. Thus, the lane centers of the initial and offset lanes are 3.725 m apart. The described dimensions are shown in the simulation and additionally marked by pylons (Fig. 4). Table 2 Obstacle avoidance track dimensions Lane Length Offset Width [m] 1 12 m – 1.1 × Vehicle width + 0.25 Fig. 5 Evasion trajectory calculated with the representative friction 2 11 m 1 m Vehicle width + 1 coefficient of the dry road 1 3 ̇𝜓 ̇𝜓 Automotive and Engine Technology Figure  8 shows the operation of the steering wheel angle control when the yaw angle  (x) and the yaw rate (x) of the evasive trajectory from Fig.  6 are used in the simulation. The yaw angle and yaw rate differences between the evasive trajectory and the dual-track model (DTM) are converted into a steering wheel angle by the steering wheel angle control. Figure  9a shows the steering wheel angles resulting from the yaw angle and yaw rate differences. Addition- ally, the steering wheel angle of the feedforward control is shown. It can be seen that the steering wheel angle of the feedforward control relieves the yaw rate and yaw angle control. The maximum lateral offset occurring between the evasive trajectory and the dual-track model (DTM) during simulation is 0.1 m, confirming the operation of the steer - ing wheel angle control on a dry road. Finally, Fig.  10 complements the evasive trajectory from Fig.  4 with the simulated lane of the dual-track (DTM) model. Fig. 6 Yaw angle and rate calculated with the representative friction coefficient of the dry road Figure 6b shows the yaw rate (x) of the evasive trajec- tory calculated by Eq. 5. The yaw angle and yaw rate are used to control the steering wheel angle of the dual track model in the simulation. This control is described in Sect. 5. 5 Control The architecture of the steering wheel angle control used in this paper is described in detail in [48]. This includes a feedforward control (FFC) as well as a yaw rate and lateral offset control. In the obstacle-avoidance maneuver, the used lateral off- set control described in [48] is replaced by a simple yaw angle control to increase driving stability when the simu- lated driving lane of the dual-track model increasingly devi- ates from the calculated evasive trajectory (Fig. 7). Fig. 7 Yaw angle control Fig. 8 Yaw angle and yaw rate control on a dry road 1 3 ̇𝜓 ̇𝜓 Automotive and Engine Technology Fig. 11 Simulated road friction coefficient sensitivity Table 3 Characteristic lateral Description Lateral offset offsets Vehicle does 3.225 m not reach the second lane Rear colli- 2 m sion with the obstacle Table 4 Selected characteristic parameter of the characteristic road condition classes Fig. 9 Functionality of the steering wheel angle control on a dry road Class Dry Wet Snow Ice Coefficient 1.0 0.6 0.3 0.15 Lateral offset 3.7 m 2.9 m 1.4 m 0.7 m y = y x = 100 m ( ) (9) end In this chapter, a function currently in series production without a friction coefficient adaption with a constant eva- sive trajectory is investigated. The maximum lateral accel- eration a of this evasive trajectory is calculated by Eq. 8 y,max and the representative friction coefficient of the dry road from Table 1. Figure 11 shows the road friction coefficient sensitivity Fig. 10 Simulation of the obstacle avoidance test on a dry road with determined in the simulation. The drawn lines illustrate a the two-track model (DTM) failure to reach the second lane and an occurring rear col- lision with the obstacle at the obstacle position (Table 3). It can be seen that the lateral offset y continuously 6 Road friction coefficient sensitivity end decreases with the road friction coefficient  . The second analysis lane is not reached when the road friction coefficient decreases from 1.0 to 0.7. A rear collision is caused when The road friction coefficient sensitivity analysis deter - the friction coefficient  is 0.4. mines to what extent the true road friction coefficient Table 4 contains the lateral offset y of the four road con- influences the operation of the automatic emergency steer end dition classes from Table 1 and illustrates that the obstacle- assist (ESA). To determine this, the true road friction coef- avoidance maneuver is only passed on a dry road. For this ficient  is gradually reduced and the lateral offset y at R end reason, the operation of a emergency steer assist has to be the obstacle position is calculated. calculated in a friction-adaptive manner to reach the second 1 3 Automotive and Engine Technology lane even on wet, snow- and ice-covered roads and to pass the coefficient  is gradually reduced and the lateral offset obstacle-avoidance maneuver. y at the obstacle position (Fig. 13a) and the additional end evasive distance x are calculated (Fig. 13b). add 7 Road friction coefficient adaption x = x  − x (11) add e E e R The road friction coefficient adaption calculates the maximum The second lane is always achieved as long as the true road lateral acceleration a of the evasive trajectory by an esti- y,max friction coefficient  equals or exceeds the estimated value mated value  of the true road friction coefficient. For this . The second lane is not reached if the true road friction purpose, the road friction coefficient  from Eq. 8 is replaced coefficient  decreases from 1.0 to 0.4. by the estimated value  . The additional evasive distance x is used as a sec- add ond characteristic parameter if the second lane is achieved a =  ⋅ g ⋅ k y,max E (10) although the estimated value  does not match with road Figure 12a shows the four evasive trajectories calculated friction coefficient  . by Eq. 8 and the representative estimated values of a dry, This method is repeated for the evasive trajectories wet, snow and ice covered road from Table 1. All evasive calculated using the estimated value  of the snow- and trajectories achieve the lateral offset y of the second lane end ice-covered road, and the lateral offset y at the obstacle end of 3.725 m at the obstacle position. This friction adaption position and the additional evasive distance x are calcu- add reduces the maximum lateral acceleration a on wet, y,max lated. These characteristic parameters are used in Chap. 8 snow- and ice-covered roads so as not to exceed the maxi- to determine the necessary accuracy requirements of the mum adhesion coefficient of the wheels. The maximum road friction coefficient estimation. lateral acceleration a decreases continuously with the y,max estimated value  (Fig. 12b). To investigate the evasive trajectory calculated with the estimated value  of the wet road, the road friction Fig. 13 Road friction coefficient adaption of the evasion trajectory Fig. 12 Variation of the calculated evasion trajectory with the estimated value of the wet road 1 3 Automotive and Engine Technology the left, because the road friction coefficient  can be both 8 Accuracy requirements of the road friction smaller and larger than the estimated values  of these roads. coefficient estimation The lines with the estimated value  of the ice-covered road run only to the left, because the road friction coefficient To determine the accuracy requirements of the road fric- can only be equal or greater than the estimated value  of tion coefficient estimation, the characteristic parameters R E the ice-covered road. The largest estimation error  corre- calculated in Chap. 7 are presented in an estimation error Err sponds to the true road friction coefficient  of the dry road. diagram. For this purpose, the estimation error  is cal- Err To determine the accuracy requirements, the maximum culated as the difference between the estimated value permissible estimation errors  in the tolerance band and road friction coefficient  and a tolerance band of the Err,max are determined. The second lane is not reached if these are characteristic parameters is defined. exceeded (Table 5). =  − Err E R (12) Subsequently, the maximum permissible estimation errors from Table 5 are converted into relative estimation This diagram was developed in [49] as part of an industrial Err,max errors  to present them as a function of the estimated cooperation with the Research Association of Automotive Err,rel value  (Table 6). The relative estimation error  must Technology (FAT) and was presented for the first time in E Err,rel not exceed about 30 % of the estimated value  at a driving [50] using the example of a friction-adaptive automatic E speed of 50 km/h to reach the second lane. emergency brake (AEB). Figure 14 shows the estimation error diagram of the fric- Err,max tion-adaptive automatic emergency steer assist with a toler- (13) Err,rel ance band determined by the lateral offset of 3.225 m from Table 3 and an additional evasive distance x of 10 m. For Figure 15 shows the estimation error diagram of the fric- add this reason, the accuracy requirements for reaching the sec- tion-adaptive automatic steer assist with a tolerance band ond lane are approximated in this estimation error diagram. The four lines are equal to the constant estimated value of a dry, wet, snow and ice covered road (Table 1). The Table 5 Accuracy requirements to reach the second track lane line with the estimated value  of the dry road runs only to Class Dry Wet Snow Ice the right, because the road friction coefficient  can only be equal or smaller than the estimated value  of the dry road. E Coefficient 1.0 0.6 0.3 0.15 The largest estimation error  corresponds to the road Err Max. permissible nega- – 0.4 0.2 0.05 friction coefficient  of the ice-covered road. tiv estimation error In contrast, the lines with the constant estimated values  Err,max Max. permissible posi- 0.3 0.2 0.1 – of the wet and snow-covered road run both to the right and to tiv estimation error Err,max Fig. 14 Estimation error diagram of the friction-adaptive automatic Emergency Steer Assist (ESA) with tolerance band for reaching the second lane lane at a driving speed of 50 km/h 1 3 Automotive and Engine Technology Table 6 Relative accuracy requirements to reach the second track Table 7 Relative accuracy requirements to avoid a rear collision with lane the obstacle Class Dry Wet Snow Ice Class Dry Wet Snow Ice Coefficient 1.0 0.6 0.3 0.15 Coefficient 1.0 0.6 0.3 0.15 Rel. permissible – 67 % 67 % 33 % Rel. permissible – 67 % 67 % 33 % negativ estimation negativ estimation error  error Err,rel Err,rel Rel. permissible posi- 30 % 33 % 33 % – Rel. permissible 60 % 58 % 100 % – tiv estimation error positiv estimation error Err,rel Err,rel determined by the lateral offset of 2 m from Table  3. For many traffic accidents still cannot be prevented today this reason, the necessary accuracy requirements to avoid an because they are due to wet, snow- and ice-covered roads. approximate rear collision are determined in this diagram. In this paper, the road friction coefficient sensitivity and The additional evasive distance x is consistent with that adaption of an automatic emergency steer assist are simula- add in Fig. 14. tively investigated. This assist overrides the driver to auto- The maximum permissible estimation error  matically execute an evasive maneuver. The driving maneu- Err,max increases when the used permissible lateral offset y is ver used is the obstacle-avoidance maneuver standardized end increased. The relative estimation error  must not in ISO 3888-2, which is transferred to the simulation and Err,rel exceed about 60 % of the estimated value  at a driving repeated on a dry, wet, snow- and ice-covered roadway. speed of 50 km/h to avoid a rear collision (Table 7). The road friction coefficient sensitivity shows that this The tolerance band used in Fig. 14 and Fig. 15 is exem- test is already failed on a wet road because the simulated plarily determined by an additional evasive distance x of vehicle does not pass the second lane without errors. It can add 10 m. The acceptance of this band is currently being deter- be seen that the lateral offset decreases continuously with the mined in further user studies on the institute’s own Dynamic true road friction coefficient. The second lane is not reached Vehicle Road Simulator (DVRS). when the road friction coefficient decreases from 1.0 to 0.7. A rear collision is caused when a road friction coefficient of 0.4 is present. For this reason, the operation of an emer- 9 Conclusion gency steer assist must be calculated in a friction-adaptive manner to reach the second lane even on wet, snow- and The number of traffic accidents with personal injury and ice-covered road. property damage is increasingly being reduced by effective The road friction coefficient adaption calculates the maxi- advanced driver assistance systems (ADAS). Nevertheless, mum lateral acceleration of the evasive trajectory using an Fig. 15 Estimation error diagram of the friction-adaptive automatic Emergency Steer Assist (ESA) with the tolerance band determined by the lateral offset of 2 m at a driving speed of 50 km/h 1 3 Automotive and Engine Technology estimated value of the true road friction coefficient. This References adaption reduces the maximum lateral acceleration on wet, 1. 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IEEE Transactions on Systems, Man, and Cyber- netics: Systems 44, 621–629 (2013). https:// doi. or g/ 10. 1109/ Author contributions TA and JI wrote the manuscript and prepared the TSMC. 2013. 22631 29 figures. All authors reviewed the manuscript. 12. Choi, J., Kim, K., Yi, K.: Emergency driving support algorithm with steering torque overlay and differential braking. Paper pre- Funding Open Access funding enabled and organized by Projekt sented at the 2011 14th International IEEE Conference on Intel- DEAL. ligent Transportation Systems (ITSC), Washington, 5–7 October 2011 (2011) Declarations 13. Choi, J., Yi, K., Suh, J., Ko, B.: Coordinated control of motor- driven power steering torque overlay and differential braking Conflict of interest The authors declare no competing interests. for emergency driving support. IEEE Trans. Veh. Technol. 63, 566–579 (2014). https:// doi. org/ 10. 1109/ TVT. 2013. 22797 19 Open Access This article is licensed under a Creative Commons Attri- 14. 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Chovan, J., Tijerina, L., Alexander, G., Hendricks, D.: Examination jurisdictional claims in published maps and institutional affiliations. of lane change crashes and potential ivhs countermeasures. Techni- cal Report DOT-VNTSC-NHTSA-93-2, National Highway Traffic Safety Administration (NHTSA), Washington, DC (March 1994) 1 3 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Automotive and Engine Technology Springer Journals

Accuracy requirements for the road friction coefficient estimation of a friction-adaptive automatic emergency steer assist (ESA)

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Abstract

The number of traffic accidents resulting in personal injury and property damage is increasingly being reduced by effective advanced driver assistance systems (ADAS). Nevertheless, many traffic accidents still cannot be prevented today because they are due to wet, snow- and ice-covered roads. For this reason, the Institute of Automotive Engineering (IAE) of the Techni- cal University of Braunschweig is investigating the road friction coefficient sensitivity and adaptation of advanced driver assistance systems (ADAS) currently in series production from 2018 to 2021 as part of the ‘Road Condition Cloud’ research project funded by the German Research Foundation (DFG) to increase driving safety, particularly on wet, snow- and ice- covered roads. In this article, the road friction coefficient sensitivity and adaptation of an automatic emergency steer assist is simulatively investigated. This assist overrides the driver to automatically execute an evasive maneuver. The driving maneuver used is a standardized obstacle-avoidance maneuver that is simulatively repeated on a dry, wet, snow- and ice-covered road. The road friction coefficient sensitivity shows that this test is already failed on a wet road because the simulated vehicle does not pass the second lane without errors. Subsequently, a road friction coefficient adaptation of the emergency steer assist is investigated. This adaptation varies the maximum lateral acceleration of the evasive trajectory depending on an estimated value of the road friction coefficient in order not to exceed the maximum adhesion coefficient of the wheels during the evasive maneuver. Ideally, the estimated value matches the true road friction coefficient so that the second lane is passed without errors even on a wet, snow- and ice-covered road. In contrast, an existing difference determines whether the second lane is reached. Finally, the necessary accuracy requirements of the road friction coefficient estimation are determined in an novel estimation error diagram. A road friction coefficient adaptation increases the driving safety of driver advanced assistance systems (ADAS) that are in series production today and future highly automated driving functions (HAF) and is necessary for automated driving because the driver is not present as a fallback level. The described results were presented before in [1]. Keywords Road friction coefficient · Road friction coefficient sensitivity · Road friction coefficient adaption · Automatic emergency steer assist · Friction-adaptive advanced driver assistance systems (ADAS) 1 Introduction The number of traffic accidents resulting in personal injury and property damage is increasingly being reduced by effec- tive advanced driver assistance systems (ADAS). Neverthe- less, many traffic accidents still cannot be prevented today * Tim Ahrenhold because they are due to wet, snow- and ice-covered roads t.ahrenhold@tu-bs.de [2]. For this reason, the road friction coefficient in particular Jannes Iatropoulos determines driving safety in road traffic. j.iatropoulos@tu-bs.de For legal reasons, automatic emergency brake assists Roman Henze (AEB) currently in series production only become active r.henze@tu-bs.de when it is no longer possible to take evasive action and the Institute of Automotive Engineering (IAE), Technical remaining relative distance falls below the last point to steer University Braunschweig, Hans-Sommer-Straße 4, distance. Because the collision-avoiding braking distance Braunschweig 38106, Niedersachsen, Germany Vol.:(0123456789) 1 3 Automotive and Engine Technology exceeds the last point to steer distance at high driving involving a sudden lane change are examined and it is speeds, automatic emergency brake assists cannot always described that many drivers often recognize an impending avoid a collision, but only at low driving speeds. collision too late. In [35] it is explained that the average In contrast, emergency steer assists (ESA) in series pro- driver often notices other road users too late to avoid a duction today become active when rapid steering by the collision. driver is detected at low relative distances. These assists Already in [36] it is recognized in the context of driving superimpose an additional torque on the driver’s steering tests with a suddenly appearing obstacle that only experi- wheel torque, which supports the driver in taking evasive enced drivers stabilize the vehicle during an evasive maneu- action [3, pp. 755-758]. As a result, a possible collision can ver. Inexperienced drivers are often unable to do so, control- always be avoided if the driver begins to steer before the last ling the vehicle response that occurs during evasive action. point to steer distance is reached. In [37], a user study recognizes that the average driver often Currently in series production, the last point to brake and reacts too late to avoid an impending collision by taking steer distance is calculated by the constant road friction coef- evasive action. The results of this study indicate that only c fi ient of a dry road, so that collisions on wet, snow- and ice- an automatic emergency steer assist that overrides the driver covered roads are not prevented. For this reason, a friction- can avoid an impending collision, especially on wet, snow- adaptive emergency steer assist (ESA) that automatically and ice-covered roads. execute an evasive maneuver has high potential to increase In [11, 14, 28, 38, 39], driving simulator studies are driving safety even on wet, snow- and ice-covered roads. described that superimpose an additional torque on the This friction-adaptive assist can be implemented through driver’s steering wheel torque during evasive action when technical advances in the development of sensors for reliable rapid driver steering is detected. The driving simulator study clearance detection, since all other sensors and actuators are in [38] illustrates that an emergency steering assist improves already available in series production [3, pp. 553–577] [4, driver behavior when a collision is imminent. The study pp. 1021–1040] [5]. in [39] examines the vehicle dynamics during an evasive For example, active lane keeping assist (LKA) systems in maneuver and highlights that driving stability is increased series production today use one or more cameras to reliably because the emergency steering assist reduces the overshoot determine the vehicle position within the lane. This position of the yaw rate. In [28], over 70 % of users favorite an auto- determines the additional torque that is superimposed on the matic emergency steering assist that overrides the driver in driver’s steering wheel torque [6–8]. emergency situations. The study in [14] illustrates that an Today, a difference is made between two groups of emer - emergency steering assist reduces the number of collisions gency steer assists. The assists of the first group superim- and decreases the humans reaction time by at least 100 ms. pose an additional torque on the driver’s steering wheel In [11], two studies with a sudden lane change are torque, which assists the driver in taking evasive action. described. In the first study, the driver’s steering wheel These assists are described in [9–15] and use as actuator, for torque is superimposed by an additional torque. To increase example, the electric motor of an electromechanical steering driving stability, the steering wheel angle is superimposed system (EPS). Because the assists in this group cooperate in the second study by an additional angle. The first study with the driver, driver models are required that represent emphasizes that an additional torque is not always sufficient human driving behavior, especially in emergency situations to prevent the vehicle from leaving the lane during a sudden such as an evasive maneuver. These models are described, lane change. In contrast, the second lane are almost always for example, in [16–20]. Further, in [21–25] different evasive traversed without error when the driver is supported by an trajectories are compared with the human driving behavior. additional angle in the second study. The assists of the second group superimpose an addi- In [40], an emergency steer assist investigated in real traf- tional angle on the steering wheel angle of the driver, which fic is described. This is activated during lane changes with cannot be overridden by the driver. These assistants are a high probability of leading to a critical driving situation studied in [26–31], among others, and use, for example, a to stabilize the driving situation or prevent a collision. This superposition transmission as actuator. Because the assists assist is able to override the driver. in this group do not interact with the driver, driver models More advanced approaches in [41–43] investigate the are not required. combination of an emergency brake assist with an emer- Critical driving situations occur when the driver fails gency steer assist that is in series production today. The to steer appropriately in an emergency situation such as an trade-off between braking and evasion is described in [9 ] evasive maneuver or a sudden lane change. In [32], traffic as a function of relative speed and road friction coefficient. accidents are studied and recognized that over 70 % of In [27, 31, 44] approaches are described that determine the deadly collisions occur on the shoulder or median strip last point to steer distance as a function of the road friction when the driver leaves his lane. In [33, 34], accidents coefficient in order not to exceed the maximum adhesion 1 3 Automotive and Engine Technology Table 1 Representative road friction coefficients Road condition class Dry Wet Snow Ice Road friction coefficient 1.0 0.6 0.3 0.15 Fig. 1 Methods Fig. 3 Input and output parameters of the used trajectory calculation 3 Function The trajectory used by the emergency steer assist is calcu- lated by an optimizer. This optimizer minimizes the evasive trajectory length x depending on two input parameters. These two input parameter are the lateral offset y to be achieved and the predefined maximum lateral acceleration a of the evasive trajectory (Fig. 3). y,max The y-coordinate y(x) of the evasion trajectory are calcu- Fig. 2 Value ranges of the road condition classes lated by a seventh degree polynomial, the lateral offset y to be achieved, and the trajectory length x . 7 6 coefficient of the wheels, especially on wet, snow- and ice- x x y(x) = y − 20 + 70 covered roads. x x e e (1) 5 4 In [42], a steer assist is described that additionally brakes x x − 84 + 35 individual wheels as desired in order not to exceed the maxi- x x e e mum adhesion coefficient of the inside and outside wheels of the curve. This additionally increases the yaw rate and The curvature (s) of the evasive trajectory is determined by shortens the length of the calculated evasive trajectories. the first and second derivatives of the coordinates x and y(x) In this paper, the road friction coefficient sensitivity and with respect to the arc length s. adaption of an automatic emergency steer assist is simula- ẋ (s)y ̈(s) − x ̈(s)ẏ (s) tively investigated using a validated dual track model. This 𝜅 (s) = (2) 3∕2 2 2 assist overrides the driver to automatically execute an eva- ẋ (s) + ẏ (s) sive maneuver along a calculated evasive trajectories. The For this, the differential quotient ds of the arc length s is driving maneuver used is the obstacle-avoidance maneuver standardized in ISO 3888-2, which is transferred to the sim- calculated by the differential quotients dx and dy of the coor - dinates x and y(x). ulation and repeated on a dry, wet, snow- and ice-covered roadway [45]. √ 2 2 ds = (dx) +(dy) (3) The yaw angle  (s) of the evasive trajectory is calculated by integrating the curvature (s) . This is used for the yaw 2 Method angle control of the emergency steer assist and described in Sect. 5. The method used takes into account the true road friction coefficient  and an estimated value  of the true road R E (s) = (s) ds (4) friction coefficient (Fig.  1). In this article, the road friction coefficient sensitivity and adaptation for the four classes of a dry, wet, snow-covered The yaw rate (s) of the evasive trajectory is calculated by and ice-covered road are investigated (Fig. 2) and representa- the curvature (s) and initial driving speed v and a side slip tive road friction coefficients are assigned to them (Table  1). angle  is neglected. 1 3 ̇𝜓 Automotive and Engine Technology (s) = 𝜅 (s) ⋅ v (5) The lateral acceleration a (s) of the used evasive trajectory is calculated like the yaw rate (s) by the curvature (s) and initial vehicle speed v . a (s) = (s) ⋅ v (6) y,max The maximum curvature  of the evasive trajectory is max determined by the maximum lateral acceleration a and y,max is not exceeded by this optimizer. −2 = a ⋅ v (7) max y,max Fig. 4 Obstacle avoidance track in the simulation The maximum lateral acceleration a of the evasive tra- y,max jectory is calculated in series production today by the accel- The evasive trajectory from Fig. 4 is calculated by Eq. 1 eration of gravity g and in particular the constant road fric- tion coefficient  of a dry road. The factor k describes the to Eq. 8 from Sect. 3 and the representative road friction coefficient  of the dry road (Table 1) from Sect. 2 (Fig. 5a). ellipse of kamm’s circle and takes values between 1.0 and 0.8 for current summer and winter tires [3, pp. 899–904]. Figure 5b shows the lateral acceleration a (x) of the eva- sive trajectory calculated by Eq. 7. This is limited by Eq. 8 a =  ⋅ g ⋅ k y,max R (8) and an assumed factor k of 0.9 [47]. Figure 6a shows the yaw angle  (x) of the evasive trajec- tory calculated by Eq. 4. This is determined by integrating the curvature (s). 4 Driving maneuver The road friction coefficient sensitivity and adaption are investigated simulatively with a validated dual track model as part of the obstacle-avoidance maneuver of ISO 3888-2. The test parameters and dimensions of this driving maneuver are described in [45]. The dual track model used includes a validated Magic Formula tire model of version 5.2 according to [46] with the individual parameters of a current winter tire. This test is used to subjectively evaluate the vehicle dynamics during an evasive maneuver. An initial lane is driven through at a constant driving speed and then changed to a second lateral offset lane. This test is passed if the lane markings are not overrun. The lengths of the initial and offset lanes are constant. The widths are determined depending on the individual vehi- cle width (Table 2). In this paper, a vehicle width of 2 m is used. Thus, the lane centers of the initial and offset lanes are 3.725 m apart. The described dimensions are shown in the simulation and additionally marked by pylons (Fig. 4). Table 2 Obstacle avoidance track dimensions Lane Length Offset Width [m] 1 12 m – 1.1 × Vehicle width + 0.25 Fig. 5 Evasion trajectory calculated with the representative friction 2 11 m 1 m Vehicle width + 1 coefficient of the dry road 1 3 ̇𝜓 ̇𝜓 Automotive and Engine Technology Figure  8 shows the operation of the steering wheel angle control when the yaw angle  (x) and the yaw rate (x) of the evasive trajectory from Fig.  6 are used in the simulation. The yaw angle and yaw rate differences between the evasive trajectory and the dual-track model (DTM) are converted into a steering wheel angle by the steering wheel angle control. Figure  9a shows the steering wheel angles resulting from the yaw angle and yaw rate differences. Addition- ally, the steering wheel angle of the feedforward control is shown. It can be seen that the steering wheel angle of the feedforward control relieves the yaw rate and yaw angle control. The maximum lateral offset occurring between the evasive trajectory and the dual-track model (DTM) during simulation is 0.1 m, confirming the operation of the steer - ing wheel angle control on a dry road. Finally, Fig.  10 complements the evasive trajectory from Fig.  4 with the simulated lane of the dual-track (DTM) model. Fig. 6 Yaw angle and rate calculated with the representative friction coefficient of the dry road Figure 6b shows the yaw rate (x) of the evasive trajec- tory calculated by Eq. 5. The yaw angle and yaw rate are used to control the steering wheel angle of the dual track model in the simulation. This control is described in Sect. 5. 5 Control The architecture of the steering wheel angle control used in this paper is described in detail in [48]. This includes a feedforward control (FFC) as well as a yaw rate and lateral offset control. In the obstacle-avoidance maneuver, the used lateral off- set control described in [48] is replaced by a simple yaw angle control to increase driving stability when the simu- lated driving lane of the dual-track model increasingly devi- ates from the calculated evasive trajectory (Fig. 7). Fig. 7 Yaw angle control Fig. 8 Yaw angle and yaw rate control on a dry road 1 3 ̇𝜓 ̇𝜓 Automotive and Engine Technology Fig. 11 Simulated road friction coefficient sensitivity Table 3 Characteristic lateral Description Lateral offset offsets Vehicle does 3.225 m not reach the second lane Rear colli- 2 m sion with the obstacle Table 4 Selected characteristic parameter of the characteristic road condition classes Fig. 9 Functionality of the steering wheel angle control on a dry road Class Dry Wet Snow Ice Coefficient 1.0 0.6 0.3 0.15 Lateral offset 3.7 m 2.9 m 1.4 m 0.7 m y = y x = 100 m ( ) (9) end In this chapter, a function currently in series production without a friction coefficient adaption with a constant eva- sive trajectory is investigated. The maximum lateral accel- eration a of this evasive trajectory is calculated by Eq. 8 y,max and the representative friction coefficient of the dry road from Table 1. Figure 11 shows the road friction coefficient sensitivity Fig. 10 Simulation of the obstacle avoidance test on a dry road with determined in the simulation. The drawn lines illustrate a the two-track model (DTM) failure to reach the second lane and an occurring rear col- lision with the obstacle at the obstacle position (Table 3). It can be seen that the lateral offset y continuously 6 Road friction coefficient sensitivity end decreases with the road friction coefficient  . The second analysis lane is not reached when the road friction coefficient decreases from 1.0 to 0.7. A rear collision is caused when The road friction coefficient sensitivity analysis deter - the friction coefficient  is 0.4. mines to what extent the true road friction coefficient Table 4 contains the lateral offset y of the four road con- influences the operation of the automatic emergency steer end dition classes from Table 1 and illustrates that the obstacle- assist (ESA). To determine this, the true road friction coef- avoidance maneuver is only passed on a dry road. For this ficient  is gradually reduced and the lateral offset y at R end reason, the operation of a emergency steer assist has to be the obstacle position is calculated. calculated in a friction-adaptive manner to reach the second 1 3 Automotive and Engine Technology lane even on wet, snow- and ice-covered roads and to pass the coefficient  is gradually reduced and the lateral offset obstacle-avoidance maneuver. y at the obstacle position (Fig. 13a) and the additional end evasive distance x are calculated (Fig. 13b). add 7 Road friction coefficient adaption x = x  − x (11) add e E e R The road friction coefficient adaption calculates the maximum The second lane is always achieved as long as the true road lateral acceleration a of the evasive trajectory by an esti- y,max friction coefficient  equals or exceeds the estimated value mated value  of the true road friction coefficient. For this . The second lane is not reached if the true road friction purpose, the road friction coefficient  from Eq. 8 is replaced coefficient  decreases from 1.0 to 0.4. by the estimated value  . The additional evasive distance x is used as a sec- add ond characteristic parameter if the second lane is achieved a =  ⋅ g ⋅ k y,max E (10) although the estimated value  does not match with road Figure 12a shows the four evasive trajectories calculated friction coefficient  . by Eq. 8 and the representative estimated values of a dry, This method is repeated for the evasive trajectories wet, snow and ice covered road from Table 1. All evasive calculated using the estimated value  of the snow- and trajectories achieve the lateral offset y of the second lane end ice-covered road, and the lateral offset y at the obstacle end of 3.725 m at the obstacle position. This friction adaption position and the additional evasive distance x are calcu- add reduces the maximum lateral acceleration a on wet, y,max lated. These characteristic parameters are used in Chap. 8 snow- and ice-covered roads so as not to exceed the maxi- to determine the necessary accuracy requirements of the mum adhesion coefficient of the wheels. The maximum road friction coefficient estimation. lateral acceleration a decreases continuously with the y,max estimated value  (Fig. 12b). To investigate the evasive trajectory calculated with the estimated value  of the wet road, the road friction Fig. 13 Road friction coefficient adaption of the evasion trajectory Fig. 12 Variation of the calculated evasion trajectory with the estimated value of the wet road 1 3 Automotive and Engine Technology the left, because the road friction coefficient  can be both 8 Accuracy requirements of the road friction smaller and larger than the estimated values  of these roads. coefficient estimation The lines with the estimated value  of the ice-covered road run only to the left, because the road friction coefficient To determine the accuracy requirements of the road fric- can only be equal or greater than the estimated value  of tion coefficient estimation, the characteristic parameters R E the ice-covered road. The largest estimation error  corre- calculated in Chap. 7 are presented in an estimation error Err sponds to the true road friction coefficient  of the dry road. diagram. For this purpose, the estimation error  is cal- Err To determine the accuracy requirements, the maximum culated as the difference between the estimated value permissible estimation errors  in the tolerance band and road friction coefficient  and a tolerance band of the Err,max are determined. The second lane is not reached if these are characteristic parameters is defined. exceeded (Table 5). =  − Err E R (12) Subsequently, the maximum permissible estimation errors from Table 5 are converted into relative estimation This diagram was developed in [49] as part of an industrial Err,max errors  to present them as a function of the estimated cooperation with the Research Association of Automotive Err,rel value  (Table 6). The relative estimation error  must Technology (FAT) and was presented for the first time in E Err,rel not exceed about 30 % of the estimated value  at a driving [50] using the example of a friction-adaptive automatic E speed of 50 km/h to reach the second lane. emergency brake (AEB). Figure 14 shows the estimation error diagram of the fric- Err,max tion-adaptive automatic emergency steer assist with a toler- (13) Err,rel ance band determined by the lateral offset of 3.225 m from Table 3 and an additional evasive distance x of 10 m. For Figure 15 shows the estimation error diagram of the fric- add this reason, the accuracy requirements for reaching the sec- tion-adaptive automatic steer assist with a tolerance band ond lane are approximated in this estimation error diagram. The four lines are equal to the constant estimated value of a dry, wet, snow and ice covered road (Table 1). The Table 5 Accuracy requirements to reach the second track lane line with the estimated value  of the dry road runs only to Class Dry Wet Snow Ice the right, because the road friction coefficient  can only be equal or smaller than the estimated value  of the dry road. E Coefficient 1.0 0.6 0.3 0.15 The largest estimation error  corresponds to the road Err Max. permissible nega- – 0.4 0.2 0.05 friction coefficient  of the ice-covered road. tiv estimation error In contrast, the lines with the constant estimated values  Err,max Max. permissible posi- 0.3 0.2 0.1 – of the wet and snow-covered road run both to the right and to tiv estimation error Err,max Fig. 14 Estimation error diagram of the friction-adaptive automatic Emergency Steer Assist (ESA) with tolerance band for reaching the second lane lane at a driving speed of 50 km/h 1 3 Automotive and Engine Technology Table 6 Relative accuracy requirements to reach the second track Table 7 Relative accuracy requirements to avoid a rear collision with lane the obstacle Class Dry Wet Snow Ice Class Dry Wet Snow Ice Coefficient 1.0 0.6 0.3 0.15 Coefficient 1.0 0.6 0.3 0.15 Rel. permissible – 67 % 67 % 33 % Rel. permissible – 67 % 67 % 33 % negativ estimation negativ estimation error  error Err,rel Err,rel Rel. permissible posi- 30 % 33 % 33 % – Rel. permissible 60 % 58 % 100 % – tiv estimation error positiv estimation error Err,rel Err,rel determined by the lateral offset of 2 m from Table  3. For many traffic accidents still cannot be prevented today this reason, the necessary accuracy requirements to avoid an because they are due to wet, snow- and ice-covered roads. approximate rear collision are determined in this diagram. In this paper, the road friction coefficient sensitivity and The additional evasive distance x is consistent with that adaption of an automatic emergency steer assist are simula- add in Fig. 14. tively investigated. This assist overrides the driver to auto- The maximum permissible estimation error  matically execute an evasive maneuver. The driving maneu- Err,max increases when the used permissible lateral offset y is ver used is the obstacle-avoidance maneuver standardized end increased. The relative estimation error  must not in ISO 3888-2, which is transferred to the simulation and Err,rel exceed about 60 % of the estimated value  at a driving repeated on a dry, wet, snow- and ice-covered roadway. speed of 50 km/h to avoid a rear collision (Table 7). The road friction coefficient sensitivity shows that this The tolerance band used in Fig. 14 and Fig. 15 is exem- test is already failed on a wet road because the simulated plarily determined by an additional evasive distance x of vehicle does not pass the second lane without errors. It can add 10 m. The acceptance of this band is currently being deter- be seen that the lateral offset decreases continuously with the mined in further user studies on the institute’s own Dynamic true road friction coefficient. The second lane is not reached Vehicle Road Simulator (DVRS). when the road friction coefficient decreases from 1.0 to 0.7. A rear collision is caused when a road friction coefficient of 0.4 is present. For this reason, the operation of an emer- 9 Conclusion gency steer assist must be calculated in a friction-adaptive manner to reach the second lane even on wet, snow- and The number of traffic accidents with personal injury and ice-covered road. property damage is increasingly being reduced by effective The road friction coefficient adaption calculates the maxi- advanced driver assistance systems (ADAS). Nevertheless, mum lateral acceleration of the evasive trajectory using an Fig. 15 Estimation error diagram of the friction-adaptive automatic Emergency Steer Assist (ESA) with the tolerance band determined by the lateral offset of 2 m at a driving speed of 50 km/h 1 3 Automotive and Engine Technology estimated value of the true road friction coefficient. This References adaption reduces the maximum lateral acceleration on wet, 1. 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Journal

Automotive and Engine Technology – Springer Journals

Published: Sep 1, 2023

Keywords: Road friction coefficient; Road friction coefficient sensitivity; Road friction coefficient adaption; Automatic emergency steer assist; Friction-adaptive advanced driver assistance systems (ADAS)

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