Collision avoidance with automatic braking and swerving

Transcription

1 Preprints of the 9th World Congress The International Federation of Automatic Control Cape Town, South Africa. August 4-9, 4 Collision aoidance with automatic braking and swering Carlo Ackermann Rolf Isermann Sukki Min Changwon Kim Institute of Automatic Control and Mechatronics, Technical Uniersity Darmstadt ( cackermann@iat.tu-darmstadt.de). Institute of Automatic Control and Mechatronics, Technical Uniersity Darmstadt ( risermann@iat.tu-darmstadt.de). Hyundai Motor Company, Seoul, Korea, ( sukkimin@hyundai.com) Hyundai Motor Company, Seoul, Korea, ( cwkim@hyundai.com) Abstract: To aoid collisions in longitudinal direction emergency braking is suitable in many situations. Howeer for higher elocites, an easie maneuer is better because it can be applied later than the braking maneuer if there is enough free space. This contribution inestigates methods for the decision-making of a collision aoidance system with regard to automatic braking and swering. The resulting system tries to use the latest possible point for interention if the drier does not react. This decision is based on certain time measures and distances. Further trajectory planning and control methods for swering are described and some simulations are gien. Keywords: Collision Aoidance; Trajectory planning; nlinear Control; Interactie ehicle control; Vehicle dynamics.. INTRODUCTION Collisions with other objects or ehicles on urban roads or highways in longitudinal direction can be aoided by automatic braking or swering, if the drier does not react in an early stage and in the right way, Isermann et al. []. This contribution extends former theoretical and experimental research for swering at higher speeds and takes into account the aailable free space. The assumed sensors are a suitable front radar system and a ideo camera and rear-left and rear-right radar systems. Some specialities of the inestigations are the calculation of the last instants to brake and to steer, which depend on the relatie elocitiy and are different. A decision making program will be deeloped which includes the estimation of aailable free space on the parallel lane considers seeral ehicles. The methods are deeloped by simulations with the comprehensie IPG CarMaker simulation enironment and include experimental results from earlier work.. CONSIDERED SCENARIO As automotie collision aoidance systems hae to consider seeral driing situations, the tested scenario has to be specified.. Sensor setup The different sensors used as shown in Fig.. A camera is installed at the windshield, which deliers information about the lane-width, the position of the ego ehicle on the lane and the lateral position of the front ehicles. Rear-left radar Rear-right radar Fig.. Schematic sensor arrangement y x Camera Front radar Three radar sensor systems (e.g. 4 or 77 GHz) are assumed, the front system detects objects driing in front of the ego ehicle. The other two radar sensors are installed at the left and right backside of the car. All radar sensors supply object lists. For each object the position relatiely to the ego ehicle and the difference elocity is proided relatiely to the obstacles. Because the rear radar sensors are turned, their information is transformed into the same coordinate system. Then Copyright 4 IFAC 694

2 9th IFAC World Congress Cape Town, South Africa. August 4-9, 4 RL High Speed Braking possible Steering possible Steering possible RM Fig.. Objects around the ego ehicle the distance and difference elocity is proided in X- and Y-coordiantes relatiely to the ego ehicle.. Objects In the following the ehicles next to the ego ehicle are considered. Four ehicles as shown in Fig. are assumed: Front-left, front-middle, rear-left, and rear-middle. The ehicles classified as left are the nearest objects on the left lane next to the ego-ehicle. The front-middle ehicle is the main object in front of the own car. For testing purposes in a first phase only the middle and the two left objects are considered in the CarMaker simulation enironment. Using the position of the ego ehicle and the object lists from the radar sensors and fusion with the camera Isermann et al. [], the releant objects can be selected. 3. Basic considerations 3. DECISION MAKING In the following it is assumed that the main object for collision aoidance is the car in front of the own () ehicle. The goal is to aoid the collision in the last possible moment. This can be either the last point to steer (LPS), then swering is the better maneuer, or the last point to brake (LPB), then braking is the better maneuer. LPB after LPS At lower elocities the braking maneuer is the maneuer which can be performed later. This is illustrated in Fig. 3. Low Speed Braking possible Steering possible Braking possible LPB LPS Fig. 4. Illustration of last point to brake and last point to steer at high elocities If swering is not possible because of missing free space, only the emergency braking helps to interent or mitigate the collision. But this has to be started at earlier time. So the information if an easie maneuer is possible at the last point to steer has to be aailable at the last point to brake. 3. Calculation of time interals For making a decision there are generally two possibilities. One is to consider the distances between all the objects. Howeer the distance has to be interpreted dependent on the elocities. The other possibility is to use time interals. These time interals indicate after which time a certain eent occurs or how long a certain eent takes. The adantage is, that only one alue has to be considered. Furthermore human reaction times can be used as reference alues. Therefore the decisions are based on time interals. They are calculated with the information from the enironmental sensors and definitions made before. Important time interals are the time to collision (TTC), the braking time (T brake ) and the easie time (T ea ). Based on these time interals the time to steer (TTS) and the time to brake (TTB) can be calculated. Time to Collision (TTC) Using the difference elocities and the distances it is possible to calculate the Time to Collision (TTC). The TTC represents the time after which a collision occurs if the two considered ehicles drie with the same elocity (Hayward [97]): LPS LPB Fig. 3. Illustration of last point to brake and last point to steer at low elocities This is the more easy case. When the last point to brake is reached, the system has to do a full braking automatically. LPS after LPB At higher elocities the braking distance is longer than the distance needed for the easie maneuer, Bender et al. [7]. This is outlined in Fig. 4. This case is more difficult than the other one. Generally the easie maneuer is the best way to aoid the collision. But an easie maneuer is of course only possible, if there is enough space sidewards and backwards to swere. So the assistance system has to ensure that the cars on the easie lane are far enough so that they are not endangered. TTC = s dx dx. () Braking Time If there is a negatie difference elocity to the car in front ( dx,fr < ), then the own car moes towards the car in front. Under the assumption that this ehicle moes with constant elocity, and a constant maximum deceleration for dry asphalt is assumed with a brake = 9.8 m s, for the braking time it holds (Ackermann et al. [4]): T brake ( dx, a brake ) = dx. () a brake Easie Time The easie time depends on the width, i.e. the lateral displacement y ea, from the easie maneuer and the maximum lateral acceleration a ea which depends on the road condition (Winner et al. [9]): T ea (y ea, a ea ) = yea a ea + τ s. (3) 695

3 9th IFAC World Congress Cape Town, South Africa. August 4-9, 4 τ s is the steering loss time and can be assumed with.s. Time to Brake (TTB) The time to brake gies the time after which a braking maneuer has to be started to preent the collision. If the TTB is smaller than, a collision can not be aoided by braking. TTB = TTC fm T brake. (4) Time to Steer (TTS) The time to steer gies the time after which an easie maneuer has to be started to preent the collision. If the TTC is smaller than, a collision can not be aoided by steering. 3.3 Selection of free space TTS = TTC fm T ea. (5) For making a decision the cars on the other lanes are considered. For simplification only the left lane is considered. Other lanes, if present, can be considered similarly. The sensor based object detection obseres the ehicles on the left lane in front and behind the ego ehicle. These two cars represent the highest potential risk. In the following a forecast of free space selection is made for the last point to steer. Assuming that the cars are moing with constant elocity, it is checked, if the easie maneuer will be possible at the last point to steer (LPS). Some equations for the forecast calculate if the easie maneuer will be possible when the last possible point to steer is reached (TTS = TTC fm T ea = ). TTS TTC fl T brake,fl TTC fl T ea TTS T ea T brake,fl Fig. 5. Graphical illustration for front-left target Front-left target Assuming constant elocities, T brake,fl and T ea stay constant and TTC fl decreases continously. Performing the easie maneuer at TTS =, TTC fl will decrease by TTS from the moment of calculation to TTS =. For the front-left target the TTC to the front-left object minus the braking and the easie time has to be higher than the TTS, because first the swering and then the braking is assumed: TTC fl T brake,fl T ea > TTS. (6) With the relation TTS = TTC fm T ea this leads to: TTC fl T brake,fl > TTC fm. (7) Rear-left target The same is done for the rear-left target with the difference that now the braking time of the rearleft ehicle is considered, which leads to: TTC rl T brake,rl > TTC fm. (8) The question if the easie maneuer will be possible at TTS = can now be answered by the following equation:, if TTC fl T brake,fl > TTC fm eapossible = TTC rl T brake,rl > TTC fm,, else. (9) 3.4 Decision rules w these calcuations are used for making a decision for the assistance system. This decision will then be gien to the collision aoidance control. For small difference elocities the braking distance is smaller than the easie distance. For big difference elocities this is opposite. The intersection can be calculated ery easily: dx;brake=ea = a brake yea a ea. () Because the system should interent at the last possible point, for difference elocities smaller than dx;brake=ea braking is better than swering, Stählin et al. [7]. For higher difference elocities the swering is the better maneuer but can only be performed when there is enough space on the easie lane. Example: Assuming a brake = 9.8 m s, a ea = 7 m s and y ea = 3.6m the intersection elocity is dx;brake=ea = 9.9 m s = 7.6 km h. Braking time reached TTC fm < T brake Easie time smaller than braking time T ea < T brake Emergency brake Easie maneuer possible? Fig. 6. Flowchart for decision making Emergency steer Easie time reached TTC fm < T ea Fig. 6 shows how the decision is made. When the braking time is reached, the system checks if the easie time is smaller than the braking time. If not, braking is in eery case the better maneuer and the system starts to brake. If not, it is considered if an easie maneuer will be possible at the last point to steer. If this is not the case, the emergency braking is performed too. If an easie maneuer will be possible, the system performs the easie maneuer at the last point to steer. 4. DESIGN OF TRAJECTORY CONTROL After the treatment of the decision-making this section deals with the control of the lateral and longitudinal dynamics of the ehicle. First, the controller for the braking maneuer is presented. Then a method for planning an easie trajectory is introduced. Finally a controller for the steering system is presented to drie along the calculated trajectory. 696

4 9th IFAC World Congress Cape Town, South Africa. August 4-9, 4 4. Brake control Because only a fullbraking is needed it is sufficient to apply maximum braking to the ehicle. The assumed maximal possible deceleration is a break = 9.8 m s for dry roads. 4. Trajectory planning For the easie maneuer the required trajectory is subject to the steering controller. The manipulated ariable is the steering angle. There are different possibilities for planning an easie trajectory. In eery case it is important to limit the lateral acceleration. Otherwise the physical limits can be exceeded. y in m Fig. 7. Transfer function t in s A simple way is to create the trajectory as a step response. In Schmitt [] a fourth order transfer function was used to predict the lane-change-trajectory for the PRORETA project. This can be also used for an easie maneuer. The following transfer function is considered: G(s) = ( + T s) 4. () This function is obtained from the transfer function G(s) = K ( + T s)( + T s)...( + T n s) B () and the assumption that all time constants match, Isermann and Münchhof []. The fourth order transfer function can also be written as a state space system: ẏ Y ȧ = Y j Y T 4 4 T 3 6 T 4 T y Y + a Y jy T 4 y ref. (3) When the easie maneuer is started, y ref is set to a step function of size B. Then an easie trajectory in timedomain y(t) follows as a step-response. T affects the shape of the trajectory and has to be determined in a way that the maximum jerk and the maximum lateral acceleration are respected. Determination of parameter T For determination of the time constant T the maximum lateral acceleration is considered, because it is included in the state ector. The maximum lateral acceleration occurs at t ay,max = T (3 3). (4) which is obtained by the solution in the time-domain of the step-response from Eq. (3). For a Y,max then holds a Y,max = B T e (3 3) ( (3 3) (3 ) 3) 3 6 (5).3 B T. w the time constant T can be determined in dependence of B and a Y,max : 4.3 Steering control Planning y y des a y,des T = B.3. a Y,max (6) -. ψ des PD Fig. 8. Structure of steering controller For steering control a two-degree-of-freedom structure is used, consisting of a feedforward and a feedback controller. Feedforward control The trajectory planning leads to the following state space system is gien: ẏ ref Y,ref ȧ Y,ref j Y,ref = T 4 4 T 3 6 T 4 T FF δ FB y ref Y,ref a Y,ref j Y,ref δ FF + δ des T 4 B ref. (7) When the easie maneuer is started, B ref as input signal is set to B. Then an easie trajectory in time-domain y ref (t) is gien as a step-response of this state space model. Furthermore a y,ref (t) is calculated. This can be used for feedforward-control. With the desired lateral acceleration the desired yawrate ψ ref can be calculated: ψ ref = a Y,ref. (8) Using the desired yawrate it is possible to calculate a desired steering angle, Schorn and Isermann [6]: δ ψ = i S l + SG. (9) 697

5 9th IFAC World Congress Cape Town, South Africa. August 4-9, 4 SG is the so-called understeer gradient and describes the steering behaiour depending on the elocity, Gillespie [99], Kiencke and Nielsen []: SG = c α,rl r + c α,f l f. () c α,f c α,r l Feedback control Schorn [7] inestigated different controllers. Finally he ended up in the relatiely simple PD-Controller, which is also used here. As the one track ehicle model shows, the lateral behaiour depends on the elocity. Therefore M different controllers depending on the elocity of the ehicle are applied. The controller outputs are weighted with membership or actiation functions and summarized as shown in Fig. 9. This approach uses local linear models (Fink et al. [999]). y Controller Controller... Controller M 95 m km/h km/h m 5 km/h Fig.. Maneuer : High difference elocity, swering possible 95 m 5 km/h km/h m 5 km/h Fig.. Maneuer : High difference elocity, swering not possible 5. Decision erification For better illustration the maximum deceleration is now assumed with 5 m s, because then the time interal between the last point to steer and the last point to brake is larger. Fig. 9. Structure of elocity dependent controllers δ fb The output of the local linear controller network is obtained from the weighted controller outputs: using δ fb = M δ LLM,i Φ i () () i= free space forecast action RL &RL steering braking LPB LPS Φ i () = µ i () M j= µ j() as actiation function. with 5. RESULTS ( µ i () = exp ( c i ) ) σ i () This section summarizes the results of the collision aoidance part. After introducing different testing scenarios, the results are presented. Here only the case of a large difference elocity is considered as an example. 5. Scenarios Maneuer : High difference elocity, swering possible In the first maneuer the ego ehicle dries with km h. In front of the own car is another ehicle, which dries ery slow. On the left lane dries a car with higher speed, which will not disturb the easie maneuer. Maneuer : High difference elocity, swering not possible The second maneuer is nearly the same like the first one. Only the car on the left dries with a higher elocity. So this car will block the easie maneuer. Fig.. Decision for scenario Fig. depicts the decision for scenario. At about. seconds at the last point to brake the decision is made. Because the forecast determines a free road, the easie maneuer is started at 3.4 seconds which is the last point to steer. free space forecast action RL &RL steering braking LPB LPS Fig. 3. Decision for scenario 698

6 9th IFAC World Congress Cape Town, South Africa. August 4-9, 4 In Fig. 3 the decision is also made at. seconds. But in this case the forecast determines a ehicle on the left lane at the last point to steer. So an emergency braking maneuer is started immediately. Hence it is illustrated, that the forecast determines the blocked lane already at the last point to brake een if there is enough space at this time instant, but not later. 5.3 Steering control y in m meas. ref (a) Control ariable δ in rad 4 Fig. 4. Steering control ay in m/s (b) Lateral acceleration ff fb (c) Manipulated steering angle For the steering the controller described before is used. In Fig. 4 the reference and the drien trajectory, the lateral acceleration and the steering angle diided in feedforward and feedback part are shown. The car follows the trajectory well and the collision is aoided. 6. CONCLUSION A drier assistance system was presented, which uses either the brake for the preenting of collisions or the steering. For swering knowledge on ehicles of the adjacent roadway is required. A method was presented which takes the aailability of the free space into account. Finally a decision is made based on the elocities, distances, gien maximum accelerations and the estimated free space to aoid the collision. Stability limits of driing physics are considered by the specification of maximum lateral acceleration and maximum deceleration. These alues hae to be chosen depending on the road condition. The system tries to use the latest possible point for interention if the drier does not react. The next step is to optimize the deeloped system. Presently the drier has the possibility to interent until the last possible point. But then the system reacts fully automatically. Therefore a warning system could be introduced. Further the inclusion of an appropriate interpretation of the drier s intentions can be inestigated. To reduce the easie time also a combination of braking and swering is conceiable. SYMBOLS ehicle elocity m/s a Y lateral acceleration m/s ψ yaw rate rad/s δ H steering wheel angle rad i S steering ratio c α cornering stiffness N/rad l wheel base m TTC time to collision s T brake braking time s T ea easie time s s dx distance in x-direction m s dy distance in y-direction m dx difference elocity in x-direction m/s REFERENCES Carlo Ackermann, Rolf Isermann, Sukki Min, and Changwon Kim. Design of a decision maker for an easie or braking maneuer. In 4th Stuttgart International Symposium, 4. Ea Bender, Michael Darms, Matthias Schorn, Ulrich Stählin, Rolf Isermann, Hermann Winner, and Kurt Landau. Anti collision system proreta on the way to the collision aoiding ehicle: Part : Basics of the system. ATZ Worldwide, 9(4): 3, 7. Alexander Fink, Olier Nelles, and Martin Fischer. Linearization based and local model based controller design. In European Control Conference, 999. Thomas D. Gillespie. Fundamentals of ehicle dynamics. Society of Automotie Engineers, Warrendale and PA, 99. John C. Hayward. Near miss determination through use of a scale of danger. Report no. TTSC75. The Pennsylania State Uniersity, 97. Rolf Isermann and Marco Münchhof. Identification of dynamical systems. Springer-Verlag, Berlin,. Rolf Isermann, Roman Mannale, and Ken Schmitt. Collision-aoidance systems proreta: situation analysis and interention control. Control Engineering Practice, ():36 46,. Uwe Kiencke and Lars Nielsen. Automotie control systems. Springer-Verlag, Berlin and New York,. Ken Schmitt. Situationsanalyse für ein Fahrerassistenzsystem zur Vermeidung on Überholunfällen auf Landstraßen, olume 763 of Fortschrittberichte VDI Reihe. VDI Verlag,. Matthias Schorn. Quer- und Längsregelung eines Personenkraftwagens für ein Fahrerassistenzsystem zur Unfallermeidung, olume 65 of Fortschrittberichte VDI Reihe. VDI-Verlag, Düsseldorf, 7. Matthias Schorn and Rolf Isermann. Automatic steering and braking for a collision aoidance ehicle. In 4th IFAC-Symposium on Mechatronic Systems: -4 September, 6. Ulrich Stählin, Matthias Schorn, and Rolf Isermann. Collision aoidance braking and steering strategies for an adanced drier assistance system. In 7th Stuttgart International Symposium, 7. Hermann Winner, Stephan Hakuli, and Gabriele Wolf. Handbuch Fahrerassistenzsysteme. ATZ- MTZ-Fachbuch. Vieweg + Teubner, Wiesbaden,