Abstract:
To determine whether an emergency braking situation exists for a vehicle, the vehicle determines at least the following state variables: its own velocity, its own longitudinal acceleration, its relative distance from an object in front, and the speed and acceleration of the object in front. A suitable evaluation method to assess whether an emergency braking situation is present is determined as a function of these state variables from a plurality of evaluation method options, including at least a movement equation evaluation method in which a movement equation system of the vehicle and of the object in front is determined, and an evaluation method in which a braking distance of the vehicle is determined.

Description:
FIELD OF THE INVENTION 
       [0001]    The present invention generally relates to a method for determining an emergency braking situation of a vehicle (e.g., risk of a rear impact), a control device for carrying out the method and a driving dynamics control system equipped with the control device. 
       BACKGROUND OF THE INVENTION 
       [0002]    It is generally known to establish equations of motion in order to determine a collision time for the current driving behavior of a vehicle and of a vehicle ahead. It is also generally known to determine target decelerations in order to avoid possible collisions. 
         [0003]    EP 1 539 523 B1 and DE10258617B4 disclose a method and a device for triggering an automatic emergency braking process of a vehicle. The speed and the acceleration of the subject vehicle are determined and a minimum distance is set as a target safety distance. Furthermore, a target relative speed between the two vehicles is set that should be reached at the end of the automatic emergency braking process. In addition, the determined currently existing relative acceleration between the two vehicles is used. 
         [0004]    DE 10 2006 019 848 84 discloses a device for reducing the effects of a vehicle collision in which an obstruction is detected with its relative distance and its relative speed and a possible collision or accident is assessed, whereupon an occupant protection device may be activated. Such systems are also known as pre-crash systems. 
         [0005]    JP 2004038245 A1 discloses an obstruction detector for vehicles with which a detected steering wheel operation is additionally used. EP 0 891 903 B1 discloses an automatic emergency brake function that assesses the possibility of avoiding an obstruction. EP 1 625 979 B1 discloses a method and a device for triggering emergency braking with which a probability of collision and furthermore a risk to the subject vehicle in the case of triggering of emergency braking are determined and the triggering threshold for the emergency braking can be varied depending on the determined risk. EP 1 803 109 B1 discloses a method for determining relevant objects close to a vehicle by which collision-relevant values are calculated from vehicle data and/or environmental sensor data including possible evasive maneuvers or braking processes. 
         [0006]    Such conventional methods have the disadvantage that, in general, they are often restricted to only special driving situations and thus do not always contribute in a timely manner to avoiding accidents by autonomous braking. Furthermore, triggering of emergency braking may also take place too early and thus possibly unnecessarily. 
         [0007]    Furthermore, various cruise control systems without emergency braking are known. For example, the Bendix-Wingman ACB adaptive cruise system with a braking property comprises a distance maintaining method for maintaining the distance to a vehicle ahead constant. Warning display signals and also emergency braking signals can be output for automatically carrying out an emergency braking process. For this purpose the distance to the vehicle ahead is measured, e.g., with radar. 
       SUMMARY OF THE INVENTION 
       [0008]    Generally speaking, it is an object of the present invention to provide a method, a corresponding control device to carry it out, and a driving dynamics control system, that enable reliable recognition of an emergency braking situation and keep the likelihood of unwarranted emergency braking low. 
         [0009]    Various methods for assessing whether an emergency braking situation is presented can be used based on the currently prevailing driving situation. 
         [0010]    According to a first assessment method, which constitutes an equation of motion assessment method, equations of motion of both a subject vehicle and also an object ahead of the vehicle are established and an assessment is made depending on the equations of motion as to whether an emergency braking situation exists. Depending on the assessment, a required deceleration can be calculated. The equations of motion can be established in the second order of time, i.e., with an initial value, a linear term and a quadratic term, so that a common system of equations or a common equation of motion of the subject vehicle and the object ahead can be formed, from which a subsequent distance less than a minimum distance and/or a collision can be determined. 
         [0011]    According to a second assessment method, a braking distance observation is carried out, in which the braking distance at least of the subject vehicle is determined and can be assessed. 
         [0012]    In a typical driving situation of a subject vehicle behind an object ahead, an emergency braking situation can be determined using equations of motion of the subject vehicle and of the object ahead. For such an equation of motion assessment method, second order equations of motion in the time domain can be formed, i.e., with a relative distance as a zero order term in the time domain, the speeds (or the relative speed) as first order terms in the time domain, and the accelerations as second order terms in the time domain. From these equations of motion, a system of equations can thus be formed, by which it can be determined whether an approach to an admissible minimum distance will occur (e.g., a minimum distance of 1 meter or even zero). In addition, response times of the brake systems of the vehicle (e.g., for supplying air to the brakes) and/or of the driver can be included, because changes through active interventions only take effect after the response time. 
         [0013]    A system of equations approach, especially using second order equations of motion in the time domain, can cause miscalculations in some situations. Second order equations of motion in the time domain with negative acceleration, i.e., braking or deceleration of the subject vehicle or of the object ahead, also mathematically include imaginary reversing following a completely stationary state of the vehicle or of the object. Such imaginary reversing is, however, physically meaningless, because a deceleration of a vehicle by means of a braking intervention or an engine retarding intervention (or even e.g., air friction) can indeed cause braking (negative acceleration) from a positive speed to the stationary state, but no further rearward acceleration of a stationary vehicle can be caused. Rather, with the vehicle stationary, the physically effective braking effect, i.e., the negative acceleration, decreases to zero, i.e., the vehicle comes to rest but reversing does not commence. 
         [0014]    Imaginary but meaningless collisions that occur during reversing, especially in the case of imaginary reversing of the object driving ahead, can thus be determined in the mathematical system of equations. 
         [0015]    Therefore, according to embodiments of the present invention, the equation of motion assessment method is only used if it is determined to be useful. Advantageously, criteria for determining different situations are used in order to select the suitable assessment method. 
         [0016]    If it is determined that the first assessment method, i.e., the equation of motion assessment method, is not useful, another assessment method is used, wherein at least one is provided as a second assessment method, preferably a braking distance assessment method with a braking distance observation. A braking distance of the subject vehicle is determined and assessed, preferably without involving the accurate equations of motion of the subject vehicle and of the object ahead. Preferably, a time-dependent admissibility criterion is defined, which compares the subject braking time of the first subject vehicle with the object braking time of the second object ahead, which constitutes a particularly simple determination and specification of the admissibility of the first or second assessment method. The subject braking time until reaching the minimum distance, while at the same time fully reducing the relative speed of the first subject vehicle to the second object ahead, can thereby be determined in advance. The object braking time is the time that the second object ahead requires to come to rest. 
         [0017]    According to an embodiment of the present invention, an advance criterion can be used regarding whether the relative distance has not already reached or fallen below the minimum distance following the response time, and thus an emergency braking situation already exists. This can be considered to be an advance (“zeroth”) assessment method, so that the first and second assessment methods do not even become relevant. 
         [0018]    The subject first acceleration can be measured by means of a longitudinal acceleration sensor and/or can be determined by time differentiation of the subject first speed. The relative distance to the object ahead can be determined by means of a distance sensor. From this, the second speed of the object can thus be determined from the time variation of the signal of the relative distance and its second acceleration can be determined as a time derivative thereof. However, in principle, the second speed of the object can also be recorded e.g., by means of a radar Doppler measurement. The assessment of the emergency braking situation can be determined by determining the required deceleration of the subject vehicle. 
         [0019]    In a distance-time diagram, the second order equations of motion in the time domain produce parabolas; for a negative acceleration, i.e., braking or deceleration, the parabolas are open at the bottom. The corresponding speed profiles form straight lines, which thus have a negative gradient for braking. 
         [0020]    The decreasing branches of a parabolic motion graph in the distance-time diagram and corresponding negative values in the speed-time diagram are assessed as physically meaningless. Such states, which result in a false assessment, are excluded by means of suitable criteria. 
         [0021]    The imaginary ease can thus be excluded in which during negative acceleration, i.e., deceleration or braking, the vehicle ahead causes a collision with the subject vehicle in a subsequent imaginary reversing movement after being at rest. 
         [0022]    In order to exclude this case of imaginary reversing that would produce a collision, a check is made as to what times or what braking distances the object and the subject vehicle require to come to rest. If the subject vehicle comes to rest earlier than or at the same time as the object ahead, according to one embodiment, the first assessment method can be applied advantageously. If the subject vehicle comes to rest later than the object ahead, however, the equation of motion assessment method is advantageously not applied because an imaginary collision case for subsequent reversing of the object ahead is determined. An admissibility criterion for the equation of motion assessment method is thus provided, wherein the second assessment method is consequently used if it is not fulfilled. 
         [0023]    With the second assessment method, in principle, the braking distances until coming to rest are used, but not the dynamics of the vehicle, i.e., its accurate equations of motion. Thus, theoretically, the case could occur in which a safety distance between the subject vehicle and the object ahead is maintained for the calculated values at the point in time of being at rest, but a collision (or falling below the minimum distance) occurs because of the actual previous dynamics of the subject vehicle. According to the inventive embodiments, the first and second assessment methods are recognized as being ideally complementary. Such collisions can already be detected by means of the equation of motion assessment method. Thus, if the admissibility criterion for the equation of motion assessment method is fulfilled and the equation of motion assessment method can be used, collisions are reliably detected until coming to rest. However, if the equation of motion assessment method cannot be used because of not fulfilling the admissibility criterion, with the second assessment method a false indication can no longer subsequently occur to the effect that, although the safety distance or minimum distance is maintained at the point in time of being at rest, a collision already occurs. Such collisions would have been detected in the equation of motion assessment procedure. 
         [0024]    Thus, a reliable method that can be implemented at relatively low computing costs is provided, which reliably detects different initial movement states of the subject vehicle and of the object ahead. Unnecessarily early emergency braking with risks arising therefrom both to the subject vehicle and possibly also to following vehicles are thereby excluded with high reliability. 
         [0025]    According to an embodiment of the present invention, both automatic emergency braking can be triggered or even a warning indication signal can be output to the driver. Accurate determination can include response times, which for an automatic emergency brake system include the equipment-related times to fill the brakes and operate the actuators, and also take into account the response time of the driver when outputting a warning indication signal to the driver. 
         [0026]    According to an embodiment, various cases are subdivided hierarchically. In principle, a first case can initially check whether the relative distance between the subject vehicle and the object ahead following the response time is less than a minimum distance that is to be maintained; if the first criterion is fulfilled, emergency braking will always be initiated immediately. Only subsequently are e.g., four cases considered, in each of which it is determined whether the first or second assessment method is to be applied. In these cases, the acceleration of the object ahead and the relative speed, especially the relative speed following the response time, are used. Thus, a case distinction can take place on the basis of only two variables, especially in four or five different cases. 
         [0027]    In these cases, initially the equation of motion assessment method may be checked and if this is not relevant, then the second assessment method is used. In two other cases, e.g., only the equation of motion assessment method or the second assessment method can be used. Furthermore, a case can exist in which the acceleration of the object ahead is positive and also the difference speed or the relative speed is positive, so that it can be recognized that there is no risk of collision at all. 
         [0028]    The control device according to an embodiment of the present invention can cap the torque of the engine, especially depending on the result of the method used to assess whether an emergency braking situation is presented, for which it e.g., outputs control signals to an engine controller. 
         [0029]    Still other objects and advantages of the present invention will in pa be obvious and will in part be apparent from the specification. 
         [0030]    The present invention accordingly comprises the features of construction, combination of elements, arrangement of parts, and the various steps and the relation of one or more of such steps with respect to each of the others, all as exemplified in the constructions herein set forth, and the scope of the invention will be indicated in the claims. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0031]    The invention is discussed in greater detail below with reference to the accompanying drawings, in which: 
           [0032]      FIG. 1  is a representation of a road scene with two vehicles traveling one after the other; and 
           [0033]      FIGS. 2 to 7  are diagrams illustrating the distances and speeds of the two vehicles and their relative distance according to different initial conditions. 
       
    
    
     LIST OF REFERENCE CHARACTERS 
       [0034]      1  subject vehicle 
         [0035]      2  object/vehicle ahead 
         [0036]      3  road 
         [0037]      4  distance sensor 
         [0038]      5  driving dynamics system 
         [0039]      6  control device 
         [0040]      7  speed sensor 
         [0041]      8  vehicle brakes 
         [0042]      9  warning display 
         [0043]    S 1  apex point of x 1   
         [0044]    S 2  apex point of x 2   
         [0045]    x 1  position of the first vehicle 
         [0046]    x 2  position of the second vehicle 
         [0047]    x 1 _ 0  position of the first vehicle at the point in time t=0 
         [0048]    x 2 _ 0  position of the second vehicle at the point in time t=0 
         [0049]    v 1  speed of the first vehicle 
         [0050]    v 1   —   t   1  speed of the first vehicle following the response time t 1   
         [0051]    v 2  speed of the second vehicle 
         [0052]    a 1  longitudinal acceleration of the first vehicle 
         [0053]    a 2  longitudinal acceleration of the second vehicle 
         [0054]    a 1   —   d _ 1  first target acceleration 
         [0055]    a 1   —   d _ 2  second target acceleration 
         [0056]    dx relative distance 
         [0057]    dx_min minimum distance 
         [0058]    dx_ 0  initial relative distance at the point in time t=0 
         [0059]    dx —   t   1  relative distance following the response time t 1   
         [0060]    dx_ 2  relative distance according to BV 2   
         [0061]    s 1   —   br  available braking distance of the first vehicle 
         [0062]    s 1   —   react  distance covered by the first vehicle during t 1   
         [0063]    s 2   —   stop  braking distance of the second vehicle until coming to rest 
         [0064]    dv relative speed 
         [0065]    dv —   t   1  relative speed following the response time t 1   
         [0066]    M 1  relative distance measurement signal 
         [0067]    M 2  speed measurement signal 
         [0068]    M 3  brake control signals 
         [0069]    Si 1  warning indication signal 
         [0070]    t time 
         [0071]    t 1  response time 
         [0072]    t 1   —   dv  subject braking time of the first vehicle (dv=0; dx=dx_min) 
         [0073]    t 2   —   stop  object braking time of the second vehicle/object to v 2 =0 
         [0074]    BV 1  assessment method  1   
         [0075]    BV 2  assessment method  2   
         [0076]    BV 0  advance assessment method 
         [0077]    K 1  first criterion 
         [0078]    K 2  further criterion 
         [0079]    K 2   a  second criterion 
         [0080]    K 2   b  third criterion 
         [0081]    K 2   c  fourth criterion 
         [0082]    K 2   d  fifth criterion 
         [0083]    Zk 1  admissibility criterion 
       DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0084]    Referring now to the drawing figures,  FIG. 1  depicts a first subject vehicle  1  driving on a road  3  behind an object ahead  2 , in this case a second vehicle  2  ahead. Only movements in the common vehicle longitudinal direction are considered below. The first subject vehicle  1  is located at a position x 1  and is traveling at a speed v 1  and with an acceleration a 1 . A braking process thus constitutes an acceleration a 1  with a negative value. Accordingly, the second vehicle ahead  2  is at a position x 2 , traveling at a second speed v 2  and with a second acceleration a 2 . All variables x 1 , v 1 , a 1 ; x 2 , v 2 , a 2  are time dependent. Consequently, second order equations of motion in the time domain are established for the two vehicles, the first subject vehicle  1  and the vehicle ahead  2 . Preferably, a constant first subject acceleration and second acceleration a 1 , a 2  are assumed here, at least until the initiation of a braking process of the subject vehicle  1 . 
         [0085]    The subject vehicle  1  comprises a distance sensor  4  for determining a relative distance dx between the first subject vehicle  1  and the vehicle  2  ahead, a driving dynamics system  5  with a control device  6 , a speed sensor  7  and vehicle brakes  8  that can be controlled by the control device  6 . The distance sensor  4  outputs a relative distance measurement signal M 1  and, correspondingly, the speed sensor  7  outputs a speed measurement signal M 2  to the control device  6 . The speed sensor  7  can also be formed by the ABS wheel revolution rate sensors. Furthermore, the control device  6  outputs brake control signals M 3  to the vehicle brakes  8 . 
         [0086]    According to an embodiment of the present invention, a case distinction is carried out depending on various criteria in various scenarios, in which different assessment processes or assessment methods are used to determine whether a collision can occur and when emergency braking may have to be initiated. 
         [0087]    All calculations take place in the first subject vehicle  1 , which thus determines the risk of a rear-end collision with the vehicle ahead  2 . Depending on the determination, subsequently either emergency braking is automatically initiated by an autonomous emergency brake system (advanced emergency braking system, AEBS) of the first subject vehicle  1  and/or a warning indication signal Si 1  is output by means of a warning display  9  to the driver of the first subject vehicle  1 . 
         [0088]    For each of the two cases, a different response t 1  can be applied. For an independent AEBS, a shorter response time t 1  can be applied, which is essentially determined by the time to build up a brake pressure in the brakes (applying air to brakes). For a collision warning (forward collision warning, FCW) to the driver, initially the response time of the driver, e.g., between one second for an attentive driver and two seconds for a distracted or inattentive driver, and additionally the required equipment-related time to build up (he internal brake pressure are to be taken into account. 
         [0089]    Assessment methods for the braking criterion, i.e., the determination of a point in time at which the emergency braking is to be initiated, are described below. 
         [0090]    The aim is to establish, where possible, the second order equations of motion of the first subject vehicle  1  and of the second vehicle ahead  2  and to determine therefrom whether emergency braking is to be initiated. Thus, a path of motion or parabola of motion is established, which in the case of negative acceleration may result in coming to rest, but mathematically also describes in the following time values a reverse movement of the first subject vehicle  1  involved and/or of the second vehicle ahead  2  involved. However, because the negative acceleration resulting from the braking effect ceases when the first subject vehicle  1  and the second vehicle ahead  2  are at rest and does not cause reversing or continued acceleration in the rearward direction(negative direction), a distinction can be made as to whether, when establishing the parabolas of motion or second order equation of motion, the physically meaningless case is detected with a situation possibly falsely indicating a collision (or falling below the minimum distance) during subsequent imaginary reversing. If the case can be excluded, the second order equations of motion in the time domain are established. However, if such a case or a similar case is recognized, a braking distance observation is carried out. 
         [0091]    Assessment Method BV 1 : 
         [0092]    The braking criterion can be determined from the second order equations of motion. The position of the second vehicle ahead  2  (object) can be represented as: 
         [0000]    
       
         
           
             
               
                 
                   
                     x 
                      
                     
                         
                     
                      
                     2 
                   
                   = 
                   
                     
                       x2_ 
                        
                       0 
                     
                     + 
                     
                       v 
                        
                       
                           
                       
                        
                       
                         2 
                         · 
                         t 
                       
                     
                     + 
                     
                       
                         1 
                         2 
                       
                        
                       a 
                        
                       
                           
                       
                        
                       
                         2 
                         · 
                         
                           
                             t 
                             2 
                           
                           . 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   1 
                 
               
             
           
         
       
     
         [0093]    where x 2 _ 0  is the position at the point in time t=0. 
         [0094]    Accordingly, the position of the subject first vehicle  1  can be represented as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     x 
                      
                     
                         
                     
                      
                     1 
                   
                   = 
                   
                     
                       x1_ 
                        
                       0 
                     
                     + 
                     
                       v 
                        
                       
                           
                       
                        
                       
                         1 
                         · 
                         t 
                       
                     
                     + 
                     
                       
                         1 
                         2 
                       
                        
                       a 
                        
                       
                           
                       
                        
                       
                         1 
                         · 
                         
                           
                             t 
                             2 
                           
                           . 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   2 
                 
               
             
           
         
       
     
         [0095]    Here, x 1  relates to the forward end point of the subject first vehicle  1 ; by contrast x 2  relates to the rearward end point, i.e., the rear of the second vehicle  2  ahead, so that the relative distance dx is directly measured by the distance sensor  4 . With dx=0 there is thus a collision or a rear-end collision. 
         [0096]    From Equations 1 and 2 the relative distance dx can be represented as follows: 
         [0000]    
       
         
           
             dx 
             = 
             
               
                 ( 
                 
                   
                     x2_ 
                      
                     0 
                   
                   - 
                   
                     x1_ 
                      
                     0 
                   
                 
                 ) 
               
               + 
               
                 
                   ( 
                   
                     
                       v 
                        
                       
                           
                       
                        
                       2 
                     
                     - 
                     
                       v 
                        
                       
                           
                       
                        
                       1 
                     
                   
                   ) 
                 
                 · 
                 t 
               
               + 
               
                 
                   1 
                   2 
                 
                 · 
                 
                   ( 
                   
                     
                       a 
                        
                       
                           
                       
                        
                       2 
                     
                     - 
                     
                       a 
                        
                       
                           
                       
                        
                       1 
                     
                   
                   ) 
                 
                 · 
                 
                   t 
                   2 
                 
               
             
           
         
       
     
         [0097]    It follows from this that: 
         [0000]    
       
         
           
             
               
                 
                   dx 
                   = 
                   
                     
                       dx_ 
                        
                       0 
                     
                     + 
                     
                       dv 
                       · 
                       t 
                     
                     + 
                     
                       
                         1 
                         2 
                       
                       · 
                       
                         ( 
                         
                           
                             a 
                              
                             
                                 
                             
                              
                             2 
                           
                           - 
                           
                             a 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         ) 
                       
                       · 
                       
                         
                           t 
                           2 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   3 
                 
               
             
           
         
       
     
         [0098]    with dv=v 2 −v 1 , i.e., the relative speed, and dx_ 0 =x 2 _ 0 −x 1 _ 0 , a relative distance dx_ 0  determined at the point in time t=0. 
         [0099]    This equation thus describes the relative movement between the first subject vehicle  1  and the second vehicle ahead  2 . This can be applied in order to avoid a collision between the first subject vehicle  1  and the second vehicle ahead  2  as late as possible. 
         [0100]    The acceleration a 1  of the subject vehicle  1  (of negative magnitude) is now determined for bringing the relative speed dv to zero while at the same time an admissible minimum distance dx_min is reached, i.e., dx=dx_min. The idea here is that for a relative speed dv=0 an approach by the first subject vehicle  1  to the second vehicle ahead  2 , which should take place on reaching the minimum distance dx_min, will no longer occur. 
         [0101]    If the two conditions dv=0 and dx=dx_min are inserted in Equation 3, the following value is given as the first target acceleration a 1   —   d   —1:    
         [0000]    
       
         
           
             
               
                 
                   
                     a1_d 
                      
                     _ 
                      
                     
                         
                     
                      
                     1 
                   
                   = 
                   
                     
                       a 
                        
                       
                           
                       
                        
                       2 
                     
                     - 
                     
                       
                         
                           dv 
                           2 
                         
                         
                           2 
                           · 
                           
                             ( 
                             
                               
                                 dx_ 
                                  
                                 0 
                               
                               - 
                               dx_min 
                             
                             ) 
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   4 
                 
               
             
           
         
       
     
         [0102]    Here, the value a 1   —   d _ 1  is referred to as the “first” target acceleration and is provided with the extension “_ 1 ”, because it is determined according to the first assessment method BV 1 , i.e., the equation of motion assessment method. 
         [0103]    In order to calculate the necessary first target acceleration a 1   —   d _ 1  of the subject vehicle  1 , the relative speed following the response time t 1  is determined as dv_t 1 . In the above equations it is thus assumed that the accelerations a 1  and a 2  are constant between the points in time t=0 and t=t 1 . The following is thus the result: 
         [0000]        dv   —   t 1 =dv +( a 2− a 1)· t 1   Equation 5
 
         [0104]    In addition, the relative distance dx 13  t 1  following the response time ti is determined for determining the first target acceleration a 1   —   d _ 1 . For this purpose, it is again assumed that the accelerations a 1  and a 2  are constant. Using the relative distance dx or dx_ 0  determined at the point in time t=0 by the distance sensor  4 , dx_t 1  can thus be calculated as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     dx_t 
                      
                     
                         
                     
                      
                     1 
                   
                   = 
                   
                     
                       dx_ 
                        
                       0 
                     
                     + 
                     
                       
                         dv 
                         · 
                         t 
                       
                        
                       
                           
                       
                        
                       1 
                     
                     + 
                     
                       
                         ( 
                         
                           
                             a 
                              
                             
                                 
                             
                              
                             2 
                           
                           - 
                           
                             a 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         ) 
                       
                       · 
                       
                         
                           
                             t 
                              
                             
                                 
                             
                              
                             
                               1 
                               2 
                             
                           
                           2 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   6 
                 
               
             
           
         
       
     
         [0105]    The required first target acceleration a 1   —   d _ 1  of the subject vehicle  1  can thus be calculated based on dv_t 1  and dx_t 1  as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     a1_d 
                      
                     _ 
                      
                     1 
                   
                   = 
                   
                     
                       a 
                        
                       
                           
                       
                        
                       2 
                     
                     - 
                     
                       
                         
                           
                             ( 
                             
                               dv_t 
                                
                               
                                   
                               
                                
                               1 
                             
                             ) 
                           
                           2 
                         
                         
                           2 
                           · 
                           
                             ( 
                             
                               
                                 dx_t 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                               - 
                               dx_min 
                             
                             ) 
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   7 
                 
               
             
           
         
       
     
         [0106]    Equation 7 is used to calculate the required first target acceleration a 1   —   d _ 1  in the following example. In the example, the second vehicle ahead  2  is accelerating with a second acceleration a 2 =−3 m/s 2 , i.e., the second vehicle  2  ahead is braking from a second initial speed v 2 =60 km/h. The subject first vehicle  1  has an initial speed of v 1 =90 km/h. The minimum distance dx_min is set to 1 m, the relative distance dx_t 0  at the point in time t=0 between the first subject vehicle  1  and the second vehicle ahead  2  is determined by the distance sensor  4  at dx_ 0 =60 m. With a response time t 1 =1 s the example results by means of Equation 7 in a required first target acceleration of a 1   —   d _ 1 =−4.3 m/s 2 . The resulting curves of motion of the first subject vehicle  1  and of the second vehicle ahead  2  are shown in  FIG. 2 . 
         [0107]    The speed curves of the first speed v 1  and of the second speed v 2  thus decrease linearly and reach the zero line. The displacement curves x 1  and x 2  form parabolas that are open below, which initially rise up to their respective apex points S 1  or S 2 , at which v 1  or v 2  thus also equal 0; the right side of the parabolas is assessed as physically meaningless because it corresponds to an imaginary reversing movement in each case. 
         [0108]    With the selected example, a stationary state of the second vehicle ahead  2  is achieved after t=5.5 s, i.e. v 2  (t=5.5 s)=0. The subject vehicle  1  reaches the stationary state v 1 =0 at t=6.8 s. 
         [0109]    With this example the inadmissible region in the diagram, i.e., the imaginary reversing movement of the second vehicle ahead  2 , thus starts from t=5.5 s. 
         [0110]    In the example of  FIG. 2 , the point at which the conditions dv=0 and dx=dx_min are fulfilled is arranged at t=9.7 s when the two lines of v 1  and v 2  intersect. However, the imaginary point of intersection already lies in the inadmissible region, wherein both vehicle speeds are actually negative at v 1 =v 2 =−44.8 km/h, i.e., each is an imaginary reversing movement. The result is thus assessed as inadmissible. 
         [0111]    A comparison of the apex points S 1  and S 2 , i.e., the positions x 1  (v 1 =0)=94.8 m and x 2  (v 2 =0)=107.1 m, shows however that with the result for a 1   —   d _ 1  in the situation a collision would have been avoided. The relative distance dx between the two vehicles  1  and  2  at the point in time of being stationary is, at 107.1 m−94.8 m=12.3 m, greater than the presumed minimum value dx_min, from which it follows that the braking or acceleration at a 1   —   d _ 1  was too high, i.e., represents a braking effect that is too high. Thus, an autonomous brake system would be activated prematurely. 
         [0112]    The weakness of the first method or first approach is especially shown in situations in which, e.g., initially, i.e., at t=0, there is a large relative distance dx between the first subject vehicle  1  and the second vehicle ahead  2  and strong braking of the vehicle ahead  2 ; in such situations the imaginary reversing movement of the vehicle ahead  2  and the subsequent imaginary collision thus occur faster during a reversing movement of the vehicle ahead  2 . In  FIG. 3 , a situation that is modified compared to  FIG. 2  is shown; with respect to  FIG. 2 , the speeds v 2 =60 km/h, v 1 =90 km/h at the point in time t=0 and the minimum distance dx_min=1 m are held constant. But now the vehicle ahead  2  is accelerating with a 2 =−6 m/s 2 , i.e., stronger braking, and the initial relative distance dx_ 0  between vehicle  1  and 2 is dx_ 0 =90 m. In this case, Equation 7 results in a first target acceleration a 1   —   d _ 1  of −73 m/s 2 . The curves of motion are shown in  FIG. 3 . 
         [0113]    In the example of  FIG. 3 , a comparison of the positions of the vehicles at their apex points S 1  and S 2 , i.e., x 1  (v 1 =0)=68.9 m and x 2  (v 2 =0)=114 m shows that the relative distance dx between them when at rest is 45.1 in. The point at which the conditions dv=0 and dx=dx_min are fulfilled also lies within the inadmissible region after the second vehicle ahead  2  has come to rest, i.e., at t=11.8 s, v 2 −195 km/h, similar to the above example of  FIG. 2 . 
         [0114]    The approach using second order equations of motion in the time domain with the boundary conditions to achieve a relative speed dv=0 (equal speeds of the vehicles) by means of the braking while simultaneously setting a minimum distance dx_min is thus not used or is rejected for such cases. 
         [0115]    In  FIG. 4 , another example is shown in which the conditions dv=0 and dx=dx_min are achieved before the vehicle ahead  2  comes to rest. The vehicle ahead  2  is braking with a 2 =−2 m/s 2  from an initial second speed of v 2 =50 km/h. The subject vehicle  1  has an initial speed of v 1 =90 km/h. The value for dx_min is set to 1 m, and the initial relative distance dx_ 0  between the two vehicles  1 ,  2  is dx_ 0 =40 m. The response time is again t 1 =1 s. For the example, Equation 7 results in a value a 1   —   d _ 1  of −5.2 m/s z . The resulting movements are shown in  FIG. 4 . The vehicle ahead  2  comes to rest after t=7 sec. The conditions dv=0 and dx=dx_min are fulfilled at t=5.1 s. In the situation, the result represents a point in time that lies within the allowed region; Equations 3 and 4 represent realistic movements of both vehicles  1 ,  2  with v 1 , v 2 &gt;0. In the situation of  FIG. 4 , the value a 1   —   d _ 1 , which is calculated on the basis of Equation 7, thus represents an admissible value that can be used for assessing the situation. 
         [0116]    Thus, it can be recognized that Equation 7 produces admissible values while both vehicles  1 ,  2  are still traveling, i.e., have not yet reached the stationary state. However, the results are inadmissible if one of the vehicles  1 ,  2  comes to rest. 
         [0117]    As graphically illustrated in the drawing figures, an inadmissible region thus starts if the paraboloid distance curve x 1  or x 2  of one of the vehicles  1 ,  2  reaches its apex point S 1  or S 2 ; accordingly, the speed lines then each intersect the zero point or the zero axis. 
         [0118]    An admissibility criterion Zk 1  is therefore applied in order to check the admissibility of the first assessment method. For this purpose, the subject braking time t 1   —   dv  that the subject vehicle  1  requires to reach the conditions dv=0 and dx=dx_min is compared with the object braking time t 2   —   stop  that the second vehicle ahead  2  requires for braking to rest. If the admissibility criterion Zk 1 : t 1   —   dv ≦t 2   —   stop  is fulfilled, it is ensured that the situation is to be assessed according to  FIG. 4 , i.e., the subject vehicle  1  reaches dv=0 and dx=dx_min before the vehicle ahead  2  comes to rest. An admissible result is thus indicated by this, i.e., the equation of motion assessment method (first assessment method) is admissible. 
         [0119]    The object braking time t 2   —   stop  can be calculated on the basis of its current second speed v 2  and second acceleration a 2 : 
         [0000]    
       
         
           
             
               
                 
                   
                     t2_ 
                      
                     stop 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             0 
                              
                             
                                 
                             
                              
                             
                               km 
                               / 
                               h 
                             
                           
                           - 
                           
                             v 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         ) 
                       
                       
                         a 
                          
                         
                             
                         
                          
                         2 
                       
                     
                     = 
                     
                       - 
                       
                         
                           
                             v 
                              
                             
                                 
                             
                              
                             2 
                           
                           
                             a 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   8 
                 
               
             
           
         
       
     
         [0120]    The subject braking time t 1   —   dv  required by the subject vehicle  1  is based on the result for a 1   —   d _ 1  from Equation 7 and can be calculated as: 
         [0000]    
       
         
           
             
               
                 
                   t1_dv 
                   = 
                   
                     
                       
                         
                           2 
                            
                           
                             ( 
                             
                               dx_t1 
                               - 
                               dx_min 
                             
                             ) 
                           
                         
                         
                           ( 
                           
                             
                               a 
                                
                               
                                   
                               
                                
                               2 
                             
                             - 
                             
                               a1_d 
                                
                               
                                   
                               
                                
                               _ 
                                
                               1 
                             
                           
                           ) 
                         
                       
                     
                     + 
                     
                       t 
                        
                       
                           
                       
                        
                       1. 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   9 
                 
               
             
           
         
       
     
         [0121]    This gives the following assessment criteria for the admissibility or validity: 
         [0122]    If the admissibility criterion a 1  is fulfilled, i.e., t 1   —   dv ≦t 2   —   stop,  then the first target acceleration a 1   —   d _ 1  applies or is admissible, i.e., the equation of motion assessment method (first assessment method) BV 1  with Equation 7 is admissible. 
         [0123]    If t 1   —   dv &gt;t 2   —   stop,  then a 1   —   d _ 1  is not admissible. 
         [0124]    In order to be able to suitably recognize the inadmissible situations, in which the determination described above does not lead to an admissible result, and to determine a second, in this case admissible, target acceleration or required deceleration a 1   —   d _ 2 , the subsequent second assessment process BV 2  or assessment method is applied: 
         [0125]    Second Assessment Process BV 2 : 
         [0126]    The second assessment process BV 2  calculates the distance that the subject vehicle  1  has available to come to rest behind the vehicle ahead  2 . 
         [0127]    Based on the distance, the second target acceleration a 1   —   d _ 2  is calculated that is required to come to rest within the distance, starting from the current speed v 1  of the subject vehicle  1 . The calculation involves all parts that contribute thereto. The parts or partial distances are:
       the current distance dx between the subject vehicle  1  and the vehicle ahead  2 ,   the distance s 2   —   stop  that the vehicle ahead  2  travels until coming to rest during the braking process with its current second acceleration a 2  (braking) from its current second speed v 2 ,   the distance s 1   —   react  that the subject vehicle travels during the response time t 1 ,   the minimum distance dx_min that should remain between the vehicles  1  and  2  after both have come to rest.       
 
         [0132]    The maximum available braking distance s 1   —   br  for the subject vehicle  1  can be calculated according to: 
         [0000]    
       
         
           
             
               
                 
                   
                     s1_br 
                     = 
                     
                       dx 
                       + 
                       
                         s2_ 
                          
                         stop 
                       
                       - 
                       
                         s1_ 
                          
                         react 
                       
                       - 
                       dx_min 
                     
                   
                   , 
                   
                     
 
                   
                    
                   with 
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   10 
                 
               
             
             
               
                 
                   
                     s2_ 
                      
                     stop 
                   
                   = 
                   
                     - 
                     
                       
                         
                           v 
                            
                           
                               
                           
                            
                           
                             2 
                             2 
                           
                         
                         
                           
                             2 
                             · 
                             a 
                           
                            
                           
                               
                           
                            
                           2 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   11 
                 
               
             
             
               
                 
                   
                     s1_ 
                      
                     react 
                   
                   = 
                   
                     
                       v 
                        
                       
                           
                       
                        
                       
                         1 
                         · 
                         t 
                       
                        
                       
                           
                       
                        
                       1 
                     
                     + 
                     
                       
                         
                           1 
                           2 
                         
                         · 
                         a 
                       
                        
                       
                           
                       
                        
                       
                         1 
                         · 
                         t 
                       
                        
                       
                           
                       
                        
                       
                         
                           1 
                           2 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   12 
                 
               
             
           
         
       
     
         [0133]    In order to calculate the required second target acceleration a 1   —   d _ 2  of the subject vehicle  1 , first the speed v 1   —   t   1  of the subject vehicle  1  following the response time t 1  is determined. This takes place under the assumption that the subject vehicle  1  is traveling with a constant acceleration a 1  during the response time t 1 : 
         [0000]        v 1 —   t 1= v 1 +a 1· t 1   Equation 13
 
         [0134]    Equation 13 thus gives the speed of the subject vehicle  1  following the response time t 1 . Based on v 1   —   t   1  and s 1   —   br,  the required acceleration of the subject vehicle  1  can be determined as a second target acceleration a 1   —   d _ 2  by: 
         [0000]    
       
         
           
             
               
                 
                   
                     a1_d 
                      
                     _ 
                      
                     2 
                   
                   = 
                   
                     - 
                     
                       
                         
                           
                             ( 
                             v1_t1 
                             ) 
                           
                           2 
                         
                         
                           2 
                           · 
                           s1_br 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   14 
                 
               
             
           
         
       
     
         [0135]    The second target acceleration a 1   —   d _ 2  that is determined in Equation 14 thus represents the required deceleration of the second assessment method BV 2  and is used in the following example. The driving situation of this example is similar to example 1 of  FIG. 2  in order to enable a direct comparison of the two approaches to calculating the target acceleration or required deceleration. The vehicle ahead  2  is accelerating (braking) at a 2 =−3 m/s 2  from an initial second speed of v 2 =60 km/h. The subject vehicle  1  has an initial speed of v 1 =90 km/h. The value for dx_min is set to 1 m and the initial relative distance dx_ 0  between the two vehicles  1  and  2  is dx_ 0 =60 m. The response time t 1  is 1 s. The second assessment method BV 2  according to Equation 14 leads to a required deceleration (second target acceleration) a 1   —   d _ 2  of −3.9 m/s 2 . However, the equation of motion assessment method BV 1  according to Equation 7 leads to a value of the first target acceleration of a 1   —   d _ 1  of −4.3 m/s 2 , which is to be considered as described above to be an inadmissible result, because Equation 7 represents a result whose point in time is after the first subject vehicle  1  and the second vehicle ahead  2  come to rest, at which the first subject vehicle  1  and the second vehicle ahead  2  are traveling backwards. In  FIG. 5 , the relationships are represented by the curves or graphs already shown in  FIG. 2  and the other curves. 
         [0136]    The second assessment method BV 2  thus only takes into account the end points of the situation if the first subject vehicle  1  and the second vehicle ahead  2  have come to rest; the braking phases are not considered separately for the first subject vehicle  1  and the vehicle ahead  2 . The braking distance s 2   —   stop  of the vehicle ahead  2  is used for the calculation of s 1   —   br.  By explicit calculation of this value, the unwanted consideration of the reversing movement of the vehicle ahead  2  is avoided. With this approach a stationary state of the second vehicle  2  ahead following the braking process is thus considered. This is illustrated by curve x 2  in  FIG. 5 . It represents the stationary state or the fixed position. In  FIG. 5  x 2 =const and v 2 =0 apply here after the second vehicle  2  ahead has come to rest. It is possible to calculate a correct target acceleration in such situations in which the subject vehicle  1  comes to rest after the vehicle ahead  2  comes to rest. 
         [0137]    The curves in  FIG. 5  thus show that Equation 14 represents the correct value for the target acceleration in this situation because it represents exactly the acceleration that is required in order to avoid a collision with the vehicle ahead  2  and for the first subject vehicle  1  to come to rest at a distance of 1 in behind the vehicle ahead  2 . Any stronger braking would also prevent a collision with the vehicle ahead  2 , but coming to rest would occur too early, i.e., at a larger relative distance dx than the target value of dx_min=1 m. This could thus lead to premature activation of the brake system with an AEBS. 
         [0138]    The second example of the previously shown equation of motion assessment method BV 1  shows another situation in which the equation of motion assessment method BV 1  results in too high a value for the first target acceleration a 1   —   d _ 1 . These situations are generally characterized by a large relative distance dx between the first subject vehicle  1  and the second vehicle ahead  2  and a strong deceleration a 2  of the vehicle ahead  2 . The example described with reference to  FIG. 3  uses an initial second speed v 2 =60 km/h of the vehicle ahead  2 , an initial speed v 1 =90 km/h of the subject vehicle  1 , a minimum distance dx_min=1 m, a second acceleration a 2   —   d _ 2 =−6 m/s 2  of the vehicle ahead  2  and an initial relative distance dx —0= 90 m. In this example, Equation 7 results in a first target acceleration of a 1   —   d _ 1  of −7.3 m/s 2 . However, Equation 14 results in a second target acceleration of a 1   —   d _ 2 =−3.6 m/s 2  in this situation. The resulting movements according to the two deceleration values are shown in  FIG. 6 . 
         [0139]    The vehicle ahead  2  comes to rest at t=2.8 s. The value for a 1   —   d _ 2  according to the equation of motion assessment method BV 1  described above is too high and leads to a distance at rest of 45.1 m, as indicated above. However, the second assessment method BV 2  leads to a value of the second target acceleration a 1   —   d _ 2  of −3.6 m/s 2 , which corresponds to the minimum deceleration that is necessary to prevent the collision with the vehicle ahead  2  in this situation.  FIG. 6  shows that the subject vehicle  1  comes to rest at t=8 s and achieves a relative distance of 1 m. 
         [0140]    By contrast, the example 3 shown above in connection with the equation of motion assessment method BV 1  provides a correct result for the first target acceleration a 1   —   d _ 1  with the equation of motion assessment method BV 1 . Here, the vehicle ahead  2  has decelerated with a 2 =−2 m/s 2  for an initial speed of 50 km/h. The subject vehicle  1  has an initial speed of 90 km/h. The value for dx_min is set to 1 m and the initial relative distance dx_ 0  between the first subject vehicle  1  and the second vehicle ahead  2  is 40 m. In this example, Equation 7 leads to a first target acceleration of a 1   —   d _ 1 =5.2 m/s 2 . Equation 14, however, leads to a result of a 1   —   d _ 2 =−5.02 m/s 2  for this situation. The resulting movements for the two acceleration values are shown in  FIG. 7 . 
         [0141]      FIG. 7  shows that deceleration with the second target acceleration a 1   —   d _ 2  determined according to the second assessment method BV 2  leads to the subject vehicle  1  coming to rest at t=6 s. The distance covered by the subject vehicle  1 , which is shown as x 1 , is 1 m smaller than the position x 2  of the vehicle ahead  2  if the vehicle ahead  2  comes to rest after t=7 s. However, before the subject vehicle  1  comes to rest for a second target acceleration a 1   —   d _ 2  the relative distance dx_ 2  between the subject first vehicle  1  and the second vehicle  2  ahead determined by the second assessment method BV 2  is less than 0. This means that the subject vehicle  1  collides with the vehicle ahead  2  before the subject vehicle  1  and the vehicle ahead  2  come to rest. Thus, the value of the second assessment method BV 2  for the second target acceleration a 1   —   d _ 2  in this example is not correct, or does not lead to a correct calculation of the deceleration value in order to prevent a collision with the vehicle ahead  2 . Rather, in such a ease the equation of motion assessment method BV 1 , i.e., a 1   —   d _ 1  according to Equation 7, is to be used. 
         [0142]    The second assessment method BV 2  thus only considers the end points of the braking situation if both vehicles  1 ,  2  have come to rest. However, it does not check the possible crossing point of the paths of motion of the two vehicles  1 ,  2  during the braking process, i.e., collisions taking place in the meantime. 
         [0143]    Thus, both assessment methods BV 1 , BV 2  are used for correct calculation of the braking criterion. 
         [0144]    For the specific case in which the vehicle ahead  2  is at rest and the subject vehicle  1  is approaching, both assessment methods BV 1 , BV 2  lead to the same result, because 
         [0000]        −dv   —   t 1= v 1 —   t 1 
         [0000]        dx   —   t 1 −dx _min= s 1 —   br    
         [0000]      a2=0 
         [0145]    Consequently, taking into account the above explanations, various cases for the use of the assessment methods BV 1  and BV 2  are thus different, essentially depending on the acceleration a 2  of the vehicle ahead  2  and the relative speed between the vehicles  1  and  2  after the response time dv_t 1  has elapsed. 
         [0146]    For checking the necessity for automatic brake operation for collision avoidance, the following cases are checked: 
         [0147]    In a first criterion K 1 , a check is made as to whether the distance dx_t 1  between the vehicles  1  and  2  after the response time t 1  is smaller than the minimum distance dx_min: dx_t 1 &lt;dx_min. 
         [0148]    If the first criterion K 1  is fulfilled, there is a need for automatic braking because the driver is unable to independently initiate deceleration. 
         [0149]    If the first criterion K 1  is not applicable, in another criterion K 2 , four cases are distinguished and checked: K 2   a,  K 2   b,  K 2   c,  K 2   d.  For case distinction, in each case the accelerations a 2  of the vehicle ahead  2  and the relative speed after expiry of the response time dv_t 1  are used. 
         [0150]    The second criterion K 2   a  is checked if a 2 &lt;0 and dv_t 1 &lt;0. Here, the equation of motion assessment method BV 1  is first checked. If this is not applicable, the second assessment method BV 2  is used. 
         [0151]    If the second criterion K 2   a  is fulfilled, i.e., the determined target acceleration a 1   —   d _ 1  or a_ 1   —   d   2  is below a limit value, there is a need for automatic braking of the subject vehicle  1  because the driver is not able to independently set the necessary level of deceleration after his/her response time has elapsed. 
         [0152]    The third criterion K 2   b  is checked if a 2 &lt;0 and dv_t 1 &gt;0. This is always checked using the second assessment method BV 2 . This avoids the weakness of the equation of motion assessment method BV 1  in those situations in which there is high deceleration of the vehicle ahead  2 . If the third criterion K 2   b  is fulfilled, i.e., the determined second target acceleration a 1   —   d _ 2  exceeds a limit value, there is a need for automatic braking of the subject vehicle  1  because the driver is not able to independently set the necessary level of deceleration after his/her response time has elapsed. 
         [0153]    The fourth criterion K 2   c  is checked if a 2 ≧0 and dv_t 1 &lt;0. This is only checked using the equation of motion assessment method BV 1  because only the assessment method BV 1  is relevant. The second assessment method BV 2  cannot be used here because no braking distance s 2   —   stop  can be determined for positive acceleration a 2  of the vehicle ahead  2 . The weakness of the equation of motion assessment method BV 1  in situations characterized by high deceleration of the vehicle ahead  2  is not relevant in such situations, because only positive values for a 2  are considered. If the fourth criterion K 2   c  is fulfilled, i.e., the determined first target acceleration a 1   —   d _ 1  exceeds a limit value, there is a need for automatic braking of the subject vehicle  1  because the driver is not able to independently set the necessary level of deceleration after his/he response time has elapsed. 
         [0154]    The fifth criterion K 2   d  is checked if a a 2 ≧0 and dv_t 1 ≧0. Here, the vehicle ahead  2  is accelerating away from the subject vehicle  1 . This case is thus completely safe, so that there is no need to initiate automatic emergency braking. 
         [0155]    The term “first, . . . fifth criterion” does not express any order or value here. 
         [0156]    Thus, according to the criteria K 1 , K 2   a  to K 2   d,  a control algorithm can he formed, according to which initially the first criterion K 1  is checked and subsequently the case distinction takes place in criteria K 2   a,  K 2   b,  K 2   c  and K 2   d,  in which as described the target acceleration (required deceleration) is determined either according to Equation 7 as a 1   —   d _ 1  or according to Equation 14 as a 2   —   d _ 2 . 
         [0157]    It will thus be seen that the objects set forth above, among those made apparent from the preceding description, are efficiently attained, and since certain changes may be made without departing from the spirit and scope of the invention, it is intended that all matter contained in the above description or shown in the accompanying drawings shall be interpreted as illustrative and not in a limiting sense. 
         [0158]    It is also to be understood that the following claims are intended to cover all of the generic and specific features of the invention herein described and all statements of the scope of the invention that, as a matter of language, might be said to fall therebetween.