DE102016218080B3 - Method and device for determining a collision probability of a vehicle with an object - Google Patents

Abstract

The invention relates to a device (1) and a method for determining a collision probability (15) of a vehicle (50) having an object (53), comprising the following steps: detecting a vehicle pose (7) and an object pose (8), calculating the Collision probability (15) by means of a calculation device (3), wherein the following steps are carried out: (a) determining a combined probability distribution (16) from the vehicle pose (7) and the object pose (8); (b) calculating a common collision surface (19) based on a vehicle surface (17) of the vehicle (50) and an object surface (18) of the object (53); (c) transforming the common collision surface (19) based on the combined probability distribution (16); (d) determining an integral of a probability density function over the transformed collision surface (20) to calculate the collision probability (15), wherein to determine the integral values are retrieved and provided from a look-up table (5) provided by a memory (4); and wherein the probability density function is a probability density function of a bivariate standard normal distribution, and outputting the calculated collision probability (15) as a collision probability signal (21) by means of an output device (6).

Description

The invention relates to a method and a device for determining a collision probability of a vehicle with an object.

Modern vehicles, especially motor vehicles, are equipped with a variety of assistance systems that assist the driver in driving the vehicle. Such assistance systems are, for example, distance control assistants or parking assistants. Increasingly, vehicles are also capable of automated or semi-automated driving.

Many assistance systems must determine what the probability of a collision of the vehicle with an object in the vicinity of the vehicle, such as an obstacle or another vehicle, is. When testing vehicle trajectories for collision, there is the problem that input data is usually subject to uncertainty. Thus, the measurements for the distance to other road users from the sensor, for example, measurement errors. Likewise, the data is subject to uncertainty for predicting the trajectories of the own vehicle and for surrounding vehicles. To account for these uncertainties in evaluating trajectories for collision freedom, it is possible to calculate the probability of a collision.

However, in view of the computation time required for this purpose, the determination of the collision probability of trajectories is very complicated, since there are often no closed solutions for this problem. One method commonly used to compute collision probabilities is based on the so-called Monte Carlo method (see Lambert, A, Gruyer, D, A Fast Monte Carlo Algorithm for Collision Probability Estimation, Control, Automation, Robotics and Vision , 2008 ICARCV 2008. 10th International Conference on IEEE, 2008). This method requires a very high number of binary collision checks for sufficient accuracy to ultimately approximate a collision probability value. This results in a very high cost in the calculation.

Other methods, such as in J. Hardy et al., Contingency Planning on Probabilistic Hybrid Obstacle Predictions for Autonomous Road Vehicles, 2010 IEEE / RSJ Int. Conference on Intelligent Robots and Systems, Taipei, Taiwan 2010 provide a strong over-approximation of collision probability at the expense of accuracy.

A method for computing bivariate normal distributions over convex polygons is described in A.R. Didonato et al., Computation of the bivariate normal distribution over convex polygon, Naval Surface Weapons Center, Virginia 1978.

The invention is based on the technical problem of providing a method and a device for determining a collision probability of a vehicle with an object in which it is possible to improve the determination of the collision probability.

The technical problem is solved by a method with the features of claim 1 and a device having the features of claim 10. Advantageous embodiments of the invention will become apparent from the dependent claims.

In particular, a method is provided for determining a collision probability of a vehicle with an object, comprising the following steps: detecting a vehicle pose by means of a detection device, wherein the vehicle pose comprises at least one vehicle position whose variance and vehicle angle, detecting a provided object pose by means of the detection device . wherein the object pose comprises at least one object position, its variance, and an object angle, calculating the collision probability by means of a calculator, the steps of: (a) determining a combined probability distribution from the vehicle pose and the object pose; (b) calculating a common collision surface based on a vehicle surface of the vehicle and an object surface of the object; (c) transforming the common collision surface based on the combined probability distribution; (d) determining an integral of a probability density function over the transformed collision surface to calculate the collision probability, wherein to determine the integral values are retrieved from a look-up table provided by a memory and provided; and wherein the probability density function is a probability density function of a bivariate standard normal distribution, and outputting the calculated collision probability as a collision probability signal by means of an output device.

Furthermore, an apparatus for determining a collision probability of a vehicle with an object is provided, comprising a detection device for detecting a vehicle pose, wherein the vehicle pose comprises at least one vehicle position, its variance and a vehicle angle, and for detecting an object pose, wherein the object pose at least one object position, whose variance and an object angle include, calculating means, wherein the calculating means is configured to determine a combined probability distribution of the vehicle pose and the object pose, to calculate a common collision area based on a vehicle area of the vehicle and an object area of the object, the common collision area Transform the basis of the combined probability distribution and an integral of a probability density function over the transformed collision surface to determine the collision probability a memory for providing a look-up table, wherein the calculating means for determining the integral retrieves values from the provided look-up table, and wherein the probability density function is a probability density function of a bivariate standard normal distribution, and output means for outputting the calculated collision probability as a collision probability signal ,

The basic idea of the invention is to transform a common collision surface formed from the vehicle and an object as a function of a combined probability distribution, which was determined from the vehicle pose and the object pose, and to integrate a probability density function over the transformed collision surface. The transforming comprises a displacement of the common collision surface and a stretching / upsetting according to the mean value and the variance of the combined probability distribution. As a result, it is possible to operate with a bivariate standard normal distribution in order to calculate the collision probability. The integral of the probability density function of the bivariate standard normal distribution over the transformed collision surface then gives the collision probability. To determine the integral, a lookup table stored in a memory is used according to the invention. This allows a very fast retrieval of values.

The advantage of the method is that significantly less computational effort is needed. Furthermore, in contrast to the aforementioned Monte Carlo method, it is deterministic, ie a repetition with the same input data leads to the same result. Despite the omission of an overapproximation, the method can be carried out with as much precision as desired. In addition, transforming to standard normal form always uses the same lookup table in each situation, so it only needs to be generated once.

The vehicle pose is detected in the form of a vehicle position (x _e , y _e ), a variance of this vehicle position (Σ _{e, x} , Σ _{e, y} ) and a vehicle angle (ψ _e ). The vehicle pose can be detected and provided, for example, by a correspondingly designed sensor system. However, it is also possible to provide calculated values, for example for a predicted trajectory, which should be traversed as part of an automated journey. The object pose is also detected in the form of an object position (x _o , y _o ), a variance of this object position (Σ _{o, x} , Σ _{o, y} ) and an object angle (ψ _o ). The object pose can be detected and determined, for example, by a surroundings sensor designed for this purpose. However, it is also possible to estimate the object pose based on, for example, map data stored in a map for the object.

In principle, it is always assumed in this context that only a single point in time is considered. The vehicle position and the object position thus correspond to estimates which correspond to normally distributed random distributions: p (x → _e ) ~ N (μ _e , Σ _e ) and p (x → _o ) ~ N (μ _o , Σ _o )

In general, the collision probability for a collision of the vehicle with the object can then be calculated from the overlap integral: ∫ _D p (x → _e ) p (x → _o ) dx → _e dx → _o with the vehicle area A and the object area B, which are each dependent on the respective center, the integration interval results in: D = {(x → _e , x → _o ) | A (x → _e ) ⋂ B (x → _o ) ≠ ∅}.

From the vehicle pose and the object pose, ie their normal distributions, the combined probability distribution is determined according to the method: p (x *) ~ N (μ _o - μ _e , Σ _e + Σ _o ) With x * = x → _o - x → _e and D * = {x * | A (0 →) ⋂ B (x → *) ≠ ∅}.

For forming the common collision surface D * based on the vehicle area A of the vehicle and the object surface B of the object, the object is moved in an orientation corresponding to the object angle along the outer contour of the object Vehicle track along the track, wherein the track of the center of the object surface when passing then forms the outer contour of the common collision surface. Mathematically, this corresponds to forming the Minkowski sum.

Subsequently, the combined probability distribution is brought to standard normal form. The common collision surface is analogously transformed on the basis of the combined probability distribution. This means that the common collision surface is shifted by the mean value .multidot. .Mu. _{X *} and undergoes rotation and compression in dependence on the entries of the covariance matrix .sigma.e + .sigma..sub.o of the combined probability distribution. The rotation results from the non-diagonal entries in the covariance matrix.

The problem of calculating the collision probability has now been reduced to the integration of a bivariate standard normal distribution over the transformed common collision surface. For this purpose, the integral of the probability density function of the combined probability function is determined via the transformed collision surface, wherein values of a lookup table provided by means of a memory are queried and provided for determining the integral.

It may be provided that the values retrieved for the determination are values of the probability density function of the bivariate standard normal distribution. The integral is then determined by means of these values over the corresponding area.

In an embodiment, it is provided that for determining the integral over the transformed collision surface, an integral is determined over an area which lies outside the transformed collision area, and wherein the integral thus determined for determining the integral over the transformed collision area then of a normalized overall probability with is subtracted from the value 1. The overall probability that a collision of the vehicle with an object occurs or that no collision of the vehicle with an object occurs is always 1. If one now knows the probability that no collision occurs, then the collision probability can be determined from this normalization. The advantage is that the calculation can be done much faster.

In a further embodiment it is provided that the vehicle surface and the object surface are each formed as polygons, so that the common collision surface is also a polygon. By means of this, the surfaces of the vehicle and of the object can be approached in a particularly simple manner, wherein nevertheless any accuracy can be achieved by adding additional corners into the respective polygon. Furthermore, it follows that the common collision surface is likewise a polygon again.

In particular, it is provided in a further embodiment that the number of corners of the polygon for describing the vehicle surface and / or the number of corners of the polygon for describing the object surface are each limited by a maximum value. This ensures that a certain degree of accuracy is not exceeded, so that a computational effort can be limited. For example, it can be provided that the vehicle surface or the outer contour of the vehicle is approximated by a polygon with four corners, that is, a rectangle. The object surface of the object can also be approximated, for example, as a polygon with four corners. The polygon of the common collision surface then gives either a polygon with 4 corners or a polygon with 8 corners depending on the vehicle angle and the object angle.

wobei P_i die mit einem Winkelstück zusammenfallende Wahrscheinlichkeit bezeichnet und N die Anzahl der Ecken des Polygons der gemeinsamen Kollisionsfläche angibt. Further, in another embodiment, to calculate the integral over the surface located outside the transformed collision surface, that surface is decomposed into contra-angles depending on a shape of the associated polygon of the transformed collision surface, a respective integral being calculated individually over each of these angles , This allows a particularly elegant calculation of the probabilities coincident with the area outside the common collision area. The collision probability then results in:

where P _i denotes the likelihood coincident with a contra-angle and N indicates the number of corners of the polygon of the common collision surface.

In a further embodiment, it is further provided that for calculating the integrals over the individual surfaces of the angle pieces from the look-up table, values for the probability coinciding with the respective angle pieces are queried and provided as a function of a radius, a first angle and a second angle. One method of calculating the angle-coincident probabilities versus these variables is, for example, AR Didonato et al., Computation of the bivariate normal distribution over convex polygon, Naval Surface Weapons Center, Virginia 1978, described. Before executing the method, the lookup table is accordingly created in such a way as to be able to provide the corresponding values in dependence on this variable and in this form.

For this purpose, provision is made in particular for the look-up table to be set up in such a way as to provide values for the probabilities P _{i of} the individual angle pieces i as a function of the radius, the first angle and the second angle.

In a further embodiment, it is further provided that the method is repeated as a function of an additionally detected variance for the vehicle angle and an additionally detected variance for the object angle, wherein a respectively determined collision probability corresponding to the selected vehicle angle and corresponding to the selected object angle weighted to a total Collision probability are added up. As a result, an uncertainty in the measurement of the vehicle angle and an uncertainty in the measurement of the object angle can additionally be taken into account.

In a further embodiment, it is further provided that the additionally detected variance for the vehicle angle is part of the vehicle pose and the additionally detected variance for the object angle is part of the object pose. As such, the vehicle pose and the object pose each represent a trivariate normal distribution.

In a further embodiment it is provided that to provide the values from the lookup table, an interpolation is performed on the basis of values stored in the lookup table. This ensures that values for areas that are not directly stored in the lookup table can also be provided. In the simplest case, the interpolation can be a linear interpolation. But it is also possible that, for example, a spline interpolation is used.

The invention will be explained in more detail with reference to preferred embodiments with reference to the figures. Hereby show:

1 a schematic representation of an embodiment of the apparatus for determining a collision probability of a vehicle with an object;

2a a schematic representation of a vehicle pose and a object pose with quadrangular polygons for the vehicle and the object;

2 B a schematic representation to illustrate the calculation of a common collision surface of the in 2a represented vehicle pose and the object pose;

2c a schematic representation for illustrating the transformation of the common collision surface based on the combined probability distribution;

2d a schematic representation to illustrate the subdivision of a lying outside of an octagonal polygon surface into individual elbows;

2e a schematic representation to illustrate the variables chosen to describe the elbows;

3 a schematic flow diagram of an embodiment of the method.

In 1 is a schematic representation of an embodiment of the device 1 for determining a collision probability of a vehicle 50 shown with an object. The device 1 is for example in a vehicle 50 arranged. The device 1 comprises a detection device 2 , a calculation device 3 , a store 4 and an output device 6 ,

The detection device 2 captures a vehicle pose for a given time 7 of the vehicle 50 and an object pose 8th of the object in an environment. The vehicle pose 7 and the object pose 8th For example, be from a suitably trained sensors 51 of the vehicle 50 provided. The vehicle pose 7 includes a vehicle position 9 , a variance 10 as a measure of the uncertainty of the vehicle position 9 and a vehicle angle 11 , The object pose 8th includes an object position 12 , a variance 13 as a measure of the uncertainty of the object position 12 and an object angle 14 , The vehicle position 9 and the object position 12 are available as normally distributed measure.

Based on the vehicle pose 7 and the object pose 8th calculates the calculation device 3 a collision probability 15 , For this purpose, the calculation device determines 3 from the normally distributed vehicle position 9 and the normally distributed object position 12 a combined probability distribution 16 , Furthermore, the calculation device calculates 3 based on a vehicle surface 17 and an object surface 18 a common collision surface 19 , The vehicle area 17 and / or the object surface 18 For example, you can also use the sensors 51 be provided or otherwise estimated. In particular, it is provided, the vehicle surface 17 and form the object surface as convex polygons. For example, the vehicle surface 17 as quadrangular Polygon (rectangle) and the object surface 18 also be designed as a square polygon (rectangle). The common collision surface 19 is then again a polygon, in the example considered an octagonal polygon.

In the next step, the calculation device transforms 3 the common collision surface 19 by means of the combined probability distribution 16 , For this purpose, a center of the common collision surface 19 moved and the joint collision area 19 is obtained by dividing the respective coordinates by the variance or the standard deviation of the combined probability distribution 16 compressed or stretched. In this way, the transformed collision surface 20 derived. Analogously, the calculation device brings 3 the combined probability distribution 16 in standard normal form, so that after this transformation there is a bivariate standard normal distribution.

Finally, the calculator determines 3 an integral of the probability density function of the bivariate standard normal distribution over the transformed collision surface 20 , This integral corresponds to the collision probability 15 , The calculator asks to determine the integral 3 For example, values for the probability density function from one using the memory 4 provided lookup table 5 from. In this lookup table 5 Values for the probability density function of the bivariate standard normal distribution are stored.

The integral over the transformed collision surface is preferred 19 however, by calculating the integral that is outside the transformed collision surface 19 lies, calculated. These are in the lookup table 5 Probabilities for specific areas outside the transformed collision area 19 deposited. The area outside the transformed collision area is particularly preferred 19 decomposed into contra angles, taking the lookup table 5 then provide the probabilities coincident with each of these contra angles. The calculation device 3 queries coincidence with each of the contra angles, sums up the individual probabilities and subtracts the accumulated probabilities from a total probability with the normalized value 1. The result is that with the transformed collision surface 19 coincident probability, which of the collision probability 15 equivalent.

In particular, it is provided here to store the individual probabilities coinciding with the angle pieces as a function of a radius, a first angle and a second angle in the lookup table and also to interrogate and provide them again as a function of these variables. This enables a particularly efficient calculation of the collision probability.

The calculated collision probability 15 is then by means of the output device 6 in the form of a collision probability signal 21 spend and can then from another device, such as an assistance system 52 of the vehicle 50 , be further processed, for example for trajectory planning. The output collision probability signal 21 This can be output both in analog and digital form, for example in the form of a data packet.

The 2a to 2e show schematic representations to illustrate individual process steps. In 2a is a schematic representation of a vehicle pose 7 and an object pose 8th with quadrangular polygons 22 . 23 as vehicle area 17 for the vehicle 50 and as an object surface 18 for the object 53 in a typical traffic situation 60 shown. The object 53 is another vehicle in this case. The vehicle pose 7 and the object pose 8th refer to a common coordinate system 24 , This can be for example a map with global coordinates. In terms of the centers 25 . 26 the vehicle area 17 and the object surface 18 correspond to the vehicle pose 7 and the object pose 8th one each around these centers 25 . 26 lying bivariate normal distribution, which indicates the probability that the vehicle 50 or the object 53 to be at a specific position at a given time. Furthermore, the vehicle pose includes 7 another vehicle angle and the object pose 8th an object angle which the respective orientation of the vehicle surface 17 or the object surface 18 to the coordinate system 24 specify.

In 2 B is a schematic representation to illustrate the calculation of a common collision surface 19 from the in the 2a illustrated vehicle pose 7 and the object pose 8th shown. For this purpose, the object surface 18 on its outer contour 27 around the outer contour 28 the vehicle area 17 guided along, without changing the vehicle angle or the object angle. The track 29 , which in this case of the center 26 the object surface 16 is described forms the outer contour 30 the common collision surface 19 , For the further explanations, it is assumed that the vehicle area 17 at the midpoint 26 the coordinates (x _e , y _e ) and the object surface 18 at the midpoint 27 the coordinates (x _o , y _o ) have. Becomes the center 32 the common collision surface 19 then set to (0, 0), the midpoint shifts 26 of Object corresponding to the coordinates (x _o - x _e , y _o - y _e ).

In 2c is a schematic representation for illustrating the transformation of the common collision surface 19 shown based on the combined probability distribution. The combined probability distribution from the bivariate standard normal distributions for the vehicle position and the object position likewise corresponds to a bivariate standard normal distribution. To transform, the common collision surface 19 by shifting around (μ _xe - μ _xo , μ _ye - μ _yo ) and rotation resulting from covariance and extension / compression resulting from the variance of the combined probability distribution Σe + Σo into the transformed collision surface 31 transferred. The middle-point 32 the transformed collision surface 31 is then ( _μxe - _μxo , _μye - _μyo ) By transforming, a bivariate standard normal distribution can then be used to calculate the collision probability (the subsequent use of a standard bivariate normal distribution can be thought of as performing the same transformation on the combined probability distribution).

In 2d is a schematic diagram illustrating the subdivision of an outside of an octagonal polygon 33 lying surface 34 in individual elbows 35 shown. Because the polygon is octagonal, the surface can be outside the polygon 33 also in eight contra angles 35 divide.

In 2e is a schematic representation to illustrate the description of the angle pieces 35 (For the sake of clarity, not all are marked with their own reference signs). An elbow 35 can be uniquely defined by the variables R for the radius of the center 36 of the polygon 33 out to the top of the contra-angle 35 and describe the two angles θ ₁ and θ ₂ . Should a probability density function over such a polygon 33 can be integrated, so can with such an angle piece 35 for example, using the method described in AR Didonato et al., Computation of the bivariate normal distribution over convex polygon, Naval Surface Weapons Center, Virginia 1978. If you subtract the sum of the individual angles 35 calculated probabilities from a normalized total probability, so that results with the polygon 33 coincident probability from the difference.

In a corresponding manner, the area outside the transformed collision surface can thus be 19 be calculated ( 2c ), so that the collision probability can be derived directly from this. These are the with the individual elbows 35 coincident probabilities P _i in a lookup table 5 deposited. A query then returns the values for the probabilities P _i as a function of the variables R, θ ₁ and θ ₂ .

In 3 FIG. 3 is a schematic flowchart of one embodiment of the method for determining a collision probability of a vehicle with an object. After the start 100 be by means of the detection device in the process steps 101 and 102 detects a vehicle pose and an object pose. For calculating the collision probability, in the subsequent method step 103 the process steps 104 to 107 executed by means of a calculation device.

In the process step 104 a combined probability distribution is determined from the vehicle pose and the object pose. Subsequently, in the process step 105 calculates a common collision surface based on a vehicle surface of the vehicle and an object surface of the object. The calculated joint collision surface is in the process step 106 transformed based on the combined probability distribution. Accordingly, the combined probability distribution by displacement and extension / compression is brought to standard normal form.

In the process step 107 For example, the probability density function of the transformed combined probability distribution, which is in standard normal form, is integrated to determine the probability of collision over the transformed collision surface. For this, values of the bivariate standard normal distribution are retrieved from a lookup table. In particular, it is provided here that only regions outside the transformed collision surface are integrated and from this the integral over the transformed collision surface is derived via the normalization condition. For this purpose, it is provided that the surface outside the transformed collision surface is split into contra-angles and that values for probabilities coinciding with the individual contra-angles are queried and provided from a look-up table.

In the last procedural step 108 the calculated collision probability is output as a collision probability signal by means of an output device. Then the process is finished 109 , It can be provided that the method is repeated for other vehicle poses and / or object poses. For this purpose, the process steps 101 to 108 repeated.

In particular, it may additionally be provided that the method is repeated for different vehicle angles and / or object angles as a function of an additionally detected variance for the vehicle angle and an additionally detected variance for the object angle, wherein the respectively calculated collision probabilities are subsequently combined to form a weighted total collision probability. This allows the uncertainties in the measurement of the vehicle angle and / or the object angle to be taken into account.

It may further be provided that the additionally detected variance for the vehicle angle is part of the vehicle pose and the additionally detected variance for the object angle is part of the object pose. As such, the vehicle pose and the object pose each represent a trivariate normal distribution.

LIST OF REFERENCE NUMBERS

1

contraption

2

detector

3

calculator

4

Storage

5

Lookup table

6

output device

7

Fahrzeugpose

8th

object pose

9

vehicle position

10

variance

11

vehicle angle

12

object position

13

variance

14

object angle

15

probability of collision

16

combined probability distribution

17

vehicle surface

18

Property area

19

common collision surface

20

transformed collision surface

21

Collision probability signal

22

polygon

23

polygon

24

coordinate system

25

Focus

26

Focus

27

outer contour

28

outer contour

29

track

30

outer contour

31

transformed collision surface

32

Focus

33

polygon

34

Surface outside the polygon

35

elbow

50

vehicle

51

sensors

52

assistance system

53

object

60

traffic situation

100-109

steps

R

radius

Θ ₁

angle

Θ ₂

angle

Claims (10)

Method for determining a collision probability ( 15 ) of a vehicle ( 50 ) with an object ( 53 ), comprising the following steps: detecting a vehicle pose ( 7 ) by means of a detection device ( 2 ), whereby the vehicle pose ( 7 ) at least one vehicle position ( 9 ) whose variance ( 10 ) and a vehicle angle ( 11 ), detecting an object pose ( 8th ) by means of the detection device ( 2 ), whereby the object pose ( 8th ) at least one object position ( 12 ) whose variance ( 13 ) and an object angle ( 14 ), calculating the collision probability ( 15 ) by means of a calculation device ( 3 ), wherein the following steps are carried out: (a) determining a combined probability distribution ( 16 ) from the vehicle pose ( 7 ) and the object pose ( 8th ); (b) calculating a common collision surface ( 19 ) based on a vehicle area ( 17 ) of the vehicle ( 50 ) and an object surface ( 18 ) of the object ( 53 ); (c) transforming the common collision surface ( 19 ) based on the combined probability distribution ( 16 ); (d) determining an integral of a probability density function over the transformed collision surface ( 20 ) for calculating the collision probability ( 15 ), wherein for determining the integral values from a memory ( 4 ) provided lookup table ( 5 ) are queried and provided; and wherein the probability density function is a probability density function of a bivariate standard normal distribution, and outputting the calculated collision probability ( 15 ) as collision probability signal ( 21 ) by means of an output device ( 6 ). A method according to claim 1, characterized in that for determining the integral via the transformed collision surface ( 21 ) an integral over an area ( 34 ) outside the transformed collision surface ( 21 ), and wherein the thus determined integral for determining the integral over the transformed collision surface ( 21 ) is then subtracted from the normalized total probability with the value 1. Method according to one of claims 1 or 2, characterized in that the vehicle surface ( 17 ) and the object surface ( 18 ) as polygons ( 22 . 23 . 33 ) are formed so that the common collision surface ( 19 ) also a polygon ( 22 . 23 . 33 ). Method according to claim 3, characterized in that the number of corners of the polygon ( 22 . 23 . 33 ) for describing the vehicle surface ( 17 ) and / or the number of corners of the polygon ( 22 . 23 . 33 ) for describing the object surface ( 18 ) are each limited by a maximum value. Method according to claim 3 or 4, characterized in that for calculating the integral over the outside of the transformed collision surface ( 21 ) ( 34 ), this area ( 34 ) depending on a shape of the associated polygon ( 33 ) of the transformed collision surface ( 19 ) in elbows ( 35 ), with a respective integral over each of these angle pieces ( 35 ) is calculated individually. A method according to claim 5, characterized in that for calculating the integrals over the individual surfaces of the angle pieces ( 35 ) from the lookup table ( 5 ) Values for the respective angle pieces ( 35 ) coincidence probability depending on a radius (R), a first angle (θ ₁ ) and a second angle (θ ₂ ) are queried and provided. Method according to one of the preceding claims, characterized in that the method as a function of an additionally detected variance for the vehicle angle ( 11 ) and an additionally detected variance for the object angle ( 14 ), wherein a respective calculated collision probability corresponding to the selected vehicle angle ( 11 ) and according to the selected object angle ( 14 ) weighted to a total collision probability ( 15 ) are added up. A method according to claim 7, characterized in that the additionally detected variance for the vehicle angle ( 11 ) Part of the vehicle pose ( 7 ) and the additionally detected variance for the object angle ( 14 ) Part of the object pose ( 8th ). Method according to one of the preceding claims, characterized in that for providing the values from the lookup table ( 5 ) an interpolation based on in the lookup table ( 5 ) stored values. Contraption ( 1 ) for determining a collision probability ( 15 ) of a vehicle ( 50 ) with an object ( 53 ), comprising: a detection device ( 2 ) for detecting a vehicle pose ( 7 ), whereby the vehicle pose ( 7 ) at least one vehicle position ( 9 ) whose variance ( 10 ) and a vehicle angle ( 11 ), and for detecting an object pose ( 8th ), whereby the object pose ( 8th ) at least one object position ( 12 ) whose variance ( 13 ) and an object angle ( 14 ), a calculation device ( 3 ), the calculation device ( 3 ) is designed such that a combined probability distribution ( 16 ) from the vehicle pose ( 7 ) and the object pose ( 7 ) to determine a common collision surface ( 19 ) based on a vehicle area ( 17 ) of the vehicle ( 50 ) and an object surface ( 18 ) of the object ( 53 ), the common collision surface ( 19 ) based on the combined probability distribution ( 16 ) and an integral of a probability density function over the transformed collision surface (FIG. 20 ) for determining the collision probability ( 15 ) to determine a memory ( 4 ) to provide a lookup table ( 5 ), the calculation device ( 3 ) for determining the integral values from the provided lookup table ( 5 ), and wherein the probability density function is a probability density function of a bivariate standard normal distribution, and an output device ( 6 ) for outputting the calculated collision probability ( 15 ) as collision probability signal ( 21 ).

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