Method and apparatus for determining the probability of collision between a vehicle and an object in three-dimensional space.

Abstract

This invention relates to a method for determining the collision probability of a vehicle (10) with an object (20, 25). The three-dimensional positions (x, y, z) and orientations of the vehicle (10) and the object (20) are detected. The vehicle (10) is approximated by at least one first geometry, wherein the at least one first geometry comprises a portion of the vehicle. The method is performed accordingly in the case of the object (20, 25). A first fuzziness (US1) and a second fuzziness (US2) are determined with respect to the geometry for either the vehicle (10) or the object (20, 25). A Minkowski difference (D') is formed for each combination of the at least one first geometry and the at least one second geometry. A third fuzziness (US3) is normalized by a transformation (TN). The transformation (TN) is used to calculate a computational volume (BK). The collision probability of the vehicle (10) with the object (20, 25) is determined based on the spatial union (D') of the computational volume (BK).

Description

Technical Field

[0001] This invention relates to a method for determining the probability of a collision between a vehicle and an object in three-dimensional space. Furthermore, this invention relates to an apparatus for determining the probability of a collision between a vehicle and an object in three-dimensional space. The invention also includes a computer program product and a computer-readable medium on which the computer program product is stored. Background Technology

[0002] The automotive industry is currently undergoing a transformation. This involves not only the shift in fleets from internal combustion engines to electric motors, but also the transformation from pure car manufacturers to mobility service providers. In the future, interaction with other modes of transport will play an increasingly important role. These other modes of transport include, in particular, air transport vehicles such as air taxis or drones. However, in such mobility services, landing procedures or docking between domains (roads and airspace) must be reliably designed.

[0003] In the automated flight path planning of air transport vehicles, it is typically necessary to evaluate individual available trajectories and select the optimal one. Collision avoidance is particularly important here. This is achieved, for example, by using integrated sensor systems to detect information about the surrounding environment or by using vehicle-to-X communication to communicate with other objects in the surrounding environment, such as other vehicles. Therefore, it is usually necessary to estimate the situation of the vehicle itself or another vehicle and plan its own trajectory based on this information.

[0004] A major challenge here is that perception and prediction always involve uncertainty due to sensor detection of the environment and the unknown intentions of other traffic participants. While the resulting uncertainty in the positions of traffic participants can be roughly estimated and used for trajectory planning, this makes trajectory planning significantly difficult. This can lead to computationally intensive trajectory planning and render realistic flight operations impossible. Furthermore, estimating collision probabilities based on simplifying assumptions often results in a significant overestimation of the probability of collisions.

[0005] Publication document DE102017215519A1 describes a method and apparatus for collision identification of a vehicle. Here, a method with at least three stages is implemented. Up to three collision checks can be performed. Here, face regions are observed stage by stage along segments of the vehicle's path of motion, wherein the face regions in each stage approximate the actual tail of the vehicle.

[0006] Publication DE102018211513A1 relates to an apparatus for determining the probability of a collision between a vehicle and an object. This apparatus is limited to two-dimensional observation and estimation of the collision probability. Three-dimensional observation methods typically require special processing of the third dimension, which is not addressed in this publication. Therefore, certain computational steps in two dimensions cannot be readily transferred to three dimensions.

[0007] Publication document DE102009045755A1 describes a method and apparatus for conflict identification. Here, the position, direction of motion, and speed of one's own flying transport vehicle and other flying transport vehicles in the airspace are determined based on sensor data. From this, trajectories for both the own flying transport vehicle and other flying transport vehicles are formed. Based on possible directional changes of the own flying transport vehicle, a group of possible trajectories for the own flying transport vehicle is calculated. The calculated group of trajectories for the own flying transport vehicle is then checked to see if it conflicts with the trajectory of any other flying transport vehicle. In the event of a conflict, information is output to the pilot of the own flying transport vehicle.

[0008] In the operation of air transport vehicles, reliable and fast trajectory planning is particularly important. A crucial component of trajectory planning is the calculation of the probability of collision between the air transport vehicle and other objects. Summary of the Invention

[0009] The objective of this invention is to more effectively design the calculation of collision probabilities for vehicles in three-dimensional space. In particular, a feasible trade-off should be achieved between speed in the calculation of collision probability and not excessively overestimating the collision probability.

[0010] Determining the collision probability of a trajectory is typically computationally intensive because a closed-form or analytical solution is often unavailable. This is especially true when common methods for tracking objects, such as the Extended Kalman Filter, describe the uncertainties of an object's state using a normal distribution. Furthermore, similar solutions are often limited to road traffic or cannot map complex realities. A frequently used method for calculating collision probabilities is based on the so-called Monte Carlo method. In this method, to achieve sufficient accuracy, numerous binary collision checks are required to approximate the collision probability. However, this leads to very high computational time requirements.

[0011] Similarly, numerical integration methods are computationally intensive when dealing with a large number of discrete parts required for sufficient quality. Significant difficulties have been demonstrated in developing autonomous vehicles (cars in road traffic) that move only in a single plane. Currently, fully autonomous vehicles capable of safely and reliably handling complex traffic situations in most cases are not yet available. For vehicles operating in three-dimensional space, such as air taxis or drones, trajectory planning must be performed not only in a single plane but also in three dimensions. Furthermore, if air vehicles are also capable of fully autonomous movement, the real-time calculation of the corresponding collision probabilities becomes crucial.

[0012] For these reasons, the present invention proposes a method for determining the probability of a collision between a vehicle and an object in three-dimensional space. Therefore, a first aspect of the invention relates to a method for determining the probability of a collision. In particular, the vehicle can be a drone, an air taxi, a helicopter, a flying vehicle, and / or an aircraft. The vehicle can be a motor vehicle. According to the method, the probability of a collision with an object should be determined. The object can be, for example, another vehicle, a flying vehicle, a motor vehicle, an animal such as a bird, a tree, a building, or a semi-static object such as a weather vane or a wind vane rotating in the wind. Weather vanes are often encountered on bridges and are mostly statically fixed to poles, wherein the vane itself is movable. Since the weather vane itself can move due to the wind, and although it cannot move completely freely due to being fixed to a pole, such an object can be called "semi-static".

[0013] First, the three-dimensional position and orientation of the vehicle and object are detected and / or received. The detection of the three-dimensional position can be performed, for example, by sensors on the vehicle or its own onboard sensor system. Additionally or alternatively, information for determining the probability of a collision can be received via the vehicle's interface. For example, local wind speed can be received as information from an external database. The three-dimensional position and orientation of the vehicle and object can be detected, for example, by means of sensor units located on the vehicle, an environmental sensor system, or an onboard sensor system. This information about the three-dimensional position and orientation can be transmitted to the interface. This information can be considered or used to determine or calculate the probability of a collision. In particular, the three-dimensional position of the vehicle and object can be expressed in Cartesian coordinates. However, the three-dimensional position can also be obtained or represented in other coordinate systems, such as spherical coordinates. In some cases, corresponding coordinate transformations may be required. In particular, the orientation of the vehicle and / or object can be three-dimensional. This means, for example, that multiple angles may exist for the orientation or orientation of the object and / or vehicle. Thus, for example, a drone may have an orientation in the xy plane, but simultaneously an orientation in the xz plane, and further an orientation in the zy plane. Therefore, three-dimensional orientation can include three orientations. Here, a common Cartesian coordinate system with known x, y, and z axes can be used as the basis. The z-axis is preferably vertically upward. Thus, a vehicle can have three degrees of freedom for position, for example, in the form of three Cartesian coordinates (x, y, z), and three additional degrees of freedom for vehicle orientation, for example, in the form of three angles (pitch, yaw, and tilt). Thus, a vehicle can have six degrees of freedom. The same applies to objects. The number of orientations can vary along the trajectory. For example, if the vehicle lands and then only moves along a plane (along the ground), then only one unique orientation is sufficient in this case. Therefore, the number of orientations can be related to the direction of the trajectory.

[0014] In the next step, the vehicle is approximated by at least one first geometry. Approximation of the vehicle can refer to its representation, proximity, or approximate presentation. Therefore, the at least one first geometry can represent, approach, or approximate the vehicle. Here, the at least one first geometry includes a portion of the vehicle. In particular, this means that at least a portion of the vehicle is included within the at least one first geometry. When approximating, three-dimensional position and / or orientation can be taken into account. For example, the vehicle can be approximated by means of multiple first geometries. For example, two spheres can be used as first geometries for approximation. Approximation is preferably performed relative to an object in a similar manner. This means that the object is approximated by at least one second geometry. Here, approximation can also refer to representation, proximity, or presentation, as explained in relation to the vehicle. Similarly, the at least one second geometry includes a portion of the object. The vehicle and / or object can be approximated by means of multiple geometries, wherein the multiple geometries can have symmetry.

[0015] For example, if an object is approximated by three spheres as a second geometry, then at least a portion of the object is contained within each of these three spheres. The entire object can be contained within these spheres. The same applies to vehicles. Ideally, an axis of symmetry can be defined for the union of the first bodies. This reduces computational costs. The same applies to the second bodies. Preferably, at least one first and / or second geometry contains a portion of the vehicle and / or object that is relevant in the event of a collision, derived from prior estimates.

[0016] In particular, the means of transport can be approximated by the at least one first geometric body. Under-approximation specifically means that the at least one first geometric body only partially, i.e., preferably not completely, contains the means of transport. Therefore, the approximation can refer to over-approximation or under-approximation. In the case of over-approximation, the means of transport is particularly completely contained within the at least one first geometric body. In this case, the volume of the at least one first geometric body exceeds the volume of the means of transport.

[0017] In a further step, a first ambiguity of the at least one first geometry and a second ambiguity of the at least one second geometry are determined and / or preset. This step arises from the recognition that all measurement data from the sensor and externally received information are subject to errors and therefore suffer from inaccuracies or uncertainties. In this regard, ambiguity specifically refers to inaccuracies, nondeterminism, uncertainty, measurement errors, data uncertainties, and / or tolerance ranges. The first and second ambiguities primarily relate to sensor data and externally received information. The first ambiguity preferably relates to the position and / or orientation of the at least one first geometry. Therefore, the first ambiguity can be indirectly related to the means of transport. The first ambiguity may be derived from the inertial uncertainty of the means of transport.

[0018] In the case of multiple first geometries, each of these first geometries can have its own first ambiguity. Each geometry can have its own ambiguity. The multiple ambiguities can be different, but for the sake of simplicity, the multiple ambiguities can be the same. Each geometry can have exactly one first ambiguity or exactly one second ambiguity. The corresponding situation can also be applied to second geometries and / or second ambiguities. The second ambiguity preferably relates to the position and / or orientation of the at least one second geometry. Thus, the second ambiguity can be understood as an (indirect) measure of the uncertainty of the position and / or orientation of an object. The first ambiguity regarding the position of a first geometry can, for example, be expressed in the form of an interval for each spatial coordinate. Thus, additional intervals with angular descriptions can express or represent the first ambiguity regarding the orientation of a first geometry or a vehicle. The description of the first ambiguity can be applied accordingly to the second ambiguity.

[0019] These first and second ambiguities are preferably taken into account in a further step of the method in order to determine a transformation necessary for determining the collision probability. The first and / or second ambiguities of the at least one first geometry and / or the at least one second geometry can be determined, in particular, based on the inaccuracies in the measurement data or received information. Therefore, inaccuracies in the sensor data and externally received data can be correspondingly transmitted to the geometry in the form of first and / or second ambiguities.

[0020] In particular, the position of a geometric object is not 100% definitive. For example, if a vehicle is approximated by a sphere, the sphere may shift accordingly depending on the degree of ambiguity. Therefore, the spatial position of this sphere cannot be precisely given as a number, but only as an interval or region in space. The larger this interval is chosen, the more reliably the sphere or a portion of it can be positioned within it. In determining the first and / or second ambiguity, a Gaussian normal distribution can be particularly considered. If, for example, the first or second ambiguity cannot be determined because, for example, the error source is not known, the first or second ambiguity can be pre-defined. If, for example, sensor information is determined using two sensors, the corresponding error propagation can be taken into account. In particular, in the case of multiple measurement errors, a known Gaussian error propagation can be used.

[0021] In the next step, a Minkowski difference is formed for each combination of the at least one first geometry and the at least one second geometry. The at least one first geometry preferably represents a means of transport. The at least one second geometry preferably represents an object. This may, for example, mean that instead of location points, intervals are used for the ambiguity of the method regarding the location of the means of transport and / or the object. The intervals can be confidence intervals or trust intervals. First and / or second ambiguities regarding the means of transport and / or the object can be inferred from the uncertainty regarding the means of transport or the object. Correspondingly, orientation may be applied alternatively or additionally. The Minkowski difference is not, in particular, a difference as common as those known in the real number range. The Minkowski difference can be described, in particular, by the following formula:

[0022] AθB:={ab:a∈A,b∈B} Formula 1

[0023] A and B are point sets. a and b are elements of sets A and B, respectively. In this method, point sets of the corresponding geometric bodies are used instead of sets A and B.

[0024] The relative distance between two entities can be determined using the so-called Minkowski difference. The Minkowski difference is specifically generated when calculating the difference between each point in set A and points in a second set B. The formation of the Minkowski difference can be viewed as a coordinate transformation to relative coordinates, in which the relative distance is expressed.

[0025] The Minkowski difference can also be understood as the Minkowski sum. In this case, the subtraction of AB is defined as the sum of sets A and -B. The Minkowski difference is particularly helpful for quickly identifying possible collisions. However, it is important to remember that due to the first and second fuzzinesses, the position of the geometry is not precisely determined. Therefore, the Minkowski difference also has fuzziness, which is called the third fuzziness. In two dimensions, the Minkowski difference is a surface; in multidimensional space, the Minkowski difference is correspondingly multidimensional. In three-dimensional space, the Minkowski difference is therefore constructed in three dimensions. However, for simplification, the Minkowski difference is usually interpreted only in two dimensions.

[0026] In a further step, a corresponding third fuzziness for each Minkowski difference is determined based on the corresponding first fuzziness of the at least one first geometry and the corresponding second fuzziness of the at least one second geometry. The third fuzziness is preferably determined by adding the first and second fuzzinesses. In particular, the third fuzziness is the sum of the first and second fuzzinesses. In the case of multiple first or second geometries, multiple Minkowski differences are generated. In particular, exactly one first geometry and exactly one second geometry can be assigned to each Minkowski difference. These two geometries can have exactly one first fuzziness and exactly one second fuzziness. The corresponding third fuzziness is preferably obtained or determined by means of these two fuzzinesses. Therefore, in the case of multiple Minkowski differences, multiple (equally many) third fuzzinesses can be determined accordingly. Each of these third fuzzinesses here specifically relates to the associated Minkowski difference. In a further step of the method, the third fuzziness is particularly needed to determine the transformation or computational operation used to determine the collision probability. Therefore, in a further step of the method, established mathematical methods can be used when determining or calculating the collision probability. This can lead to a simpler and more efficient calculation of collision probabilities.

[0027] In a further step, the corresponding third fuzziness is standardized by a corresponding transformation. Here, in particular, the corresponding transformation is determined. Standardization of the third fuzziness, especially in three dimensions, results in a unit sphere around the origin. To determine the corresponding computational volume from the corresponding Minkowski difference, the same corresponding transformation is applied to the corresponding Minkowski difference. Multiple third fuzzinesses can also be standardized. If only one unique Minkowski difference exists, then correspondingly only one unique computational volume is determined. Standardization of the third fuzziness can, in particular, mean that the relevant covariance matrix is ​​transformed into a standard normal distribution. In the case of multiple third fuzzinesses, multiple covariance matrices can be transformed or transformed into a standard normal distribution respectively. Thus, multiple third fuzzinesses can be standardized. A transformation can be understood as a computational operation on a transformation matrix in three-dimensional space. Transformations can include stretching, translation, compression, twisting, rotation, and / or mirroring. The transformations required for this purpose are then preferably applied to the corresponding Minkowski differences. Therefore, standardization is particularly used to determine the corresponding transformation that derives the relevant computational volume from the Minkowski differences. Depending on the characteristics of the transformation, this can lead to translation, extension, distortion, stretching, and / or compression of the Minkowski difference.

[0028] In the process of standardization, especially the standardization of measurements, the arithmetic mean, standard deviation, and / or covariance matrix can be considered. In two dimensions, standardization can be viewed as a modification of the density function of a normal distribution. During standardization in two dimensions, the density function or density curve is stretched or compressed such that the standard deviation is 1 along the spatial direction, while the area (probability) of the density curve remains generally unchanged. This approach can be similarly applied to multidimensional distributions. Alternatively, when standardizing for a third or other dimension, appropriate scaling factors can be additionally used. Standardization of a parameter in one dimension can be viewed as a shift, stretching, and / or compression of a normal distribution. When standardizing in a multidimensional space (dimension greater than 2), a separate scaling factor can be used for each dimension. For example, a distribution with a specific preset standard deviation can thus be transformed into another distribution with a correspondingly different standard deviation. Since the probability represented here, especially below the density curve, should be preserved, the corresponding density function is shifted and / or stretched accordingly. When “standardization of Minkowski difference” is mentioned below, it preferably refers to standardizing the corresponding third fuzziness by means of the corresponding transformation, and applying the same transformation to the corresponding Minkowski difference.

[0029] The collision probability between the vehicle and the object is determined based on the union of the computational volumes or an approximation of the union. The collision probability is determined, in particular, based on the union of the computational volumes or an approximation of the union. The union is, in particular, a spatial union. Specifically, the computational volume can be constructed, in particular, as a spatial volume, such as an ellipsoid, a cube, etc. For example, a sphere can thus be transformed into an ellipsoid. Multiple Minkowski differences can be correspondingly transformed into multiple new computational volumes through corresponding transformations, which are determined by standardization using a corresponding third fuzziness. Minkowski differences can be constructed as geometrical bodies in three-dimensional space, like computational volumes, wherein preferably the subject of the Minkowski difference differs from the subject of the computational volume. Through corresponding transformations, in particular, the subject representing the Minkowski difference is transformed or reshaped into a new computational volume. In the case of multiple Minkowski differences, multiple computational volumes can be correspondingly derived. Therefore, not only Minkowski differences but also computational volumes can be understood as sets of points in space or as subjects in three dimensions, respectively. In higher dimensions (n-dimensional; n > 3), this method can correspondingly lead to n-dimensional volumes.

[0030] For approximation, the computational volume is particularly different from the at least one first geometry and at least one second geometry. The computational volumes can, in particular, partially overlap or intersect. The collision probability can be determined, in particular, based on a probability density function. For this purpose, the probability density function can be integrated or summed via the union of the computational volumes. In most cases, analytical integration cannot be performed. Therefore, summing with respect to the union is preferred. This summation can be performed based on discrete points. The union can be understood, in particular, as a mathematical term. Therefore, the union preferably represents the total volume of all volumes of the normalized Minkowski difference, where overlapping regions are counted only once. If A and B are considered as sets, then the union A with B is a set in which the following applies:

[0031] A∪B={x|x∈A∨x∈B} Formula 2

[0032] The probability of a collision involving a means of transport can be determined, in particular, by integrating over the spatial domain of the corresponding probability density function or function. For this purpose, the following formula can be used, for example:

[0033]

[0034] p Z (z) is a probability density function containing the first and second fuzzinesses for the geometry of the vehicle and the object; z E It is from Z E A vector of the means of transport, which takes into account the first fuzziness of the means of transport vector; θ(z) E Z represents the basic volume of a means of transport; T ,θ(zT ), z T This relates to objects. P(C) here represents the collision probability.

[0035] The general formula for the integral or summation used to calculate collision probabilities can often be further simplified. This leads to the following formula:

[0036]

[0037] The difference between Formula 4 and Formula 3 is that Formula 4 uses its own separate probability density function not only for vehicles but also for objects. In Formula 4, D can be the volume used to calculate the collision probability. For example, D can be the volume of an enclosing cube, sphere, prism, etc.

[0038] If the vehicle and the object act independently of each other, the formula according to Equation 4 can be applied. This is often the case. For example, when a drone moves in the airspace, this mostly occurs independently of another object, such as a bird. The probability density function can be constructed as a multivariate normal distribution. An exemplary normal distribution for three-dimensional space is given by the following formula:

[0039]

[0040] ∑ is the covariance matrix; z in Equation 5 is the corresponding position vector for the vehicle or object; μ is the corresponding expected value.

[0041] Such probability density functions can be assumed or calculated not only for vehicles but also for objects. To calculate Equation 4, the product of two probability density functions can first be formed, and then integration can be performed (numerically). For the integration with respect to volume, the volume of the spatial union or another volume can be used as an approximation. Thus, the probability of a collision between a vehicle and an object can be determined or calculated.

[0042] This invention allows for the calculation of collision probabilities with a significant computational time advantage over Monte Carlo methods and other numerical integration methods. The loss of accuracy can remain relatively low, while real-time calculation of collision probabilities is achieved simultaneously. In particular, the complete trajectory of an object or vehicle, including all collision probabilities to be calculated, can be performed within 0.1 seconds. Preferably, the calculation of collision probabilities can be performed in real time. The advantages of this method are amplified when a large number of samples are required for the necessary quality in Monte Carlo simulations, as the proposed method specifically requires an estimable, constant computational runtime. This method enables real-time requirements, even in complex systems where many different trajectories must be checked for collisions. Instead of binary collision checks as in other methods, quantitative collision probabilities can be calculated. The resulting uncertainties can be appropriately mapped during the decision-making process. Overall, this method achieves a computational runtime advantage with high accuracy. With this method, the positional uncertainties generated by traffic participants can be mapped into collision probabilities and used for trajectory planning. Therefore, the risk of the planned trajectory can be estimated and thus minimized accordingly. This enables the safe manipulation of air transport vehicles in three-dimensional space.

[0043] Additional or alternative implementations of the method can be configured to determine the volume of the geometry of the vehicle and the object based on digital resources. These digital resources can, in particular, be available computing power. Additionally or alternatively, the volume of the body can be determined based on the speed of the vehicle and / or the object. Thus, for example, in the case of an airborne vehicle, a body can be selected that is positioned at a location on the airborne vehicle oriented along the flight direction. Preferably, the volume of the body encompasses the area of ​​the vehicle most likely to be affected in the event of a collision. Therefore, the volume of the body can preferably be limited to the potential collision site between the vehicle and another object. Thus, even with relatively limited available computing power, a value for the probability of collision can always be determined with acceptable accuracy. For example, the probability of a drone colliding with an object in the rear region is relatively low.

[0044] Both the object and the vehicle can be approximated by a spherical shape. In this case, the main body is constructed as a sphere. The vehicle and the object can be approximated by multiple spheres. Here, the corresponding volumes in their union respectively contain the entire vehicle or the entire object. When approximating by multiple spheres, it is preferable to achieve an acceptable increase in volume. Other vehicles in adjacent cockpits or flight corridors can mostly pass without problems. Approximation using a spherical main body has the following advantages: orientation can be ignored. This is mainly due to the special symmetry of the sphere. Rotation of an ideal sphere results in the same sphere. The size or volume of the geometry can also be determined based on the speed of the vehicle or object. It is generally meaningful to set a larger volume for the main body when the vehicle speed is higher. Depending on the application and safety requirements, vehicles with relatively low computational power can also have their collision probabilities determined in order to determine the corresponding flight trajectory. For example, this may be the case in the case of non-critical package delivery.

[0045] Additional or alternative embodiments of the method are configured such that the at least one first body completely comprises a vehicle, while the at least one second body completely comprises an object. The at least one first body preferably relates to a vehicle. The at least one second body relates to an object. Alternatively, the at least one first body may be configured to under-approximate a vehicle, while the at least one second body may under-approximate an object. In particular, under-approximation occurs when the volumes represented by the vehicle or the object are approximated to be smaller than the volumes of the vehicle and / or the object, respectively. Under-approximation occurs when the at least one first and / or second geometry is selected or determined such that its volume is smaller than the volume of the vehicle or the object. Therefore, in under-approximation, the calculated collision probability is underestimated. This is preferably configured in situations with low computational power. Depending on available digital resources or computational power, over-approximation or under-approximation may be configured.

[0046] For example, in an over-approximation, the vehicle can be completely surrounded by a correspondingly large sphere. Similarly, multiple smaller spheres can also collectively contain the vehicle within their volume. The same applies to objects. Instead of spheres, other bodies such as cubes, prisms, pyramids, tetrahedrons, cones, octahedrons, etc., can be used for approximation. This implementation is particularly meaningful if collisions should be eliminated as much as possible. For example, in this case, it can be determined whether the vehicle merely grazed another object rather than colliding with it. Thus, this scenario can be taken into account. If multiple first bodies completely or entirely contain the vehicle, any contact between the vehicle and other objects can be determined using the collision probabilities calculated therefrom. While this implementation is of interest for safety-critical scenarios, in some cases, stronger requirements may be placed on the available computational power.

[0047] Additional or alternative implementations of the method are configured such that the first and / or second ambiguities are determined based on a Gaussian normal distribution and / or error propagation. The first and / or second ambiguities arise, in particular, from erroneous sensor data, similarly erroneous externally transmitted information, and / or from the corresponding inertial uncertainties of the vehicle or object. In most cases, to reasonably calculate the collision probability, it can be assumed that the measured values ​​follow a Gaussian normal distribution around the expected value. For example, if a temperature sensor records a value of 19.5 degrees Celsius, the corresponding Gaussian normal distribution can yield a tolerance range of 19.0 to 20.0 degrees Celsius. The corresponding standard deviation and the desired confidence level can also affect this tolerance range. Depending on the application, the ambiguity arising from the Gaussian normal distribution can be scaled using additional factors. The first, second, and / or third ambiguities can be expressed as intervals or tolerance ranges. In particular, intervals for spatial location and orientation can be determined. In the case of Cartesian spatial coordinates, a tolerance range can be determined for each spatial coordinate. For example, if a spatial coordinate, such as geodetic height z, is related to multiple sensor values, then the ambiguity for geodetic height z can be determined through the corresponding error propagation.

[0048] The first and second ambiguities of the first and second geometries can be mathematically expressed, in particular, by means of the covariance matrix. In the case of a normal distribution of position coordinates, the corresponding ambiguities can be determined via linear error propagation according to Gaussian. In particular, the first ambiguity of the at least one first geometries is determined here from the uncertainty of the means of transport. Correspondingly, the second ambiguity of the at least one second geometries can be determined from the uncertainty of the object. Equation 6 particularly represents sensor uncertainty or sensor measurement error. Equations 7 to 9 particularly refer to a sphere as the subject used for approximation. This can be expressed, for example, by the following formula:

[0049]

[0050]

[0051]

[0052]

[0053]

[0054] Formulas 6 through 9 specifically involve a sphere as the subject used for approximation. In Formula 7, distance represents the distance between the center points of the respective associated ambiguity regions. X E / T Y E / T and Z E / T Especially representing the spatial location of a means of transport or an object. AαE / T Bβ E / T ,Γγ E / T In particular, this represents the orientation of a vehicle or object in space. The ambiguity region can be represented in the form of an ellipsoid. Equation 7 specifically addresses the case where the vehicle or object is first approximated using a single principal sphere, and then approximated using multiple subspheres. `distance` specifically refers to the distance between the ambiguity of the principal sphere and one ambiguity of each corresponding subsphere. The parameter `distance` can be chosen symmetrically with respect to the multiple subspheres, so that the first ambiguity is the same for each subsphere, and therefore the transformation used to standardize the third ambiguity or to transform the Minkowski difference into a computational volume only needs to be calculated once. In particular, the mentioned formulas start from the normal distribution of position coordinates and take into account the propagation of linear uncertainty according to Gaussians. It should be considered here that the spatial attitude of the vehicle or object is already six-dimensional, because in addition to the three spatial coordinates... In addition, three directional coordinates α, β, and γ are also assumed. The corresponding case applies to the spatial coordinates of the object. Random vector as well as and It can involve any entity.

[0055]

[0056] z E and z T The vector z represents the position of the means of transport or object without uncertainty. According to Equation 6, through the corresponding mapping rule, vector z... E and z T This can be achieved by using a random vector Z E and Z T Conversion. Z E and Z T In particular, it contains uncertainties. Accordingly, ambiguities for the geometry can be determined. R(α, β, γ) specifically describes the rotation matrix in at least three-dimensional space related to the oriented coordinates or angles α, β, γ.

[0057] Two vectors z E and z T These can be combined into a common vector z, which is twelve-dimensional. In this case, z is a twelve-dimensional vector, not a geodesic altitude. In this case, the following applies:

[0058] in,

[0059] Regarding sensor data functionality and prediction algorithms, we can assume that the random variables follow a common normal distribution.

[0060] The covariance matrix for vehicles or objects particularly includes the corresponding uncertainties of the underlying sensors or information. The matrix regions marked with an asterisk in Equation 6 are irrelevant to further calculations, as these calculations do not affect the collision probability.

[0061] An additional or alternative implementation of the method is configured to detect the three-dimensional position and / or orientation of the object multiple times at different time points to determine the three-dimensional trajectory of the object, and select the trajectory with the lowest collision probability from multiple trajectories for the vehicle based on the object's trajectory. Orientation may have three degrees of freedom in the form of three angles. Multiple trajectories for the object may be generated due to the uncertainty or ambiguity of the object's position or due to ambiguity regarding the object's behavior (action assumption). In order to reliably determine the object's trajectory, the three-dimensional position and / or orientation of the object are detected multiple times at different time points in this case. Predictable object behavior can be considered to determine the three-dimensional trajectory. A probability function as an action assumption can describe the object's behavior. For example, this can be used in the case of birds. Then, for example, based on the bird's object recognition or holding behavior, it can be determined whether the bird stays in one place, begins to fly, or changes its flight path. This different behavior can additionally lead to further trajectories of the bird. Similar analysis can also be performed in the case of other flying vehicles or drones.

[0062] In particular, multiple collision probabilities at multiple points can be combined into a unique collision probability for a single trajectory. Therefore, multiple collision probabilities can be converted into a (total) collision probability for a single trajectory. Preferably, the trajectory with the lowest collision probability is selected. For this purpose, in particular, control signals are generated, designed to activate the corresponding actuators of the vehicle to manipulate it along the trajectory with the lowest collision probability. Estimates of the behavior of other objects can be mathematically expressed through action hypotheses. An action hypothesis can be understood as a probability at which a particular action is performed. For example, in the case of a bird, this would be the probability of it flying away. This means that, in addition to determining the collision probability, other probabilities regarding the action hypothesis can be additionally considered when determining the collision probability in order to identify and / or select the trajectory with the lowest collision probability. Therefore, the safest flight trajectory can be selected for the vehicle.

[0063] Additional or alternative implementations of the method are configured to determine the collision probability separately for multiple points along the trajectory of the vehicle. This allows the collision probability to be determined not only at possible collision points but also along the entire trajectory. Similarly, the (total) collision probability for the entire trajectory can be determined by multiple collision probabilities for multiple points. Preferably, multiple points are selected in each region, which can be understood as a potential collision area. This ensures that the collision probability involves not only a single point but also represents the trajectory of the vehicle.

[0064] Additional or alternative embodiments of the method are configured to approximate the transport vehicle and the object respectively by at least one polyhedron, and to approximate the union of the computational volumes by means of a prism, wherein the prism completely contains the union. Preferably, the prism is considered instead of the union when determining the collision probability. In particular, the prism is an approximation of the union. In particular, the prism can be constructed to be straight and regular. In particular, the prism can be a right prism with the smallest volume enclosing the union. This in particular means that the size of the prism is just sufficient to completely enclose or contain the union of the computational volumes. For example, a square can be chosen whose size is just sufficient to completely enclose the union of the computational volumes. In this regard, "smallest volume" means, in particular, finding or selecting a prism with the smallest possible volume that still completely or entirely contains the union of the computational volumes.

[0065] To calculate or determine the collision probability, the product of the probability density functions (according to Equation 4) can be summed or integrated with respect to the spatial volume of the union. Alternatively, the probability density function involving the third ambiguity can be summed or (numerically) integrated with respect to the volume of the union of the computational volumes or with respect to its approximation. In the case of multiple third ambiguities, a separate probability density function can be defined, determined, and / or pre-defined for each third ambiguity. In the case of multiple third ambiguities, multiple corresponding probability density functions can be considered to determine the collision probability. In this embodiment of the method, the vehicle and the object are preferably approximated by means of corresponding polyhedra. In over-approximation, the corresponding polyhedron completely contains the vehicle or the object.

[0066] By approximating the volume using a right prism with the minimum volume under ideal conditions of boundedness, the calculation of collision probability can be reduced by one dimension. Therefore, it may only be necessary to determine the probability density function on one face. Due to the right prism, the third dimension can be easily considered.

[0067] Preferably, all the bodies are convex for approximation. In particular, all polyhedra are convex. If an overestimation of the collision probability is not required, any convex representation of the at least one first body and / or the at least one second body can be chosen, i.e., any convex polyhedron. Preferably, the base is parallel to the cover face of the prism. This creates a spatial volume that is easy to calculate. To determine the collision probability, the volume of the prism can be used instead of the spatial union. In particular, the volume of the prism is an approximation of the union. Since the volume of the prism completely contains the union, the collision probability is not underestimated. To avoid unnecessarily overestimating the collision probability, it is meaningful to choose the prism with the smallest volume accordingly. Therefore, when determining the collision probability, it is preferable to consider the prism instead of the union.

[0068] Alternatively, the collision probability of a binary variable can be determined for the base of the prism. In the case of a regular right prism, the calculation of the collision probability can be decomposed into a two-dimensional component and a one-dimensional component of the collision probability. In particular, this allows the two collision probabilities to be determined separately and then combined. In the case of the two-dimensional component of the collision probability, the collision probability is determined by the corresponding inverse probability. This means that the faces outside the prism are considered, not the faces inside the prism. The base of the prism is, in particular, a polygon. The outer region of the polygon can be divided into corresponding angular segments by extending the sides of the polygon accordingly. When calculating the two-dimensional component of the collision probability, the faces outside the polygon can be considered in particular. These faces outside the polygon can be represented by corresponding angular segments. Here, the property of the probability density function can be used, that is, as the distance increases, the probability density function becomes smaller and decreases to zero. This can be explained figuratively by the following: as the distance increases, the collision probability is zero at some point.

[0069] The one-dimensional component of the collision probability can be determined by multiplying it by the height or difference of the cumulative probability density function, where the difference of the cumulative probability density function is defined at different vertical positions. In Equation 12, 1∑P i The two-dimensional component representing the collision probability, term The first component represents the one-dimensional probability of a collision. Therefore, for each angular segment around the polygon, the corresponding probability density function can be integrated or summed. This determines a probability value indicating that a collision does not occur. Conversely, the collision probability in this case corresponds exactly to the inverse event. The third component in three-dimensional space can be considered through the corresponding cumulative probability density function. This leads to the following formula:

[0070]

[0071] P i : The probability corresponding to the angle segment;

[0072] P": Position within the prism;

[0073] The probability density function evaluated at the maximum position within the z-direction of the prism, for example, at the capping surface of the prism. In the case of Equation 12, the third dimension z is random and independent. The subscript i indicates the corresponding angular segment of the polygon surrounding the prism.

[0074] Additional or alternative implementations of the method are configured such that the computational volume is approximated by a plurality of contacting prisms. In particular, the prisms can be symmetrical to each other. The plurality of prisms can be congruent to each other. However, these prisms can also be moved or offset relative to each other. In this case, the third dimension (typically spatial coordinate z) is discretized, especially to improve accuracy. The plurality of contacting prisms here represents discretization along the spatial direction z. This specifically means that, after forming the Minkowski difference, not a single right prism, but a plurality of contacting right prisms, ideally the smallest in volume, are determined or selected for enclosure. Thus, the computational volume is enclosed according to the discretization steps, with a tighter aperture. The calculation of the collision probability can be performed similarly to the example described above. Because generally, for all prisms, the same uncertainty distribution can serve as a basis, the same transformation can be used to form the computational volume and therefore to determine the corresponding prisms. That is, the transformation required for the computational volume must ideally be determined only once.

[0075] Therefore, the collision region can be approximated by using multiple contacting prisms, or the true collision probability can be approximated by discretizing the 3D region into multiple sub-prisms. Discretization or discretization steps allow for a balance between computational time requirements and accuracy. In particular, the number of contacting prisms, i.e., the discretization, can be determined based on digital resources, such as available computing power. Thus, the accuracy of collision probability determination can be achieved more precisely, while simultaneously saving computational time.

[0076] An additional or alternative implementation of the method is configured such that the vehicle and the object are each approximated by at least one sphere, and the union of the computational volumes is approximated by a cube, wherein the cube completely contains the union. Preferably, the cube is considered instead of the union when determining the collision probability. In particular, the cube represents an approximation of the union. The sphere is preferably an ideal geometric sphere. The vehicle or object can be approximated by multiple spheres. In this implementation of the method, it is particularly important to examine whether the at least one sphere for the vehicle can overlap with at least one sphere for the object, i.e., collide. For this purpose, it is particularly sufficient if at least one sphere of the vehicle coincides with one sphere of the object. Therefore, the collision probability is less than the collision probability of all possible variations of the collision between the sphere of the vehicle and the sphere of the object. This can be expressed by the following formula:

[0077] P(C) < P(C) ms ) Formula 13

[0078] P(C ms )=P(coll(c1,c3)∨coll(c1,c4)∨coll(c1,c5)∨coll(c2,c3)…) Formula 14

[0079] P(C ms Let ) represent the collision probability of multiple spheres, where the actual collision probability P(C) is overestimated. The expression coll(i,j) here represents the event (here, collision), and p(coll(i,j)) represents the probability of the event, i.e., the collision probability. Different collision events are usually not independent of each other. The probability of the intersection of the spheres is not known in advance. Therefore, evaluating the event individually is usually impractical. Therefore, it is preferable, in this case, to form a corresponding third ambiguity for each combination of the first ambiguity of the spheres of the vehicle and the second ambiguity of the object, and then to normalize this third ambiguity. The transformation required for this is specifically used to calculate or determine the corresponding computational volume from the corresponding Minkowski difference. The combination region of the computational volume forms, in particular, the computational basis for the sought collision probability.

[0080] The uncertainty or ambiguity of the corresponding sphere can be determined from the uncertainty of the means of transport. This is done according to the normal distribution, specifically by propagating the linear uncertainty according to Gaussian. Here, the previously mentioned formulas 6 to 9 can be applied. In the case of these multiple spheres, many Minkowski differences can now be formed accordingly by utilizing the ambiguities of each of the coordinates x, y, and z. From the radius r of the sphere of the means of transport... i And the radius r of the sphere of the object j In particular, they are generated as having a radius r = r i +rj The sphere at the origin and the uncertainty Σ i,j The corresponding Minkowski difference in three dimensions is specifically for spheres surrounding the origin. Since the spheres themselves are perfectly symmetrical, orientation information can be ignored. If a symmetrical arrangement of multiple spheres is chosen, the transformations used for standardization of the third fuzziness or determination of the computational volume are particularly similar and must be computed in a reduced manner accordingly.

[0081] The standardization of the third fuzziness specifically leads to a transformation used to determine the computational volume. The union of these computational volumes can be used to determine the collision probability. However, the computational cost can be reduced by approximating the union by considering an axis-parallel polyhedron, i.e., a cube, around the union. Here, the cube should be designed to minimize volume, similar to the example with prisms. The probability generated by the cube again overestimates the collision probability. Ideally, the determination of the collision probability, taking into account the cube, would only result in a slight overestimation of the collision probability, but with significantly less computational cost. In a standardized normal distribution, all spatial coordinates are independent of each other. In this case, the probabilities for the x, y, and z coordinates can be evaluated individually by the standardized distribution function. In this case, the distribution function is called the cdf and represents the cumulative probability density function. The collision probability associated with the cube can be determined by the following formula:

[0082]

[0083] D ∨ "It is the volume and area of ​​the calculated volume." It relates to the collision probability of the cube. cdf is the corresponding cumulative probability density function.

[0084] Additional or alternative implementations of the method are configured to detect the object type by object recognition and determine a second ambiguity for the at least one second body based on the object type. For example, object recognition can be performed using a trained neural network. Depending on the object type, different uncertainties can arise for the object, and therefore different uncertainties for the at least one second body. For example, a drone as an object has different ambiguities than a bird. In the case of a bird, the bird's behavior may be more difficult to predict than the behavior of a controlled drone. For example, another drone can provide its intentional flight path or trajectory through a suitable interface (vehicle-to-X communication). Therefore, in the case of a drone, the probability of a particular behavior, such as a sudden turn, is very small. In the case of a bird, it is not known firstly how the bird will specifically behave in its flight path. These different behaviors can be expressed mathematically by means of different action assumptions. As already explained, these different action assumptions can lead to correspondingly different collision probabilities for the trajectory. For example, in the case of a drone, it is unlikely that the drone will deviate from its planned trajectory, but this cannot be assumed in the case of a bird. Therefore, the determination of the second ambiguity can be adapted to the object type. Consequently, the determination or calculation of the collision probability along the trajectory can be designed more realistically.

[0085] Additional or alternative implementations of the method are configured such that all bodies used to approximate the vehicle and the object are convex. In particular, a convex body is especially considered convex if the associated connecting paths lie entirely within that body for all point pairs. Therefore, the calculation of collision probabilities can be designed more reliably and easily. In the case of non-convex bodies, such as hollow cylinders or rings, the corresponding algorithms can produce unrealistic results or even cause the algorithm to crash. While this is not always the case, it has been shown that particularly high reliability can be achieved by approximating the vehicle and / or object using convex bodies for calculating collision probabilities.

[0086] Additional or alternative embodiments of the method are configured to generate control signals for maneuvering the vehicle and / or output instruction signals for the driver of the vehicle, based on a determined collision probability. Accordingly, control signals can be generated for a determined trajectory with a low collision probability. Alternatively or additionally, the determined collision probability can be used to adjust the vehicle. Here, the trajectory of the vehicle can be adapted according to the determined collision probability. The control signals for maneuvering the vehicle are preferably generated by the autonomous vehicle. This is, for example, the case in unmanned aerial vehicles (UAVs). On the other hand, if the vehicle is, for example, an air taxi requiring a driver, it may be sufficient to output instruction signals for the driver instead of control signals. Based on the instruction signals, the driver can accordingly control the vehicle to prevent a collision. In the case of autonomous flying vehicles, the control signals are particularly designed to manipulate and influence the corresponding actuator systems of the vehicle, thereby reliably avoiding collisions. In the case of vehicles controlled by a pilot, triggering safety functions may be sufficient. Depending on the collision probability, temporary automatic control, similar to emergency braking assistance in automobiles, can be additionally configured.

[0087] A second aspect of the invention relates to an apparatus for determining the probability of a collision between a vehicle and an object in three-dimensional space. This three-dimensional space is, in particular, traffic space open to airborne vehicles. The apparatus has at least one sensor unit for detecting the three-dimensional position and orientation of the vehicle and the object. Additionally or alternatively, the apparatus has an interface for receiving information regarding the three-dimensional position and orientation of the vehicle and the object. The apparatus also has a control unit. The control unit is configured to approximate the vehicle by at least one first geometry, wherein the at least one first geometry contains a portion of the vehicle. In particular, the vehicle can be under-approximated by at least one first geometry. Under-approximation, in particular, means that the at least one first geometry only partially, i.e., preferably not completely, contains the vehicle. Therefore, approximation can mean over-approximation or under-approximation. In the case of over-approximation, the vehicle is particularly completely contained within the at least one first geometry. In this case, the volume of the at least one first geometry exceeds the volume of the vehicle. Therefore, the volume of the at least one first geometry is greater than the volume of the vehicle.

[0088] The control unit is also configured to approximate an object using at least one second geometry, wherein the at least one second geometry comprises a portion of the object. The explanations regarding approximation, under-approximation, and / or over-approximation in relation to vehicles can be similarly applied to the approximation of objects. An object can be over-approximated or under-approximated using the at least one second geometry. During approximation, the position and / or orientation of the vehicle or object can be incorporated separately.

[0089] The control unit is capable of determining and / or presetting a first ambiguity of the at least one first geometry and a second ambiguity of the at least one second geometry. The control unit is configured to form a Minkowski difference for each combination of the at least one first geometry for a vehicle and the at least one second geometry for an object. The control unit is also configured to determine a corresponding third ambiguity for each Minkowski difference based on the first ambiguity of the at least one first geometry and the second ambiguity of the at least one second geometry. The control unit is configured to normalize the corresponding third ambiguity by a corresponding transformation and apply the same corresponding transformation to the correspondingly formed Minkowski difference to determine the corresponding computational volume from the corresponding Minkowski difference. Furthermore, the control unit is configured to determine or calculate the collision probability between the vehicle and the object based on the union of the computational volumes or an approximation of the union.

[0090] The sensor unit may include multiple sensors. Therefore, the sensor unit may include a temperature sensor, a camera, a lidar sensor, a pressure sensor, an ultrasonic sensor, and / or a radar sensor. For example, vector data can be received from an external data source via an interface. Similarly, information from other vehicles or flying objects can be received via an interface. The device may have a neural network that performs object recognition. For this purpose, for example, a neural network can be used to evaluate corresponding camera images.

[0091] The extensions and implementation schemes of the first aspect can be applied to the second aspect in the same sense and similarly, and vice versa. Therefore, all methodological features can be interpreted as representative device features. This also applies conversely.

[0092] In particular, the control unit may include a computer, a microcontroller, an integrated circuit, or a neural network. Alternatively, the control unit may include a combination of real or virtual computers. The control unit may also be configured as a processor or a microchip. Therefore, the control unit may have hardware or software elements to implement the illustrated method and its extensions. For this purpose, the control unit may additionally access a storage unit. This storage unit may be configured as permanent memory or non-permanent working memory. Therefore, the control unit may have a processor device configured to implement all embodiments of the method. For this purpose, the processor device may have at least one processor and / or at least one microcontroller and / or at least one FPGA (Field Programmable Gate Array) and / or at least one DSP (Digital Signal Processor). Furthermore, the processor device may have program code configured to execute embodiments of the method when implemented by the processor device. This program code may be stored in the data memory of the processor device.

[0093] The sensor unit can be configured as an environmental sensor system. This environmental sensor system is particularly capable of generating sensor data or sensor signals that map, represent, or reproduce the surrounding environment of the vehicle.

[0094] The invention also includes a computer program product comprising instructions that cause the apparatus to perform the method steps. The computer program product can exist in the form of program code. Corresponding instructions can be stored in the program code, which, when appropriately implemented, can carry out the method steps of claim 1 and all further extensions of the method.

[0095] The present invention also includes a computer-readable medium on which a computer program product is stored. In particular, the computer-readable medium contains program code with corresponding instructions capable of implementing the method according to claim 1. The computer-readable medium may be a memory card, a hard disk, or other non-volatile memory.

[0096] The present invention also includes extensions to the method according to the invention, which have the features described in connection with the extension to the motor vehicle according to the invention. For this reason, corresponding extensions to the method according to the invention will not be described again here.

[0097] The present invention also includes combinations of features of the described embodiments. Attached Figure Description

[0098] Several embodiments of the present invention are described below. For this purpose:

[0099] Figure 1 An exemplary illustration of a vehicle along with multiple objects in three-dimensional space and multiple possible trajectories for the vehicle is shown.

[0100] Figure 2 An exemplary flowchart illustrating a possible method for the present invention is shown;

[0101] Figure 3 shows an exemplary illustration of a method in which the approximation of a vehicle and an object is made by means of multiple spheres;

[0102] Figure 4 An exemplary illustration shows a vehicle and object approximated by a polyhedron;

[0103] Figure 5 shows an exemplary two-dimensional illustration for forming the Minkowski difference, for standardizing the third fuzziness, and for forming the computational volume;

[0104] Figure 6An exemplary illustration is shown for approximating a computational volume using one or more right prisms. Detailed Implementation

[0105] The embodiments described below are a preferred embodiment of the present invention. In this embodiment, the described portions constitute corresponding individual features of the invention to be considered independently of each other, and these features also independently further improve the invention, and therefore can be considered as part of the invention individually or in a manner different from the combinations shown. Furthermore, the described embodiments can also be supplemented by other features among the features already described in the invention. In the figures, functionally identical elements are given the same reference numerals.

[0106] Figure 1 A possible traffic situation for vehicle 10 is illustrated exemplarily. Besides vehicle 10, in... Figure 1 The drawing also depicts two objects, 20 and 25, and a car, 30. Like vehicle 10, object 25 is also a flying vehicle. In this example, the flying vehicle is constructed as a drone. Object 20 is a bird. Figure 1 Seven possible trajectories TR1 to TR7 are shown. The seventh trajectory, TR7, indicates the direction in which car 30 will travel. Since car 30 is not an air transport vehicle, its seventh trajectory TR7 lies in the xy plane. Therefore, Figure 1 A Cartesian coordinate system KS with typical axes x, y, and z is shown. Bird 20 has a sixth trajectory TR6, while another drone, acting as object 25, can use two possible trajectories, namely the fourth and fifth trajectories TR4 and TR5. The transport vehicle 10 has a sensor unit 12, an interface 15, and a control unit 14. Multiple sensors can form the sensor unit 12. These sensors can be, for example, cameras, lidar sensors, radar sensors, ultrasonic sensors, pressure sensors, temperature sensors, radiation sensors, venturi tubes, pitot tubes, or other sensors used for environmental detection. The control unit 14 can have a microcontroller, a processor device, and / or a neural network. Figure 1 In the scenario shown, the transport vehicle 10 needs to travel from a first point P1 to a second point P2. In particular, it is crucial to reliably avoid collisions with birds 20 and other drones 25.

[0107] In the field of collision recognition, so-called Monte Carlo methods are frequently used. However, these Monte Carlo methods tend to be very computationally intensive, and their computation time is dependent on the number of samples. Furthermore, Monte Carlo methods are stochastic and therefore not deterministic; there is no lower or upper bound that can be estimated. At best, a certain confidence interval can be given. Other methods attempt to calculate collision probabilities through numerical integration with appropriate adaptations. So far, this approach has failed primarily because these methods are extremely computationally intensive or their computation time is dependent on the number of discretization steps. Although implementations often reduce degrees of freedom through clever transformations and reshaping, this often leads to another drawback: in many cases, accuracy is compromised, resulting in collision probabilities no longer being accurately calculated. Attempting to re-establish this inaccuracy through correspondingly finer discretization further impacts computation time. Therefore, reliably, i.e., accurately and quickly enough, calculating or determining collision probabilities is extremely difficult.

[0108] The method proposed in this application provides a solution that offers a good trade-off between computation time and accuracy in determining collision probabilities. Furthermore, many methods focus only on collision avoidance in road traffic, i.e., they only consider collisions in two-dimensional space. If collisions are considered in three-dimensional space, this is typically done without considering the uncertainty UN. However, when air traffic space is compressed, considering the uncertainty UN becomes important.

[0109] Figure 1 The transport vehicle 10 is an aircraft, which can be optionally manned or unmanned. The transport vehicle 10 has three possible trajectories TR1, TR2, and TR3 to choose from. The objective is to determine a trajectory for the transport vehicle 10 that minimizes the possibility of collisions with birds 20 or other objects 25. To achieve this, the selected trajectories TR1, TR2, and TR3 need to be optimized. i A criticality assessment is performed. This assessment specifically involves calculating or determining the collision probability. The collision probability is determined, particularly for each point along the trajectory. If the collision probability is determined for multiple points along the trajectory, then the overall collision probability for that trajectory can be determined accordingly.

[0110] exist Figure 1 In the example, the second trajectory TR2 shows some points. Figure 1In this case, the second trajectory TR2 is selected. This second trajectory TR2 is the one with the lowest collision probability among the three trajectories TR1 to TR3. Therefore, the probability of colliding with the bird 20 or other drone 25 along this trajectory is extremely small. In the case of unmanned vehicles or autonomous vehicles with occupants, it can be set to completely avoid collisions. However, in the case of manned vehicles 10, it can be set to only provide warnings to the driver of vehicles 10 in order to mitigate critical situations in advance.

[0111] Figure 2 An exemplary flowchart of a possible method is shown. In the first step S1, the three-dimensional positions x, y, z and orientations α, β, γ of the transport vehicle 10 and the object 25 are detected or received. In particular, the orientation of the transport vehicle 10 and the object can be three-dimensional. Therefore, the orientation can have three angles. In the second step S2, through at least one first geometry c i ,py i To approximate the transport vehicle 10. Therefore, the transport vehicle 10 is traversed by the at least one first geometric shape c. i ,py i To represent, approximate, and / or represent. Here, the at least one first geometric body c i ,py i It includes at least a portion of the transport vehicle 10. Objects 20 and 25 can be approximated accordingly in a similar manner.

[0112] In the third step S3, a first ambiguity US1 and a second ambiguity US2 are determined and / or preset. The first ambiguity US1 relates to a first body, and the second ambiguity relates to a second body. In the fourth step S4, at least one first geometric shape c for the transport vehicle 10 is formed. i ,py i With at least one second geometry c for objects 20, 25 j ,py j The Minkowski difference D' for each combination. This can result in multiple Minkowski differences D'. In the fifth step S5, the third fuzziness US3 can be calculated from the corresponding first fuzziness US1 and second fuzziness US2, for example, by adding the first and second fuzzinesses. The third fuzziness US3 can be normalized by the corresponding transformation TN. Furthermore, in the fifth step S5, the same transformation TN used to normalize the third fuzziness US3 can be applied to the associated Minkowski difference D'. This is used to obtain the corresponding computational volume BK. In the sixth step S6, the collision probability of the vehicle 10 with the objects 20, 25 can be determined based on the spatial union D” of the computational volume BK. In particular, the corresponding probability density functions for the vehicle 10 and the objects 20, 25 can be considered here.

[0113] In a dynamic environment, the behavior of other traffic participants or objects 20, 25 is often unknown. Therefore, the environment of the vehicle 10 can be cyclically detected, especially with the help of sensor unit 12 or interface 15. The states of the detected objects 20, 25 can be predicted for the future. Based on this information, motion or trajectory can be planned. The trajectory TR thus determined... i This can be forwarded to the actuator system or control unit 14 for implementation. This can be implemented, in particular, in the form of control signals. Here, motion planning or trajectory planning should, in particular, perform a criticality evaluation, as proposed in this application, which preferably should be performed in real time. In particular, it is applicable here to consider the sensor unit 12 and the uncertainty UN of the prediction. Criticality is expressed or mapped, in particular, by the collision probability.

[0114] The control unit 14 can, in particular, consider the behavior of other objects 20, 25 to determine the collision probabilities for trajectories TR1 to TR7. The behavior of these other objects 20, 25 can be expressed mathematically through so-called action hypotheses. Multiple action hypotheses for the various other objects 20, 25 can be considered discretizedly. In particular, the following formula can be used for this purpose:

[0115]

[0116] Here, in Formula 16, the applicable formula is: P(h) TR2 p(h) represents the collision probability for the second trajectory TR2. g,k p(C) represents the probability of hypothesis g occurring in object k. i,g,k Let p(C) represent the probability of collision with object k. The purpose of this method is particularly to address p(C) i,g,k The calculation of p(C). i,g,k ) can be considered as the local or instantaneous collision probability at time or time step i. If we further consider the assumption that p(h) g,k The probability of ) then at multiple time points t i Above, we can calculate P(h) for the second trajectory. TR2 The probability of p(h). For the hypothesis p(h) g,k The probability of an object can, for example, map the probability of how the object behaves.

[0117] Similarly, the trajectory TRi can be decomposed into multiple time points t. i Therefore, on the lower plane, it can be determined that at a time point t, the distance between the two objects is... i The instantaneous collision probability at time t. This is especially true for the collision probability between vehicle 10 and objects 20 and 25. Subsequently, multiple time points t iThe individual probabilities can be summed to form the total probability for the second trajectory TR2. Therefore, from a specific spatial point or time point t... i Starting from the collision probability, we can also determine the TR for the entire trajectory. i The probability of collision.

[0118] Figure 3 illustrates, exemplarily, a possible method for determining the probability of a collision, in which the vehicle 10 and the object 25 are connected by means of multiple spheres c i To approximate. The means of transport 10 is approximated by a vector z for the means of transport 10. E Description, object 25 is described by means of vector z T Description (see Formula 10).

[0119] Therefore, a system with twelve degrees of freedom can be formulated for the vehicle 10 and the object 25. This can be achieved by means of Equation 11, in which the vector z is twelve-dimensional.

[0120] However, in reality, the determination or estimation of the state of an object always involves uncertainty. This is subject to uncertainty UN. Uncertainty UN in Figure 3a The ellipsoid is represented by a dashed ellipse. Multiple ellipses shown around the vehicle 10 or object 25 represent ellipses with corresponding three-dimensional orientations. Uncertainties UN or different ambiguities US1, US2, US3 should be understood in three dimensions. For clarity or simplification only, the ellipsoid is shown as a two-dimensional ellipse. Similarly, for the same reason, the Minkowski difference D' should be considered a circle rather than a sphere. Figure 3c The normalized third ambiguity US3 is shown as a dashed circle. In this case, the third ambiguity US3 also represents a sphere. Vehicle 10 in Figure 3a The expression contains three ellipses, which are actually ellipsoids. Each of these ellipses or ellipsoids represents a corresponding confidence interval or region of confidence. The explanation of confidence intervals mentioned above can be applied to... Figures 3a to 3d .

[0121] Uncertainty UN can be generated by inertial uncertainty, measurement error, erroneous sensor data, etc. Figure 3b The sphere c shown i It also cannot be accurately located. The sphere is affected by a first ambiguity US1 or a second ambiguity US2. If the relevant first or second ambiguity US1 or US2 is considered for all twelve degrees of freedom, this also results in a twelve-dimensional random vector Z. In sensor data fusion and prediction algorithms, the corresponding random variables can usually be assumed to be normally distributed. The determination of the random vector Z can be performed similarly to Equations 6 to 9.

[0122]

[0123] The collision probability can be determined using the following equation.

[0124] P(C)=∫ D pz(z)dz, where,

[0125] Here, the capital letter D represents the global integration region for the collision, θ(z E () represents a set of points in space, which are determined by the transportation vehicle 10 according to the vector z. E Occupied. The corresponding case applies to θ(z) T For the case where the probability functions for vehicle 10 and object 25 are independent, their respective probability density functions can be used. Equation 5 illustrates an exemplary computational possibility for this case.

[0126] In the following text, by means of Figures 3a to 3d The determination of collision probability is illustrated by using a sphere ci as an approximation of the geometry of the transport vehicle 10 and the object 25. Therefore, Figures 3a to 3d This vividly illustrates how Formula 4 can be effectively and efficiently evaluated. Figure 3a The image shows a vehicle 10 and an object 25. These two objects are at a distance large enough to reliably prevent a collision. The corresponding uncertainties UN of their three-dimensional spatial positions x, y, and z are schematically illustrated using multiple ellipses. This means that the vector z... E and z T The respective uncertainties (UN) cause some ambiguity. When using a sphere c... i In approximate cases, this is completely unnecessary, because sphere c i This is true even during rotation. Therefore, a sphere, in particular, lacks directional information.

[0127] exist Figure 3b As can be seen, the transport vehicle 10 is approximated by two spheres c1 and c2, while the object 25 is approximated by three spheres c3, c4, and c5. The first fuzziness US1 or the second fuzziness US2 can be derived from the uncertainty UN. Figure 3b In the example, there are multiple spheres c. i Each of the following is completely surrounded by the transport vehicle 10, or multiple spheres c j Each completely surrounds the object 25. Figure 3b The example assumes that the vehicle 10 is still at a sufficient distance from the object 25 to avoid a collision. If the object 25 gets further closer to the vehicle 10, a collision can no longer be avoided. Figure 3bThe diagram shows an approximation. In this case, the actual collision probability is slightly overestimated. A collision can occur if at least one combination of spheres from vehicle 10 collides with another sphere from object 25. This can be mathematically expressed by formulas 13 and 14.

[0128] exist Figure 3c The left side exemplarily illustrates a unique Minkowski difference D' as a sphere around the origin. Typically, each combination of subspheres forms its own Minkowski difference D'. However, for clarity, only a unique Minkowski difference D' is shown. Figure 3c It is assumed that object 25 and vehicle 10 have come closer together. In addition to the Minkowski difference D', several third ambiguities US3 are also indicated. Since the vehicle is approximated using two spheres c1 and c2, while object 20 is approximated using three spheres c3, c4, and c5, a total of six possible combinations are generated. This results in six Minkowski differences D', and also six third ambiguities US3.

[0129] If we assume that the sphere c is for the transportation vehicle 10 i radius r i and sphere c for object 25 j radius r j Then the Minkowski difference D' is especially a sphere with radius r = r i +r j The Minkowski difference D' also has a third fuzziness US3, which is the sum of the corresponding first fuzziness US1 and second fuzziness US2. Ideally, this involves attempting to select multiple spheres c. i,j The arrangement is symmetrical. In this case, some computational steps or operations are similar and need to be implemented with a corresponding reduction.

[0130] The third fuzziness, US3, is further standardized through a transformation TN. This is in... Figure 3c As shown in the diagram. This normalization, specifically by each corresponding third fuzzyness US3, generates a unit sphere around the origin. Since multiple third fuzzies US3 are normalized, multiple unit spheres are correspondingly generated. Multiple unit spheres can overlap at the same radius, so that only one unique sphere is visible.

[0131] This transformation TN is used to form or determine the computational volume BK. For this purpose, the same transformation TN used to normalize the third fuzziness US3 is applied to the Minkowski difference D' associated with the corresponding third fuzziness. This is in Figure 3dThe diagram shows that the transformation TN can be a matrix containing stretching, twisting, translation, reflection, compression, etc. The same transformation TN that transforms the third fuzziness US3 into a unit sphere will transform the corresponding Minkowski difference D' into the corresponding computational volume BK. For each Minkowski difference D' or each third fuzziness US3, a separate transformation TN may be required. In the case of Figure 3, there are six Minkowski differences D', and therefore six transformations TN. Due to the geometry c... i ,py i With a symmetrical arrangement, the number of transformations TN can be reduced, or the computational cost can be decreased. The union D” of these multiple ellipsoids representing the computational volume BK forms the basis for calculating the collision probability. The probability density functions for the vehicle 10 and the object 25 can be integrated or summed over the region of the union D”.

[0132] However, due to the multiple ellipsoids, the joint region D” is not always mathematically readily obtainable. For this reason, the present invention proposes, in this case, placing a cube BB around the multiple ellipsoids. Ideally, the cube BB completely contains the entire union D”. Simultaneously, the cube BB should not be chosen to be too large, i.e., preferably implemented with a minimum volume. While this slightly overestimates the collision probability, it significantly reduces computational complexity. In a normalized normal distribution, the coordinates x, y, and z are independent. Therefore, the probabilities in the x, y, and z directions can be evaluated individually by the normalized distribution function cdf. The distribution function cdf here corresponds to the cumulative probability density function. This is achieved, in particular, using Equation 15.

[0133] exist Figure 4 The image also shows a transport vehicle 10 and an object 25. Unlike Figure 3, the transport vehicle 10 or the object 25 is not composed of multiple spheres c. i,j It is not an approximation, but rather an approximation by the first polyhedron py1 and the second polyhedron py2. Figure 4 In this case, these polyhedra py i,j The implementation is a cube (BB). In principle, the methods used to calculate or determine the collision probability are the same as... Figures 3a to 3d Similar to what is described in the text. Figure 4 and Figure 3b Correspondingly, the condition is to replace the sphere with the polyhedron py. i,j Used for approximation. For Figures 3a to 3d The explanation also applies to polyhedra py i,j The polyhedron was used as an approximation. However, slight deviations exist, which are caused by... Figure 6 To illustrate.

[0134] exist Figure 6The diagram shows the first prism PR1 and the second prism PR2. The second prism PR2 is indicated only by dashed lines. Within the first prism PR1, three squares BB can be seen. These three squares BB represent the corresponding computational volume BK. The volumes of these three squares BB together form a union D". These three squares BB can intersect or overlap. Figure 3d In the example, the union D” can also be approximated by using simpler geometry. However, in Figure 6 In the example, this is not a cube, but a first prism PR1. Ideally, the first prism is a right prism PR1 with the smallest volume that completely encloses the union D". Figure 6 In the diagram, for clarity, the first prism PR1 is drawn slightly larger. Preferably, the first prism PR1 and all other prisms PR... i The bottom and top surfaces are positioned parallel to each other. In this case, the collision probability can be calculated by integrating the probability density function of the vehicle 10 and the object 25 over the volume of the first prism PR1. Alternatively, the collision probability can be calculated via the corresponding inverse probability. Formula 12 can be used for this.

[0135] Alternatively, the computational mechanism BK can be discretized using multiple prisms. Figure 6 The example illustrates a second prism PR2. The second prism PR2 can move relative to the first prism PR1 (unlike in the figure), where it is always parallel to the first prism PR1. The second prism PR2 can move relative to the first prism PR1, where the two prisms remain in contact. After forming the computational volume BK, instead of selecting a single right prism PR1, multiple contacting right prisms PR1 with the ideal minimum volume are selected. i This is used to enclose the computational volume BK. Thus, the computational volume BK can be enclosed with tighter apertures depending on the discretization steps. Typically, multiple polyhedra py... i,j They have the same first or second ambiguity US1, US2. Therefore, for multiple Minkowski differences D', multiple prisms PR can be addressed. i The same transformation TN is obtained. Ideally, the transformation TN only needs to be determined once.

[0136] To further illustrate this, Figure 5 schematically shows, as an example, the determination of the collision probability in two-dimensional space. Figure 5a Method steps S1 to S3 are illustrated schematically. Two objects are approximated using rectangles. The corresponding first or second ambiguities US1, US2 are represented by corresponding ellipses. The underlying covariance matrix and normal distribution are implemented in two dimensions. From... Figures 5a to 5bThe transition, in particular, represents the fourth step S4 of the method. This corresponds to the formation of the Minkowski difference D'. It can be schematically seen here that the two rectangles have been moved multiple times in order to shape the Minkowski difference D'. Figure 5b The third fuzziness, US3, is preferably the sum of the first fuzziness, US1, and the second fuzziness, US2. Because... Figure 5b The Minkowski difference D' is shown, therefore the coordinate axes are relative coordinates.

[0137] from Figures 5b to 5c The transition specifically represents the fifth step S5, namely the standardization of the third fuzziness US3. The standardization process results in the elliptical third fuzziness US3 being transformed into a unit circle around the origin. This transformation TN, which generates the standard circle and origin from arbitrarily arranged ellipses, can also be applied to the Minkowski difference D'. The result here is specifically the computational volume BK. Here, multiple computational volumes BK can be generated or appear due to multiple transformations TN. It can be clearly seen that after the standardization of the third fuzziness US, the third fuzziness US3 is no longer an ellipse, but rather circles around the origin (…). Figure 5c The transformation TN required for this can include translation, rotation, and / or scaling. The same transformation TN that transforms the third fuzziness US3 from an ellipse to a circle with the origin is applied accordingly to the Minkowski difference D'. This results in... Figure 5c The computational body BK. In this case, the computational body BK also corresponds to the union D". The normalization process is a known method or procedure in stochastic physics. However, it can be demonstrated, especially by means of Figure 5, from Figures 5b to 5c The transition illustrates the standardization process more vividly.

[0138] In summary, this invention demonstrates that collision probabilities can be determined using the methods described herein and their additional embodiments, offering significant computational advantages compared to other methods, such as Monte Carlo methods or other numerical integration methods. These advantages enable the use of collision probabilities instead of binary collision checks, even in complex systems with real-time requirements (which must be applied to collision checks of many different trajectories), and thus appropriately shaping uncertainty in the decision-making process. In conclusion, there is therefore a significant advantage in computational runtime with high accuracy. Therefore, for closed-loop mobility services that also include air transport vehicles, the transition between the road domain and airspace can be reliably designed. This is particularly relevant in situations where traffic spaces are relatively dense, creating a need for rapid and reliable determination of collision probabilities. Compared to other methods, this invention provides a deterministic method for determining collision probabilities, the computational runtime of which is estimable. Furthermore, the computational runtime according to the method and this invention is significantly reduced compared to other methods for calculating collision probabilities. Therefore, multiple trajectories TR can be calculated respectively. iThe relevant collision probabilities are determined. This reduced computation time enables the trajectory of vehicle 10 to be determined in real time.

[0139] The following formula symbols are used in this application. Additionally, the variables are explained in the corresponding formulas. Subscript E relates to means of transport. The corresponding formula symbol (Z) for objects... T ,θ(z T (etc.) have the subscript T:

[0140] A, B: Sets A and B

[0141] μ E For a random vector Z E Expected value

[0142] ∑: Covariance matrix for a random vector Z

[0143] ∑ E For a random vector Z E covariance matrix

[0144] Z E A random vector of transportation vehicle vectors

[0145] θ(z E A set of points, defined by a transport vehicle based on vector z. E occupy

[0146] According to vector z E For a random vector z E probability density function

[0147] p Z(z) Based on the probability density function of the state (vector) z for a random vector Z,

[0148] z E Transportation vehicle vector

[0149] According to vector Z E For a random vector z E probability density function

[0150] R(α,β,γ): Rotation matrix

[0151] distance: The distance between the center points of the related fuzziness of different geometries.

[0152] List of reference numerals

[0153] 10. Means of transport

[0154] 20 objects, birds

[0155] 25 objects, drones

[0156] TR i Corresponding trajectory

[0157] KS Cartesian coordinate system

[0158] P1 First point

[0159] P2 Second point

[0160] 12 sensor units

[0161] 14 Control Unit

[0162] 15 Interfaces

[0163] 30 cars

[0164] Steps S1 to S6 (First to Sixth Steps)

[0165] US1 First Ambiguity

[0166] US2 Second Ambiguity

[0167] US3 Third Ambiguity

[0168] BK Computational Entity

[0169] TN transformation

[0170] D' Minkowski difference

[0171] c i,j The corresponding sphere

[0172] py i,j The corresponding polyhedron

[0173] t i One or more time points

[0174] PR i The corresponding prism

[0175] D” Union or an approximation of the union.

[0176] x, y, z 3D position, corresponding coordinates

[0177] BB square

[0178] i is the footer for the time point, time step, and / or the first geometry.

[0179] j is the subscript for the second geometry.

[0180] UN uncertainty

Claims

1. A method for determining the probability of collision between a vehicle (10) and an object (20, 25) in three-dimensional space by performing the following method steps: a) Detect and / or receive (S1) the three-dimensional position (x,y,z) and orientation (α,β,γ) of the transport vehicle (10) and the object (20,25); b) Through at least one first geometry (c) i ,py i To approximate the transport vehicle (10) (S2), wherein, The at least one first geometric body (c) i ,py i ) includes a portion of the transport vehicle (10) and is connected by at least one second geometry (c j ,py j To approximate the object (20, 25), wherein the at least one second geometric body (c j ,py j ) contains a portion of the object (20, 25); c) Determine and / or preset (S3) the at least one first geometry (c i ,py i The first ambiguity (US1) and the at least one second geometry (c) j ,py j The second ambiguity (US2); d) For the at least one first geometry (c) i ,py i ) and the at least one second geometry (c j ,p yj Each combination of ) forms the (S4) Minkowski difference (D'); e) Based on the at least one first geometry (c) i ,py i The corresponding first ambiguity (US1) and the at least one second geometry (c) j ,py j The corresponding second fuzziness (US2) is used to determine the corresponding third fuzziness (US3) for each Minkowski difference (D'); f) The corresponding third fuzziness (US3) is standardized (S5) by the corresponding transformation (TN), and the same corresponding transformation (TN) is applied to the corresponding formed Minkowski difference (D') to determine the corresponding computational volume (BK) from the corresponding Minkowski difference (D'). g) Determine (S6) the collision probability of the vehicle (10) and the object (20,25) based on the union (D'') of the computational body (BK) or an approximation of the union (D'').

2. The method according to claim 1, wherein, The geometry (c) for the vehicle (10) and the object (20, 25) is determined based on digital resources. i,j ,py i,j The volume of ).

3. The method according to claim 1 or 2, wherein, For the at least one first body (c) of the transport vehicle (10) i ,py i The first or second body (c) completely comprises the transport vehicle (10), while the second body (c) for the object (20, 25) is... j ,py j ) completely contains the object (20, 25), or the at least one first body (c i ,py i The first or second body (c) is not nearly identical to the transport vehicle (10), while the second or second body (c) is not nearly identical to the transport vehicle (10). j ,py j The object (20, 25) is not approximated.

4. The method according to claim 1 or 2, wherein, The first ambiguity (US1) and / or the second ambiguity (US2) are determined based on a Gaussian normal distribution and / or error propagation.

5. The method according to claim 1 or 2, wherein, At different time points (t) i The three-dimensional position (x, y, z) and / or orientation (α, β, γ) of the object (20, 25) are repeatedly detected to determine the three-dimensional trajectory (TR) of the object. i ), and based on the trajectory (TR) of the object (20,25) i ), select the trajectory with the lowest collision probability from multiple trajectories (TRi) for the vehicle (10).

6. The method according to claim 5, wherein, For the trajectory (TR) of the transport vehicle (10) i The collision probability is determined by multiple points.

7. The method according to claim 1 or 2, wherein, Through at least one polyhedron (py) i,j The transport vehicle (10) and the objects (20, 25) are approximated by means of prisms (Pr i The union (D'') of the computational volume (BK) is approximated, wherein the prism (Pr) i The union (D'') completely contains the union.

8. The method according to claim 7, wherein, The computational volume (BK) is constructed through multiple phase-contact prisms (Pr). i )approximate.

9. The method according to claim 1 or 2, wherein, The transport vehicle (10) and the object (20, 25) respectively pass through at least one sphere (c i,j The union (D'') of the computational volume (BK) is approximated by a square volume (BB), wherein the square volume (BB) completely contains the union (D'').

10. The method according to claim 1 or 2, wherein, The object type of the object (20, 25) is detected by object recognition.

11. The method according to claim 1 or 2, wherein, All bodies (c) used to approximate the means of transport (10) and the objects (20, 25) i,j ,py i,j It is convex.

12. The method according to claim 1 or 2, wherein, Based on the determined collision probability, control signals are generated for maneuvering the vehicle (10) and / or instruction signals are output to the driver of the vehicle (10).

13. The method according to claim 7, wherein, When determining the collision probability (S6), the prism (Pr) is considered instead of the union (D''). i ).

14. The method according to claim 8, wherein, The prism (Pr) i They are symmetrical to each other.

15. The method according to claim 9, wherein, When determining the collision probability (S6), the cube (BB) is considered instead of the union (D'').

16. The method of claim 10, wherein, Determine the target for at least one second body (c) based on the object type. j ,py j The second ambiguity (US2).

17. An apparatus for determining the probability of collision between a vehicle (10) and an object (20, 25) in three-dimensional space, the apparatus comprising: - At least one sensor unit (12), said at least one sensor unit is used to detect (S1) the three-dimensional position (x,y,z) and orientation (α,β,γ) of the transport vehicle (10) and the object (20,25) and / or receive (S1) information related to the three-dimensional position (x,y,z) and orientation (α,β,γ) of the transport vehicle (10) and the object (20,25) by means of an interface (15). - Control unit (14), the control unit being configured to: *Through at least one first geometry (c) i ,py i The transport vehicle (10) is approximated (S2), wherein, The at least one first geometric body (c) i ,py i ) includes a portion of the transport vehicle (10) and is connected by at least one second geometry (c j ,py j The object (20, 25) is approximated (S2), wherein the at least one second geometric body (c j ,py j ) contains a portion of the object (20, 25); *Determine and / or preset (S3) the at least one first geometry (c i ,py i The first ambiguity (US1) and the at least one second geometry (c) j ,py j The second ambiguity (US2); *For the at least one first geometry (c) i ,py i ) and the at least one second geometry (c j ,py j Each combination of ) forms the (S4) Minkowski difference (D'); *According to the at least one first geometry (c) i ,py i The corresponding first ambiguity (US1) and the at least one second geometry (c) j ,py j The corresponding second fuzziness (US2) is used to form the corresponding third fuzziness (US3) for each Minkowski difference (D'); * The corresponding third fuzziness (US3) is standardized (S5) by the corresponding transformation (TN), and the same corresponding transformation (TN) is applied to the correspondingly formed Minkowski difference (D') to determine the corresponding computational volume (BK) from the Minkowski difference (D'). *The collision probability of the vehicle (10) with the object (20,25) is determined (S6) based on the union (D'') of the computational body (BK) or an approximation of the union (D'').

18. A computer program product comprising instructions that cause the apparatus of claim 17 to perform the steps of the method of claim 1.

19. A computer-readable medium on which a computer program product according to claim 18 is stored.

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