Method for assessing a potential collision between a mobile device and an object

Abstract

The invention relates to a method for assessing a potential collision between a mobile device, intended to move in an environment, and an object in the environment, comprising: providing a first data set indicating an approximate representation (501) of an outer shape of the mobile device and a position of the mobile device in relation to the approximate representation of the outer shape of the mobile device; providing a second data set indicating an approximate representation (502) of an outer shape of the object and a position (510) of the object in relation to the approximate representation of the outer shape of the object; assessing whether an overdetermination (506b) exists for a Minkowski sum of the first data set and the second data set, which overdetermination does not include a vector of the position of the mobile device and the position of the object, and if an overdetermination (506b) of this type exists, determining that there is no collision between the mobile device and the object.

Description

[0001]R.406617 - 1 - Description Title Method for assessing a potential collision between a mobile device and an object The present invention relates to a method for assessing a potential collision between a mobile device that is supposed to move in an environment and an object in the environment, a computing unit and a computer program for carrying out the method and a mobile device. Background of the invention Mobile devices, in particular robots, drones or at least partially automated vehicles such as so-called AGVs (“Automated Guided Vehicles”), are used in various areas. Such mobile devices typically move along a trajectory or a movement path in an environment such as a home, in a garden, in a factory hall or on the street, in the air or in water. A collision with objects in the environment should be avoided as far as possible.Disclosure of the Invention According to the invention, a method for assessing a potential collision between a mobile device and an object, a computing unit and a computer program for carrying out the method, as well as a mobile device having the features of the independent patent claims are proposed. Advantageous embodiments are the subject of the subclaims and the following description. R.406617 The invention generally relates to mobile devices that move or are intended to move, for example, along a trajectory in an environment. A trajectory in this case comprises, in particular, a movement path and a speed profile along the movement path. The trajectory can, for example, contain positions and / or orientations of the mobile device and, in addition, a speed profile, e.g.Times at which these positions and / or orientations should apply; thus, a certain speed is also specified along or on the movement path. In an environment, there are usually objects that can be regarded as obstacles for the mobile device, so that a collision between the mobile device and an object should be avoided. Examples of such mobile devices are, for example, robots and / or drones and / or partially or (fully) automated vehicles (on land, water, or in the air). Robots that can be considered include, for example, household robots such as vacuum and / or mop robots, floor or street cleaning devices, or lawnmower robots, as well as other so-called service robots, as well as at least partially automated vehicles, e.g., passenger transport vehicles or goods transport vehicles (also so-called industrial trucks, e.g.in warehouses, including automated forklifts), but also aircraft such as drones or watercraft. Furthermore, parts of robots, e.g. a robot arm with a manipulator, can be considered as mobile devices. In all these cases, there may be objects such as other (mobile) devices, walls, furniture, people, animals or other objects with which a collision must be avoided. Various options can be considered to check whether two objects may collide, in particular whether there is or could be a potential collision between a mobile device that is supposed to move in an environment and an object in the environment. This can be taken into account in particular when determining or planning movement paths or trajectories for the mobile device. R.406617 Objects can be defined for this purpose, for example, as sets (of e.g.points or vectors in space) are considered, which then describe, for example, an external shape of the objects. Differential constraints that describe whether two sets overlap or not are useful, for example, in optimization-based collision-free planning techniques. They not only allow the assessment of whether these two sets actually overlap and thus collide, but the partial derivatives of the constraints also provide information about the direction in which the sets must be shifted to undo an overlap, as well as about how, for example, the requirements for collision-freeness can be weighed against the costs of minimizing the path length. In predictive path planning or trajectory generation, this facilitates the efficient calculation of optimal collision-free paths or trajectories.An example of a condition that states that two (hyper-)spheres are in a Euclidean space with center positions ^. ^ , ^ ^ and the radii ^ ^ , ^ ^ not intersect, can be written, differentiable, as: (^ ^ − ^ ^ ) ^ (^ ^ − ^ ^ ) ≥ (^ ^ + ^ ^)² . Alternatively, it can be indirectly proven that two convex sets do not intersect by finding a separating hyperplane. In other words, when considering a 2D plane, two convex sets (e.g., circles) do not intersect if any line can be drawn between them (so-called separating hyperplane). The existence of a trajectory for the separating hyperplane at any time is a necessary and sufficient condition for the trajectory to be collision-free. However, the separating hyperplane can be different at different times. However, it has now been found that a particularly efficient way to assess a potential collision between a mobile device and an object involves taking a Minkowski sum for representations of the external shape of the mobile device on the one hand and the object on the other hand.406617, and then to check or assess whether there is an overdetermination for this Minkowski sum, for which overdetermination the vector between the position of the mobile device and the position of the object is not contained in the overdetermination. Instead of vector, one can also speak of an offset or a (directed) distance. If ^ and ℬ are two sets, if ^ is an approximation of ℬ, and if ^ ⊃ ℬ, then ^ is an overapproximation of ℬ. If such an overdetermination exists, it can be determined that there is no collision between the mobile device and the object. In particular, it is not only possible to check whether a collision (at all) exists or not, but also to obtain the gradient information, i.e. in which direction the potential position of the mobile device should be changed to avoid a collision.Since the collision avoidance condition is differentiable, the advantages of this approach can be exploited to a greater extent when using gradient information. In particular, the Minkowski sum is determined from two sets of vectors, where one set of vectors specifies the interior and surface of the mobile device (as far as approximately represented) and a set of vectors specifies the interior and surface of the object (as far as approximately represented). The external shape of the mobile device, which is relevant when checking for a potential collision, should be taken into account at least approximately. For this purpose, a first data set is provided that specifies an approximate representation of an external shape of the mobile device and a position of the mobile device with respect to the approximate representation of the external shape of the mobile device.For example, this approximate representation of the external shape can be an ellipsoid (or, in 2D, an ellipse as a special case of the ellipsoid) or, more generally, a Minkowski sum of ellipsoids. In the case of an ellipsoid, the position of the mobile device can, for example, correspond to the center point R.406617 of the ellipsoid. Further details will be explained in the figure description. Other shapes that can be described, for example, by Minkowski sums of ellipsoids are (hyper-)rectangles (a Minkowski sum of orthogonal line segments that effectively correspond to degenerate ellipsoids), (hyper-)parallelograms (a Minkowski sum of non-orthogonal line segments), and (hyper-)capsules (a Minkowski sum of line segments with circles or ellipsoids). This applies accordingly to the object for which a corresponding second data set is provided.This proposes a novel alternative to the separating hyperplane approach to check whether two objects, which can in particular be described by the Minkowski sum of ellipsoids, intersect, which is compatible with numerical optimization methods, e.g., for optimization-based trajectory generation. An existing approach for overdetermining (or overapproximating) the Minkowski sum of two sets (e.g., ellipsoids) can be used. Only a condition is formulated to determine whether the two sets (ellipsoids) intersect, and their signed distance can be determined. Overdetermination can also be used to perform the above calculation between a pair of Minkowski sums of ellipsoids. The unique insight is that, although overdeterminations are used, the results for the signed distance are exact.In one embodiment, a trajectory is determined for a mobile device that is to move in an environment while avoiding a collision with an object in the environment. For this purpose, a potential position of the mobile device and a position of an object in the environment R.406617 are provided. In this case, sensors of the mobile device can be used, for example, to detect the environment and thus also to determine the distance to and the external shape of objects. It is then determined according to a method described above whether a collision will occur between the mobile device, the external shape of which can be predetermined, at the potential position and the object. If it is determined that no collision will occur, the trajectory of the mobile device is determined using the potential position of the mobile device, and the trajectory is then provided.As mentioned, the gradient information can also be used to determine the direction in which the potential position of the mobile device should be changed. For example, based on the trajectory, movement control variables for the mobile device can be determined, the movement control variables can then be provided, and / or the mobile device can be moved based on the movement control variables. Although the invention is primarily described in connection with the control of autonomous mobile devices such as robots on wheels, an application to other mobile devices such as robot manipulators is also conceivable. Examples of possible applications include shuttles, autonomous professional floor cleaning machines, baggage handling robots at airports and robots on construction sites, autonomous vacuum cleaner robots, and other types of mobile devices already mentioned. Applications in related fields such as automotive engineering, aviation, etc., but also in more distant areas such as toy motors, chemical engineering, biotechnology, etc. are also possible, in particular where non-overlaps (and / or distances between) Minkowski sums of ellipsoids may be relevant (e.g. molecules, cells). A computing unit according to the invention, e.g. a control device or a control unit of a mobile device, or a server or other computer, is configured, R.406617 in particular in terms of programming, to carry out a method according to the invention. The invention also relates to a mobile device, e.g. a robot, a drone, or an at least partially automated vehicle (e.g. an AGV), which is configured to receive a trajectory or motion control variables. The mobile device then has a drive system and a control or regulating unit for controlling the drive system based on the adapted trajectory and / or the motion control variables.The mobile device can also have a computing unit according to the invention, i.e. the trajectory and / or the movement control variables can be determined on the mobile device or its computing unit. However, it is also expedient if the trajectory and / or the movement control variables are determined on a higher-level computing unit, e.g. a server or in the so-called cloud, from where the mobile device then receives the trajectory and / or the movement control variables. The implementation of a method according to the invention in the form of a computer program or computer program product with program code for carrying out all method steps is also advantageous, since this entails particularly low costs, in particular if an executing control unit is also used for other tasks and is therefore already present. Finally, a machine-readable storage medium is provided with a computer program stored thereon as described above.Suitable storage media or data carriers for providing the computer program are in particular magnetic, optical and electrical memories, such as hard disks, flash memories, EEPROMs, DVDs, etc. Downloading a program via computer networks (Internet, intranet, etc.) is also possible. Such a download can be wired or cable-based or wireless (e.g. via a WLAN network, a 3G, 4G, 5G or 6G connection, etc.). Further advantages and embodiments of the invention emerge from the description and the accompanying drawings. R.406617 The invention is shown schematically in the drawing using an exemplary embodiment and is described below with reference to the drawings. Brief description of the drawings Figure 1 shows a schematic view of a mobile device in an environment to explain the invention. Figures 3 to 5 show schematic representations to explain the invention.Figure 6 shows a schematic sequence of a method according to the invention in a preferred embodiment. Embodiment(s) of the invention Figure 1 schematically shows a mobile device 100 in an environment 120, with reference to which the invention will be explained. By way of example, the mobile device 100 is a self-driving vehicle, e.g. an AGV. It is understood that the mobile device can also be of a different type, as explained above. The mobile device 100 has a computing unit 108 designed as a control unit, which is connected, for example, to the higher-level computing unit 110 in a wireless data-transmitting manner, and also, by way of example, a lidar sensor 106. Furthermore, the mobile device 100 has a drive system 104 and a control or regulating unit 102 for controlling the drive system 104 based on trajectory or movement control variables.In the environment 120, a possible trajectory 130 is indicated by way of example, according to which the mobile device 100 is to be moved or travel, for example. The trajectory 130 can not only indicate the movement path ultimately to be followed by the mobile device (alternative possible R.406617 movement paths could also be present), but also a speed in this case. In addition, an object 140 is shown in the environment as an example. When determining the trajectory 130, it is desirable that it is planned in such a way that a collision between the mobile device 100 and the object 140 (in the sense of an obstacle) is avoided. In this case, a potential collision between the mobile device and the object is assessed. For this purpose, in particular an approximate representation of an external shape of the mobile device 100 and its position, and an approximate representation of an external shape of the object 140 and its position are required.While the external shape of the mobile device 100 can be predetermined or known, the shape of the object 140 can be determined at least approximately, for example using the aforementioned lidar sensor. The positions of the mobile device and object can be specified as a relative position between the two, which is sufficient for collision avoidance. The position of the object can be determined relative to the mobile device, for example also using the lidar sensor. The following will explain how a possible collision between two objects or a mobile device and an object can be assessed within the scope of the present invention, in particular with the fundamentals thereof. Figure 2 shows two sets ^ and ℬ which do not overlap in illustration (a) (there would be no collision here) and do overlap in illustration (b). For this purpose, a distance can first be defined. Let ^ ⊂ ^. ^ and ℬ ⊂ ^ ^two compact sets. Then the distance between the two sets can be defined as ^^^^ ( ^, ℬ ) = ^ i ∈ n ^ f ^{ |^| | ^ ∩ ( ℬ + ^ ) ≠ ∅} where ℬ + ^ is the translation of the set ℬ around the vector ^ ∈ ^ ^ R.406617 Furthermore, a penetration can be defined. The penetration between two sets is ^^^^ ( ^, ℬ ) = ^ i ∈ n ^ f ^{ |^| | ^ ∩ ( ℬ + ^ ) = ∅}. Furthermore, a signed distance can be defined. The signed distance between two sets is defined as ^^ ( ^, ℬ ) = ^^^^ ( ^, ℬ ) − ^^^^ ( ^, ℬ ) . If the two sets do not intersect, ^^^^ ( ^, ℬ ) > 0, ^^^^ ( ^, ℬ ) = 0 and therefore ^^ ( ^, ℬ ) > 0. The distance ^^^^( ^, ℬ ) − is equal to the smallest distance between points in the set ^ and points in the set ℬ. If the two sets intersect, then ^^^^ ( ^, ℬ ) = 0, ^^^^ ( ^, ℬ ) > 0 and thus ^^ ( ^, ℬ ) < 0. The penetration ^^^^ ( ^, ℬ ) is equal to the minimum length of the linear translation vector ^ separating the two sets. The Minkowski sum of two sets ^ ⊂ ^ ^ and ℬ ⊂ ^ ^ can be defined as ^ ⊕ ℬ ≔ {^ + ^ | ∀^ ∈ ^ ^^^ ^ ∈ ℬ} The Minkowski difference of two sets ^ ⊂ ^ ^ and ℬ ⊂ ^ ^ can be defined as ^ ⊖ ℬ ≔ {^ − ^ | ∀^ ∈ ^ ^^^ ^ ∈ ℬ} The signed distance between two closed sets ^ ⊂ ^ ^ and ℬ ⊂ ^ ^ is equivalent to the signed distance between its Minkowski difference ^ ⊖ ℬ and its origin {0}: ^^ ( ^, ℬ )= ^^({0}, ^ ⊖ ℬ). R.406617 This can be proven as follows: . To prove this, it is therefore sufficient to prove that ^^^^ ( ^, ℬ ) = ^^^^ ( {0}, ^ ⊖ ℬ ) , if two sets are separate, and ^^^^(^, ℬ) = ^^^^({0}, ^ ⊖ ℬ) if the two sets overlap. First, the case is considered when two sets are separate. For ^ ∗ , ^ ∗ ≔ arg ^∈ m^i,^n∈ℬ ( ^ − ^ )^ ( ^ − ^ ) applies ^ ^ ≔ ^ ∗ − ^ ∗ ∈ ^ ⊖ ℬ Therefore ^^^^({0}, ^ ⊖ ℬ) ≤ ^^^^({0}, {^ ^}) = ^^^^(^, ℬ) Conversely, let ^ ∗ the point in the set ^ ⊖ ℬ that has the shortest distance to the origin, there exists a ^ ^ ∈ ^ and ^ ^ ∈ ℬ, such that ^′: = ^′ + ^ ∗ . Therefore ^^^^(^, ℬ) ≤ ||^ ∗|| = ^^^^({0}, ^ ⊖ ℬ) Using the last two equations, it can be concluded that ^^^^(^, ℬ) = ^^^^({0}, ^ ⊖ ℬ). If two sets overlap, ^^^^({0}, ^ ⊖ ℬ) = ^^^^(^, ℬ) can be shown similarly. R.406617 There are various notations for ellipsoids. In the following, the following notation for an ellipsoid should be used. ℇ(^, ^) ∶= {^| ( ^ − ^ )^ ^ ^^( ^ − ^ ) ≤ 1} ⊂ ^ ^ Where ^ ∈ ^ ^ is the center of the ellipsoid and ^ ∈ ^ ^ ^ is a positive semi-definite matrix. Figure 3 shows two ellipsoids (or ellipses, in 2D) 301, 302, both of which have the same center point 310. The Minkowski sum and the Minkowski difference of two origin-centered ellipsoids are then equivalent: In Figure 3, this is indicated by the ellipses indicated by the vectors ^, ^. The theorem can now be stated that the signed distance between two ellipsoids ℇ(^ ^ , ^ ^ ) and ℇ(^ ^ , ^ ^ ) is equivalent to the signed distance between the Minkowski sum of the two ellipsoids and the difference of their centers: This can be shown as follows. Based on the above theorem, the following can be easily obtained: The Minkowski difference remains the same if the same translation is made over both ellipsoids: R.406617 = ^^ ( {^ ^ − ^ ^}, ℇ(0, ^ ^ ) ⊖ ℇ(0, ^ ^ ) ) . It can then be concluded from the above: Thus, the signed distance between two sets can be determined based on the Minkowski sum of the two sets and their position difference. The above-mentioned overdetermination will be explained in more detail below. Reference is also made to Figure 4, which again shows two ellipsoids or ellipses 401, 402 (similar to Figure 3), as well as their Minkowski sum 405 and a superdetermination 406. Two ellipsoids ℇ ( 0, ^ ^ ) and ℇ ( 0, ^ ^ ) be considered, e.g. the ellipses or ellipsoids 401 and 402. Their Minkowski sum ℇ ( 0, ^ ^ ) ⊕ ℇ ( 0, ^ ^ ) or 405 in Figure 4 is not itself an ellipsoid, but their sum can be overdetermined. For every β > 0, ℇ ( 0, ^ ^ ) ⊕ ℇ ( 0, ^ ^ ) ⊆ ℇ^0, ^ ^ (^, ^ ^ , ^ ^ )^ where The theorem shall apply according to which and R.406617 For each ^ ∈ Rn and two ellipsoids ℇ ( 0, ^ ^ ) and ℇ ( 0, ^ ^ ) , there exists a β ∗ so that ^^ ^ = ^^ ^ . Now assume that the shape of a robot (or other mobile device) is defined by an ellipsoid ℇ ( 0, ^ ^) and the shape of an object by an ellipsoid ℇ ( 0, ^ ^) can be specified, at least approximately. In addition, the centers of the robot and the object, ie their positions, ^ ^ and ^ ^ The condition that no collision occurs between the two is then of the following type: ^^(ℇ ( ^ ^ , ^ ^) , ℇ ( ^ ^ , ^ ^)) ≥ 0. It can be assumed that the position of the robot can be specified, which is typical when determining trajectories and the movement of the robot. An optimization problem with an objective function ^ ( ^ ^ , ^ ^) for the condition that no collision occurs, then This optimization problem can be reformulated as follows: min ^ ^ ^ , ^, ^ ^ ^ ^ ^ ^ ,^ ( , ^ , ^ ) ^. ^. ℎ ( ^ ^ , ^, ^ ^ , ^ ^ , ^ ^) ≥ 0, where R.406617 Since ℇ(0, ^ ^ (^, ^ ^ , ^ ^ )) is an overdetermination for ^ > 0, then ℎ ( ^ ^ , ^, ^ ^ , ^ ^ , ^ ^)≥ 0 is a sufficient, but not necessary, condition for avoiding a collision. In Figure 5, the three images (a), (b), and (c) each show two ellipsoids or ellipses 501, 502, as well as a respective overdetermination 506a, 506b, 506c. A center point of the ellipse 502 is designated 510. The two ellipses 501, 502 can be viewed here as an approximate representation of an external shape of the mobile device or object. A position of the object can be position 510. Based on the two ellipses 501, 502, it can be seen that there is no collision between the mobile device and the object; the signed distance is positive. The three figures (a), (b), and (c) show the overdeterminations 506a, 506b, and 506c with values ​​for ^ = 0.4, ^ = 2.0, and ^ = 10.0. For the value ^ = 2.0, position 510 lies outside the overdetermination; in the other two cases, it lies within.As has now been shown and follows from the above considerations, it is sufficient if a value for ^ can be found for which the position lies outside the overdetermination. Then there is no intersection of the two ellipses and thus no collision. It is irrelevant that there are values ​​for ^ for which this is not the case. While this was explained above for ellipsoids as a more approximate representation of the external shape of the mobile device and object, this also applies to other representations, such as rectangles and rectangular cuboids. This can be illustrated for a simple 2D case as follows. It can also be shown that this is not limited to axis-oriented rectangles. R.406617 The optimization problem can then be written in the following form: A rectangle can be viewed as the Minkowski sum of two line segments, and a line segment can be viewed as an ellipsoid with one semiaxis zero: ^ ( ^, ^, ^ ) = ℇ ^^, ^^ ^ 0^^ ⊕. ℇ ^^, ^0 0 ^^. 0 0 0 ^ ^ Taking into account the overdetermination of the Minkowski sum of two ellipsoids, the following can be obtained: ^(^, ^, ^) ⊂ ℇ(^, ^ ^ (^, ^, ^)), where (1 + 1 / ^) ^ ^ ^ 0 (^, ^, ^):= ^ 0 (1 + ^)^^. Thus, the optimization problem can be written as follows: where ℎ(^ ^ , ^, ^ ^ , ^ ^ , ^ ^ , ^ ^ , ^ ^ , ^ ^ , ^ ^ ):= ^(^ ^ − ^ ^ ) ^ ^ ^ ^^(^, ^ ^ ^ , ^ ^^ ) (^ ^ − ^ ^ ) − 1 ^ ^^ : = ^ ^ (^ ^ , ^ ^ , ^ ^ ), ^ ^^ : = ^ ^ (^ ^ , ^ ^ , ^^ ), R.406617 If the rectangles are not axis-oriented, the orientations of the mobile device and object θ ^ and ^ ^ Then Figure 6 schematically shows a method according to the invention in a preferred embodiment. Here, a trajectory for a mobile device that is to move in an environment while avoiding a collision with an object in the environment is to be determined. For example, this can be the situation shown in Figure 1, in which the robot is not to collide with the object. Here, in step 600, a potential position 602 of the mobile device and a position 604 of an object in the environment are provided. This can be done, for example, as a relative position to one another, ie the position 602 of the mobile device can be assumed to be zero or at the origin, relative to which the position of the object is or will be determined. The latter can be done, for example, using the aforementioned lidar sensor or other sensors, with which, for example, the distance can be determined.It is then assessed in step 610 whether or how a collision will (or would) occur between the mobile device at the potential position and the object, and in particular also how a collision can then be avoided. For this purpose, in step 620, a first data set 622 is provided which indicates an approximate representation of an external shape of the mobile device and a position of the mobile device with respect to the approximate representation of the external shape of the mobile device. The shape of the mobile device can, for example, be approximated as a rectangle represented as a Minkowski sum of ellipsoids. The center of the rectangle can correspond to the position of the mobile device. In addition, in step 630, a second data set 632 is provided which indicates an approximate representation of an external shape of the object and a position of the R.406617 object with respect to the approximate representation of the external shape of the object.The shape of the object can, for example, also be approximated as a rectangle or as an ellipse, which is represented as a Minkowski sum of ellipsoids. The center of the rectangle or ellipse can correspond to the position of the object. As already mentioned, it is usually sufficient if the position of the object relative to the position of the mobile device is known, which can be determined using the lidar sensor. Likewise, the shape of the object can, for example, be detected or determined using the lidar sensor in order to suitably approximate it. In a step 640, it is then assessed whether an overdetermination exists for a Minkowski sum of the first data set and the second data set, for which overdetermination a vector between the position of the mobile device and the position of the object is not included in the overdetermination. For this purpose, an optimization problem can be created and solved as described above.If such an overdetermination can be found or if one exists, it is determined that there is no collision between the mobile device and the object. If, on the other hand, it is determined that a collision does occur, it can be determined in particular in which direction or generally how the trajectory of the mobile device should be changed or shifted in order to avoid the collision. The derivation of the aforementioned condition for collision avoidance can be used for this purpose. It should be noted that steps 610 to 640 can be sub-steps of step 610 or can be regarded as such, since they represent a concrete way of assessing and, in particular, avoiding the potential collision. If it is determined that there will be no collision, then in step 650 the trajectory of the mobile device is determined using the potential position of the mobile device.In step 660, the trajectory can be provided, i.e., used for navigation for the mobile device. R.406617 It is understood that potential collisions can be repeatedly assessed in this way, e.g., while the mobile device is moving, and the trajectory is repeatedly adjusted if necessary, whereby the derivation of the aforementioned condition for collision avoidance can be used for this purpose. If, for example, a collision were to occur for a potential position of the mobile device, this potential position can be disregarded for the trajectory, or the trajectory can be determined differently, as mentioned above.

Claims

R.406617 Claims 1. Method for assessing a potential collision between a mobile device (100), in particular a robot, or an at least partially automated vehicle that is intended to move in an environment (120), and an object (140) in the environment, comprising: providing (620) a first data set (622) that specifies an approximate representation (501) of an external shape of the mobile device and a position of the mobile device with respect to the approximate representation of the external shape of the mobile device, providing (630) a second data set (632) that specifies an approximate representation (502) of an external shape of the object and a position (510) of the object with respect to the approximate representation of the external shape of the object, assessing (640) whether an overdetermination (406, 506a, 506b, 506c) for a Minkowski sum (405) of the first data set and the second data set exists,for which overdetermination a vector between the position of the mobile device and the position of the object is not included in the overdetermination, and if such an overdetermination (506b) exists, determine that there is no collision between the mobile device (100) and the object (140).

2. The method according to claim 1, wherein for checking (640) whether the overdetermination exists for a Minkowski sum of the first data set and the second data set, an optimization problem is solved.

3. The method according to claim 1 or 2, wherein the approximate representation of the external shape of the mobile device and / or the approximate, R.406617 Representation of the external shape of the object corresponds to a Minkowski sum of ellipsoids or an ellipsoid.

4. Method according to one of the preceding claims, wherein the approximate representation of the external shape of the mobile device corresponds to an ellipse or a rectangle, wherein the position of the mobile device corresponds in particular to a center point of the ellipse or the rectangle.

5. Method according to one of the preceding claims, wherein the approximate representation of the external shape of the object corresponds to an ellipse or a rectangle, wherein the position of the object corresponds in particular to a center point of the ellipse or the rectangle. 6.A method for determining a trajectory (130) for a mobile device (100) that is to move in an environment (120) while avoiding a collision with an object (140) in the environment, comprising: providing (600) a potential position (602) of the mobile device and a position (604) of an object in the environment, determining (610) according to a method of any of the preceding claims whether a collision will occur between the mobile device at the potential position and the object if it is determined that no collision will occur, determining (650) the trajectory of the mobile device using the potential position of the mobile device, and providing (660) the trajectory.

7. The method of claim 6, further comprising: determining, based on the trajectory, motion control variables for the mobile device, and providing the motion control variables and / or moving the mobile device based on the motion control variables. 8.Computing unit (108) which is configured to carry out all method steps of a method according to one of the preceding claims. R.406617 9. Mobile device (100) which is set up to receive a trajectory (130) which has been determined according to a method according to claim 6, or movement control variables which have been determined according to claim 7, with a drive system (104) and a control or regulating unit (102) for controlling the drive system based on the trajectory and / or the movement control variables, and in particular with a computing unit (108) according to claim 8, and further in particular with at least one sensor unit (106) for detecting objects in the environment.

10. Mobile device (100) according to claim 9, which is designed as an at least partially automated vehicle, in particular as a passenger transport vehicle or as a goods transport vehicle, or as a robot, in particular as a household robot, e.g., a vacuum and / or mop robot, a floor or street cleaning device, or a lawnmower robot, or as a drone. 11.A computer program comprising instructions which, when executed by a computer, cause the computer to carry out the method according to claims 1 to 7.

12. A computer-readable data carrier on which the computer program according to claim 11 is stored.

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