DE102022122761A1 - METHOD FOR PATH PLANNING FOR AN AUTOMATED MOTOR VEHICLE, COMPUTER PROGRAM PRODUCT, PARKING ASSISTANCE SYSTEM AND VEHICLE - Google Patents

Abstract

The present invention relates to a method for planning a route for an automated motor vehicle. The method includes the following steps: determining a parking space (103a) on a lateral side relative to a street (100); planning a first movement in a forward direction with an S shape; and planning a second movement in a reverse direction into the parking space, the second movement immediately following the first movement. The first movement is planned when a lateral object distance (DVO) between the vehicle (1) and an object on the other lateral side of the road (100) is smaller than an object threshold and/or a lateral parking space distance (DVP) between the vehicle (1) and the parking space (102) is larger than a parking space threshold.

Description

The present invention relates to a method for planning a route for an automated motor vehicle from an initial position of the motor vehicle to a parking position in the vicinity of the motor vehicle. In particular, the present invention relates to a method for planning the path of a vehicle in tight parking situations or other situations in which a collision with an external object must be avoided. The present invention also relates to a parking assistance system which is designed to carry out the aforementioned method. The present invention further relates to a computer program product. The present invention also relates to a vehicle with an aforementioned parking assistance system.

Path planning, also known as motion planning, is one of the most important sub-functions for various applications for automated driving assistance systems or autonomous driving systems. Different types of parking such as parallel parking, perpendicular parking, diagonal parking, etc. are essential parking functions provided by the automated driving assistance systems. Existing approaches to path planning for parking a motor vehicle use a single planned path of interconnected circular, then straight, and finally circular segments to allow the vehicle to reverse into a parking space in one step from a specific starting position. The planned path is adjusted according to such a starting position, which must have a tolerance in the longitudinal direction (X) and in the transverse direction (Y) to a parking space entrance corner 101, which tolerance must be below certain minimum thresholds, as in 1 shown. The outer corner, which delimits the minimum space in which the vehicle can safely park, defines the entry corner into the parking space. Adjusting the planned path involves calculating the radius of rotation and change in orientation over the circular segments and the length of the straight segment. The most important limitation to the starting position from which the system can plan the intended reverse path for the vehicle to enter the parking space in one piece is that there must be enough space around the vehicle to allow the maneuver to be carried out in tight parking situations or in Situations in which the vehicle is very close to an obstacle can be carried out without a collision. Furthermore, existing path planning approaches result in a low degree of path smoothness and generally longer paths required to connect an initial position of the vehicle to a parking position of the vehicle.

An object of the present invention is to provide a technique for generating an optimal path for safely maneuvering a vehicle from an initial position to a parking space in tight parking environments or other environments in which the vehicle is very close to an obstacle. The present invention is based on the observation that the vehicle to be parked is limited by a parking space on one lateral side of a street and a large number of objects on the other lateral side of the street. Furthermore, the parking space is defined in the direction of vehicle movement between a front object and a rear object. The front object is also called the start object and the back object is called the end object. In such tight parking environments, the vehicle must be automatically maneuvered from an initial position to a parking position in the parking space without colliding with the plurality of objects, the front and rear objects. The front and rear objects, if they are parked vehicles, are parked in an orientation that is substantially the same direction as the intended parking direction of the vehicle. Furthermore, it may be that the vehicle to be parked has not yet completely passed or crossed the parking space in the direction of travel. That is, the initial position of the vehicle is shifted laterally from the front and rear objects and lies between the front and rear objects.

According to a first aspect, a method for planning a route for an automated motor vehicle from an initial position of the motor vehicle to a parking position in the surroundings of the motor vehicle is described. The method includes the following steps: determining a parking space on a lateral side relative to a street; planning a first movement in a forward direction with an S shape; and planning a second movement in a reverse direction into the parking space, the second movement immediately following the first movement. The first movement is planned when a lateral object distance between the vehicle and an object on the other lateral side of the road is less than an object threshold and/or a lateral parking space distance between the vehicle and the parking space is greater than a parking space threshold. In order to avoid collisions with the above objects, the vehicle will start forward movement to exclude collision with the objects until it can reach the target position suitable for backward movement to directly enter the parking space. Advantageously, the present invention creates the narrowest possible, collision-free, S-shaped A sufficient forward path is created for the parking maneuver so that the vehicle reaches the parking space without colliding with other objects. Furthermore, the path planned according to the invention has a significantly higher smoothness and requires fewer steering maneuvers in tight parking environments.

In one aspect, the vehicle is preferably a passenger car or a truck. Preferably, the vehicle may be of any type capable of carrying passengers and/or goods.

In one aspect, the street is a one-way street or carriageway.

In one aspect, the path of the vehicle when moving forward is planned to follow a Bezier curve, where the path of the vehicle when moving backward may also follow a Bezier curve. The Bezier curve may be, for example, a first-order Bezier curve or a second-order Bezier curve or a third-order Bezier curve or a combination thereof.

In one aspect, the lateral object distance and the lateral parking space distance serve as trigger points to initiate the first forward movement of the vehicle and the second backward movement based on the one or more constraints defined above.

According to a further embodiment of the method, the method includes providing sensor information describing at least an initial position of the vehicle, the parking space and information relating to a plurality of objects on the other side of the road, the parking space being between a front object and a rear one Object is defined in a vehicle movement direction; evaluating the sensor information provided to determine a parking position in the parking space, the lateral object distance and the lateral parking space distance; and planning the first movement to maneuver the vehicle from the initial position to a target position and the second movement to maneuver the vehicle from the target position to the parking position, the target position being a first longitudinal distance (Δx) from the initial position is located along the vehicle movement direction and at a first transverse distance (Δy) from the initial position, and an orientation of the vehicle in the initial position is equal to an orientation of the vehicle in the target position.

In particular, a sensor device of the vehicle provides the sensor information that describes an environment of the vehicle. The sensor device includes several sensors such as ultrasonic sensors and/or cameras and/or a radar and/or a LiDAR. For example, the ultrasonic sensor data and/or camera data and/or radar data and/or LiDAR data are merged and used to provide the sensor information. The environment is determined by a detection range of the sensor device. A processing device is used to determine the parking position information that describes the parking position and the parking space. This is done by evaluating the sensor information provided and preferably vehicle dimension information that describes the dimensions of the vehicle. Parking space preferably means a representation of a real place in the area. Preferably the representation has a rectangular shape when viewed from above. The dimensions of a representation of the vehicle (when viewed from above), including a safe distance to each side of the vehicle, must fit within the representation. The parking space including the vehicle surroundings can be shown to the driver of the vehicle e.g. B. displayed via the human-machine interface.

The initial position of the vehicle corresponds to a predefined or predetermined position of the vehicle. The initial position may, for example, correspond to a current position of the vehicle at a time when the route planning method is carried out. On the other hand, the parking position is not predefined and is determined by processing the sensor information. Furthermore, the target position is not predefined, but can be viewed as an intermediate result of the method in the sense that by defining the initial position and determining the path that connects the initial position to the target position, the target position is also determined. However, one or more boundary conditions may apply that limit the target position. In some implementations, the constraints may be predefined. The positions mentioned are preferably described by coordinates and/or an angle as orientation information. The coordinates as well as the angle information can be determined with respect to a center point of a rear axle of the vehicle. In particular, the initial position of the vehicle is defined by the coordinates and an orientation of the vehicle in the initial position. Analogously, the target position of the vehicle is defined by the coordinates and an orientation of the vehicle in the target position. Similarly, the parking position of the vehicle is defined by the coordinates and an orientation of the vehicle in the parking position.

According to a further embodiment of the method, the S-shape of forward movement consists of a pair of circular segments connected by a straight segment.

According to another embodiment of the method, planning the first movement includes determining a minimum lateral distance from an opposite side boundary line based on a radius of rotation in the front extreme corner of the vehicle and a radius of rotation of the vehicle by steering the vehicle at a maximum steering angle. The opposing side boundary line defines a boundary of the plurality of opposing objects. In one aspect, the opposite side boundary line may be asymptotically represented by a straight line covering the plurality of objects.

According to a further embodiment of the method, the method includes constructing a target line that is laterally displaced by the minimum transverse distance from the opposite side boundary line and is parallel to both the opposite side boundary line and a longitudinal axis of the vehicle in the initial position, wherein the target position of the vehicle is on the target line. Planning the first movement further includes determining the first longitudinal distance, the first transverse distance, an orientation change across the circular segments, and a rotation radius of the circular segments that results in a front right extreme corner of the vehicle being tangent to a parking space front line, if the Vehicle reaches the target position, with the parking space front line defining a boundary between the front object and the rear object. In one aspect, the opposite parking space front line may be asymptotically represented by a straight line that includes the front object and the rear object.

The minimum transverse distance corresponds to a distance between the plurality of objects on the other side of the road and the target line. The minimum lateral distance can be considered as the smallest possible distance that the vehicle can achieve given a predefined set of constraints. A boundary condition is a maximum steering angle of the vehicle. Since the lateral distance that the vehicle travels during the steering maneuver is proportional to the steering angle of the vehicle, the minimum lateral distance to avoid a collision is taken into account during the maximum steering maneuver. In addition, for example, the wheelbase of the vehicle can correspond to a boundary condition. The shorter the wheelbase, the shorter the vehicle's radius of rotation at the center of the rear axle (distance from the center of rotation to the center of the rear axle) and the shorter the minimum transverse distance. Furthermore, for example, a front wheel angle of the vehicle corresponds to a further boundary condition.

Advantageously, the minimum transverse distance ensures that the backward movement, i.e. H. the movement in the opposite direction, without collision with the large number of objects, takes place after the vehicle has reached the target position. In other words: The target position of the vehicle is selected so that the backward movement occurs without collision with the large number of objects.

The first transverse distance corresponds to a transverse distance between the initial position of the vehicle and the target position of the vehicle, and the first longitudinal distance corresponds to a longitudinal distance between the initial position of the vehicle and the target position of the vehicle. During the first movement, the vehicle is maneuvered so that it moves from the initial position to the target position. In other words: The target position results from the initial position, shifted by the transverse distance along an initial transverse axis and shifted by the longitudinal distance along the initial longitudinal axis. The initial longitudinal axis and the initial transverse axis can be understood as the longitudinal axis and transverse axis of the vehicle according to the initial orientation, in particular with respect to the reference coordinate system.

As already explained, the orientation of the vehicle in the initial position is also the same as the orientation of the vehicle in the target position. As a result, the vehicle follows an S-shape when moving forward, that is, the first time it moves in the forward direction. First circular, then straight, then circular segments (CSC) define the S-shaped maneuver, with the two circular segments assumed to be the same. The parameters that define the S-shaped maneuver are therefore the radius of rotation of the two circular arcs (R), the change in orientation across the two circular arcs (θ), the length of the straight segment (S), the longitudinal distance traveled after the S-shape ( Δx) or the first longitudinal distance, and the transverse distance according to the S-shape (Δy) or the first transverse distance. These parameters determine the target position of the vehicle, and these parameters are calculated by applying a predefined set of constraints so that the S-shaped maneuver is guaranteed to be drivable. One boundary condition that applies is that the vehicle must not collide with the object behind during forward movement. Another boundary condition that applies is that the The rotation radius of the vehicle must not be less than the minimum rotation radius, which corresponds to the maximum steering. Another boundary condition that applies is that the vehicle must travel a shorter path or an optimal path, that is, the path on which the vehicle moves is tangential to the parking space front line of the rear object when the vehicle moves forward. In other words, the outermost corner of the vehicle is tangent to the parking space front line as the vehicle moves forward. This results in the first transverse distance being as short as possible, so that the path of forward movement is shorter and at the same time the vehicle does not collide with the object behind.

According to another embodiment, the method includes determining the first transverse distance (Δy) based on the minimum transverse distance between the opposite side boundary line and the target line, the vertical distance between the X-axis of the global reference coordinates, the opposite side boundary line and the vertical Coordinate of the vehicle in its initial position.

According to a further embodiment, the method includes determining the radius of rotation (R) of the circular segments based on at least one of the following elements: an angle between the parking space front line and the initial position of the vehicle, the first transverse distance, a length of the vehicle, a width of the vehicle, and a distance between the rear axle and the rear bumper of the vehicle.

Furthermore, the first longitudinal distance (Δx) is determined based on the first transverse distance (Δy) and the radius of rotation (R) of the circular segments and an orientation change across the circular segments is determined based on the first longitudinal distance and the first transverse distance.

According to a further embodiment of the present invention, the parking space front line runs parallel to the target line. In this parking environment, the parking assistance system creates a drivable and collision-free S-shaped path that leads from the initial position to the target position and ends in the target position with a certain orientation that is parallel to the parking space front line of the front and rear objects.

According to a further embodiment of the present invention, the parking space front line runs obliquely to the target line. In this parking environment, the parking assistance system creates a drivable and collision-free S-shaped path that leads from the initial position to the target position and ends in the target position with a certain orientation that is not parallel to the parking space front line of the front and rear objects.

In a further embodiment, the first transverse distance is in the range between 0.1 m and 5 m.

According to a further embodiment, the first longitudinal distance is in the range between 0.5 m and 10 m.

In a further embodiment, the object threshold value is in the range between 30 cm and 300 cm.

In a further embodiment, the lateral parking space distance is in the range between 4 m and 8 m.

According to a further aspect of the invention, a computer program product is proposed. The computer program product includes instructions that, when a computer executes the program, cause the computer to perform the method as explained. A computer program product, such as a computer program medium, may be in the form of a storage device, such as a storage medium, a USB flash drive, a CD-ROM, a DVD, etc., and/or in the form of a digital file stored by a server on a computer network or The like can be downloaded. For example, this can be achieved by transferring the corresponding file over a wireless network.

According to a further aspect of the invention, a parking assistance system for planning a first movement in a forward direction with an S-shape and for planning a second movement in a backward direction into the parking space is provided. The second movement follows the first movement, and the parking assistance system includes at least one detection device and at least one electronic computing device. This parking assistance system has the same advantages that are described for the aforementioned method. The embodiments and features that are proposed for the method can also be features and embodiments of the parking assistance system.

According to a further aspect, a vehicle comprising such a parking assistance system is provided. The parking assistance system can include at least one sensor, in particular ultrasonic sensors and/or a camera and/or a radar and/or a LiDAR, for detecting the environment around the vehicle.

The invention will be explained in more detail below with reference to the attached drawings and on the basis of preferred embodiments. The features described may represent an aspect of the invention both individually and in combination. Features of different example embodiments may be transferred from one example embodiment to another.

• 1 ist ein schematisches Diagramm eines beispielhaften Fahrzeugwegs gemäß dem Stand der Technik.
• 2 ist eine schematische Darstellung eines Fahrzeugs mit einer beispielhaften Implementierung eines Parkassistenzsystems gemäß einer Ausführungsform der vorliegenden Erfindung.
• 3 ist eine schematische Darstellung eines Einparkszenarios des Kraftfahrzeugs gemäß einer Ausführungsform der vorliegenden Erfindung.
• 4 zeigt eine schematische Darstellung der Variablen, die beim Bestimmen eines minimalen Querabstands von einer Begrenzungslinie der gegenüberliegenden Seite gemäß einer Ausführungsform der vorliegenden Erfindung beteiligt sind.
• 5 zeigt eine schematische Darstellung von Parametern des S-förmigen Manövers gemäß einer Ausführungsform der vorliegenden Erfindung.
• 6a zeigt eine schematische Darstellung der Variablen, die beim Bestimmen des Rotationsradius des kreisförmigen Wegs der Vorwärtsbewegung bei gegebenem Anfangsrahmen gemäß einer ersten beispielhaften Ausführungsform der vorliegenden Erfindung beteiligt sind.
• 6b zeigt eine schematische Darstellung der Variablen, die beim Bestimmen des Rotationsradius des kreisförmigen Wegs der Vorwärtsbewegung bei gegebenem Zielrahmen parallel zur gegebenen Frontlinie gemäß einer zweiten beispielhaften Ausführungsform der vorliegenden Erfindung beteiligt sind.
• 6c zeigt eine schematische Darstellung der Variablen, die beim Bestimmen des Rotationsradius des kreisförmigen Wegs der Vorwärtsbewegung beteiligt sind, wenn der Zielrahmen gemäß einer dritten beispielhaften Ausführungsform der vorliegenden Erfindung nicht parallel zur gegebenen Frontlinie verläuft.
• 7 zeigt eine schematische Darstellung eines Einparkszenarios, bei dem eine Solllinie gemäß einer Ausführungsform der vorliegenden Erfindung parallel zu einer Parklückenfrontlinie verläuft.
• 8 zeigt eine schematische Darstellung eines Einparkszenarios, bei dem eine Solllinie gemäß einer weiteren Ausführungsform der vorliegenden Erfindung unter einem Winkel zu einer Parklückenfrontlinie verläuft.
• 9 ist ein Flussdiagramm, das ein Verfahren zum Erzeugen eines tangentialen fahrbaren S-förmigen Wegs gemäß einer Ausführungsform der vorliegenden Erfindung zeigt.

In order to complete the description and provide a better understanding of the invention, a set of drawings is provided. The drawings form an integral part of the description and illustrate an embodiment of the invention, which should not be construed as limiting the scope of the invention, but merely as an example of how the invention may be carried out. The drawings include the following characteristics.

• 1 is a schematic diagram of an exemplary vehicle path according to the prior art.
• 2 is a schematic representation of a vehicle with an exemplary implementation of a parking assistance system according to an embodiment of the present invention.
• 3 is a schematic representation of a parking scenario of the motor vehicle according to an embodiment of the present invention.
• 4 Fig. 12 shows a schematic representation of the variables involved in determining a minimum transverse distance from an opposite side boundary line in accordance with an embodiment of the present invention.
• 5 shows a schematic representation of parameters of the S-shaped maneuver according to an embodiment of the present invention.
• 6a Fig. 12 shows a schematic representation of the variables involved in determining the radius of rotation of the circular path of forward motion given an initial frame according to a first exemplary embodiment of the present invention.
• 6b shows a schematic representation of the variables involved in determining the radius of rotation of the circular path of forward movement given the target frame parallel to the given front line according to a second exemplary embodiment of the present invention.
• 6c shows a schematic representation of the variables involved in determining the radius of rotation of the circular path of forward movement when the target frame is not parallel to the given front line according to a third exemplary embodiment of the present invention.
• 7 shows a schematic representation of a parking scenario in which a target line runs parallel to a parking space front line according to an embodiment of the present invention.
• 8th shows a schematic representation of a parking scenario in which a target line according to a further embodiment of the present invention runs at an angle to a parking space front line.
• 9 is a flowchart showing a method for generating a tangential drivable S-shaped path according to an embodiment of the present invention.

Embodiments of the present application are explained below, by way of example, with reference to the accompanying drawings. Throughout the description, like or similar reference numerals represent like or similar parts. The following description of the embodiments with reference to the drawings is intended to explain the general inventive concept of the present application rather than limiting it to the present invention.

In the following detailed description, numerous specific details are set forth for explanatory purposes in order to provide a thorough understanding of the disclosed embodiments. However, it should be understood that one or more embodiments may be implemented without these specific details.

2 is a schematic representation of a vehicle with an exemplary implementation of a parking assistance system according to an embodiment of the present invention. How out 2 As can be seen, the parking assistance system 2 is integrated in the vehicle 1. The parking assistance system 2 includes an electronic computing device 3 that can plan a path for the vehicle that connects an initial position of the vehicle with a parking position. The parking assistance system 2 further includes an environmental sensor system 5, which is connected to the computing device 3. The environmental sensor system 5 may, for example, include multiple sensors such as ultrasonic sensors and/or cameras and/or a radar and/or a LiDAR. For example, the ultrasonic sensor data and/or camera data and/or radar data and/or LiDAR data are merged and used to provide the sensor information. These sensors can be strategically located at various locations on the vehicle, such as the front bumper, rear bumper, front bumper, and rear bumper. The electronic computing device 3 receives input data including environmental sensor data generated by the environmental sensor system 5 and can plan the route depending on the sensor information.

Optionally, the parking assistance system 2 additionally includes a status sensor system 4 and/or an input device 6. The status sensor system 4 can, for example, include a speed sensor, a steering angle sensor and/or a yaw rate sensor. The input device 6 can, for example, include direction indicators of the vehicle 1, which are to be operated by the driver of the vehicle. The condition sensor system 4 may generate corresponding condition sensor data about a current condition of the vehicle, and/or an input device 6 may generate a corresponding user input signal. The user input signal and/or the condition sensor data may also be part of the input data, and the electronic computing device 3 may take these into account to plan the path in some implementations.

The functionality of the parking assistance system 2 as well as corresponding embodiments of computer-implemented methods for path planning according to the invention are described below with reference to 3 until 9 explained in more detail.

3 is a schematic representation of a parking scenario of the motor vehicle according to an embodiment of the present invention. An example parking environment is in 3 shown. How out 3 As can be seen, the vehicle 1 to be parked is limited by obstacles on both sides of the road 100. For example, a plurality of objects 101a, 101b, 101c are located on a lateral side of the road 100, and these objects are located along the vehicle movement direction. Further, a parking space 102c, which is bounded by a front object 102b and a rear object 102a, is located on the other side of the road 100, and the vehicle 1 to be parked is in an initial position 103a or a starting position on the road. How out 3 As can be seen, the vehicle 1 to be parked has not yet completely crossed or passed the parking space 102c in the direction of movement. In another aspect, it is also possible that the vehicle 1 to be parked has crossed the parking space 102c in the direction of movement of the vehicle. In one aspect the road can be a one-way street. In another aspect, the road may be a carriageway. For example, the plurality of objects 101a, 101b, 101c, the front object 102a and the rear object 102b may be motor vehicles. Although in 1 Motor vehicles are shown on both sides of the road 100, any other obstacles can replace one or more motor vehicles. In such tight parking environments, the vehicle 1 must be automatically maneuvered from an initial position 103a to a parking position 103c in the parking space 102c without colliding with the plurality of objects 101a, 101b, 101c, the front object 102a and the rear object 102b . The front and rear objects 102a, 102b, if they are parked vehicles, are parked in an orientation that is essentially the same direction as the parking direction of the vehicle. The parking space 102c preferably means a representation of a real place in the area. Preferably, the representation has a rectangular shape when viewed from above. The dimensions of a representation of the vehicle (when viewed from above), including a safe distance to each side of the vehicle, must fit within the representation. The parking space including the vehicle surroundings can be displayed to the driver of the vehicle 1, for example via the human-machine interface.

The present invention provides a method for generating a path for optimal and safe maneuvering of a vehicle 1 from the initial position 103a to the parking position 103c in the tight parking environments described above. In the first step, the method includes obtaining data that relate to the surroundings of the vehicle 1. This data corresponds to the information supplied by the environmental sensor system 5 of the parking assistance system 2. The sensor information may include information about the target parking position 103c of the vehicle 1, the objects 101a, 101b, 101c, 102a, 102b located on both sides of the road 100, including the plurality of objects 101a, 101b, 101c on one side and the front and rear objects 102b, 102a on the other side of the street 100, as well as the available parking space 102c and their dimensions. The initial position 103a is preferably described by coordinates and/or an angle as orientation information. The coordinates as well as the angle information can be determined with respect to a center point of a rear axle of the vehicle 1.

After receiving the sensor information, the method includes evaluating the sensor information by the computing device 3 of the parking assistance system 2 to determine a parking position in the parking space 102c, a lateral object distance D _VO between the vehicle 1 and an object on the other lateral side of the road and a lateral parking space distance D _VP between vehicle 1 and parking space 102c. At least one of these two distances can serve as a trigger point for the parking assistance system 2 to create a path for maneuvering the vehicle. In order not to collide with the objects 101a, 101b, 101c, 102a, 102b on the street 100 in the tight parking environment, the method includes planning a first movement in the forward direction and planning a second movement in the backward direction into the parking space 102c, the second movement immediately follows the first movement. In one aspect, the first movement is planned when a lateral object distance (D _VO ) between the vehicle 1 and an object on the other lateral side of the road 100 is less than an object threshold and/or a lateral parking space distance (D _VP ) between the vehicle 1 and the parking space 102c is greater than a parking space threshold value. In one aspect, the object threshold ranges between 30 cm and 300 cm. Furthermore, the lateral parking space distance is between 4 m and 8 m.

The first movement is to maneuver the vehicle from the initial position 103a to a target position 103b, and the second movement is to maneuver the vehicle from the target position 103b to the parking position 103c, with the target position 103b at a first longitudinal distance (Δx ) from the initial position along the vehicle movement direction and at a first transverse distance (Δy) from the initial position, and an orientation of the vehicle in the initial position 103a is equal to an orientation of the vehicle in the target position 103b.

To plan the path for the first movement or the forward movement, the method determines a minimum transverse distance (Δy _min ) from an opposite side boundary line 105 that defines a boundary of the plurality of objects on the opposite side 101a, 101b, 101c. The boundary line of the opposite side 105 can be asymptotically represented by a straight line covering the plurality of objects 101a, 101b, 101c, as shown in 3 shown. The minimum transverse distance (Δy _min ) can be considered as the smallest possible distance that can be realized by the vehicle 1 when a predefined set of constraints applies. An applicable boundary condition is a maximum steering angle of vehicle 1. Since the minimum lateral distance that the vehicle covers during the steering maneuver is proportional to the steering angle of vehicle 1, the minimum lateral distance to avoid a collision is taken into account during the maximum steering maneuver. In addition, for example, the wheelbase of the vehicle can correspond to a boundary condition. The shorter the wheelbase, the shorter the radius of rotation of the vehicle 1 at the center of the rear axle (distance from the center of rotation to the center of the rear axle) and the shorter the minimum transverse distance. Furthermore, for example, a front wheel angle of the vehicle 1 corresponds to a boundary condition. Advantageously, this minimum transverse distance ensures that the second movement or the backward movement occurs without collision with the plurality of objects 101a, 101b, 101c after the vehicle 1 has reached the target position 103b. In other words: The target position 103b of the vehicle 1 is selected so that the backward movement occurs without collision with the large number of objects 101a, 101b, 101c.

wobei R_min und R_omin der minimale Rotationsradius entsprechend der maximalen Lenkung in der Mitte der Hinterachse (Abstand vom Rotationsmittelpunkt zur Mitte der Hinterachse) bzw. am äußersten Eckpunkt (Abstand vom Rotationsmittelpunkt zum äußersten Eckpunkt) sind. Unter der Annahme, dass das Fahrzeug 1 eine Gesamtlänge (L), eine Breite (w) und einen Abstand von der Hinterachse bis zum hinteren Stoßfänger (rr) hat, kann R_omin wie folgt berechnet werden: $$R_{o_{min}}=\sqrt{{\left(R_{min}+\frac{w}{2}\right)}^2+{\left(L-rr\right)}^2}$$

Der minimale Rotationsradius entsprechend der maximalen Lenkung in der Mitte der Hinterachse kann unter Berücksichtigung des Radstands (Wb) des Fahrzeugs 1 und des maximalen Lenkwinkels (φ) für das Rückwärtslenken bestimmt werden. $$R_{min}=\frac{Wb}{\text{tan}\left(\phi \right)}$$

4 shows a schematic representation of the variables involved in determining the minimum transverse distance (Δy _min ) from the opposite side boundary line 105 according to an embodiment of the present invention. Regarding 4 applies: $$\Delta y_{min}=R_{O_{min}}-R_{min}$$

where R _min and R _{o min} the minimum rotation radius corresponding to the maximum steering in the center of the rear axle (distance from the center of rotation to the center of the rear axle) or at the outermost corner point (distance from the center of rotation to the outermost corner point). Assuming that the vehicle 1 has an overall length (L), a width (w) and a distance from the rear axle to the rear bumper (rr), R _{o min} be calculated as follows: $$R_{O_{min}}=\sqrt{{\left(R_{min}+\frac{w}{2}\right)}^2+{\left(L-rr\right)}^2}$$

The minimum rotation radius corresponding to the maximum steering at the center of the rear axle can be determined taking into account the wheelbase (Wb) of the vehicle 1 and the maximum steering angle (φ) for reverse steering. $$R_{min}=\frac{Wb}{\text{tan}\left(\phi \right)}$$

By replacing R _min and R _{o min} From equations 2 and 3 to equation 1, the minimum transverse distance (Δy _min ) can be calculated.

After determining the minimum transverse distance (Δy _min ), the method includes constructing a target line (T) that is laterally offset by the minimum transverse distance (Δy _min ) from the opposite side boundary line 105, as in 3 and 4 shown. How out 3 and 4 As can be seen, the target line T runs parallel to the boundary line of the opposite side 105 and to the longitudinal axis of the vehicle in the initial position, with the target position 103b of the vehicle lying on the target line T.

After constructing the target line (T), the procedure involves planning the path for the forward movement or the first movement in the forward direction. As discussed, the target position 103b of the vehicle 1 is on the target line T, and the orientation of the vehicle 1 in the target position and the initial position are substantially the same. As a result, the vehicle follows an S-shape as it moves forward. First circular, then straight, then circular segments (C-S-C) define the S-shaped maneuver, with the two circular segments assumed to be the same.

5 shows a schematic representation of parameters of the S-shaped maneuver according to an embodiment of the present invention. The parameters that define the S-shaped maneuver are the radius of rotation (R) of the two circular arcs, the change in orientation (θ) over the two circular arcs, the length of the straight segment (S), the one traveled after the S-shape (Δx). Longitudinal distance or the first longitudinal distance, and the transverse distance according to the S-shape (Δy) or the first transverse distance. These parameters determine the target position 103b of the vehicle 1, and these parameters are calculated by applying a predefined set of constraints so that the S-shaped maneuver is guaranteed to be drivable. A boundary condition that applies here is that the vehicle 1 must not collide with the front object 102a during the forward movement. The further boundary condition that applies is that the rotation radius of the vehicle 1 must be larger than the minimum rotation radius corresponding to the maximum steering. A further boundary condition that applies is that the vehicle 1 must cover a shorter path or an optimal path, ie the path on which the vehicle moves tangentially to the parking space front line (S) of the front object 102a when the vehicle 1 moves forward. In other words, the outermost corner of vehicle 1 is tangential to the parking space front line (S) when vehicle 1 moves forward. The parking space front line (S) defines a boundary between the front object 102a and the rear object 102b, as shown 3 is visible. The parking space front line (S) can be represented asymptotically by a straight line. This results in the first transverse distance (Δx) being as short as possible, so that the path of forward movement is shorter and at the same time the vehicle does not collide with the front object 102a.

$$\Delta y=2R\left(1-cos\left(\theta \right)\right)+Ssin\left(\theta \right)$$

The parameters that define the S-shaped maneuver are in 5 shown. Based on the in 5 The following relationships can be established using the geometry shown: $$\Delta x=2Rsin\left(\theta \right)+ScOs\left(\theta \right)$$

$$\Delta y=2R\left(1-cOs\left(\theta \right)\right)+Ssin\left(\theta \right)$$

By multiplying equation [4] by cos(θ) and equation [5] by sin(θ) and adding the results, the following equation is obtained: $$\begin{array}{l}\Delta xcOs\left(\theta \right)+\Delta ysin\left(\theta \right)\\ =2Rsin\left(\theta \right)cOs\left(\theta \right)+ScO{s}^2\left(\theta \right)+2R\left(1-cOs\left(\theta \right)\right)sin\left(\theta \right)+Ssi{n}^2\left(\theta \right)\\ \Delta xcOs\left(\theta \right)+\Delta ysin\left(\theta \right)=2Rsin\left(\theta \right)+S\\ \text{2R}sin\left(\theta \right)=\Delta xcOs\left(\theta \right)+\Delta ysin\left(\theta \right)-S\end{array}$$

Multiplying equation [4] by sin(θ) and equation [5] by cos(θ) and subtracting the results gives the following equation: $$\begin{array}{l}\Delta xsin\left(\theta \right)-\Delta ycOs\left(\theta \right)\\ =2Rsi{n}^2\left(\theta \right)+Ssin\left(\theta \right)cOs\left(\theta \right)-2R\left(1-cOs\left(\theta \right)\right)cOs\left(\theta \right)\\ -Ssin\left(\theta \right)cOs\left(\theta \right)\\ \\ \Delta xsin\left(\theta \right)-\Delta ycOs\left(\theta \right)=2R\left(1-cOs\left(\theta \right)\right)\\ 2R\left(1-cOs\left(\theta \right)\right)=\Delta xsin\left(\theta \right)-\Delta ycOs\left(\theta \right)\end{array}$$

$$\theta ={\text{cos}}^{-1}\left(\frac{{\left(\Delta x+S\right)}^2-\Delta y^2}{{\left(\Delta x+S\right)}^2+\Delta y^2}\right)$$

$$\Delta y=2R-\sqrt{4R^2-{\left(\Delta x\right)}^2+S^2}$$

$$\Delta x=\sqrt{4\left(\Delta y\right)R-{\left(\Delta y\right)}^2+S^2}$$

By dividing equations [6] / [7] and solving, one obtains the following equations for θ, Δx and Δy: $$R=\frac{{\left(\Delta x\right)}^2+{\left(\Delta y\right)}^2-{\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="DE102022122761A1\_0063.png,DE102022122761A1\_0072.png"\; state="\{\{state\}\}">S</figure-callout>}}^2}{4\left(\Delta y\right)}$$

$$\theta ={\text{cos}}^{-1}\left(\frac{{\left(\Delta x+S\right)}^2-\Delta y^2}{{\left(\Delta x+S\right)}^2+\Delta y^2}\right)$$

$$\Delta y=2R-\sqrt{4{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="DE102022122761A1\_0063.png,DE102022122761A1\_0072.png"\; state="\{\{state\}\}">R</figure-callout>}}^2-{\left(\Delta x\right)}^2+{\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="DE102022122761A1\_0063.png,DE102022122761A1\_0072.png"\; state="\{\{state\}\}">S</figure-callout>}}^2}$$

$$\Delta x=\sqrt{4\left(\Delta y\right)R-{\left(\Delta y\right)}^2+{\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="DE102022122761A1\_0063.png,DE102022122761A1\_0072.png"\; state="\{\{state\}\}">S</figure-callout>}}^2}$$

• Da der Rotationsradius des Fahrzeugs unterhalb des minimalen Rotationsradius (R_min) entsprechend der maximalen Lenkung liegen muss, muss eine weitere Einschränkung des berechneten Rotationsradius in den Berechnungsfunktionen berücksichtigt werden. Liegt der berechnete Rotationsradius unterhalb des kleinstmöglichen Werts, wird er auf das Minimum gesetzt, und die Eingabeparameter werden so korrigiert, dass sie der Beschränkung auf den minimalen Radius entsprechen. Auf diese Weise ist gewährleistet, dass die erzeugte S-Kurve fahrbar ist.

Using equations [4], [5], [8], [9], [10] and [11], any two parameters of the S-shaped maneuver can be calculated given the other three parameters. For example, the distance between the straight segments (S) is assumed to be a known fixed value (~1 m), which ensures that the steering controller has enough time to predict the required steering angle change along the path. There are therefore six possible combinations of the other two parameters of the S-shaped maneuver from which the remaining two parameters must be calculated. The six possible combinations of the given inputs can be listed as follows:

• Since the rotation radius of the vehicle must be below the minimum rotation radius (R _min ) corresponding to the maximum steering, a further restriction on the calculated rotation radius must be taken into account in the calculation functions. If the calculated rotation radius is below the smallest possible value, it is set to the minimum and the input parameters are corrected to meet the minimum radius constraint. This ensures that the S-curve created is mobile.

According to a first variant, the following equation describes the calculation of R, θ, Δx taking into account the parameters Δx, Δy, S: $$\begin{array}{l}\left[R,\theta ,\Delta x\right]=\text{Create\_S-Shape\_1}\left(\Delta x,\Delta y,S\right)\\ R=\frac{{\left(\Delta x\right)}^2+{\left(\Delta y\right)}^2-{\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="DE102022122761A1\_0063.png,DE102022122761A1\_0072.png"\; state="\{\{state\}\}">S</figure-callout>}}^2}{4\left(\Delta y\right)}\\ wennR<R_{min}\\ R=R_{min}\\ \Delta x=\sqrt{4\left(\Delta y\right)R-{\left(\Delta y\right)}^2+{\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="DE102022122761A1\_0063.png,DE102022122761A1\_0072.png"\; state="\{\{state\}\}">S</figure-callout>}}^2}\\ \theta ={\text{cos}}^{-1}\left(\frac{{\left(\Delta x+S\right)}^2-\Delta y^2}{{\left(\Delta x+S\right)}^2+\Delta y^2}\right)\end{array}$$

According to a second variant, the following equation describes the calculation of the parameters θ,, Δx when the parameters R, Δy, S are given. $$\begin{array}{l}\left[\Delta x,\theta \right]=\text{Create\_S-Shape\_2}\left(R,\Delta y,S\right)\\ \Delta =\sqrt{4\left(\Delta y\right)R-{\left(\Delta y\right)}^2+{\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="DE102022122761A1\_0063.png,DE102022122761A1\_0072.png"\; state="\{\{state\}\}">S</figure-callout>}}^2}\\ \theta ={\text{cos}}^{-1}\left(\frac{{\left(\Delta x+S\right)}^2-{\left(\Delta y\right)}^2}{{\left(\Delta x+S\right)}^2+{\left(\Delta y\right)}^2}\right)\end{array}$$

According to a third variant, the following equation describes the calculation of the parameters Δy, θ when the parameters R, Δx, S are given. $$\begin{array}{l}\left[\Delta y,\theta \right]=\text{Create\_S-Shape\_3}\left(R,\Delta x,S\right)\\ \Delta y=2R-\sqrt{4{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="DE102022122761A1\_0063.png,DE102022122761A1\_0072.png"\; state="\{\{state\}\}">R</figure-callout>}}^2-{\left(\Delta x\right)}^2+{\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="DE102022122761A1\_0063.png,DE102022122761A1\_0072.png"\; state="\{\{state\}\}">S</figure-callout>}}^2}\\ \theta ={\text{cos}}^{-1}\left(\frac{{\left(\Delta x+S\right)}^2-{\left(\Delta y\right)}^2}{{\left(\Delta x+S\right)}^2+{\left(\Delta y\right)}^2}\right)\end{array}$$

According to a fourth variant, the following equation describes the calculation of the parameters Δx, Δy when the parameters R, θ, S are given. $$\begin{array}{l}\left[\Delta x,\Delta y\right]=\text{Create\_S-Shape\_4}\left(R,\theta ,S\right)\\ \Delta x=2Rsin\left(\theta \right)+ScOs\left(\theta \right)\\ \Delta y\_2R\left(1-cOs\left(\theta \right)\right)+Ssin\left(\theta \right)\end{array}$$

According to a fifth variant, the following equation describes the calculation of the parameters R, Δy,, Δx when the parameters Δx, θ, S are given. $$\begin{array}{l}\left[R,\Delta y,\Delta x\right]=Er\mathrm{e.g}euGe\_S-FOrm\_5\left(\Delta x,\theta ,S\right)\\ R=\frac{\Delta x-ScOs\left(\theta \right)}{2sin\left(\theta \right)}\\ wennR<R_{min}\\ R=R_{min}\\ \Delta x=2Rsin\left(\theta \right)+ScOs\left(\theta \right)\\ \Delta y=2R\left(1-cOs\left(\theta \right)\right)+Ssin\left(\theta \right)\end{array}$$

According to a sixth variant, the following equation describes the calculation of the parameters R, Δy,, Δx when the parameters Δy, θ, S are given. $$\begin{array}{l}\left[R,\Delta x,\Delta y\right]=Er\mathrm{e.g}euGe\_S-FOrm\_6\left(\Delta y,\theta ,S\right)\\ R=\frac{\Delta y-Ssin\left(\theta \right)}{2\left(1-cOs\left(\theta \right)\right)}\\ wennR<R_{min}\\ R=R_{min}\\ \Delta y=2R\left(1-cOs\left(\theta \right)\right)+S\text{sin}\left(\theta \right)\\ \Delta x=2Rsin\left(\theta \right)+ScOs\left(\theta \right)\end{array}$$

As already mentioned, one of the constraints that applies when determining the S-shape parameters is that the vehicle must follow an optimal path, i.e. H. the path along which the vehicle moves tangentially to the parking space front line (S) of the front object 102a when the vehicle 1 performs the forward movement.

The radius of rotation (R) of the circular path over which the vehicle 1 can maneuver so that its outer front corner is tangent to a given line must be calculated using the given parameters. According to a first exemplary embodiment, the method describes calculating a radius of rotation (R) of the circular path of forward movement given the initial position of the vehicle. According to a second exemplary embodiment, the method describes calculating the radius of rotation (R) of the tangential circular path at a given target position parallel to the parking space front line (S). According to a third exemplary embodiment, the method describes calculating the radius of rotation (R) of the tangential circular path at a given target position not parallel to the parking space front line (S).

6a Fig. 12 shows a schematic representation of the variables involved in determining the radius of rotation of the circular path of forward motion given an initial frame according to a first exemplary embodiment of the present invention. As in 6a shown, the initial frame of the vehicle (x ₀ ,y ₀ ) is shown, and the parking space front line (S) is given. The angle between the given initial frame or position and the front line is θ ₀ and the perpendicular distance from the initial frame to the front line is Δy. Based on the in 6a Using the geometry shown, the following equation can be set up: $$R\text{cos}\left({\theta }_0\right)+\Delta y=R_O$$

• Der Rotationsradius (R) ist in dieser Gleichung ein Absolutwert (R > 0). $$=\frac{-\frac{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="DE102022122761A1\_0063.png,DE102022122761A1\_0072.png"\; state="\{\{state\}\}">w</figure-callout>}}{2}+\left(\Delta y\right)\text{cos}\left({\mathrm{\theta }}_0\right)+\sqrt{{\left(\frac{w}{2}\right)}^2{\text{cos}}^2\left({\theta }_0\right)-w\left(\Delta y\right)\text{cos}\left({\theta }_0\right)+{\left(\Delta y\right)}^2-{\left(L-rr\right)}^2{\text{sin}}^2\left({\theta }_0\right)}}{{\text{sin}}^2\left({\theta }_0\right)}$$
  

R _o is the radius of rotation of the outer front corner of the vehicle, and by substituting R _o from Equation [2] into Equation [12] and solving, one obtains:

• The radius of rotation (R) in this equation is an absolute value (R > 0). $$=\frac{-\frac{w}{2}+\left(\Delta y\right)\text{cos}\left({\mathrm{\theta }}_0\right)+\sqrt{{\left(\frac{w}{2}\right)}^2{\text{cos}}^2\left({\theta }_0\right)-w\left(\Delta y\right)\text{cos}\left({\theta }_0\right)+{\left(\Delta y\right)}^2-{\left(L-rr\right)}^2{\text{sin}}^2\left({\theta }_0\right)}}{{\text{sin}}^2\left({\theta }_0\right)}$$
  

$$Term={\left(\frac{w}{2}\right)}^{2}co{s}^2\left({\theta }_0\right)-w\left(\Delta y\right)cos\left({\theta }_0\right)+{\left(\Delta y\right)}^2-{\left(L-rr\right)}^{2}si{n}^2\left({\theta }_0\right)$$

$$R=\frac{-\frac{w}{2}+\left(\Delta y\right)\text{cos}\left({\theta }_0\right)+\sqrt{Term}}{{\text{sin}}^2\left({\theta }_0\right)}$$

So, to create a circular path tangent to a given line at a given initial position, the following function can be formulated: $$\left[R\right]=Er\mathrm{e.g}euGe\_tanGential-kreisf\ddot{O}rmiGen\_WeG\_1\left(\Delta y,{\theta }_0,w,L,rr\right)$$

$$Term={\left(\frac{w}{2}\right)}^{2}cO{s}^2\left({\theta }_0\right)-w\left(\Delta y\right)cOs\left({\theta }_0\right)+{\left(\Delta y\right)}^2-{\left(L-rr\right)}^{2}si{n}^2\left({\theta }_0\right)$$

$$R=\frac{-\frac{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="DE102022122761A1\_0063.png,DE102022122761A1\_0072.png"\; state="\{\{state\}\}">w</figure-callout>}}{2}+\left(\Delta y\right)\text{cos}\left({\theta }_0\right)+\sqrt{Term}}{{\text{sin}}^2\left({\theta }_0\right)}$$

The calculated rotation radius must be within the range [R _min , R _max ]. R _min is due to the maximum steering limit, while R _max is due to the maximum storage limit for the rotation radius value $$\begin{array}{l}wennR>R_{max}\\ R=R_{max}\\ wennR<R_{min}\\ \left(KeinekOllisiOnsfreieL\ddot{O}sunG\right)\end{array}$$

If the radius of rotation leading to the tangential path is greater than R _max , it can be set to R _max as this is guaranteed to be collision-free even if it is not tangential. On the other hand, if the rotation radius leading to the tangential path is smaller than R _min , there is no possible way to avoid a collision. However, such a case could occur if the vehicle 1 has a large angle relative to the front line.

6b shows a schematic representation of the variables involved in determining the radius of rotation of the circular path of forward movement given the target frame parallel to the given front line according to a second exemplary embodiment of the present invention.

As in 6b shown, if the target position 103b of the vehicle 1 is given, which the vehicle 1 should reach after the tangential circular maneuver and the displacement distance (ss) to the parallel given parking space front line (S), the rotation radius (R) of the intended circular path can be calculated as follows : Based on the geometry in 6b the following equation can be set up: $$\begin{array}{l}{\mathrm{<figure-callout\; id="2"\; label="R\; O"\; filenames="DE102022122761A1\_0063.png,DE102022122761A1\_0072.png"\; state="\{\{state\}\}">R</figure-callout>}}_O^{}={\left(R+\frac{w}{2}\right)}^2+{\left(L-rr\right)}^2={\left(R+ss\right)}^2\\ R=\frac{{\left(\frac{w}{2}\right)}^2+{\left(L-rr\right)}^2-s{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="DE102022122761A1\_0063.png,DE102022122761A1\_0072.png"\; state="\{\{state\}\}">s</figure-callout>}}^2}{2ss-w}\end{array}$$

To create a circular path tangential to a given line at a given target position that runs parallel to the parking space front line (S), the following function can be formulated: $$\begin{array}{l}\left[R\right]=Er\mathrm{e.g}euGe\_tanGential-kreisf\ddot{O}rmiGen\_WeG\_2\left(ss,w,L,rr\right)\\ R=\frac{{\left(\frac{w}{2}\right)}^2+{\left(L-rr\right)}^2-s{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="DE102022122761A1\_0063.png,DE102022122761A1\_0072.png"\; state="\{\{state\}\}">s</figure-callout>}}^2}{2\left(ss-\frac{w}{2}\right)}\\ wennR<R_{min}\\ R=R_{min}\\ wennR>R_{max}\\ KeinekOllisiOnsfreieL\ddot{O}sunG\end{array}$$

If the radius of rotation leading to the tangential path is less than R _min , it can be set to R _min as this is guaranteed to be collision-free even if it is not tangential. On the other hand, if the rotation radius leading to the tangential path is larger than R _max , there is no possible way to avoid a collision. However, such a case could occur if the target line is too close to the front line $\left(ss-\frac{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="DE102022122761A1\_0063.png,DE102022122761A1\_0072.png"\; state="\{\{state\}\}">w</figure-callout>}}{2}\approx 0\right).$

6c shows a schematic representation of the variables involved in determining the radius of rotation of the circular path of forward movement when the target frame is not parallel to the given front line according to a third exemplary embodiment of the present invention.

As in 6c shown, the final position that the vehicle reaches after the circular movement is given. The final frame has a relative orientation (θ _f ) to the given parking space front line (S) and a perpendicular distance (Δy) to the given parking space front line (S). Based on the geometry in 6c the following relationship can be established: $$R\text{cos}\left({\theta }_f\right)+\Delta y=R_O$$

R _o is the radius of rotation of the outer front corner of the vehicle, and by substituting R _o from Equation [2] into Equation [15] and solving, one obtains: $$R=\frac{-\frac{w}{2}\left(\Delta y\right)\text{cos}\left({\theta }_f\right)+\sqrt{{\left(\frac{w}{2}\right)}^2{\text{cos}}^2\left({\theta }_f\right)-w\left(\Delta y\right)\text{cos}}\left({\theta }_f\right)+{\left(\Delta y\right)}^2-{\left(L-rr\right)}^2{\text{sin}}^2\left({\theta }_f\right)}{{\text{sin}}^2\left({\theta }_f\right)}$$

To create a circular path tangential to a given line at a given target position that is not parallel to the parking space front line, the following function can be formulated: $$\begin{array}{l}\left[R\right]=Er\mathrm{e.g}euGe\_tanGential-kreisf\ddot{O}rmiGen\_WeG\_3\left(\Delta y,{\theta }_f,w,L,rr\right)\\ Term={\left(\frac{w}{2}\right)}^{2}cO{s}^2\left({\theta }_f\right)-w\left(\Delta y\right)cOs\left({\theta }_f\right)+{\left(\Delta y\right)}^2-{\left(L-rr\right)}^2{\text{sin}}^2\left({\theta }_f\right)\\ R=\frac{-\frac{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="DE102022122761A1\_0063.png,DE102022122761A1\_0072.png"\; state="\{\{state\}\}">w</figure-callout>}}{2}+\left(\Delta y\right)\text{cos}\left({\theta }_f\right)+\sqrt{Term}}{{\text{sin}}^2\left({\theta }_f\right)}\\ wennR>R_{max}\\ R=R_{max}\\ wennR<R_{min}\\ KeinekOllisiOnsfreieL\ddot{O}sunG\end{array}$$

7 shows a schematic representation of a parking scenario in which a target line runs parallel to the parking space front line according to an exemplary embodiment of the present invention. 8th shows a schematic representation of a parking scenario in which a target line according to a further exemplary embodiment of the present invention runs at an angle to a parking space front line. The following description explains how to create a path for optimal, safe maneuvering, especially in tight scenarios, by calculating various parameters for two different exemplary parking scenarios.

$$\left[R\right]=Erzeuge\_tangential-kreisf\ddot{o}rmigen\_Weg\_2\left(\Delta ,w,L,rr\right)$$

$$\left[\Delta x,\theta \right]=Erzeuge\_S-Form\_2\left(R,\Delta y,S\right)$$

For the in 7 In the exemplary parking scenario shown, the method describes the calculation of various parameters for generating a drivable and tangential S-shaped path, which is intended to make the outer corner of the vehicle 1 run tangentially to the predetermined parking space front line (S). Since in the symmetrical S-shape the second circular forward maneuver is tangential to the parking space front line (S) and ends parallel to it, the radius of rotation (R) of the S-shaped path can be calculated using equation [14]. After the radius of rotation (R) is calculated, the method calculates other S-shaped parameters Δx and θ based on the in 5 described function 2, since both Δy and the length of the straight segment (S) of the S-shaped path are given. Thus, to generate the S-shaped path, the following function can be formulated: It is understood that Δy = Δy _min - Δy _Opp-Init is calculated with Δy _min in equation [1], and Δy _Opp-Init is the transverse distance between the initial position of the vehicle and the opposite side. $$\left[R,\Delta x,\theta \right]=Er\mathrm{e.g}euGe\_S-FOrm\_tanGential-parallel\left(\Delta ,\Delta y,S,w,L,r\right)$$

$$\left[R\right]=Er\mathrm{e.g}euGe\_tanGential-kreisf\ddot{O}rmiGen\_WeG\_2\left(\Delta ,w,L,rr\right)$$

$$\left[\Delta x,\theta \right]=Er\mathrm{e.g}euGe\_S-FOrm\_2\left(R,\Delta y,S\right)$$

For the in 8th In the exemplary parking scenario shown, the method describes the calculation of various parameters for generating a drivable and tangential S-shaped path, which should make the outer corner of the vehicle tangential to the predetermined parking space front line. How out 8th As can be seen, the target line containing the end frame of the S-shape is in a lateral displacement Δy from the initial frame of the vehicle, where Δy = Δy _min - Δy _Opp-Init is calculated with Δy _min in equation [1] and Δy _{Opp- Init} is the transverse distance between the initial position of the vehicle and the opposite side. The intersection of the target line (T) with the parking space front line (S) is indicated by an intersection with the reference number 110. The longitudinal distance in the direction of vehicle orientation from its initial frame to the intersection point is referred to as X _s . The parking space front line already has a relative orientation θ _s with the orientation of the vehicle at the time of the initial frame. θ _s is defined as the angle between the target line and the parking space front line. $${\mathrm{\theta }}_s=WinkelFrOntlinie-WinkelSOlllinie.$$

Δy can be calculated using equation [1], and X _s can be calculated from the direct geometric intersection of the two known given lines. Finally, Δ is the perpendicular distance between the S-shaped vehicle frame and the given parking space front line. Out of 8th the following geometric relationship can be derived between Δ, Δx, θ _s and X _s : $$\Delta =\left(X_s-\Delta x\right)\text{sin}\left({\theta }_s\right)$$

To generate the intended tangential collision-free S-shaped path, the method calculates the unknown parameters of the S-shape {R, Δx, θ} besides the parameter Δ.

Reformulation of equation [16]: $$\begin{array}{l}\Delta =-\left(\text{sin}\left({\theta }_s\right)\right)\Delta x+\left(\text{sin}\left({\theta }_s\right)\right)X_s\\ \Delta =a\Delta x+b\end{array}$$

Reformulation of equation [8]: $$\begin{array}{l}R=\left(\frac{1}{4\left(\Delta y\right)}\right){\left(\Delta x\right)}^2+\left(\frac{\left(\Delta y\right)}{4}-\frac{{\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="DE102022122761A1\_0063.png,DE102022122761A1\_0072.png"\; state="\{\{state\}\}">S</figure-callout>}}^2}{4\left(\Delta y\right)}\right)\\ R=c{\left(\Delta x\right)}^2+d\end{array}$$

Reformulation of equation [9]: $$\theta =cO{s}^{-1}\left(\frac{{\left(\Delta x+S\right)}^2-\Delta y^2}{{\left(\Delta x+S\right)}^2+\Delta y^2}\right)$$

Reformulation of equation [13]: $$\begin{array}{l}Term={\left(\frac{w}{2}\right)}^{2}cO{s}^2\left({\theta }_s\right)-w\left(\Delta \right)cOs\left({\theta }_s\right)+{\left(\Delta \right)}^2-{\left(L-rr\right)}^2{\text{sin}}^2\left({\theta }_s\right)\\ Term={\left(\Delta \right)}^2-\left(wcOs\left({\theta }_s\right)\right)\left(\Delta \right)+\left({\left(\frac{w}{2}\right)}^{2}cO{s}^2\left({\theta }_s\right)-{\left(L-rr\right)}^2{\text{sin}}^2\left({\theta }_s\right)\right)\\ Term={\mathrm{<figure-callout\; id="2"\; label="\Delta "\; filenames="DE102022122761A1\_0063.png,DE102022122761A1\_0072.png"\; state="\{\{state\}\}">\Delta </figure-callout>}}^2+e\left(\Delta \right)+f\\ R=\frac{-\frac{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="DE102022122761A1\_0063.png,DE102022122761A1\_0072.png"\; state="\{\{state\}\}">w</figure-callout>}}{2}+\left(\Delta \right)cOs\left({\theta }_s\right)+\sqrt{Term}}{{\text{sin}}^2\left({\theta }_s\right)}\\ Term={\left(\left({\text{sin}}^2\left({\theta }_s\right)\right)R-\left(cOs\left({\theta }_s\right)\right)\Delta +\frac{w}{2}\right)}^1\\ Term={\left(GR+H\Delta +\frac{w}{2}\right)}^2\\ {\left(GR+H\Delta +\frac{w}{2}\right)}^2-\left({\mathrm{<figure-callout\; id="2"\; label="\Delta "\; filenames="DE102022122761A1\_0063.png,DE102022122761A1\_0072.png"\; state="\{\{state\}\}">\Delta </figure-callout>}}^2+e\left(\Delta \right)+f\right)=0\end{array}$$

Solving equations [17], [18], [19] and [20] for the unknowns {R, Δx, θ, Δ} leads to a fourth-order polynomial equation. In order to solve the equation more efficiently, equation [19], which represents the tangency condition, can be reformulated into an inequality condition, which represents the collision freedom. Such an inequality condition can be more efficient to simplify the problem, which can be represented by a binary search or other direct loop search.

kann der Rotationsradius des Fahrzeugs (R) auf den tangentialen Radius begrenzt werden, um eine Kollision zu vermeiden. $$R\le R_t$$

$$R\le \frac{-\frac{w}{2}+\left(\Delta \right)\text{cos}\left({\theta }_s\right)+\sqrt{Term}}{{\text{sin}}^2\left({\theta }_s\right)}$$

$$Term\ge {\left(\left({\text{sin}}^2\left({\theta }_s\right)\right)R-\left(\text{cos}\left({\theta }_s\right)\right)\Delta +\frac{w}{2}\right)}^2$$

$$Term\ge {\left(gR+h\Delta +\frac{w}{2}\right)}^2$$

$$Term={\left(\Delta \right)}^2-\left(wcos\left({\theta }_s\right)\right)\left(\Delta \right)+\left({\left(\frac{w}{2}\right)}^{2}co{s}^2\left({\theta }_s\right)-{\left(L-rr\right)}^{2}si{n}^2\left({\theta }_s\right)\right)$$

$$Term={\Delta }^2+e\left(\Delta \right)+f$$

$${\Delta }^2+e\left(\Delta \right)+f\ge {\left(gR+h\Delta +\frac{w}{2}\right)}^2$$

$${\Delta }^2+e\left(\Delta \right)+f-{\left(gR+h\Delta +\frac{w}{2}\right)}^2\ge 0$$

Since the radius of rotation corresponding to the tangential path from equation [11] is formulated as follows: $$R_t=\frac{-\frac{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="DE102022122761A1\_0063.png,DE102022122761A1\_0072.png"\; state="\{\{state\}\}">w</figure-callout>}}{2}+\left(\Delta \right)\text{cos}\left({\theta }_s\right)+\sqrt{Term}}{{\text{sin}}^2\left({\theta }_s\right)}$$

The vehicle's rotation radius (R) can be limited to the tangential radius to avoid a collision. $$R\le R_t$$

$$R\le \frac{-\frac{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="DE102022122761A1\_0063.png,DE102022122761A1\_0072.png"\; state="\{\{state\}\}">w</figure-callout>}}{2}+\left(\Delta \right)\text{cos}\left({\theta }_s\right)+\sqrt{Term}}{{\text{sin}}^2\left({\theta }_s\right)}$$

$$Term\ge {\left(\left({\text{sin}}^2\left({\theta }_s\right)\right)R-\left(\text{cos}\left({\theta }_s\right)\right)\Delta +\frac{w}{2}\right)}^2$$

$$Term\ge {\left(GR+H\Delta +\frac{w}{2}\right)}^2$$

$$Term={\left(\Delta \right)}^2-\left(wcOs\left({\theta }_s\right)\right)\left(\Delta \right)+\left({\left(\frac{w}{2}\right)}^{2}cO{s}^2\left({\theta }_s\right)-{\left(L-rr\right)}^{2}si{n}^2\left({\theta }_s\right)\right)$$

$$Term={\mathrm{<figure-callout\; id="2"\; label="\Delta "\; filenames="DE102022122761A1\_0063.png,DE102022122761A1\_0072.png"\; state="\{\{state\}\}">\Delta </figure-callout>}}^2+e\left(\Delta \right)+f$$

$${\mathrm{<figure-callout\; id="2"\; label="\Delta "\; filenames="DE102022122761A1\_0063.png,DE102022122761A1\_0072.png"\; state="\{\{state\}\}">\Delta </figure-callout>}}^2+e\left(\Delta \right)+f\ge {\left(GR+H\Delta +\frac{w}{2}\right)}^2$$

$${\mathrm{<figure-callout\; id="2"\; label="\Delta "\; filenames="DE102022122761A1\_0063.png,DE102022122761A1\_0072.png"\; state="\{\{state\}\}">\Delta </figure-callout>}}^2+e\left(\Delta \right)+f-{\left(GR+H\Delta +\frac{w}{2}\right)}^2\ge 0$$

$$H\left(\Delta x\right)\ge 0$$

$$H\left(\Delta x\right)={\left(a\left(\Delta x\right)+b\right)}^2+e\left(a\left(\Delta x\right)+b\right)+f-{\left(g\left(c{\left(\Delta x\right)}^2+d\right)+h\left(a\left(\Delta x\right)+b\right)+\frac{w}{2}\right)}^2$$

wobei $$a=-\left(\text{sin}\left({\theta }_s\right)\right)$$

$$b=\left(\text{sin}\left({\theta }_s\right)\right)X_s$$

$$c=\left(\frac{1}{4\left(\Delta y_{min}\right)}\right)$$

$$d=\left(\frac{\left(\Delta y_{min}\right)}{4}-\frac{S^2}{4\left(\Delta y_{min}\right)}\right)$$

$$e=-\left(wcos\left({\theta }_s\right)\right)$$

$$f=\left({\left(\frac{w}{2}\right)}^{2}co{s}^2\left({\theta }_s\right)-{\left(L-rr\right)}^{2}si{n}^2\left({\theta }_s\right)\right)$$

$$g=\left({\text{sin}}^2\left({\theta }_s\right)\right)$$

$$h=-\left(\text{cos}\left({\theta }_s\right)\right)$$

By substituting [17] and [18], the inequality condition to guarantee freedom from collision can then only be a function of Δx, which is represented in equation [20]. $${\left(a\Delta x+b\right)}^2+e\left(a\Delta x+b\right)+f-{\left(G\left(c{\left(\Delta x\right)}^2+d\right)+H\left(a\Delta x+b\right)+\frac{w}{2}\right)}^2\ge 0$$

$$H\left(\Delta x\right)\ge 0$$

$$H\left(\Delta x\right)={\left(a\left(\Delta x\right)+b\right)}^2+e\left(a\left(\Delta x\right)+b\right)+f-{\left(G\left(c{\left(\Delta x\right)}^2+d\right)+H\left(a\left(\Delta x\right)+b\right)+\frac{w}{2}\right)}^2$$

where $$a=-\left(\text{sin}\left({\theta }_s\right)\right)$$

$$b=\left(\text{sin}\left({\theta }_s\right)\right)X_s$$

$$c=\left(\frac{1}{4\left(\Delta y_{min}\right)}\right)$$

$$d=\left(\frac{\left(\Delta y_{min}\right)}{4}-\frac{{\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="DE102022122761A1\_0063.png,DE102022122761A1\_0072.png"\; state="\{\{state\}\}">S</figure-callout>}}^2}{4\left(\Delta y_{min}\right)}\right)$$

$$e=-\left(wcOs\left({\theta }_s\right)\right)$$

$$f=\left({\left(\frac{w}{2}\right)}^{2}cO{s}^2\left({\theta }_s\right)-{\left(L-rr\right)}^{2}si{n}^2\left({\theta }_s\right)\right)$$

$$G=\left({\text{sin}}^2\left({\theta }_s\right)\right)$$

$$H=-\left(\text{cos}\left({\theta }_s\right)\right)$$

In this way, different parameters of the S-shaped path can be generated for the forward movement of the vehicle 1 from the initial position 103a to the target position 103b in the tight parking environments. When the vehicle 1 reaches the target position 103b, the method further includes planning the path for the second movement from the target position 103b in the reverse direction into the parking space 102c. In one aspect, the backward path may have an S-shape. For example, the path of the vehicle in the reverse direction may follow a Bezier curve. The Bezier curve may be, for example, a first-order Bezier curve or a second-order Bezier curve or a third-order Bezier curve or a combination thereof.

9 is a flowchart showing a method for generating a tangential drivable S-shaped path according to an embodiment of the present invention.

In step S1, the method includes receiving various input parameters such as the length of the vehicle (L), the distance from the rear axle to the rear bumper (rr), an angle between the target front line and the parking space front line (θ _s ), the width of the vehicle (w ), the minimum rotation radius corresponding to the maximum steering at the center of the rear axle (R _min ), the opposite side line Y, the parking space front line (S) and the length of the straight segment (S) of the S-shaped path. The opposite side line Y is the vertical distance between the X-axis of the global reference coordinates and the parallel boundary line of the opposite side 105.

• R_omin : minimaler Rotationsradius, der dem äußersten Eckpunkt entspricht (Abstand vom Rotationsmittelpunkt zum äußersten Eckpunkt), $$R_{o_{min}}=\sqrt{{\left(R_{min}+\frac{w}{2}\right)}^2+{\left(L-rr\right)}^2}$$
  
• Δy_min: einen minimalen Querabstand von einer Begrenzungslinie der gegenüberliegenden Seite $$\Delta y_{min}=R_{o_{min}}-R_{min}$$
  
• Solllinie (T): Linie parallel zur Anfangsorientierung des Fahrzeugs und um Δy_min von der gegebenen Linie der gegenüberliegenden Seite 105 verschoben
• Schnittpunkt: Schnittpunkt zwischen der Solllinie und der Parklückenfrontlinie
• X_s = Abstand vom Anfangsrahmen des Fahrzeugs zum Schnittpunkt in Richtung der Anfangsorientierung des Fahrzeugs.

In step S2, the method includes calculating the following values:

• R _{o min} : minimum rotation radius corresponding to the outermost corner point (distance from the center of rotation to the outermost corner point), $$R_{O_{min}}=\sqrt{{\left(R_{min}+\frac{w}{2}\right)}^2+{\left(L-rr\right)}^2}$$
  
• Δy _min : a minimum transverse distance from a boundary line on the opposite side $$\Delta y_{min}=R_{O_{min}}-R_{min}$$
  
• Target line (T): Line parallel to the initial orientation of the vehicle and shifted by Δy _min from the given line of the opposite side 105
• Intersection: Intersection between the target line and the parking space front line
• X _s = distance from the vehicle's initial frame to the intersection point in the direction of the vehicle's initial orientation.

In step S3, the method includes comparing the calculated X _S with the X _{s min} and _{Xs Max} . If it is determined that the target line (T) is parallel to the parking space front line (S) (if X _s ≤ X _{s min} or X _s ≥ X _{s Max} ), the method calculates the various S-shape parameters that are in 7 for generating the S-shape path were discussed as indicated in step S4. If it is determined that the target line is not parallel to the parking space front line (X _{s min} < _Xs < _{Xs Max} ), the method calculates the various S-shape parameters that are in 8th for generating the S-shaped path, as indicated in step S5. X _{s Max} is the upper threshold of X _S , while X _{s min} is the lower threshold of X _s . For example, the upper threshold of X _s is about 30 m and the lower threshold of X _s is about 0.5 m.

It is understood that the parking assistance system 2 carries out various procedural steps, as described above.

According to another aspect of the invention, a computer program product is provided. The computer program product includes instructions that, when the program is executed by a computer, cause the computer to perform the method according to the first and/or second and/or third aspects. A computer program product, such as a computer program medium, may be in the form of a storage device, such as a storage medium 100, a USB flash drive, a CD-ROM, a DVD, etc., and/or in the form of a digital file stored by a server on a computer network or the like can be downloaded. For example, this can be achieved by transferring the corresponding file over a wireless network.

Those skilled in the art will recognize that the present invention is by no means limited to the preferred embodiments described above. On the contrary, many modifications and variations are possible within the scope of the appended claims. One skilled in the art will also readily recognize that the various embodiments described herein can be freely combined to obtain new combinations.

In addition, variations to the disclosed embodiments may be understood and effected by those skilled in the art in practicing the claimed invention from a review of the drawings, the disclosure and the appended claims. In the claims, the word “comprising” does not exclude any other elements or steps, and the indefinite article “a” or “an” does not exclude a plurality. The mere fact that certain measures are given in separate dependent claims does not indicate that a combination of these measures cannot be used advantageously.

REFERENCE MARKS

101

Corner to the entrance to the parking space

100

Street

1

vehicle

2

Parking assistance system

3

Computing device

4

Condition sensor system

5

Environmental sensor system

6

Input device

101a, 101b, 101c:

Variety of objects

102a

Front object

102b

Rear object

102c

parking lot

103a

Initial position of the vehicle

103b

Target position of the vehicle

103c

Parking position of the vehicle

105

Boundary line of the opposite side

T

target line

S

Parking space front line

900

flow chart

S1

Procedural step

S2

Procedural step

S3

Procedural step

S4

Procedural step

S5

Procedural step

Claims (19)

Method for planning a route for an automated motor vehicle (1), the method comprising the following steps: determining a parking space (103a) on a lateral side relative to a street (100); planning a first S-shaped movement in the forward direction; planning a second movement in a reverse direction into the parking space, the second movement immediately following the first movement; and wherein the first movement is planned when a lateral object distance (D _VO ) between the vehicle (1) and an object (101) on the other lateral side of the road (100) is smaller than an object threshold and / or a lateral parking space distance (D _VP ) between the vehicle (1) and the parking space (102) is greater than a parking space threshold value. Procedure according to Claim 1 , wherein the method comprises: providing sensor information that describes at least an initial position (103a) of the vehicle (1), the parking space (102c) and a plurality of objects (101a, 101b, 101c) on the other side of the road (100). , wherein the parking space (102c) is defined between a front object (102a) and a rear object (102b) in a vehicle movement direction; Evaluating the sensor information provided to determine at least one parking position (103c) in the parking space (102), the lateral object distance and the lateral parking space distance; and planning the first movement for maneuvering the vehicle from the initial position (103a) to a target position (103b) and the second movement for maneuvering the vehicle from the target position (103b) to the parking position (103c), the target position (103b) being in a first longitudinal distance (Δx) from the initial position (103a) along the vehicle movement direction and at a first transverse distance (Δy) from the initial position, and an orientation of the vehicle in the initial position (103a) equal to an orientation of the vehicle (1) in the target position ( 103b). Procedure according to Claim 1 , where the S-shape comprises a pair of circular segments connected by a straight segment. A method according to any one of the preceding claims, wherein planning the first movement includes determining a minimum lateral distance (Δy _min ) from an opposite side boundary line (105) based on a radius of rotation at the front extreme corner (R _{o min} ) of the vehicle and a radius of rotation of the vehicle (R _min ) by steering the vehicle (1) with a maximum steering angle, the boundary line of the opposite side (105) defining a boundary of the plurality of objects (101a, 101b, 101c). Procedure according to Claim 4 , wherein the method includes constructing a target line (T) that is laterally displaced by the minimum transverse distance (Δy _min ) from the opposite side boundary line (105) and to both the opposite side boundary line (105) and to a longitudinal axis of the vehicle (1) in the initial position (103a) is parallel, and the target position (103b) of the vehicle lies on the target line (T). Procedure according to Claim 4 , wherein planning the first movement further includes determining the first longitudinal distance (Δx), the first transverse distance (Δy), a change in orientation (θ) across the circular segments, and a radius of rotation (R) of the circular segments resulting in a front right extreme corner of the vehicle runs tangentially to a parking space front line (S) when the vehicle (1) reaches the target position (103b), wherein the parking space front line (S) includes a boundary between the front object (102a) and the rear object (102b) defined. Procedure according to Claim 5 and 6 , whereby the parking space front line (S) runs parallel to the target line (T). Procedure according to Claim 5 and 6 , whereby the parking space front line (S) runs at an angle to the target line (T). Procedure according to Claim 6 , wherein the method involves determining the first transverse distance (Δy) by means of $$\Delta y=\Delta y_{min}-\left(GeGen\ddot{u}berlieGendeSeitenlinieY-y_0\right)$$

includes, where Δy _min is the minimum transverse distance between the boundary line of the opposite side (105) and the target line (T), opposite side line Y is the vertical distance between the X-axis of the global reference coordinates and the parallel boundary line of the opposite side (105) and y ₀ is the vertical coordinate of the vehicle (1) in its initial position (103a). Procedure according to Claim 6 and Claim 7 , wherein the method includes determining the radius of rotation (R) of the circular segments based on at least one of the following elements: an angle (θ _o ) between the parking space front line (S) and the initial position (103a) of the vehicle, the first transverse distance (Δy) , a length (L) of the vehicle (1), a width (w) of the vehicle (1) and a distance between the rear axle and the rear bumper (rr) of the vehicle (1). Procedure according to one of the Claims 6 until 8th , wherein the method includes determining the first longitudinal distance (Δx) based on the first transverse distance (Δy) and the radius of rotation (R) of the circular segments. Procedure according to one of the Claims 6 until 9 , the method including determining a change in orientation (θ) across the circular segments based on the first longitudinal distance (Δx) and the first transverse distance (Δy). Procedure according to Claim 2 , where the first transverse distance (Δy) is in the range between 0.1 m and 5 m. Procedure according to Claim 2 , where the first longitudinal distance (Δx) is in the range between 0.5 m and 10 m. Procedure according to Claim 1 , where the object threshold is in the range between 30 cm and 300 cm. Procedure according to Claim 1 , whereby the lateral parking space distance is between 4 m and 8 m. Computer program product with program means stored in a computer-readable medium to implement the method according to one of the preceding Claims 1 until 16 to be carried out when the computer program product is executed on a processor of an electronic computing device (3). Computer-readable storage medium comprising a computer program product according to Claim 17 . Parking assistance system (2) for planning a first movement in a forward direction with an S-shape and for planning a second movement in a backward direction into the parking space, the second movement following the first movement and the parking assistance system (2) having at least one detection device (5 ) and at least one electronic computing device (3), wherein the parking assistance system (2) for carrying out a method according to one of Claims 1 until 16 is configured.

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