DE102022203683A1 - Method for determining a travel trajectory for a vehicle - Google Patents

Abstract

The invention relates to a method (100) for determining a travel trajectory (316) for a vehicle (305), comprising: - receiving (101) map data of a map representation of the surroundings of a vehicle (305); - receiving (103) data of an occupancy grid the environment of the vehicle (305); - determining (105) at least one road segment (304) of the road (301) to be traveled by the vehicle (305) based on the map data; - determining (107) for each road segment (304) of a plurality of width line segments (311); - reducing (109) a length of each width line segment (311) by at least one width of the vehicle (305); - determining (111) for each width line segment (311) a support point (311) positioned on the width line segment (311). 313);- Connecting (113) the support points to form a travel trajectory (316); and - outputting (115) the travel trajectory (316) along the roadway (301).

Description

The invention relates to a method for determining a travel trajectory for a vehicle. The invention further relates to a method for controlling a vehicle along a travel trajectory determined according to the invention.

State of the art

Driving trajectories are essential for controlling vehicles. The determination of a travel trajectory must take place while the vehicle is driving and must be carried out taking into account the nature of the surroundings and in particular the road to be traveled on. The investigation must therefore be carried out quickly and precisely in order to enable accident-free and safe control of the vehicle.

It is therefore an object of the invention to provide an improved method for determining a travel trajectory for a vehicle and an improved method for controlling a vehicle.

This task is solved by the method for determining a travel trajectory for a vehicle and by the method for controlling a vehicle of the independent claims. Advantageous refinements are the subject of the subordinate claims.

• Empfangen von Kartendaten einer Kartendarstellung einer Umgebung eines Fahrzeugs, wobei die Kartendarstellung Information bezüglich wenigstens einer durch das Fahrzeug zu befahrenden Fahrbahn umfasst;
• Empfangen von Daten eines Belegungsgitters des Umfelds des Fahrzeugs, wobei das Belegungsgitter wenigstens ein wenigstens teilweise auf der Fahrbahn positioniertes Objekt darstellt;
• Bestimmen wenigstens eines Fahrbahnsegments der durch das Fahrzeug zu befahrenden Fahrbahn basierend auf den Kartendaten, wobei ein Fahrbahnsegment ein in einer Fahrtrichtung vor der Position des Fahrzeugs angeordnetes Teilstück der Fahrbahn ist;
• Bestimmen für jedes Fahrbahnsegment einer Mehrzahl von in vorbestimmten Abständen zueinander entlang einer Längsrichtung der Fahrbahn nacheinander angeordneten Breitenliniensegmenten, wobei ein Breitenliniensegment als ein entlang einer Breitenausdehnung der Fahrbahn verlaufendes Liniensegment ausgebildet ist, wobei das Breitenliniensegment zwischen seitlichen Abgrenzungen der Fahrbahn oder zwischen einer seitlichen Abgrenzung der Fahrbahn und einem wenigstens teilweise auf der Fahrbahn positionierten Objekt oder zwischen zwei wenigstens teilweise auf der Fahrbahn positionierten Objekten verläuft, und wobei eine Länge eines Breitenliniensegments eine für eine Befahrung durch das Fahrzeug zur Verfügung stehende Breite der Fahrbahn beschreibt;
• Reduzieren einer Länge eines jeden Breitenliniensegments um wenigstens eine Breite des Fahrzeugs, wobei zur Längenreduktion jedes Breitenliniensegment an jedem Ende des Breitenliniensegments um wenigstens eine halbe Breite des Fahrzeugs reduziert wird;
• Bestimmen für jedes Breitliniensegment einer auf dem Breitenliniensegment positionierte Stützstelle; und
• Verbinden der Stützstellen zu einer Fahrtrajektorie
• Ausgeben der Fahrtrajektorie entlang der Fahrbahn.

According to one aspect of the invention, a method for determining a travel trajectory for a vehicle is provided, comprising:

• Receiving map data of a map representation of an environment of a vehicle, the map representation comprising information regarding at least one roadway to be traveled by the vehicle;
• Receiving data from an occupancy grid of the surroundings of the vehicle, the occupancy grid representing at least one object positioned at least partially on the roadway;
• determining at least one roadway segment of the roadway to be traveled by the vehicle based on the map data, wherein a roadway segment is a portion of the roadway arranged in a direction of travel in front of the position of the vehicle;
• Determining for each roadway segment a plurality of width line segments arranged one after the other at predetermined distances from one another along a longitudinal direction of the roadway, a widthline segment being designed as a line segment running along a width extent of the roadway, the widthline segment between lateral boundaries of the roadway or between a lateral boundary of the roadway and an object positioned at least partially on the roadway or between two objects positioned at least partially on the roadway, and wherein a length of a width line segment describes a width of the roadway available for travel by the vehicle;
• reducing a length of each width line segment by at least a width of the vehicle, wherein to reduce length each width line segment is reduced at each end of the width line segment by at least half a width of the vehicle;
• Determine for each width line segment a support point positioned on the width line segment; and
• Connecting the support points to form a travel trajectory
• Outputting the travel trajectory along the road.

In this way, the technical advantage can be achieved that an improved method for determining a travel trajectory for a vehicle can be provided. For this purpose, road segments of a road to be traveled by a vehicle are created based on map data and based on data from an occupancy grid of a vehicle's surroundings. Furthermore, width line segments arranged one after the other at predetermined distances from one another along a longitudinal direction of the roadway are generated for each roadway segment. The extent of the width line segments describes the width of the road.

For the purposes of the application, the width of the roadway is an extension of the roadway in a direction perpendicular to the longitudinal direction.

The wide line segments are defined here as line segments and run between two side boundaries of the road, between a side boundary of the road and an object at least partially arranged on the road or between two objects at least partially arranged on the road. According to the invention, support points are defined for each width line segment, with one support point being arranged on a width line segment. To generate the travel trajectory, the support points are each connected with a continuous line element. The line element represents a course of the route generated in this way The travel trajectory generated in this way primarily includes position information in which the positions of the individual support points as well as the positions of the line element connecting the support points serve as position information for controlling the vehicle along the travel trajectory. Alternatively, the travel trajectory can also include speed information in addition to the position information.

For this purpose, the width line segments or the roadway segments are generated based on the map data of the map display and in particular taking into account the position information stored there. In addition, GPS information regarding the position of the vehicle can be taken into account in order to localize the vehicle relative to the map display. According to the invention, the data of the occupancy grid of the vehicle's surroundings can be based on surroundings sensor data and can describe an occupancy of the surroundings, which are divided into spatial segments, with objects, in particular static objects.

By reducing the lengths of the width line segments by at least one width of the vehicle, it can be ensured that the vehicle is able to travel along the roadway without collision when driving on the travel trajectory running through the support points. Collision-free driving on the road by the vehicle is possible for any support points positioned on the reduced-length width line segments. This requires that when the vehicle is controlled along the travel trajectory, a geometric center of the vehicle is positioned on the travel trajectory.

According to one embodiment, each support point is positioned centrally on the respective width line segment.

In this way, the technical advantage can be achieved that a simple determination of the support points on the respective latitude line segments is made possible. Since the width line segments are reduced in length by at least the width of the vehicle, central positioning of the support points on the respective width line segments can ensure that the vehicle can be controlled along the road without collision when driving along the travel trajectory running through the support points.

• Verbinden von einer auf einem ersten Breitenliniensegment positionierten ersten Stützstelle mit einer auf einem unmittelbar hinter dem ersten Breitenliniensegment angeordneten zweiten Breitliniensegment positionierten zweiten Stützstelle mit einer geraden Verbindungslinie;
• Ermitteln eines Schnittpunkts der geraden Verbindungslinie mit einem unmittelbar hinter dem zweiten Breitenliniensegment angeordneten dritten Breitenliniensegment; und
• Positionieren einer auf dem dritten Breitenliniensegment angeordneten dritten Stützstelle auf dem Schnittpunkt der geraden Verbindungslinie mit dem dritten Breitenliniensegment oder auf einer Position mittig zwischen dem Schnittpunkt und einer aktuellen Position der dritten Stützstelle; oder
• Positionieren der dritten Stützstelle an einem Ende des dritten Breitenliniensegments, falls kein Schnittpunkt zwischen der geraden Verbindungslinie und dem dritten Breitenliniensegment besteht; und Iteratives Ausführen der Schritte.

According to one embodiment, determining the support points includes:

• Connecting a first support point positioned on a first width line segment with a second support point positioned on a second width line segment arranged immediately behind the first width line segment with a straight connecting line;
• Determining an intersection of the straight connecting line with a third width line segment arranged immediately behind the second width line segment; and
• Positioning a third support point arranged on the third width line segment at the intersection of the straight connecting line with the third width line segment or at a position midway between the intersection and a current position of the third support point; or
• positioning the third support point at an end of the third width line segment if there is no intersection between the straight connecting line and the third width line segment; and executing the steps iteratively.

In this way, the technical advantage can be achieved that precise positioning of the support points on the different width line segments is possible.

• Verbinden von einer auf einem ersten Breitenliniensegment positionierten ersten Stützstelle mit einer auf einem hinter dem ersten Breitenliniensegment angeordneten dritten Breitliniensegment positionierten dritten Stützstelle mit einer geraden Verbindungslinie;
• Ermitteln eines Schnittpunkts der geraden Verbindungslinie mit einem zwischen dem ersten Breitenliniensegment und dem dritten Breitenliniensegment angeordneten zweiten Breitenliniensegment; und
• Positionieren einer auf dem zweiten Breitenliniensegment angeordneten zweiten Stützstelle auf dem Schnittpunkt der geraden Verbindungslinie mit dem zweiten Breitenliniensegment oder auf einer Position mittig zwischen dem Schnittpunkt und einer aktuellen Position der zweiten Stützstelle; oder
• Positionieren der zweiten Stützstelle an einem Ende des zweiten Breitenliniensegments, falls kein Schnittpunkt zwischen der geraden Verbindungslinie und dem zweiten Breitenliniensegment besteht; und Iteratives Ausführen der Schritte.

According to one embodiment, determining the support points includes:

• Connecting a first support point positioned on a first width line segment with a third support point positioned on a third width line segment arranged behind the first width line segment with a straight connecting line;
• determining an intersection of the straight connecting line with a second width line segment arranged between the first width line segment and the third width line segment; and
• Positioning a second support point arranged on the second width line segment at the intersection of the straight connecting line with the second width line segment or at a position midway between the intersection and a current position of the second support point; or
• Positioning the second support point at an end of the second width line segment if there is no intersection between the straight connecting line and the second width line segment; and executing the steps iteratively.

In this way, the technical advantage can be achieved that precise positioning of the support points on the width line segments is possible.

• Reduzieren der Länge eines Breitenliniensegments um einen maximalen Lenkwinkeleinschlagsbeitrag, wobei der maximale Lenkwinkeleinschlagsbeitrag einen maximalen Lenkwinkeleinschlag des Fahrzeugs berücksichtigt, den das Fahrzeug ohne eine Kollision mit einer seitlichen Fahrbahnbegrenzung der Fahrbahn und/oder mit einem wenigstens teilweise auf der Fahrbahn positionierten Objekt ausführen kann; und wobei das Reduzieren der Länge umfasst:
• Ermitteln eines Schnittpunkts einer geraden Verbindungslinie von einem ersten Breitenliniensegment mit einem unmittelbar hinter dem ersten Breitenliniensegment angeordneten zweiten Liniensegment, wobei die gerade Verbindungslinie von einem Endpunkt des ersten Breitenliniensegments aus verläuft und zum ersten Breitenliniensegment einen Winkel α aufweist, wobei der Winkel α den maximalen Lenkwinkel des Fahrzeugs beschreibt;
• Bestimmen des Schnittpunkts der geraden Verbindungslinie mit dem zweiten Breitenliniensegment als einen neuen Endpunkt des zweiten Breitenliniensegments.

According to one embodiment, the method further comprises:

• Reducing the length of a width line segment by a maximum steering angle contribution, the maximum steering angle contribution taking into account a maximum steering angle of the vehicle that the vehicle can execute without a collision with a side road boundary of the road and / or with an object positioned at least partially on the road; and wherein reducing the length includes:
• Determining an intersection of a straight connecting line from a first width line segment with a second line segment arranged immediately behind the first width line segment, the straight connecting line extending from an end point of the first width line segment and having an angle α to the first width line segment, the angle α being the maximum steering angle of the vehicle describes;
• Determine the intersection of the straight connecting line with the second width line segment as a new end point of the second width line segment.

In this way, the technical advantage can be achieved that a maximum steering angle of the vehicle can be taken into account when driving on the road along the travel trajectory. The maximum steering angle is defined in the sense of the application as the steering angle that can be made when driving on the road without this leading to a collision of the vehicle with objects or road boundaries. By reducing the width line segments by the respective determined amount of the maximum steering angle angle, the positioning of the support points can also be positioned further away from the respective objects or the road boundaries, whereby the safety of driving on the resulting travel trajectory can be further improved.

• Anpassen einer Spline-Funktion an die Stützstellen durch Ausführen eines Anpassungsprozesses.

According to one embodiment, connecting the support points to the travel trajectory includes:

• Adjusting a spline function to the support points by executing an adjustment process.

In this way, the technical advantage can be achieved that a simple and precise connection of the support points for determining the travel trajectory is made possible. By using the spline function, the smoothest possible course of the driving trajectory can be achieved, which runs through the support points and along the road without strong steering movements. This makes it possible to achieve pleasant and safe driving behavior of the vehicle. An adaptation process is a fit process in the sense of registration.

According to one embodiment, the spline function is designed as a basic spline function with control points.

In this way, the technical advantage can be achieved that an easy-to-use and reliable adaptation of the spline function to the support points is possible.

• Minimieren von Abständen der Spline-Funktion zu den Stützstellen, sodass die Spline-Funktion einen Schnittpunkt mit jedem Breitenliniensegment aufweist;
• und/oder
• Minimieren einer Krümmung der Spline-Funktion entlang eines Verlaufs der Spline-Funktion; und/oder
• Minimieren einer Ableitung der Krümmung der Spline-Funktion nach einer Weglänge der Spline-Funktion entlang des Verlaufs der Spline-Funktion.

According to one embodiment, adapting the spline function to the support points includes:

• Minimizing distances from the spline function to the vertices so that the spline function has an intersection with each width line segment;
• and or
• Minimizing a curvature of the spline function along a course of the spline function; and or
• Minimizing a derivative of the curvature of the spline function according to a path length of the spline function along the path of the spline function.

In this way, the technical advantage can be achieved that by minimizing the distances between the spline function and the support points, the resulting travel trajectory runs through the support points as precisely as possible. In this way, the safest possible course of the travel trajectory can be achieved, in which the vehicle is controlled as far away as possible from the road boundaries or the objects that are at least partially arranged on the road. By minimizing the curvature or the derivative of the curvature of the spline function, the smoothest possible course of the driving trajectory can be achieved without large or strong steering movements. This enables the vehicle to drive as pleasantly and safely as possible.

• Ermitteln für jedes Breitenliniensegment einer Abtaststellte der Spline-Funktion, für die die Spline-Funktion einen Wert aufweist, der zwischen Endpunkten des Breitenliniensegments liegt; und
• Minimieren eines Abstands der Abtaststelle der Spline-Funktion und einer senkrechten Projektion der Abtaststelle auf das Breitenliniensegment.

According to one embodiment, minimizing the distances between the spline function and the support points includes:

• Determining, for each width line segment, a sample location of the spline function for which the spline function has a value that lies between end points of the width line segment; and
• Minimize a distance of the spline function sampling point and a perpendicular project tion of the sampling point to the width line segment.

In this way, the technical advantage can be achieved that a precise and easy-to-calculate minimization of the distances between the spline function and the support points is possible.

According to one embodiment, minimizing is accomplished by performing a gradient process.

In this way, the technical advantage can be achieved that a precise and quick minimization of the above-mentioned sizes is possible.

• Bestimmen eines Endpunkts der Fahrtrajektorie, falls die Breite des Fahrzeugs kleiner oder gleich der Länge eines Breitenliniensegments ist, wobei der Endpunkt der Fahrtrajektorie durch die Stützstelle des in Fahrtrichtung des Fahrzeugs letzten Breitenliniensegments gegeben ist, das eine Länge aufweist, die größer als die Breite des Fahrzeugs ist.

According to one embodiment, the method further comprises:

• Determining an end point of the travel trajectory if the width of the vehicle is less than or equal to the length of a width line segment, the end point of the travel trajectory being given by the support point of the last width line segment in the direction of travel of the vehicle, which has a length that is greater than the width of the vehicle is.

In this way, the technical advantage can be achieved that a safe driving trajectory can be determined. If the above-mentioned length reductions of the width line segments result in a width line segment that has a shorter length than the width of the vehicle, the last width line segment in the direction of travel with a length greater than the width of the vehicle is defined as the end point of the travel trajectory. A width line segment with a shorter length than the width of the vehicle would lead to a collision of the vehicle with either the road boundaries or one or a plurality of objects positioned at least partially on the road when driving on the vehicle. To avoid collisions, according to the invention, the travel trajectory is ended before reaching such a latitude line segment at an end point of the travel trajectory. This can prevent the vehicle from colliding with road boundaries or objects.

• Empfangen von Umfeldsensordaten wenigstens eines Umfeldsensors des Fahrzeugs, wobei die Umfeldsensordaten das Umfeld des Fahrzeugs abbilden; und

According to one embodiment, the method further comprises:

• Receiving environment sensor data from at least one environment sensor of the vehicle, the environment sensor data depicting the environment of the vehicle; and

Generating an occupancy grid of the vehicle's surroundings based on the surroundings sensor data.

In this way, the technical advantage can be achieved that a precise occupancy grid of the vehicle's surroundings and, associated with this, precise detection of objects can be provided.

• Ausführen des Verfahrens zum Bestimmen einer Fahrtrajektorie für ein Fahrzeug nach einer der voranstehenden Ausführungsformen; und
• Steuern des Fahrzeugs entlang der berechneten Fahrtrajektorie.

According to a further aspect, a method for controlling a vehicle is provided, comprising:

• Executing the method for determining a travel trajectory for a vehicle according to one of the preceding embodiments; and
• Controlling the vehicle along the calculated travel trajectory.

In this way, the technical advantage can be achieved that an improved method for controlling a vehicle can be provided. The vehicle is controlled along a travel trajectory determined according to the method according to the invention for determining a travel trajectory for a vehicle with the above-mentioned technical advantages.

According to a further aspect, a computing unit is provided which is set up to carry out the method for determining a travel trajectory for a vehicle according to one of the preceding embodiments and/or the method for controlling a vehicle.

According to a further aspect, a computer program product is provided comprising commands which, when the program is executed by a data processing unit, cause it to carry out the method for determining a travel trajectory for a vehicle according to one of the preceding embodiments and/or the method for controlling a vehicle.

• 1 eine graphische Darstellung eines Verfahrens zum Bestimmen einer Fahrtrajektorie für ein Fahrzeug gemäß einer Ausführungsform;
• 2 eine graphische Darstellung eines Schritts des Verfahrens in 1;
• 3 eine weitere graphische Darstellung eines weiteren Schritts des Verfahrens in 1;
• 4 ein Flussdiagramm des Verfahrens zum Bestimmen einer Fahrtrajektorie für ein Fahrzeug gemäß einer Ausführungsform;
• 5 ein Flussdiagramm eines Verfahrens zum Steuern eines Fahrzeugs; und
• 6 eine schematische Darstellung eines Computerprogrammprodukts.

Embodiments of the invention are explained using the following drawings. Shown in the drawings:

• 1 a graphical representation of a method for determining a travel trajectory for a vehicle according to an embodiment;
• 2 a graphical representation of a step of the method in 1 ;
• 3 a further graphical representation of a further step of the method in 1 ;
• 4 a flowchart of the method for determining a travel trajectory for a vehicle according to an embodiment;
• 5 a flowchart of a method for controlling a vehicle; and
• 6 a schematic representation of a computer program product.

1 shows a graphical representation of a method 100 for determining a travel trajectory 316 for a vehicle 305 according to an embodiment.

Graphic a) shows a roadway 301 and a vehicle 305 traveling on the roadway 301. The roadway 301 has roadway boundaries 302 arranged on the right and left relative to a longitudinal direction 306 of the roadway 301. In the illustration shown, an object 303 is arranged on the right edge of the road 302 and on the left edge of the road 302, which is at least partially arranged on the road 301. The objects 303 can be, for example, parked vehicles, stopped vehicles, construction site boundaries or other primarily statically arranged objects that can usually occur in road traffic.

The vehicle 305 also has at least one environment sensor 307, by means of which an environment detection of the vehicle's surroundings is possible. The environment sensor 307 can be designed, for example, as a camera sensor, LIDAR sensor or radar sensor. The vehicle can also include several different environmental sensors. The vehicle 305 also has a computing unit 309.

By means of the computing unit 309, the vehicle 305 is set up to carry out the method according to the invention for determining a travel trajectory.

For this purpose, the computing unit 309 takes into account map data of a map representation of a traffic network comprising the roadway 301. The map display can be designed, for example, as a topological road map. Furthermore, data from an occupancy grid of the surroundings of the vehicle 305 are taken into account by the computing unit 309. The occupancy grid describes an occupancy of various spatial segments of the surroundings of the vehicle 305 by objects 303 arranged in the surroundings of the vehicle.

According to one embodiment, the occupancy grid is based on surroundings sensor data from the surroundings sensor 307, so that by recording the surroundings sensor data, by means of which the surroundings of the vehicle 305 and in particular the roadway 301 and possibly the objects 303 at least partially arranged thereon are imaged, a corresponding occupancy grid based on the received Environmental sensor data can be generated.

According to one embodiment, the computing unit 309 can further take into account position data from a global navigation system, for example a GPS system, in order to bring about a position comparison of the vehicle 305 with the map data of the map display.

Based on the map data of the map display, the data of the occupancy grid and the position data of the navigation system, roadway segments 304 are calculated according to the invention for the roadway 301 traveled by the vehicle 305.

Graphic b) shows a roadway segment 304 calculated in this way. The roadway segment 304 shown describes the course of the roadway 301 from graphic a) and further includes the two roadway boundaries 302. Furthermore, the two objects 303 arranged on the right and left edge of the roadway 301 are at least are partially positioned on the roadway 301.

To calculate the travel trajectory, in a first step 304 width line segments 311 are calculated for each road segment. The width line segments 311 are designed as line segments and run in a direction oriented perpendicular to the longitudinal direction 306 of the roadway 301. The width line segments 311 are arranged one behind the other at predetermined distances from one another along the longitudinal direction 306 in the direction of travel. The width line segments 311 run either between the two roadway boundaries 302 or between a roadway boundary 302 and an object 303 that is at least partially arranged on the roadway 301 or between two objects 303 that are at least partially arranged on the roadway 301.

A length of the width line segments 311 describes a width of the travel corridor of the roadway 301 that is available for travel by the vehicle 305. The travel corridor can be given either by the width of the roadway, which is defined by the two roadway boundaries 302. Alternatively, when positioning the objects 303, the available travel corridor can be defined by the distance between the respective object 303 and the opposite road boundary 302 or by the distance between two opposite objects 303.

Graphic c) shows the width line segments 311 of the roadway segment 304 shown in graphic B. In graphic C, some of the width line segments 311, in particular the width line segments 311, which are arranged in the direction of travel D of the vehicle 305 immediately behind the two objects 303 shown in graphic b), are reduced in length in the respective end regions 312. By reducing the length of the width line segments 311 shown, a maximum steering angle of the vehicle 305 is taken into account. The maximum steering angle describes the steering angle that the vehicle 305 can make when driving on the road 301 without the vehicle 305 colliding with a road boundary 302 or an object 303. Since the vehicle 305 cannot execute a full steering angle immediately behind the objects 303 when driving on the road 301 due to the length of the vehicle when passing the objects 303 without causing a collision with the objects, the corresponding width line segments arranged immediately behind the objects 303 are 311 reduced in length. As already mentioned, the length of a width line segment 311 describes the travel corridor that can be traveled by the vehicle 305 without the risk of a collision. The corresponding width line segments 311 are therefore only reduced in length in the end regions 312, which are arranged in the immediate vicinity of the respective object 303.

Graphic d) shows the latitude line segments 311 from graphic c). The width line segments 311 shown in graphic d) also have an additional reduction in length by a width of the vehicle 305. The width line segments 311 are reduced by at least half the width of the vehicle 305 at the two opposite end regions 312 of each width line segment 311. By reducing the length of the width line segments 311 by at least the width of the vehicle 305, the available travel corridor can be further reduced. By reducing the size of the travel corridor, the safety of the vehicle 305 traveling along the travel corridor of the roadway along the travel trajectory can be further increased. A travel trajectory that runs anywhere through the width line segments 311 shown with reduced length in graphic d) can ensure safe travel of the vehicle 305 along the roadway 301. By positioning the vehicle 305 relative to the travel trajectory with reference to a geometric center of the vehicle 305, the length reduction of the width line segments 311 shown can be achieved at both end regions 312 by at least half the vehicle width, that when positioning the geometric center of the vehicle 305 at any point of the reduced-length width line segments 311, a collision of the vehicle 305 with the road boundary 302 or the objects 303 arranged as shown in graphic a) can be avoided.

Graphic e) shows the correspondingly reduced length width line segments 311 from graphic d). Furthermore, each reduced-length width line segment 311 has a support point 313. In the embodiment shown, the support point 313 is positioned centrally on the respective width line segments 311. Alternatively, any positioning of the support point 313 on a width line segment 311 is possible. For a more precise description of the positioning of the support points 313, see the description 3 referred.

According to the invention, in order to determine a travel trajectory 316, the support points 313 of the latitude line segments 311 shown in graphic e) are connected. Graphic f) shows such a connection of the support points 313 from graphic e). Graphic f) shows a connection of the support points 313 with a spline function 314. In the illustration shown, the spline function 314 is shown as a basic spline with control points 315.

According to one embodiment of the method according to the invention, the support points 313 are connected by adapting the spline function 314 to the support points 313 using an adaptation process known from the prior art (fit process). The spline function 314 adapted in this way to the support points 313 is defined as a travel trajectory 316 according to the method according to the invention and is provided for further control of the vehicle 305. The travel trajectory 316 primarily includes position information, in which each function value of the spline function includes at least one position information of the travel trajectory relative to the map representation of the road 301. The position information is based on the position information of the map display. According to one embodiment, the spline function 314 is designed as a two-dimensional function and has position information regarding an X-axis and a Y-axis arranged perpendicular thereto of a reference coordinate system. The reference coordinate system can relate to the position information of the map display and can be given, for example, by the coordinate system of the map display.

Alternatively, the corresponding describes, while the Y-axis defines a direction that is perpendicular to the direction of travel D and oriented horizontally. In addition to the position information, the travel trajectory can also include speed information.

2 shows a graphical representation of a step of the method 100 in 1 , in particular a graphical representation of the length reduction of width line segments 311 taking into account the maximum steering angle.

In graphic a) a first width line segment 317 and a second width line segment 318 are shown. The latitude line segments 317, 318 each have end points 321. The width line segments 317, 318 are each arranged one behind the other with respect to the direction of travel D of the vehicle 305. To determine the length reduction, connecting lines 323 are formed at the two end points 321 of the first width line segment 317 arranged at the front in the direction of travel D. The connecting lines 323 have an angle α to the first width line segment 317. The angle α ^- describes the maximum steering angle that can be carried out by the vehicle due to the technical design of the vehicle 305. According to the invention, intersection points with the second width line segment 318 arranged immediately after the first width line segment 317 in the direction of travel D are determined for the two connecting lines 323.

In the graphic a) shown, the second width line segment 318 has an intersection with one of the two connecting lines 323. To reduce the length of the second latitude line segment 318, the intersection of the second latitude line segment 318 with the connecting line 323 is defined as a new end point 322 of the second latitude line segment 318. The length-reduced second width line segment 318 thus runs between the new end point 322 and the opposite original end point 321. The corresponding length reduction of the second width line segment 318 takes into account the maximum steering angle due to any objects 303 that may be arranged. The correspondingly generated driving corridor can therefore take place without the risk of a collision with the road boundaries 302 or objects 303.

However, if the second width line segment 318 arranged immediately behind the first width line segment 317 in the direction of travel D does not have any intersections with the two connecting lines 323, then there is no reduction in the length of the second width line segment 318. A corresponding case is shown in graphic b).

3 shows another graphical representation of another step of the method 100 in 1 .

Graphics a) and b) show two graphic representations of two similar methods for positioning support points 313 on width line segments 311. The two graphics a) and b) each have three width line segments 311 arranged one behind the other in the direction of travel D, a first width line segment 317 second width line segment 318 and a third width line segment 319. A first support point 324 is arranged on the first width line segment 317. A second support point 325 is positioned on the second width line segment 318. A third support point 326 is positioned on the third latitude line segment 319.

To position the support points 313, a straight connecting line 329 is now defined starting from the first support point 324 of the first width line segment 317. In graphic a), the straight connecting line 329 runs between the first support point 324 of the first width line segment 317 and the third support point 326 of the third width line segment 319. Alternatively, the straight connecting line 329 in graphic b) runs between the first support point 324 of the first width line segment 317 and the second support point 325 of the second latitude line segment 318.

To position the second support point 325 of the second width line segment 318, an intersection point between the straight connecting line 329 and the second width line segment 318 is determined in the method in graphic a). A new second support point 329 is positioned in the embodiment shown at the position of the intersection of the connecting line 329 with the second width line segment 318. Alternatively, the new support point 327 can be positioned at half a distance between the current position of the second support point 325 and the intersection of the connecting line 329 and the second with the width line segment 318.

In graphic b), an intersection point between the connecting line 329 and the third width line segment 319 is determined to position the third support point 326 of the third width line segment 319. A new third support point 328 is positioned in the embodiment shown at the position of the intersection of the connecting line 329 with the third width line segment 319.

Alternatively, the new third support point 328 can be half the distance between the third support point 326 and the intersection between the connecting line 329 and the third width line segment 319 can be positioned.

The methods shown in graphics a) and b) can be carried out iteratively for all width line segments 311 of the roadway segment 304. For this purpose, the methods in graphics a) and b) can be carried out alternatively to each other or simultaneously or one after the other.

The initial positioning of the support points 313 can, for example, be a central positioning in a geometric center of the width line segments 311. Alternatively, the support points 313 can be positioned anywhere on the width line segments 311. The execution of the above-mentioned steps can then be carried out iteratively based on the support points 313 positioned arbitrarily on the width line segments 311.

4 shows a flowchart of the method 100 for determining a travel trajectory 316 for a vehicle 305 according to an embodiment.

According to the invention, in a first method step 101, map data of a map representation of an environment of a vehicle 305 is received. The map representation includes information regarding at least one roadway 301 to be traveled by the vehicle 305. The map representation can be, for example, a topological road map.

In a further method step 155, in the embodiment shown, environment sensor data from at least one environment sensor 307 of a vehicle 305 is received. The surrounding sensor data represent an environment of the vehicle 305 and in particular the road 301 to be traveled on. The environmental sensor data can include, for example, camera data, LIDAR data or radar data.

In a further method step 157, an occupancy grid of the surroundings of the vehicle 305 is generated based on the surroundings sensor data. The occupancy grid describes occupancies of spatial segments of the surroundings of the vehicle 305 and includes information regarding objects 303 within the surroundings of the vehicle 305. The objects 303 taken into account here primarily include stationary objects that have a comparatively small change in their positioning over a predetermined period of time. According to the invention, particular attention is paid to objects 303 that are at least partially positioned on the roadway 301 to be traveled by the vehicle 305. Such objects can be, for example, parked or stopped vehicles, construction site boundaries or similar primarily statically positioned objects that can be found in normal road traffic.

In a further method step 103, data from the previously generated occupancy grid of the surroundings of the vehicle 305 are received.

In a further method step 105, at least one roadway segment 304 of the roadway 301 to be traveled by the vehicle 305 is generated based on the map data. For this purpose, data or information regarding the positioning of the vehicle can also be taken into account, which is provided, for example, by information from a navigation system. Positioning the vehicle based on the position data enables positioning of the vehicle relative to the map display and, associated with this, localization of the vehicle within the map display.

In a further method step 107, a plurality of width line segments 311 arranged one after the other at predetermined distances from one another along a longitudinal direction 306 of the roadway 301 are determined for each roadway segment 304. The width line segments 311 describe line elements that are oriented in a direction perpendicular to the longitudinal direction 306 of the roadway 301 and either between two roadway boundaries 302 of the roadway 301, between a roadway boundary 302 and an object 303 positioned at least partially on the roadway 301, or between two at least partially Objects 303 positioned on the roadway 301 run. A length of the width line segment 311 describes a width of a travel corridor of the road that can be traveled by the vehicle 305.

In a further method step 135, lengths of width line segments 311 are reduced by a maximum steering angle contribution. The maximum steering angle contribution takes into account a maximum steering angle of the vehicle 305, with which the vehicle 305 can be steered along the roadway 301 without fear of a collision of the vehicle 301 with roadway boundaries 302 and/or objects 303 positioned at least partially on the roadway 301.

For this purpose, in a method step 137, at least one intersection of a straight connecting line 323 is determined starting from a first width line segment 317 with a second width line segment 318 arranged immediately behind the first width line segment 317. The straight connecting line 323 goes from one end point 321 of the first width line segment 317 and has an angle α ^- to the first width line segment 317. The angle α ^- describes the maximum steering angle of the vehicle 305.

In a further method step 139, the determined intersection of the straight connecting line 323 with the second latitude line segment 318 is defined as a new end point 322 of the second latitude line segment 318. However, if the second latitude line segment 318 does not have an intersection with the at least two straight connecting lines 323 of the first latitude line segment 317, there is no reduction in the length of the second latitude line segment 318.

In a further method step 109, a further reduction in the length of each latitude line segment 311 is carried out. For this purpose, at least half the vehicle width of the vehicle 305 is subtracted from each end region 312 of each width line segment 311.

In a further method step 111, a support point 313 positioned on the width line segment 311 is determined for each width line segment 311. According to one embodiment, the support point 313 can be positioned centrally on the respective width line segment 311.

To determine the support points 313, in a further method step 117 a connection is made between a first support point 324 positioned on a first width line segment 317 and a second support point 325 positioned on a second width line segment 318 arranged immediately behind the first width line segment 317 via a straight connecting line 329.

In a further method step 119, an intersection of the straight connecting line 329 with a third width line segment 319 arranged immediately behind the second width line segment 318 is determined.

In a further method step 121, a third support point 326 arranged on the third width line segment 319 is positioned at the intersection of the straight connecting line 329 with the third width line segment 319 or at a position centrally between the intersection and the current position of the third support point 319.

Alternatively, in a method step 123, the third support point 326 is positioned at one end of the third width line segment 319 if there is no intersection between the straight connecting line 329 and the third width line segment 319.

In a further method step 125, the above-mentioned method steps 117 to 123 are carried out iteratively.

In a further method step 127, the first support point 324 of the first width line segment 317 is alternatively or additionally connected to the third support point 326 of the third width line segment 319 via a straight connecting line 329.

In a further method step 129, an intersection of the straight connecting line 329 with the second width line segment 318 arranged between the first and third width line segments 317, 319 is determined.

In a further method step 131, the second support point 325 of the second width line segment 318 is positioned at the intersection of the straight connecting line 329 with the second width line segment 318 or at a position centrally between the intersection and the current position of the second support point 325.

Alternatively, the second support point 325 is positioned at one end of the second width line segment 318 if there is no intersection between the straight connecting line 329 and the second width line segment 318.

In method step 125 an iterative execution of method steps 127 to 133 is also effected.

Before carrying out method steps 117 to 123, the support points 313 can be positioned either in the middle as described above or at any desired location on each width line segment 311. Starting from these positions, the method steps 117 to 133 mentioned can be carried out.

In a further method step 113, the support points 313 of the width line segments 311 are connected to form a travel trajectory 316.

For this purpose, in a method step 141, an adaptation of a spline function 314 to the support points 313 of the width line segments 311 is carried out. The adjustment can be carried out in the form of an adjustment process (fit process). This fit process can be carried out taking into account a least squares method. The spline function 314 may be designed as a basic spline function with control points, according to one embodiment.

To adapt the spline function 314 of the support points 313, a further method is used Step 143 minimizes the distances between the spline function 314 and the support points 313 in such a way that the spline function has an intersection with each width line segment 311 of the roadway segment 304.

For this purpose, a sampling point of the spline function 314 is determined for each width line segment 311 in a method step 149, for which the spline function 314 has a value that lies between the end points 321 of the respective width line segment 311.

In a further method step 151, the distances between the sampling points of the spline function 314 and a vertical position of the sampling point on the respective width line segment 311 are minimized.

In a further method step 145, in order to adapt the spline function 314 to the support points 313, a curvature of the spline function 314 is minimized along a course of the spline function 314.

In a further method step 147, a derivation of the spline function 314 or the curvature of the spline function is further minimized according to a path length of the spline function along the course of the spline function 314.

In a further method step 153, an end point of the travel trajectory 316 is determined if the width of the vehicle 305 is greater than or equal to a length of a width line segment 311. The end point of the travel trajectory 316 is defined by the support point 313 of the last width line segment 311 in the direction of travel D of the vehicle 305, which has a length that is greater than the width of the vehicle 305.

In a further method step 115, the correspondingly generated travel trajectory 316 is output.

nach einer Bogenlänge s(t) der Spline-Funktion 314 berechnet. Zur Minimierung der Krümmung κ(t) und der Ableitung der Krümmung $\frac{d\kappa }{ds}\left(t\right)$

werden eine Mehrzahl von Abtaststellten t ermittelt und die genannten Größen für die jeweiligen Abtaststellen t ermittelt. Die Abtaststellen werden hierbei in vorbestimmten Abständen zueinander ermittelt, wobei die Abstände vorzugsweise den Abständen der Breitenliniensegmente 311 entsprechen.The adaptation of the spline function 314 to the plurality of calculated support points 311 is effected using the least squares method. When adapting the spline function 314 to the support points 313, it is taken into account that the spline function 314 has an intersection with each width line segment 311 for which a support point 313 was calculated. Furthermore, a minimization of a curvature κ(t) and a minimization of a derivative of the curvature $\frac{d\kappa }{ds}\left(t\right)$

calculated according to an arc length s(t) of the spline function 314. To minimize the curvature κ(t) and the derivative of the curvature $\frac{d\kappa }{ds}\left(t\right)$

A plurality of sampling points t are determined and the variables mentioned are determined for the respective sampling points t. The scanning points are determined at predetermined distances from one another, the distances preferably corresponding to the distances of the width line segments 311.

The plurality of support points of the width line segments, each connected to straight line elements, represents a polyline. The aim of adapting the spline function is to find a smooth curve through the individual support points, which can serve as a vehicle's travel trajectory. The individual points of the polyline, i.e. the support points, do not have any associated parameter values. For this reason, parameter values are generated for each support point by assigning the value (i-1)/(n-1) to the i-th support point. The parameter n describes the number of support points 313.

aufweisen. Derartige Fahrtrajektorien 316 können zu starken Lenkradeinschlägen und damit zu unruhigen Fahrverhalten des Fahrzeugs 305 führen. Um dies zu vermeiden, wird ferner die bereits angesprochenen Minimierung der Krümmung κ(t) und der Ableitung der Krümmung $\frac{d\kappa }{ds}\left(t\right)$

durchgeführt.In a further step, two spline functions can be adapted independently of one another to the x coordinates and y coordinates of the support points 313. The curve generated in this way runs along the road 301 and can serve as a travel trajectory 316 for a vehicle 305. However, a travel trajectory 316 generated in this way can have large fluctuations in the course between the individual support points 313 and, associated with this, large values of the curvature κ (t) and the derivative of the curvature $\frac{d\kappa }{ds}\left(t\right)$

exhibit. Such driving trajectories 316 can lead to strong steering wheel turns and thus to unsteady driving behavior of the vehicle 305. To avoid this, the already mentioned minimization of the curvature κ(t) and the derivative of the curvature $\frac{d\kappa }{ds}\left(t\right)$

carried out.

As already mentioned, the adaptation of the spline function 314 to the support points 313 is carried out in such a way that the spline function 314 has an intersection with each width line segment 311. For this purpose, a vertical projection onto a respective latitude line segment 311 is calculated for each sampling point t. In this context, in the course of the adaptation, a distance between each scanning point t and the respective vertical projection onto the corresponding width line segment 311 of the scanning point t is minimized. For this purpose, the positions of the scanning points t are shifted in such a way that the distance to the respective projection of the scanning point t becomes minimal.

Ferner kann ein Schnittpunktterm definiert werden, mittels dem neben einem Schnitt der Spline-Funktion 314 mit dem i-ten Breitenliniensegment 311 ein Abstand zu der jeweiligen Stützstelle 313 des i-ten Breitenliniensegments 311 bestimmt werden kann: $$h_i=\frac{\left(G_i-A_i\right)\cdot \overrightarrow{A_l{B}_l}}{\overrightarrow{A_l{B}_l}\cdot \overrightarrow{A_l{B}_l}}$$

For this purpose, let G _i (t _i ) be a function value of the spline function 314 at an i-th sampling point t _i . Furthermore, let A _i and B _i be two end points 321 of an i-th mash ten line segment 311. The orthogonal projection Hi onto the i-th latitude line segment 311 can hereby be defined as follows, $H_i=A_i+\overrightarrow{A_l{b}_l},$

Furthermore, an intersection term can be defined, by means of which, in addition to an intersection of the spline function 314 with the i-th latitude line segment 311, a distance to the respective support point 313 of the ith latitude line segment 311 can be determined: $$H_i=\frac{\left(G_i-A_i\right)\cdot \overrightarrow{A_l{b}_l}}{\overrightarrow{A_l{b}_l}\cdot \overrightarrow{A_l{b}_l}}$$

The factor h _i is the position of H _i relative to A _i and B _i . To minimize the distance of the i-th sampling point t to the respective orthogonal projection on the respective latitude line segment 311, the following expression is minimized: $${\displaystyle \sum _i^n{\left(G_i-H_i\right)}^2}$$

die Ableitung der Krümmung κ(t) nach s(t) definiert. Ziel der Anpassung der Spline-Funktion an die Stützstellen 311 ist es, die Krümmung κ(t) und die Ableitung $\frac{d\kappa }{ds}\left(t\right)$

entlang der Verlauf der Spline-Funktion 314 nahe oder gleich Null zu bringen. Eine derartige Fahrtrajektorie 316 würde eine nahezu gerade Verlauf aufweisen und nahezu keine Lenkbewegungen wären nötig, um der Fahrtrajektorie folgen zu können. Durch die Berücksichtigung der Ableitung $\frac{d\kappa }{ds}\left(t\right)$

können ferner die Geschwindigkeit, mit denen Lenkbewegungen durchzuführen sind, reduziert werden. Hierdurch können ruckartige Hin-und-Her-Bewegungen des Lenkrads vermieden werden, die zu keiner wirklichen Richtungsänderung des Fahrzeugs 305 führen. Ziel der Optimierung ist es vielmehr, möglichst langsame Drehung des Lenkrads zu erreichen, was zu angenehmeren Fahrverläufen des Fahrzeugs 305 führt. Da die Größen κ(t) und $\frac{d\kappa }{ds}\left(t\right)$

die Krümmung und die Ableitung an Abtaststellen der Spline-Funktion bestimmen, und da es ein Ziel der Optimierung ist, κ(t) und $\frac{d\kappa }{ds}\left(t\right)$

entlang dem Verlauf der Spline-Funktion 314 gegen Null zu minimieren, ist die folgenden Relation zu minimieren: $${\displaystyle {\int }_0^1\kappa \left(t\right)}dt$$

For a smooth course of the spline function 314 and the later travel trajectory 316, the curvature of the spline function 314 is also minimized. Let κ(t) be the curvature at a sampling point t along the course of the spline function 314. Furthermore, let s(t) be the arc length along the course of the spline function up to the sampling point t. Furthermore, be with me $\frac{d\kappa }{ds}\left(t\right)$

the derivative of the curvature κ(t) with respect to s(t) is defined. The aim of adapting the spline function to the support points 311 is the curvature κ(t) and the derivative $\frac{d\kappa }{ds}\left(t\right)$

along the course of the spline function 314 to bring it close to or equal to zero. Such a travel trajectory 316 would have an almost straight course and almost no steering movements would be necessary in order to be able to follow the travel trajectory. By taking the derivative into account $\frac{d\kappa }{ds}\left(t\right)$

The speed at which steering movements are to be carried out can also be reduced. This makes it possible to avoid jerky back-and-forth movements of the steering wheel, which do not lead to any real change in direction of the vehicle 305. The aim of the optimization is rather to achieve the slowest possible rotation of the steering wheel, which leads to more pleasant driving characteristics of the vehicle 305. Since the quantities κ(t) and $\frac{d\kappa }{ds}\left(t\right)$

determine the curvature and the derivative at sampling points of the spline function, and since it is a goal of optimization, κ(t) and $\frac{d\kappa }{ds}\left(t\right)$

To minimize towards zero along the course of the spline function 314, the following relation must be minimized: $${\displaystyle {\int }_0^1\kappa \left(t\right)}dt$$

This integral can be approximated by the following relationships, where m is a tuning parameter: $${\displaystyle \sum _i^m\kappa {\left(\frac{i-1}{m-1}\right)}^2}$$

Similarly, minimizing the derivative of curvature can be accounted for by minimizing the following expression: $${\displaystyle \sum _i^m\frac{d\kappa }{dt}{\left(\frac{i-1}{m-1}\right)}^2}$$

The sum according to the counting parameter i takes into account the sampling points t up to the mth sampling point.

der Krümmung nach der Bogenlänge s und die zweite Ableitung der Krümmung $\frac{d^s\kappa }{d{s}^2}\left(t\right)$

nach der Bogenlänge s des Verlaufs der Spline-Funktion 314. Zur Berechnung der genannten Größen werden für in regelmäßigen Abständen bestimmte Abtastwerte t entsprechende Werte der Spline-Funktion 314 beziehungsweise der genannten Größen bestimmt bzw. berechnet.To adapt the spline function, the following values are calculated for a plurality of sampling points t: the arc length s along the course of the spline function 314, the x coordinate, the y coordinate of the two-dimensional spline function 314, the curvature κ( t), the derivative $\frac{d\kappa }{ds}\left(t\right)$

the curvature according to the arc length s and the second derivative of the curvature $\frac{d^s\kappa }{d{s}^2}\left(t\right)$

according to the arc length s of the course of the spline function 314. To calculate the quantities mentioned, corresponding values of the spline function 314 or the quantities mentioned are determined or calculated for sample values t determined at regular intervals.

The x coordinate and the y coordinate can refer to a coordinate system that is firmly connected to the ego vehicle. The x-axis of the coordinate system can be oriented along the direction of travel D of the vehicle 305, while the y-axis can be oriented in a horizontal and perpendicular direction to the direction of travel D. Alternatively, the coordinate system can be a fixed coordinate system of the map display, where the x and y axes can refer to cardinal directions.

direkt berechnet werden können. Um die Schreibweise zu vereinfachen, wird definiert: $$\begin{array}{l}ƒ\left(t\right)=\frac{dx}{dt}\left(t\right)\cdot \frac{d^{2}y}{d{t}^2}\left(t\right)-\frac{d^{2}x}{d{t}^2}\left(t\right)\cdot \frac{dy}{dt}\left(t\right)\\ g\left(t\right)={\left(\frac{dx}{dt}\left(t\right)\right)}^2+{\left(\frac{dy}{dt}\left(t\right)\right)}^2\end{array}$$

fSince the parameters taken into account in the adaptation of the spline function 314 are chosen to be proportional to the arc length, s and t are highly correlated. The scanning therefore also takes place at regular intervals with the arc length. To adapt the spline function 314, function values of the spline function 314 are determined for a plurality of sampling points. The number of sampling points t corresponds to the number of Support points 213 of the width line segments 211. The width line segments 211 are generated at regular intervals from one another. According to the invention, the sampling points t of the spline function 214 are arranged at comparable distances from one another. The distances between the scanning points t preferably correspond to the distances between the width line segments 211. According to the invention, the six quantities mentioned above are calculated for each scanning point t. The calculation of the coordinates x(t) and y(t) includes an evaluation of the spline function 314 with respect to the respective coordinate axes. A property of spline functions, especially basis spline functions, is that the derivatives $$\frac{dx}{dt}\left(t\right),\frac{d^{2}x}{d{t}^2}\left(t\right),\frac{d^{3}x}{d{t}^3}\left(t\right)\cdots \frac{dy}{dt}\left(t\right),\frac{d^{2}y}{d{t}^2}\left(t\right),\frac{d^{3}y}{d{t}^3}\left(t\right)$$

can be calculated directly. To simplify the notation, it is defined: $$\begin{array}{l}ƒ\left(t\right)=\frac{dx}{dt}\left(t\right)\cdot \frac{d^{2}y}{d{t}^2}\left(t\right)-\frac{d^{2}x}{d{t}^2}\left(t\right)\cdot \frac{dy}{dt}\left(t\right)\\ G\left(t\right)={\left(\frac{dx}{dt}\left(t\right)\right)}^2+{\left(\frac{dy}{dt}\left(t\right)\right)}^2\end{array}$$

f

Since f and g are simple combinations of x(t) and y(t) and their derivatives with respect to t, the derivatives of f and g with respect to t can be calculated. The curvature of general curves can therefore be calculated as follows: $$\kappa \left(t\right)=\frac{ƒ\left(t\right)}{G\left(t\right)\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$$

It should be noted that the calculation of the curvature κ(t) shown does not use the derivatives of x and y according to the arc length s, but rather according to the sampling point t. However, this is identical because the arc length s is a monotonically increasing function of t. For general curves, s(t) and g(t) can be related as follows: $$s\left(t\right)={\displaystyle {\int }_0^p\sqrt{G\left(t\right)}}dt$$

The function s(t) can be approximated as follows by interpreting the calculated functions x(t) and y(t) as polylines of a plurality of sampling points. The derivatives can therefore be related as follows: $$\frac{ds}{dt}\left(t\right)=\sqrt{G\left(t\right)}$$

Using the rule of inverse derivation: $$\frac{dt}{ds}\left(t\right)=\frac{1}{\sqrt{G\left(t\right)}}$$

berechnet werden, was wie folgt möglich ist: $$\frac{d\kappa }{ds}\left(t\right)=\frac{2\cdot \frac{dƒ}{dt}\cdot g\left(t\right)-3\cdot ƒ\left(t\right)\cdot \frac{dg}{dt}}{g\left(t\right)\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$$

In addition, the derivatives of the curvature must be included $\frac{d\kappa }{dt}$

can be calculated, which is possible as follows: $$\frac{d\kappa }{ds}\left(t\right)=\frac{2\cdot \frac{dƒ}{dt}\cdot G\left(t\right)-3\cdot ƒ\left(t\right)\cdot \frac{dG}{dt}}{G\left(t\right)\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$$

For a derivation of the curvature κ according to the arc length s, the chain rule results: $$\frac{d\kappa }{ds}\left(t\right)=\frac{d\kappa }{dt}\left(t\right)\cdot \frac{dt}{ds}\left(t\right)=\frac{2\cdot \frac{dƒ}{dt}\cdot G\left(t\right)-3\cdot ƒ\left(t\right)\cdot \frac{dG}{dt}}{G{\left(t\right)}^3}$$

an einer Abtaststelle t verwendet. Ein ähnlicher Ansatz kann verwendet werden, um eine geschlossene Lösung für zweifache Ableitung der Krümmung $\frac{d{\kappa }^2}{d{s}^2}\left(t\right)$

herzuleiten. Die zweifache Ableitung $\frac{d{\kappa }^2}{d{s}^2}\left(t\right)$

kann hierbei durch Berechnung einer numerischen Differenzierung von $\frac{d\kappa }{ds}\left(t\right)$

approximiert werden.The latter formula is used to calculate the derivative of the curvature $\frac{d\kappa }{ds}\left(t\right)$

used at a sampling point t. A similar approach can be used to provide a closed-form solution for twofold derivatives of curvature $\frac{d{\kappa }^2}{d{s}^2}\left(t\right)$

to derive. The double derivative $\frac{d{\kappa }^2}{d{s}^2}\left(t\right)$

can be done by calculating a numerical differentiation of $\frac{d\kappa }{ds}\left(t\right)$

be approximated.

Minimizing the above-mentioned sizes in the course of adapting the spline function 314 to the support points 313 can be achieved by carrying out a gradient method.

5 shows a flowchart of a method 200 for controlling a vehicle 305.

In a first method step 201, the method 100 according to the invention for determining a travel trajectory 316 for a vehicle 305 is first carried out according to one of the above-mentioned embodiments and a corresponding travel trajectory 316 is generated.

In a further method step 203, the vehicle 305 is controlled according to the travel trajectory 316 determined in method step 201. Controlling the vehicle 305 includes outputting corresponding control signals from the computing unit 309 to actuators of the vehicle 305.

6 shows a schematic representation of a computer program product 400, comprising commands which, when the program is executed by a computing unit, cause the program to execute the method 100 for determining a travel trajectory 316 for a vehicle 305 and/or the method 200 for controlling a vehicle 305.

The computer program product 400 is stored on a storage medium 401 in the embodiment shown. The storage medium 401 can be any storage medium known from the prior art.

Claims (15)

Method (100) for determining a travel trajectory (316) for a vehicle (305), comprising: - Receiving (101) map data of a map representation of an environment of a vehicle (305), the map representation comprising information regarding at least one roadway (301) to be traveled by the vehicle (305); - Receiving (103) data from an occupancy grid of the surroundings of the vehicle (305), the occupancy grid representing at least one object (303) positioned at least partially on the roadway (301); - Determining (105) at least one roadway segment (304) of the roadway (301) to be traveled by the vehicle (305) based on the map data, wherein a roadway segment (304) is a section arranged in front of the vehicle (305) in a direction of travel (D). the roadway (301); - Determine (107) for each roadway segment (304) a plurality of width line segments (311) arranged one after the other at predetermined distances from one another along a longitudinal direction (306) of the roadway (301), a width line segment (311) being one along a width extension of the roadway ( 301) extending line segment is formed, wherein the width line segment (311) between lateral boundaries (302) of the roadway (301) or between a lateral boundary (302) of the roadway (301) and an object (301) positioned at least partially on the roadway (301) 303) or runs between two objects (303) positioned at least partially on the roadway (301), and wherein a length of a width line segment (311) describes a width of the roadway (301) available for the vehicle (305) to travel on; - Reducing (109) a length of each width line segment (311) by at least one width of the vehicle (305), wherein to reduce the length each width line segment at each end of the width line segment (311) is reduced by at least half the width of the vehicle (305); - Determine (111) for each width line segment (311) a support point (313) positioned on the width line segment (311); - Connecting (113) the support points to form a travel trajectory (316); and - Outputting (115) the travel trajectory (316) along the road (301). Procedure (100) according to Claim 1 , each support point (313) being positioned centrally on the respective width line segment (311). Procedure (100) according to Claim 1 or 2 , wherein determining (111) the support points comprises: connecting (117) a first support point (324) positioned on a first width line segment (317) with a second support point (318) positioned on a second width line segment (318) arranged immediately behind the first width line segment (317). Support point (325) via a straight connecting line (329); Determining (119) an intersection of the straight connecting line (329) with a third width line segment (319) arranged immediately behind the second width line segment (318); and positioning (121) a third support point (326) arranged on the third width line segment (319) at the intersection of the straight connecting line (329) with the third width line segment (319) or at a position midway between the intersection and a current position of the third support point (319); or positioning (123) the third support point (326) at an end of the third width line segment (319) if there is no intersection between the straight connecting line (329) and the third width line segment (319); and iteratively (125) executing the above method steps (117, 119, 121, 123). Procedure (100) according to Claim 1 , 2 or 3 , wherein determining (111) the support points comprises: connecting (127) a first support point (324) positioned on a first width line segment (317) with a third support point positioned on a third width line segment (319) arranged behind the first width line segment (317). (326) via a straight connecting line (329); Determining (129) an intersection of the straight connecting line (329) with a second width line segment (318) arranged between the first width line segment (317) and the third width line segment (319); and positioning (131) a second support point (325) arranged on the second width line segment (318) at the intersection of the straight connecting line (329) with the second width line segment (318) or at a position midway between the intersection and a current position of the second support point (325); or positioning (133) the second support point (325) at an end of the second width line segment (318) if there is no intersection between the straight connecting line (329) and the second width line segment (318); and Iteratively (125) performing the preceding steps. Method (100) according to one of the preceding claims, further comprising: reducing (135) the length of a width line segment (311) by a maximum steering angle angle amount, wherein the maximum steering angle angle amount takes into account a maximum steering angle angle of the vehicle (305) that the vehicle (305) without can carry out a collision with a side road boundary (302) of the road (301) and/or with an object (303) positioned at least partially on the road (301); and wherein reducing (135) the length comprises: determining (137) an intersection of a straight connecting line (323) of a first width line segment (317) with a second width line segment (318) arranged immediately behind the first width line segment (317), the straight Connecting line (323) starts from an end point (321) of the first width line segment (317) and has an angle (α ^- ) to the first width line segment (317), the angle (α ^- ) describing the maximum steering angle of the vehicle (305); Determining (139) the intersection of the straight connecting line (323) with the second width line segment (318) as a new end point (322) of the second width line segment (318). Method (100) according to one of the preceding claims, wherein connecting (113) the support points (313) to the travel trajectory (316) comprises: adapting (141) a spline function (314) to the support points (313). Procedure (100) according to Claim 6 , wherein the spline function (314) is designed as a basic spline function with control points. Procedure (100) according to Claim 6 or 7 , wherein adapting (141) the spline function (314) to the support points (313) includes: minimizing (143) the distances of the spline function (314) to the support points (313), so that the spline function (314) has an intersection with each latitude line segment (311); and/or minimizing (145) a curvature of the spline function (314) along a course of the spline function (314); and/or minimizing (147) a derivative of the curvature of the spline function (314) according to a path length of the spline function (314) along the course of the spline function (314). Procedure (100) according to Claim 8 , wherein minimizing (143) distances from the spline function (314) to the support points (313) includes: determining (149) for each latitude line segment (311) a sampling point of the spline function (314) for which the spline function (314) has a value that lies between end points (321) of the width line segment (311); and minimizing (151) a distance of the sample location of the spline function (314) and a perpendicular projection of the sample location onto the latitude line segment (311). Procedure (100) according to Claim 8 and 9 , where the minimization is effected by performing a gradient process. Method (100) according to one of the preceding claims, wherein connecting (113) the support points (311) with the travel trajectory (316) comprises: Determining (153) an end point of the travel trajectory (316) if the width of the vehicle (305) is greater than or equal to the length of a width line segment (311), the end point of the travel trajectory (316) being defined by the support point (313) of the travel direction (313) D) the last width line segment (311) of the vehicle (305) is given, which has a length that is greater than the width of the vehicle. Method (100) according to one of the preceding claims, further comprising: Receiving (155) environment sensor data from at least one environment sensor (307) of the vehicle (305), the environment sensor data depicting the environment of the vehicle (305); and Generating (157) the occupancy grid of the surroundings of the vehicle (305) based on the surroundings sensor data. Method (200) for controlling a vehicle, comprising: executing (201) the method (100) for determining a travel trajectory (316) for a vehicle (305) according to one of the preceding Claims 1 until 12 ; and controlling (203) the vehicle (305) along the calculated travel trajectory (316). Computing unit (309), which is set up, the method (100) for determining a travel trajectory (316) for a vehicle (305) according to one of the above Claims 1 until 12 and/or the method for controlling a vehicle (301). Claim 13 to carry out. Computer program product (400) comprising commands which, when the program is executed by a data processing unit, cause it to carry out the method (100) for determining a travel trajectory for a vehicle according to one of the preceding Claims 1 until 12 and/or the method for controlling a vehicle (301). Claim 13 to carry out.

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