DE102022205090A1 - Method for planning a trajectory - Google Patents

Abstract

The invention relates to a method for planning a trajectory for a driving maneuver of a vehicle based on a search space that limits the duration of the trajectory, the search space being based on the current kinematic state of the vehicle, the kinematic state of the vehicle to be achieved and at least one further boundary parameter of the driving maneuver is determined.

Description

The invention relates to a method for planning a trajectory for a driving maneuver of a vehicle, in which a driving situation-dependent search space, which relates to the duration of the trajectory, is first determined and several trajectories are calculated within the search space, one of which is based on a selection criterion is selected to carry out the driving maneuver.

Methods for planning a trajectory from a starting state to a final state are already known in the prior art. In the known methods, a search interval for the trajectory duration is defined before trajectory planning. Several trajectories that have different trajectory durations are then calculated in the search interval. After the trajectories have been calculated, it is checked which trajectories can be driven without collision and the trajectory that has the lowest costs (costs in terms of driving comfort and/or other specified goals) is selected.

The problem with the known planning methods is that the search space is determined in a very unspecific manner. In the search space, a large number of the calculated trajectories do not meet the specified boundary conditions, so that they have to be rejected later. This means that a large number of impermissible trajectories are calculated, which leads to ineffective use of the available computing resources.

Based on this, it is the object of the invention to provide a method for planning a trajectory of a vehicle, which enables a permissible trajectory to be calculated in a computationally efficient manner.

The task is solved by a method with the features of independent patent claim 1. Preferred embodiments are the subject of the subclaims. A driver assistance system for planning a trajectory of a vehicle is the subject of independent claim 15.

• Zunächst wird ein am Ende der Trajektorie zu erreichender kinematischer Zielzustand des Fahrzeugs empfangen oder berechnet. Der kinematische Zielzustand ist zumindest durch eine erste und eine zweite kinematische Größe des Fahrzeugs definiert, wobei die zweite kinematische Größe die zeitliche Ableitung der ersten kinematischen Größe ist. Der kinematische Zielzustand kann beispielsweise den Abstand zu einem stationären oder bewegten Zielobjekt (beispielsweise einem vorausfahrenden Fahrzeug) angeben, an dem sich das Fahrzeug nach Durchfahren der Trajektorie befinden soll. Zudem kann der kinematische Zielzustand die Geschwindigkeit angeben, die das Fahrzeug im kinematischen Zielzustand haben soll.

According to a first aspect, the invention relates to a method for planning a trajectory for a driving maneuver of a vehicle. The procedure includes the following steps:

• First, a kinematic target state of the vehicle to be achieved at the end of the trajectory is received or calculated. The kinematic target state is defined at least by a first and a second kinematic quantity of the vehicle, the second kinematic quantity being the time derivative of the first kinematic quantity. The kinematic target state can, for example, indicate the distance to a stationary or moving target object (for example a vehicle in front) at which the vehicle should be after traveling through the trajectory. In addition, the kinematic target state can indicate the speed that the vehicle should have in the kinematic target state.

A minimum time duration of a trajectory is then determined which, based on the current kinematic state of the vehicle, also referred to as the kinematic start state, is necessary to reach the kinematic target state of the vehicle. The kinematic target state is in particular a time-variant state. The minimum time period can be the time period that is at least required to reach the kinematic target state, taking into account the physical boundary conditions and the current driving situation. The minimum time period is determined based on the first and second kinematic quantities and at least one maximum value and at least one minimum value of a third kinematic quantity, the third kinematic quantity being the time derivative of the second kinematic quantity.

A search space for the duration of the trajectory to be planned is then determined based on the minimum duration of the trajectory. The search space specifies an interval for the duration of the trajectory to be planned. The previously determined minimum duration of the trajectory specifies the lower limit of the search space or interval.

After determining the search space, several different values of time durations of trajectories within the search space are determined.

A trajectory is then calculated for the determined values of time durations of trajectories. This creates a set of trajectories with different time durations that lie in the search space.

Finally, the trajectories are compared with each other and a trajectory is selected based on at least one selection criterion. Preferably, a driving process is then carried out at least temporarily based on the selected trajectory.

The technical advantage of the method according to the invention is that an effective determination of the search space is possible by calculating a minimum time duration of the search space. As a result, the search space can be determined depending on the kinematic starting state and the kinematic target state of the ego vehicle in such a way that it is adapted very specifically to the respective driving situation - without a separate application. This minimizes the computational effort required to calculate a suitable trajectory, as the probability of determining unsuitable trajectories is reduced.

According to an exemplary embodiment, the first kinematic quantity is the distance to a target position of the vehicle to be reached, the second kinematic quantity is the speed of the vehicle relative to an surrounding object and the third kinematic quantity is the longitudinal acceleration of the vehicle relative to an surrounding object. A relative speed and/or relative acceleration is preferably used as a second and/or third kinematic variable when the target position to be reached is itself a moving position, for example a position selected at a certain distance from a vehicle in front (e.g. when controlling the vehicle by an adaptive cruise control). This means that the method can be used to plan trajectories in which the kinematic target state is determined by a distance, for example to an object in front, the speed and the acceleration.

According to one exemplary embodiment, the first kinematic variable is the lateral offset of the vehicle to a target line to be reached that runs in the direction of travel, the second kinematic variable is the lateral speed of the vehicle and the third kinematic variable is the lateral acceleration of the vehicle. This means that the method can be used to plan lateral trajectories. It is understood that the method can also be used to plan trajectories in which the vehicle is to be controlled to a kinematic target state, which is defined by target parameters specified in the longitudinal and transverse directions. In the case of lateral vehicle control, a relative coordinate system in the form of a Frenet coordinate system can be used.

According to one exemplary embodiment, the first kinematic quantity is the longitudinal speed of the vehicle, the second kinematic quantity is the longitudinal acceleration of the vehicle and the third kinematic quantity is the longitudinal jerk of the vehicle. This means that the method can be used to plan trajectories that do not depend on an environmental object, for example a vehicle in front, but are used, for example, only for trajectory planning when using a cruise control system without being restricted by a vehicle in front.

According to one embodiment, the target state is time-variant and defined by the origin of a relative coordinate system. An example of a time-variant state is when the ego vehicle is supposed to use the trajectory to reach a specific position that moves along with an environmental object (for example a third-party vehicle).

According to one exemplary embodiment, the minimum duration of the trajectory is determined by the vehicle being moved in a first sub-area of the trajectory, first taking into account a maximum value of the third kinematic variable, and in a subsequent second sub-area of the trajectory taking into account a minimum value of the third kinematic variable. The third kinematic variable can be, for example, the longitudinal acceleration of the vehicle relative to an environmental object. This results in a theoretically possible minimum duration of the trajectory, using the maximum value and the minimum value of the third kinematic quantity. The minimum duration of the trajectory can, for example, be determined in the manner described above if the ego vehicle is currently slower than in the kinematic target state to be achieved.

According to one exemplary embodiment, the minimum duration of the trajectory is determined by the vehicle in a first sub-area of the trajectory initially taking into account a minimum value of the third kinematic variable and in a subsequent second sub-area of the trajectory rie is moved taking into account a maximum value of the third kinematic variable. The third kinematic variable can in turn be, for example, the longitudinal acceleration of the vehicle relative to an environmental object. This results in a theoretically possible minimum duration of the trajectory, using the maximum value and the minimum value of the third kinematic quantity. The minimum duration of the trajectory can, for example, be determined in the manner described above if the ego vehicle is currently faster than in the kinematic target state to be achieved.

According to one exemplary embodiment, a maximum value for the second kinematic variable is provided. The minimum duration of the trajectory is calculated taking into account the maximum value of the second kinematic quantity. This allows speed limitations to be taken into account when calculating the minimum trajectory duration.

According to one embodiment, a maximum value and a minimum value are provided for a fourth kinematic quantity, the fourth kinematic quantity being the time derivative of the third kinematic quantity. The minimum duration of the trajectory is calculated taking into account the maximum value and/or the minimum value of the fourth kinematic quantity. The fourth kinematic variable can in particular be the longitudinal jerk and/or the transverse jerk of the vehicle. The maximum value can define a positive threshold value and the minimum value can define a negative threshold value for the longitudinal jerk and/or transverse jerk. By taking into account the maximum value and/or the minimum value of the fourth kinematic variable, when calculating the minimum trajectory duration, it can be taken into account that, for reasons of comfort, an immediate switch from a maximum longitudinal or lateral acceleration to a minimum longitudinal or lateral acceleration or vice versa is not possible, but rather Limitations of longitudinal and/or transverse jerk must be observed. This enables a more realistic determination of the minimum duration of the trajectory.

According to one embodiment, the upper limit of the search space is determined based on the minimum duration of the trajectory and a predetermined length of the search space. This means that the search spaces each have the same length, regardless of the driving situation.

According to one embodiment, the upper limit of the search space is determined based on the length of time in which an environmental object is temporarily in the travel corridor. The environmental object can, for example, cross the driving corridor of the ego vehicle. This means that the environmental object is only relevant for trajectory planning for a limited time. The upper limit of the search space, i.e. the maximum time period of the trajectory to be planned, can be selected such that it corresponds to the time period in which the environmental object is in the travel corridor of the ego vehicle.

Alternatively, with iterative trajectory calculation, the upper limit of the search space can be determined based on the minimum duration of the trajectory and the last determined trajectory duration. This allows the length of the search space to be determined based on the previously obtained results of the trajectory calculation.

According to one exemplary embodiment, the time durations based on which the trajectories are calculated are selected to be uniformly distributed at least at times in the search space. This applies in particular when planning a trajectory that takes into account for the first time a kinematic target state to be achieved or an environmental object that influences the kinematic target state. This means that the trajectories cover the search space evenly.

According to one exemplary embodiment, the trajectory of the vehicle is iteratively recalculated, with the recalculation of the trajectory resulting in a changed discretization or distribution of the time durations in the search space, in such a way that the distance between the time durations in a first area of the search space is increased by a time period that is one assigned to the trajectory selected in a previous iteration step is chosen narrower than outside this first area of the search space. Due to the uneven distribution of the trajectory durations in the search space depending on the duration of the selected trajectory of the previous iteration step, a trajectory that is advantageous for the driving maneuver can be found more quickly and efficiently. The uneven distribution of the trajectory durations in the search space also has the advantage that the absolute length of the search space plays a subordinate role, since even with a generous design of the search space length, support points in the area of the relevant trajectory duration are preferably selected.

According to one exemplary embodiment, the at least one selection criterion is based on the maximum longitudinal jerk of the vehicle in the direction of travel, the lateral jerk of the vehicle and/or the jerk integral of the vehicle movement predetermined by the trajectory. This makes it possible, for example, to obtain a trajectory that is optimized for comfort. Alternatively, other criteria, for example the trajectory duration, can also be used to select a trajectory.

According to one embodiment, the trajectories are trajectories described by a polynomial function. This allows the trajectories to be calculated with reduced computational effort.

According to another exemplary embodiment, the trajectories are determined by a numerical optimization method.

• - Empfangen oder berechnen eines am Ende der Trajektorie zu erreichenden kinematischen Zielzustands des Fahrzeugs, der zumindest durch eine erste und eine zweite kinematische Größe des Fahrzeugs definiert ist, wobei die zweite kinematische Größe die zeitliche Ableitung der ersten kinematischen Größe ist;
• - Bestimmen einer minimalen Zeitdauer einer Trajektorie, die ausgehend vom aktuellen kinematischen Zustand des Fahrzeugs zum Erreichen des kinematischen Zielzustands des Fahrzeugs nötig ist, basierend auf der ersten und zweiten kinematischen Größe und zumindest einem Maximalwert und zumindest einem Minimalwert einer dritten kinematischen Größe, wobei die dritte kinematische Größe die zeitliche Ableitung der zweiten kinematischen Größe ist;
• - Bestimmen eines Suchraums für die Zeitdauer der zu planenden Trajektorie basierend auf der minimalen Zeitdauer der Trajektorie;
• - Ermitteln mehrerer unterschiedlicher Werte von Zeitdauern von Trajektorien innerhalb des Suchraums;
• - Berechnen der Trajektorien zu den ermittelten Werten von Zeitdauern von Trajektorien;
• - Vergleichen der Trajektorien untereinander und Auswählen einer Trajektorie basierend auf zumindest einem Auswahlkriterium.

According to a further aspect, the invention relates to a driver assistance system for planning a trajectory for a driving maneuver of a vehicle. The driver assistance system includes at least one computing unit. The at least one computing unit is configured to carry out the following steps:

• - receiving or calculating a kinematic target state of the vehicle to be achieved at the end of the trajectory, which is defined at least by a first and a second kinematic quantity of the vehicle, the second kinematic quantity being the time derivative of the first kinematic quantity;
• - Determining a minimum time period of a trajectory that is necessary, based on the current kinematic state of the vehicle, to reach the target kinematic state of the vehicle, based on the first and second kinematic quantities and at least one maximum value and at least one minimum value of a third kinematic quantity, the third kinematic quantity is the time derivative of the second kinematic quantity;
• - determining a search space for the duration of the trajectory to be planned based on the minimum duration of the trajectory;
• - Determining several different values of time durations of trajectories within the search space;
• - Calculating the trajectories based on the determined values of time durations of trajectories;
• - Comparing the trajectories with each other and selecting a trajectory based on at least one selection criterion.

Further developments, advantages and possible applications of the invention also emerge from the following description of exemplary embodiments and from the figures. All described and/or illustrated features, individually or in any combination, are fundamentally the subject of the invention, regardless of their summary in the claims or their relationship. The content of the claims is also made part of the description.

• 1 beispielhaft eine schematische Darstellung einer Fahrsituation eines Fahrzeugs, für die eine Trajektorie geplant werden soll;
• 2 beispielhaft ein Weg-Geschwindigkeitsdiagramm, das die kinematischen Zusammenhänge zum Erreichen eines kinematischen Zielzustands verdeutlicht;
• 3 beispielhaft ein Weg-Geschwindigkeitsdiagramm, das die kinematischen Abläufe eines Fahrzeugs, die ausgehend von einem kinematischen Startzustand zur Erreichung eines kinematischen Zielzustands basierend auf einer Trajektorie mit minimaler Trajektorienzeitdauer vollzogen werden, verdeutlicht;
• 4 beispielhaft ein Weg-Geschwindigkeitsdiagramm ähnlich dem der 3, wobei die maximal erreichbare Geschwindigkeit sowie der maximale Ruck beim Übergang von der maximalen Beschleunigung zur minimalen Beschleunigung begrenzt sind;
• 5 beispielhaft der Beschleunigungsverlauf zu den kinematischen Abläufen gemäß 4;
• 6 beispielhaft die Darstellung eines Suchraums, der durch die minimale Trajektorienzeitdauer t_min und die maximale Trajektorienzeitdauer t_max definiert ist, wobei der Stern die Trajektorienzeitdauer der ausgewählten Trajektorie des vorherigen Iterationsschritts und die Punkte die nicht-äquidistante Diskretisierung des Suchraums illustrieren.
• 7 beispielhaft die kinematischen Abläufe eines Fahrzeugs während einer Geschwindigkeitsregelung (cruise control), die ausgehend von einem auf den kinematischen Zielzustand bezogenen kinematischen Startzustand S zur Erreichung des kinematischen Zielzustands Z basierend auf einer Trajektorie mit minimaler Trajektorienzeitdauer vollzogen werden und bei denen ein oberes Beschleunigungslimit Anwendung findet;
• 8 beispielhaft die kinematischen Abläufe eines Fahrzeugs während einer Geschwindigkeitsregelung ähnlich der 7, wobei kein Beschleunigungslimit Anwendung findet;
• 9 beispielhaft und schematisch die Veranschaulichung eines lateralen Fahrmanövers in Form eines Spurwechsels, bei dem ebenfalls das beschriebene Verfahren zur Anwendung kommen kann; und
• 10 beispielhaft ein Blockdiagramm, das die Verfahrensschritte des Verfahrens zur Planung einer Trajektorie für ein Fahrmanöver eines Fahrzeugs veranschaulicht.

The invention is explained in more detail below using the figures and exemplary embodiments. Show it:

• 1 By way of example, a schematic representation of a driving situation of a vehicle for which a trajectory is to be planned;
• 2 an example of a path-velocity diagram that illustrates the kinematic relationships for achieving a kinematic target state;
• 3 by way of example, a path-velocity diagram that clarifies the kinematic processes of a vehicle that are carried out starting from a kinematic starting state to achieve a kinematic target state based on a trajectory with a minimum trajectory duration;
• 4 For example, a path-velocity diagram similar to that of 3 , where the maximum achievable speed and the maximum jerk are limited during the transition from maximum acceleration to minimum acceleration;
• 5 For example, the acceleration curve for the kinematic processes according to 4 ;
• 6 For example, the representation of a search space that is defined by the minimum trajectory time period t _min and the maximum trajectory time period t _max , where the star represents the trajectory time period selected trajectory of the previous iteration step and the points illustrate the non-equidistant discretization of the search space.
• 7 For example, the kinematic processes of a vehicle during cruise control, which are carried out starting from a kinematic starting state S related to the kinematic target state to achieve the kinematic target state Z based on a trajectory with a minimum trajectory duration and in which an upper acceleration limit is applied;
• 8th For example, the kinematic processes of a vehicle during speed control similar to this 7 , where no acceleration limit applies;
• 9 an exemplary and schematic illustration of a lateral driving maneuver in the form of a lane change, in which the method described can also be used; and
• 10 By way of example, a block diagram that illustrates the procedural steps of the method for planning a trajectory for a driving maneuver of a vehicle.

1 shows, by way of example and schematically, a driving situation in which a vehicle 1 moves along a trajectory planned by a driver assistance system of the vehicle 1 in a direction of travel FR. The vehicle 1 travels through a driving route FS.

The trajectory planned by the driver assistance system determines the kinematic states of the vehicle 1 along the route that is traveled based on the trajectory. The trajectory has in particular a kinematic target state Z and a kinematic starting state S. The kinematic target state Z is defined, for example, as the origin of a relative coordinate system. The kinematic target state can, for example, indicate the position, the speed and the acceleration of the vehicle 1 at the end of the trajectory relative to an object surrounding the vehicle. The position, speed and acceleration can relate to the longitudinal and/or transverse direction. The kinematic starting state S can indicate the position, the speed and the acceleration of the vehicle 1 at the start of the trajectory relative to the kinematic target state Z. The position, speed and acceleration can in turn relate to the longitudinal and/or transverse direction.

The vehicle 1 has a sensor system 3 which is designed to record environmental information. The sensor system 3 can, for example, include at least one radar sensor, ultrasonic sensors, at least one camera and/or at least one LIDAR sensor. Furthermore, the vehicle 1 has at least one computing unit R, which is designed to assess the surrounding information and to make driving decisions.

In the exemplary embodiment shown, the surrounding object 2, in the case shown a third vehicle, is located in front of the vehicle 1 in the same lane. The environmental object 2 can move itself. Deviating from the exemplary embodiment shown, the environmental object 2 can only be present temporarily in the travel path FS of the vehicle, for example crossing the travel path.

The computing unit R of the vehicle 1 is preferably configured to determine the kinematics of the surrounding object 2 and, for example, to predict the trajectory of the object 2. This allows the ego trajectory of the vehicle 1 to be calculated taking into account the movement of the surrounding object 2.

In known methods for trajectory planning, it is necessary to define a search space for the duration of the trajectory to be determined. A method is described below that makes it possible to advantageously limit the search space for the trajectory duration, so that the number of trajectories to be calculated and thus the computational effort in determining a drivable trajectory that also fulfills at least one predetermined selection criterion is reduced.

The search space SR for the duration of a trajectory has a minimum duration t _min and a maximum duration t _max . The method first determines the minimum time period t _min based on the kinematic starting state S of the vehicle 1 and the kinematic target state Z of the vehicle 1. In addition, when calculating the minimum time period t _min , boundary conditions of the kinematics of the vehicle 1, such as the maximum permissible longitudinal - and/or lateral acceleration and/or the maximum permissible longitudinal or lateral jerk is taken into account.

2 shows a diagram that clarifies the kinematic relationships for achieving a kinematic target state Z. In the 2 The distance between the current position of the vehicle 1 (position at the kinematic starting state S) and the target position (position of the vehicle at the kinematic target state Z) is shown in the horizontal direction. In the vertical direction is in 2 the speed of the vehicle 1 is plotted relative to the speed at the kinematic target state Z.

In general, the minimum time period t _min to achieve the kinematic target state can also be made taking into account other kinematic variables, namely a first kinematic variable and a second kinematic variable, where the second kinematic variable is the time derivative of the first kinematic variable.

The kinematic target state Z can refer to a stationary target position or to a target position that moves itself, for example due to the movement of a vehicle in front, as shown in 1 is shown.

Kinematic states in the first and fourth quadrants of the coordinate system in 2 have a first kinematic size that is above the first kinematic size of the target state Z. Accordingly, the second and third quadrants include kinematic states whose first kinematic magnitude is below the first kinematic magnitude of the target state Z.

Kinematic states in the first and second quadrants of the coordinate system in 2 have a second kinematic size that is above the second kinematic size of the target state Z. Accordingly, the third and fourth quadrants of the coordinate system include kinematic states whose second kinematic magnitude is below the second kinematic magnitude of the target state Z.

The curved lines drawn in the second and fourth quadrants of the coordinate system refer to kinematic boundary conditions that must be taken into account when planning the trajectory. In general, the kinematic boundary conditions include a maximum value and a minimum value of a third kinematic quantity. The third kinematic quantity is the time derivative of the second kinematic quantity.

In the exemplary embodiment 2 the curved, dashed line in the second quadrant refers to the minimum longitudinal acceleration of the vehicle 1, where the minimum longitudinal acceleration can be a relative longitudinal acceleration (relative to a moving surrounding object 2). In an analogous manner, the curved, dotted line in the fourth quadrant refers to the maximum longitudinal acceleration of the vehicle 1, where the maximum longitudinal acceleration can be a relative longitudinal acceleration (relative to a moving surrounding object 2). It should be noted that due to the relative coordinate system originating in the target state, it is also possible, depending on the driving situation, for both the minimum and maximum longitudinal acceleration to lie in the same quadrant.

3 illustrates in a simplified representation, by way of example, the kinematic processes of the vehicle 1, which are carried out starting from a kinematic starting state S to achieve the kinematic target state Z based on a trajectory with a minimum trajectory time duration. The kinematic processes are illustrated by the solid line.

The kinematic starting state S is characterized in that the vehicle 1 is currently further away from the target position ZP than desired in the kinematic target state Z and that the vehicle 1 currently has a lower speed than desired in the kinematic target state Z.

The kinematic target state Z can be achieved in a minimum of time by initially accelerating the vehicle 1 with the maximum permissible acceleration, starting from the kinematic starting state S. This increases the speed of the vehicle 1 and the current kinematic state moves in the direction of 3 marked switching point at which the minimum acceleration curve is reached. When this switching point is reached, the vehicle is braked with minimum acceleration, ie with the maximum possible deceleration. This means that the current kinematic state follows the in 2 drawn curve with minimal acceleration until the kinematic target state Z is reached.

wobei $v_u=\sqrt{a_{min}\cdot \frac{v_0^2-2\cdot a_{max}\cdot s_0}{a_{min}-a_{max}}}$

und wobei s₀ der Abstand des Fahrzeugs zur Zielposition, v_u die Geschwindigkeit des Fahrzeugs am Umschaltpunkt und v₀ die Relativgeschwindigkeit des Fahrzeugs jeweils zum Beginn der Trajektorie sind und wobei a_min und a_max die minimale und die maximale Relativbeschleunigung des Fahrzeugs 1 relativ zum kinematischen Zielzustand (beispielsweise einem bewegten Umgebungsobjekt 2) sind.The minimum time period t _min can be in the in 3 The driving scenario shown, ie the kinematic starting state S is below the S-shaped curve, can be calculated as follows: $$t_{min}=\frac{v_u-v_0}{a_{max}}+\frac{0-v_u}{a_{min}};$$

where $v_u=\sqrt{a_{min}\cdot \frac{{\mathrm{<figure-callout\; id="0"\; label="v"\; filenames="DE102022205090A1\_0023.png"\; state="\{\{state\}\}">v</figure-callout>}}_0^2-2\cdot a_{max}\cdot s_0}{a_{min}-a_{max}}}$

and where s ₀ is the distance of the vehicle to the target position, v _u is the speed of the vehicle at the switching point and v ₀ is the relative speed of the vehicle at the start of the trajectory and where a _min and a _max are the minimum and maximum relative acceleration of the vehicle 1 relative to the kinematic target state (for example a moving environmental object 2).

If the kinematic starting state S is above the S-shaped curve, the minimum trajectory duration is determined based on the inverse processes in order to achieve the kinematic target state Z based on a trajectory with a minimum trajectory duration. This means that a trajectory is determined for the vehicle 1, in which the vehicle 1 is first decelerated to the maximum until the curve with maximum acceleration is reached (dotted line) and then the vehicle 1 is accelerated with the maximum permissible acceleration until the kinematic target state Z is reached.

wobei $v_u=\sqrt{a_{max}\cdot \frac{v_0^2-2\cdot a_{min}\cdot s_0}{a_{max}-a_{min}}}$

und
wobei wiederum s₀ der Abstand des Fahrzeugs zur Zielposition und v₀ die Relativgeschwindigkeit des Fahrzeugs jeweils zum Beginn der Trajektorie sind, wobei a_min und a_max die minimale und die maximale Relativbeschleunigung des Fahrzeugs 1 relativ zum kinematischen Zielzustand (beispielsweise einem bewegten Umgebungsobjekt 2) und wobei v_u die Geschwindigkeit des Fahrzeugs am Umschaltpunkt sind.If the kinematic starting state S is above the S-shaped curve, the minimum time period t _min can be calculated as follows: $$t_{min}=\frac{v_u-v_0}{a_{min}}+\frac{0-v_u}{a_{max}};$$

where $v_u=\sqrt{a_{max}\cdot \frac{{\mathrm{<figure-callout\; id="0"\; label="v"\; filenames="DE102022205090A1\_0023.png"\; state="\{\{state\}\}">v</figure-callout>}}_0^2-2\cdot a_{min}\cdot s_0}{a_{max}-a_{min}}}$

and
where again s ₀ is the distance of the vehicle to the target position and v ₀ is the relative speed of the vehicle at the start of the trajectory, where a _min and a _max are the minimum and maximum relative acceleration of the vehicle 1 relative to the kinematic target state (for example a moving environmental object 2) and where v _u is the speed of the vehicle at the switching point.

It is understood that a sudden change from maximum acceleration to maximum deceleration of the vehicle 1 leads to an infinitely high longitudinal jerk, which is not physically possible and is therefore only assumed for simplified calculation. In order to carry out the calculation of the minimum trajectory duration t _min on a more realistic basis, a maximum and a minimum value of a fourth kinematic quantity can be used. The fourth kinematic quantity is the time derivative of the third kinematic quantity. The fourth kinematic variable can in particular be the longitudinal jerk or the transverse jerk of the vehicle 1.

4 shows a representation similar to this 3 , but with the difference that due to a limitation of the maximum speed to the value v _max and the limitation of the longitudinal jerk, there is no abrupt transition at the switching point, as is the case with 3 the case is. 5 shows the course of acceleration a over time t for the kinematic processes as shown in 4 . It can be seen that the time course of the acceleration is not rectangular, that is, the edges on which the acceleration changes are not vertical, but rather the edges have a predetermined slope that corresponds to the maximum permissible longitudinal jerk of the vehicle 1. Taking limitations of the fourth kinematic variable, in particular the longitudinal jerk, into account leads to a more realistic determination of the minimum trajectory duration t _min .

After determining the minimum time duration of the trajectory t _min , the search space SR for the trajectory durations can be determined, ie the search space of trajectory durations in which several trajectories are calculated in order to select one of these calculated trajectories based on at least one selection criterion.

The search space SR can include a predetermined time period, ie the maximum time period of the trajectory t _max is calculated by adding the predetermined time period to the minimum time period of the trajectory t _min .

Alternatively, the upper limit of the search space SR, ie the maximum time period of the trajectory t _max , can be determined by the time period in which an environmental object 2 is actually relevant for the trajectory calculation. The environmental object 2 can, for example, be an object that is temporarily in the driving route FS and leaves it again after a certain period of time. The surrounding object 2 can, for example, be a third vehicle crossing the route of the vehicle 1.

After defining the search space, several trajectories each with a different trajectory duration, which lie in the search space SR, are calculated.

After calculating several different trajectories of the vehicle 1 with different trajectory durations, these trajectories are compared with one another. After comparing the trajectories, one of the calculated trajectories is selected based on a selection criterion. The vehicle 1 is then moved at least over a certain distance based on this selected trajectory.

For example, the maximum longitudinal jerk of the vehicle 1 and/or the jerk integral can be used as a selection criterion. A combination of these criteria for selecting the travel trajectory is also possible.

wobei s₀ der Abstand des Fahrzeugs zur Zielposition, wobei a_min und a_max die minimale und die maximale Relativbeschleunigung des Fahrzeugs 1 relativ zum kinematischen Zielzustand (beispielsweise einem bewegten Umgebungsobjekt 2) und j_min und j_max die untere und obere Schwelle des Längsrucks sind und wobei: $$v_0=v_s+\frac{a_{max}^2-a_s^2}{2j_{max}}$$

$$v_3=\frac{a_{min}^2}{2j_{max}}$$

$$v_2=\frac{a_{min}\left(a_{min}-a_{max}\right)}{2j_{min}}+\sqrt{\frac{a_{min}}{a_{min}-a_{max}}\left[v_0^2-2a_{max}{s}_0+\frac{a_{max}{a}_{min}^3}{12j_{max}^2}-\frac{{\left(a_{min}-a_{max}\right)}^3{a}_{max}}{12j_{min}^2}\right]}$$

$$v_1=v_2-\frac{a_{min}^2-a_{max}^2}{2j_{min}}.$$

Für den Fall, dass der kinematische Startzustand S oberhalb der S-förmigen Kurve liegt, wird die minimale Zeitdauer t_min unter Berücksichtigung von Begrenzungen des Längsrucks wie folgt berechnet: $$t_{min}=\frac{a_{min}-a_s}{j_{min}}+\frac{v_1-v_0}{a_{min}}+\frac{a_{max}-a_{min}}{j_{max}}+\frac{v_3-v_2}{a_{max}}-\frac{a_{max}}{j_{min}}$$

wobei s₀ der Abstand des Fahrzeugs zur Zielposition, wobei a_min und a_max die minimale und die maximale Relativbeschleunigung des Fahrzeugs 1 relativ zum kinematischen Zielzustand (beispielsweise einem bewegten Umgebungsobjekt 2) und j_min und j_max die untere und obere Schwelle des Längsrucks sind und wobei: $$v_0=v_s+\frac{a_{min}^2-a_s^2}{2j_{min}}$$

$$v_3=\frac{a_{max}^2}{2j_{min}}$$

$$v_2=\frac{a_{max}\left(a_{max}-a_{min}\right)}{2j_{max}}-\sqrt{\frac{a_{max}}{a_{max}-a_{min}}\left[v_0^2-2a_{min}{s}_0+\frac{a_{min}{a}_{max}^3}{12j_{min}^2}-\frac{{\left(a_{max}-a_{min}\right)}^3{a}_{min}}{12j_{max}^2}\right]}$$

$$v_1=v_2-\frac{a_{max}^2-a_{min}^2}{2j_{max}}.$$

The calculation of the minimum time period t _min taking into account limitations of the longitudinal jerk can be calculated as follows in the case that the kinematic starting state S is below the S-shaped curve: $$t_{min}=\frac{a_{max}-a_s}{j_{max}}+\frac{{\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="DE102022205090A1\_0021.png"\; state="\{\{state\}\}">v</figure-callout>}}_1-v_0}{a_{max}}+\frac{a_{min}-a_{max}}{j_{min}}+\frac{{\mathrm{<figure-callout\; id="3"\; label="v"\; filenames="DE102022205090A1\_0021.png"\; state="\{\{state\}\}">v</figure-callout>}}_3-v_2}{a_{min}}-\frac{a_{min}}{j_{max}}$$

where s ₀ is the distance of the vehicle to the target position, where a _min and a _max are the minimum and maximum relative acceleration of the vehicle 1 relative to the kinematic target state (for example a moving environmental object 2) and j _min and j _max are the lower and upper thresholds of the longitudinal jerk and where: $${\mathrm{<figure-callout\; id="0"\; label="v"\; filenames="DE102022205090A1\_0023.png"\; state="\{\{state\}\}">v</figure-callout>}}_0=v_s+\frac{a_{ma\mathrm{<figure-callout\; id="2"\; label="x"\; filenames="DE102022205090A1\_0021.png"\; state="\{\{state\}\}">x</figure-callout>}}^2-a_{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="DE102022205090A1\_0021.png"\; state="\{\{state\}\}">s</figure-callout>}}^2}{2j_{max}}$$

$${\mathrm{<figure-callout\; id="3"\; label="v"\; filenames="DE102022205090A1\_0021.png"\; state="\{\{state\}\}">v</figure-callout>}}_3=\frac{a_{min}^2}{2j_{max}}$$

$${\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="DE102022205090A1\_0021.png"\; state="\{\{state\}\}">v</figure-callout>}}_2=\frac{a_{min}\left(a_{min}-a_{max}\right)}{2j_{min}}+\sqrt{\frac{a_{min}}{a_{min}-a_{max}}\left[{\mathrm{<figure-callout\; id="0"\; label="v"\; filenames="DE102022205090A1\_0023.png"\; state="\{\{state\}\}">v</figure-callout>}}_0^2-2a_{ma\mathrm{<figure-callout\; id="0"\; label="x\; s"\; filenames="DE102022205090A1\_0023.png"\; state="\{\{state\}\}">x</figure-callout>}}{s}_{}{}_0+\frac{a_{max}{a}_{min}^3}{12j_{ma\mathrm{<figure-callout\; id="2"\; label="x"\; filenames="DE102022205090A1\_0021.png"\; state="\{\{state\}\}">x</figure-callout>}}^2}-\frac{{\left(a_{min}-a_{max}\right)}^3{a}_{max}}{12j_{min}^2}\right]}$$

$${\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="DE102022205090A1\_0021.png"\; state="\{\{state\}\}">v</figure-callout>}}_1={\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="DE102022205090A1\_0021.png"\; state="\{\{state\}\}">v</figure-callout>}}_2-\frac{a_{min}^2-a_{ma\mathrm{<figure-callout\; id="2"\; label="x"\; filenames="DE102022205090A1\_0021.png"\; state="\{\{state\}\}">x</figure-callout>}}^2}{2j_{min}}.$$

In the event that the kinematic starting state S is above the S-shaped curve, the minimum time period t _min is calculated as follows, taking into account limitations of the longitudinal jerk: $$t_{min}=\frac{a_{min}-a_s}{j_{min}}+\frac{{\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="DE102022205090A1\_0021.png"\; state="\{\{state\}\}">v</figure-callout>}}_1-v_0}{a_{min}}+\frac{a_{max}-a_{min}}{j_{max}}+\frac{{\mathrm{<figure-callout\; id="3"\; label="v"\; filenames="DE102022205090A1\_0021.png"\; state="\{\{state\}\}">v</figure-callout>}}_3-v_2}{a_{max}}-\frac{a_{max}}{j_{min}}$$

where s ₀ is the distance of the vehicle to the target position, where a _min and a _max are the minimum and maximum relative acceleration of the vehicle 1 relative to the kinematic target state (for example a moving environmental object 2) and j _min and j _max are the lower and upper thresholds of the longitudinal jerk and where: $${\mathrm{<figure-callout\; id="0"\; label="v"\; filenames="DE102022205090A1\_0023.png"\; state="\{\{state\}\}">v</figure-callout>}}_0=v_s+\frac{a_{min}^2-a_{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="DE102022205090A1\_0021.png"\; state="\{\{state\}\}">s</figure-callout>}}^2}{2j_{min}}$$

$${\mathrm{<figure-callout\; id="3"\; label="v"\; filenames="DE102022205090A1\_0021.png"\; state="\{\{state\}\}">v</figure-callout>}}_3=\frac{a_{ma\mathrm{<figure-callout\; id="2"\; label="x"\; filenames="DE102022205090A1\_0021.png"\; state="\{\{state\}\}">x</figure-callout>}}^2}{2j_{min}}$$

$${\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="DE102022205090A1\_0021.png"\; state="\{\{state\}\}">v</figure-callout>}}_2=\frac{a_{max}\left(a_{max}-a_{min}\right)}{2j_{max}}-\sqrt{\frac{a_{max}}{a_{max}-a_{min}}\left[{\mathrm{<figure-callout\; id="0"\; label="v"\; filenames="DE102022205090A1\_0023.png"\; state="\{\{state\}\}">v</figure-callout>}}_0^2-2a_{min}{s}_0+\frac{a_{min}{a}_{max}^3}{12j_{min}^2}-\frac{{\left(a_{max}-a_{min}\right)}^3{a}_{min}}{12j_{max}^2}\right]}$$

$${\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="DE102022205090A1\_0021.png"\; state="\{\{state\}\}">v</figure-callout>}}_1={\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="DE102022205090A1\_0021.png"\; state="\{\{state\}\}">v</figure-callout>}}_2-\frac{a_{ma\mathrm{<figure-callout\; id="2"\; label="x"\; filenames="DE102022205090A1\_0021.png"\; state="\{\{state\}\}">x</figure-callout>}}^2-a_{min}^2}{2j_{max}}.$$

The method is preferably carried out iteratively in several successive iteration cycles. Preferably, in a first iteration step of the method, the trajectories are calculated based on a uniform discretization of the search space SR. This means that the distances between the successive discrete values of the trajectory duration are the same.

After the first iteration step, the trajectory of the vehicle 1 is preferably iteratively recalculated. During this recalculation of the trajectory, the search space SR cannot be discretized equidistantly, as in 6 is shown. In particular, the discretization can be chosen narrower in a range that is close to the trajectory duration of the vehicle 1, which was selected in the previous iteration step (indicated by the star), than in a range that is further away from this trajectory duration. The points in 6 illustrate the non-equidistant discretization.

7 and 8th illustrate by way of example the kinematic processes of a vehicle 1 during cruise control, which are carried out starting from a kinematic starting state S to achieve the kinematic target state Z based on a trajectory with a minimum trajectory duration. The kinematic processes are illustrated by the solid line.

The essential difference is that the kinematic starting state S and the kinematic target state Z of the vehicle 1 are determined by the parameters first kinematic variable speed v, the second kinematic variable acceleration a and a maximum and minimum value of a third kinematic variable, namely the longitudinal jerk j .

The limitation of the longitudinal jerk j leads to the 7 and 8th drawn S-shaped curves, whereby the curve section located in the second quadrant results from the lower limit (minimum) of the longitudinal jerk and the curve section located in the fourth quadrant results from the upper limit (maximum value) of the longitudinal jerk.

7 shows the case that the specified maximum acceleration a _max is reached before the curve specified by the limitation of the longitudinal jerk has been reached in the second quadrant. This results in two switching points S1 and S2.

In this case, the minimum trajectory duration t _min can be determined in such a way that it is assumed that the vehicle is accelerated from the kinematic starting state S based on the maximum longitudinal jerk up to the maximum acceleration a _max (first switching point S1), then this maximum acceleration a _max is maintained until the second switching point S2 is reached, and then the vehicle 1 reaches the kinematic target state Z with the minimum longitudinal jerk.

wobei

• v₀: Geschwindigkeit des Fahrzeugs am kinematischen Startzustand S;
• a₀: Beschleunigung des Fahrzeugs am kinematischen Startzustand S;
• a_max: maximal zulässige Beschleunigung des Fahrzeugs;
• j_min: minimal zulässiger Längsruck des Fahrzeugs;
• j_max: maximal zulässiger Längsruck des Fahrzeugs.

In this case, the minimum trajectory time duration t _min can be calculated as follows: $$t_{min}=\frac{a_{max}}{2j_{max}}-\frac{a_{max}}{2j_{min}}+\frac{a_0^2}{2j_{max}{a}_{max}}-\frac{a_0}{j_{max}}-\frac{v_0}{a_{max}};$$

where

• v ₀ : speed of the vehicle at the kinematic starting state S;
• a ₀ : Acceleration of the vehicle at the kinematic starting state S;
• a _max : maximum permissible acceleration of the vehicle;
• j _min : minimum permissible longitudinal jerk of the vehicle;
• j _max : maximum permissible longitudinal jerk of the vehicle.

8th illustrates the case in which the maximum permissible acceleration a _max of the vehicle 1 is not reached before the curve of the minimum longitudinal jerk of the vehicle in the second quadrant has been reached. In this case there is only a single switching point, similar to this 3 .

wobei $v_u=\sqrt{j_{min}\cdot \frac{a_0^2-2\cdot j_{max}\cdot v_0}{j_{min}-j_{max}}}$

wobei v₀ die Geschwindigkeit und a₀ die Beschleunigung des Fahrzeugs 1 zum Startzeitpunkt, a_u die Beschleunigung des Fahrzeugs im Schaltpunkt und j_min und j_max der minimal und der maximal zulässige Längsruck des Fahrzeugs 1 sind.In this case, the minimum trajectory time duration t _min can be calculated as follows: $$t_{min}=\frac{a_u-a_0}{j_{max}}-\frac{a_u}{j_{min}};$$

where $v_u=\sqrt{j_{min}\cdot \frac{a_0^2-2\cdot j_{max}\cdot v_0}{j_{min}-j_{max}}}$

where v ₀ is the speed and a ₀ is the acceleration of vehicle 1 at the starting time, a _u is the acceleration of the vehicle at the switching point and j _min and j _max are the minimum and maximum permissible longitudinal jerk of vehicle 1.

7 and 8th each show an initial situation in which the kinematic starting states S lie below the S-shaped curve, which relates to the minimum or maximum permissible longitudinal jerk of the vehicle.

In the event that the kinematic starting states S are above the S-shaped curve and the maximum permissible acceleration a _max of the vehicle 1 is reached before the S-shaped curve of the minimum or maximum longitudinal jerk of the vehicle has been reached, the minimum trajectory time duration t _min can be calculated as follows: $$t_{min}=\frac{a_{min}}{2j_{min}}-\frac{a_{min}}{2j_{max}}+\frac{a_0^2}{2j_{min}{a}_{min}}-\frac{a_0}{j_{min}}-\frac{v_0}{a_{min}}$$

wobei $v_u=\sqrt{j_{max}\cdot \frac{a_0^2-2\cdot j_{min}\cdot v_0}{j_{max}-j_{min}}.}$

In the event that the kinematic starting states S are above the S-shaped curve and the maximum permissible acceleration a _max of the vehicle 1 is not reached before the S-shaped curve of the minimum or maximum longitudinal jerk of the vehicle has been reached, the minimum Trajectory time duration t _min can be calculated as follows: $$t_{min}=\frac{a_u-a_0}{j_{min}}-\frac{a_u}{j_{max}};$$

where $v_u=\sqrt{j_{max}\cdot \frac{a_0^2-2\cdot j_{min}\cdot v_0}{j_{max}-j_{min}}.}$

9 shows an exemplary embodiment in which the previously described method is applied to the lateral guidance of the vehicle 1.

The main difference to the aforementioned exemplary embodiments is that the method is used to carry out trajectory planning in the transverse direction instead of or in addition to trajectory planning in the longitudinal direction. The first kinematic variable is preferably the lateral offset to the target position ZP to be achieved, the second kinematic variable is preferably the lateral speed and the third kinematic variable is preferably the lateral acceleration of the vehicle 1.

In the exemplary embodiment, for example, a lane change is carried out from a first lane to a second lane. In this exemplary embodiment, too, the kinematic states of the vehicle 1 are carried out in relation to the kinematic target state Z to be achieved by the trajectory, in such a way that the kinematic states of the vehicle 1 are measured, for example, in relation to a Frenet reference frame, the origin of which the kinematic target state Z of vehicle 1 is. In the exemplary embodiment shown, the first coordinate (x _frenet ) is oriented in the longitudinal direction (ie parallel to the lane boundary) and the second coordinate (y _frenet ) is oriented in the transverse direction (ie perpendicular to the lane boundary).

10 shows a schematic block diagram that illustrates the processes of the method for planning a trajectory for a driving maneuver of a vehicle 1.

First, a kinematic target state of the vehicle to be achieved at the end of the trajectory is received or calculated. This is defined at least by a first and a second kinematic quantity of the vehicle, the second quantity being the time derivative of the first quantity.

A minimum time duration of a trajectory is then determined which, based on the current kinematic state of the vehicle, is necessary to reach the target kinematic state of the vehicle. The determination of the minimum time period is based on the first and second kinematic quantities and at least one maximum value and at least one minimum value of a third quantity, the third quantity being the time derivative of the second quantity (S11).

A search space for the duration of the trajectory to be planned is then determined based on the minimum duration of the trajectory (S12).

Within this search space, several different values of time durations of trajectories are then determined (S13). Trajectories are subsequently calculated for these determined values of time durations of trajectories (S14).

Finally, the trajectories are compared with each other and a trajectory is selected based on at least one selection criterion (S15).

The invention has been described above using exemplary embodiments. It is understood that numerous changes and modifications are possible without departing from the scope of protection defined by the patent claims.

Reference symbol list

1

vehicle

2

Environment object

3

Sensors

FR

Direction of travel

FS

Driving tube

R

Computer unit

s

Distance

S

kinematic starting state

S.R

Search space

Z

kinematic target state

ZP

Target position

Claims (15)

Method for planning a trajectory for a driving maneuver of a vehicle (1), the method comprising the following steps: - receiving or calculating a kinematic target state (Z) of the vehicle (1) to be achieved at the end of the trajectory, which is at least through a first and a second kinematic quantity of the vehicle (1) is defined, the second kinematic quantity being the time derivative of the first kinematic quantity (S10); - Determining a minimum time period (t _min ) of a trajectory that is necessary, based on the current kinematic state (S) of the vehicle (1), to reach the kinematic target state (Z) of the vehicle (1). is, based on the first and second kinematic quantities and at least a maximum value and at least a minimum value of a third kinematic quantity, the third kinematic quantity being the time derivative of the second kinematic quantity (S11); - Determining a search space (SR) for the duration of the trajectory to be planned based on the minimum duration (t _min ) of the trajectory (S12); - Determining several different values of time durations of trajectories within the search space (SR) (S13); - Calculating the trajectories based on the determined values of time durations of trajectories (S14); - Comparing the trajectories with each other and selecting a trajectory based on at least one selection criterion (S15). Procedure according to Claim 1 , characterized in that the first kinematic variable is the distance (s) to a target position (ZP) to be reached of the vehicle (1), the second kinematic variable is the speed of the vehicle (1) relative to an environmental object (2) and the third kinematic Size that is the longitudinal acceleration of the vehicle (1) relative to an environmental object (2). Procedure according to Claim 1 , characterized in that the first kinematic quantity is the lateral offset of the vehicle (1) to a target line running in the direction of travel, the second kinematic quantity is the lateral speed of the vehicle (1) and the third kinematic quantity is the lateral acceleration of the vehicle (1). Procedure according to Claim 1 , characterized in that the first kinematic quantity is the longitudinal speed of the vehicle (1), the second kinematic quantity is the longitudinal acceleration of the vehicle (1) and the third kinematic quantity is the longitudinal jerk of the vehicle (1). Method according to one of the preceding claims, characterized in that the target state (Z) is time-variant and is defined by means of a relative coordinate system. Method according to one of the preceding claims, characterized in that the minimum duration of the trajectory (t _min ) is determined by the vehicle (1) in a first sub-area of the trajectory initially taking into account a maximum value of the third kinematic variable and in a subsequent one second portion of the trajectory is moved taking into account a minimum value of the third kinematic variable. Method according to one of the preceding claims, characterized in that the minimum duration of the trajectory (t _min ) is determined by the vehicle in a first sub-area of the trajectory initially taking into account a minimum value of the third kinematic variable and in a subsequent second sub-area of the Trajectory is moved taking into account a maximum value of the third kinematic variable. Method according to one of the preceding claims, characterized in that a maximum value for the second kinematic quantity is provided and that the calculation of the minimum duration of the trajectory (t _min ) takes place taking into account the maximum value of the second kinematic quantity. Method according to one of the preceding claims, characterized in that a maximum value and a minimum value are provided for a fourth kinematic quantity, the fourth kinematic quantity being the time derivative of the third kinematic quantity and that the calculation of the minimum duration of the trajectory (t _min ) taking into account the maximum value and / or the minimum value of the fourth kinematic variable. Procedure according to Claim 9 , characterized in that the fourth kinematic quantity is the longitudinal jerk and/or the transverse jerk of the vehicle (1). Method according to one of the preceding claims, characterized in that the upper limit of the search space (SR) is determined based on the minimum duration of the trajectory (t _min ) and a predetermined length of the search space (SR). Procedure according to one of the Claims 1 until 10 , characterized in that the upper limit of the search space (SR) is determined based on the period of time in which an environmental object (2) is temporarily in the travel corridor, or that in an iterative trajectory calculation, the upper limit of the search space (SR) is determined based on the minimum duration of the trajectory (t _min ) and the last determined trajectory duration. Method according to one of the preceding claims, characterized in that the time durations based on which the trajectories are calculated are chosen to be uniformly distributed at least at times in the search space (SR). Method according to one of the preceding claims, characterized in that the trajectory of the vehicle (1) is iteratively recalculated, such that when the trajectory is recalculated, a changed discretization or distribution of the time durations in the search space (SR) takes place, in such a way that the distance the time durations in a first area of the search space (SR) are chosen to be narrower than outside this first area of the search space (SR) by a time period that is assigned to a trajectory selected in a previous iteration step. Driver assistance system for planning a trajectory for a driving maneuver of a vehicle (1), comprising at least one computing unit (R), wherein the at least one computing unit (R) is configured to carry out the following steps: - receiving or calculating a at the end of the trajectory kinematic target state (Z) of the vehicle (1) to be achieved, which is defined at least by a first and a second kinematic quantity of the vehicle (1), the second kinematic quantity being the time derivative of the first kinematic quantity; - Determining a minimum time duration of a trajectory (t _min ) that is necessary, starting from the current kinematic state (S) of the vehicle (1), to reach the kinematic target state (Z) of the vehicle (1), based on the first and second kinematic variables and at least one maximum value and at least one minimum value of a third kinematic quantity, the third kinematic quantity being the time derivative of the second kinematic quantity; - Determining a search space (SR) for the duration of the trajectory to be planned based on the minimum duration of the trajectory (t _min ); - Determining several different values of time durations of trajectories within the search space (SR); - Calculating the trajectories based on the determined values of time durations of trajectories; - Comparing the trajectories with each other and selecting a trajectory based on at least one selection criterion.

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