Reduced-effort trajectory planning for a vehicle

Abstract

Method (400) for determining a trajectory (112) for a driving maneuver of a vehicle (100), wherein the method (400) comprises, - Determining (401) an approximate end time for the end of the driving maneuver, wherein the approximate end time is determined by determining a preliminary trajectory based on a trajectory shape having reduced complexity compared to a trajectory shape of the trajectory to be determined; - Determining a target end state of the vehicle (100), wherein the target end state comprises a lateral positioning of the vehicle (100) at the end of the driving maneuver; - Limiting (402) a search space (121, 122) to determine the trajectory (112) depending on the approximated end time and the target end state; - Determining (403) the trajectory (112) using the limited search space (121, 122); and - Controlling and / or regulating the lateral and / or longitudinal guidance of the vehicle (100) depending on the determined trajectory (112).

Description

[0001] The invention relates to a method and a corresponding device for determining a trajectory for controlling and / or regulating the lateral / longitudinal guidance of a vehicle during a driving maneuver.

[0002] The realization of partially or highly automated driving operation for vehicles (especially road vehicles) is being pursued both in research and increasingly in the automotive industry. A key aspect of partially or highly automated driving operation is planning the most optimal trajectory possible for the vehicle, thereby avoiding collisions with other road users. Determining such a trajectory (e.g., an evasive trajectory) involves a high level of computational effort, which is typically not possible or only possible to a limited extent with the control units in a vehicle.

[0003] German patent application DE 10 2008 016 377 A1 proposes a method for operating a motor vehicle in which the driver's steering action during an evasive maneuver is supported to avoid a collision. In this method, when an imminent collision between the motor vehicle and an obstacle is detected, and when the driver initiates an evasive maneuver, the steering torque is adjusted to support evasive action along a determined trajectory, provided that the collision can be avoided by such evasive action.

[0004] DE 10 2012 203 187 A1 describes a method for predicting and adapting the motion trajectories of a motor vehicle to support the driver in their driving task and / or to prevent a collision or mitigate the consequences of an accident. The method involves creating an intersection of situationally necessary motion trajectories, determined using environmental sensors, and physically possible motion trajectories. These physically possible motion trajectories result from the vehicle's dynamic properties and the coefficient of friction between the tires and the road surface, up to a maximum possible limit coefficient of friction. Only motion trajectories within this intersection are considered.

[0005] German patent application DE 10 2014 215 244 A1 describes a method and a corresponding device for determining a target trajectory for controlling the lateral / longitudinal guidance of a vehicle. In particular, a method is described which includes the detection of one or more objects in the vehicle's environment based on environmental data. Furthermore, the method includes performing global planning to determine a multitude of potentially possible driving maneuvers based on the one or more detected objects, as well as selecting one driving maneuver from this multitude. The method also includes performing local planning to determine a target trajectory for the longitudinal and / or lateral guidance of the vehicle for the selected driving maneuver.

[0006] This document addresses the technical challenge of determining the most optimal trajectory for a vehicle with reduced computational effort. In particular, the computational effort should be reduced to such an extent that trajectory planning can be implemented on the vehicle's control unit.

[0007] The problem is solved by the independent claims. Advantageous embodiments are described, among other things, in the dependent claims.

[0008] According to one aspect, a method for determining a trajectory for a driving maneuver of a vehicle (in particular a road vehicle) is described. The driving maneuver typically involves the longitudinal and / or lateral control of the vehicle. The method can, for example, be executed on a control unit of the vehicle. The determined trajectory can be used to provide automatic assistance to the driver of the vehicle with regard to the longitudinal and / or lateral control of the vehicle. In particular, depending on the determined trajectory, a steering input for the vehicle's electronic power steering and / or a deceleration input for the vehicle's braking system and / or a input for the vehicle's propulsion system can be determined and, if necessary, controlled.

[0009] The procedure involves determining an approximate end time for the completion of a driving maneuver. Specifically, it can determine the approximate time the vehicle will need to execute the maneuver. The approximate end time can be determined based on a vehicle model that is less complex than the vehicle model used to determine the trajectory. In other words, to determine the approximate end time, a preliminary trajectory can be calculated, described by a preliminary polynomial with an order lower than that of the polynomial used to describe the trajectory to be determined.In other words, to determine the approximate end time, a preliminary trajectory can be calculated based on a trajectory shape that has reduced complexity compared to the trajectory shape of the trajectory to be determined. The approximate end time can thus be determined with a moderate computational effort.

[0010] The procedure further includes limiting a search space to determine the trajectory depending on the approximated end time. In particular, the search space for determining the trajectory for the driving maneuver can be limited to a specific region around the approximated end time. For example, the search space can be limited to a region of 10% of the approximated end time around the approximated end time.

[0011] Furthermore, the procedure includes determining the trajectory using the limited search space. This trajectory determination can be restricted to the limited search space and, in particular, to end times within that space.

[0012] This method allows the trajectory of a driving maneuver to be determined with reduced computational effort. This is particularly true for driving maneuvers with a relatively long time horizon (i.e., with relatively high possible values ​​for an end time).

[0013] Determining an approximate end time can involve determining a target state variable, particularly an average target state variable, for the vehicle during the maneuver. In other words, a (possibly average) target value for the behavior of a state variable during the maneuver can be determined. Specifically, a target acceleration can be determined that the vehicle should exhibit (possibly on average) during the maneuver, or should not fall below or exceed (possibly on average). The approximate end time can then be determined as a function of the (possibly average) target state variable. In particular, it can be determined what the duration of the maneuver would be if the vehicle exhibited the target state variable (especially the target acceleration) during the maneuver (possibly on average). In this way, the approximate end time can be determined precisely and efficiently.

[0014] The driving maneuver may involve accelerating or decelerating the vehicle in the longitudinal direction. The approximate end time can then depend on an initial velocity at the beginning of the driving maneuver and a final velocity at the end of the driving maneuver. In particular, the approximate end time t̂ f of the driving maneuver as |s˙ziel−s˙(0)|s¨m to be determined, where ṡ ziel the final velocity is, ṡ(0) the initial velocity is and s̈ m The average target longitudinal acceleration is given by the above formula. This formula applies particularly when describing a preliminary trajectory with a second-order polynomial.

[0015] Alternatively or additionally, the maneuver may involve moving the vehicle laterally (i.e., a distance from a reference position). In this case, the approximate end time may depend on an initial movement at the beginning of the maneuver and an end movement at the end of the maneuver. In particular, the approximate end time t̂ f of the driving maneuver as t^f=2|dziel−d(0)|d¨m to be determined, where d̈ m where d(0) is the mean target lateral acceleration, d(0) is the initial position, and d ziel The final storage location is the formula above. This formula applies particularly when describing a preliminary trajectory with a second-order polynomial.

[0016] The procedure further includes determining an approximate final state or a target final state of the vehicle at the end of the driving maneuver. This approximate final state or target final state includes, in particular, the vehicle's lateral position at the end of the maneuver and—optionally—its speed at the end of the maneuver. The search space for determining the trajectory is also limited depending on the approximate final state or target final state, for example, to a limited area (e.g., 10%) around the approximate final state or target final state. This further reduces the computational effort required to determine a trajectory. The approximate final state or target final state can be specified by a driver assistance function (e.g., as a lane to be achieved with the driving maneuver or as a driving speed to be achieved with the driving maneuver).

[0017] Determining a trajectory can involve identifying a multitude of possible trajectories for the driving maneuver. These possible trajectories are limited to the restricted search space. By identifying a large number of different possible trajectories, it can be ensured that the most optimal trajectory (e.g., optimal with regard to collision avoidance, comfort, and / or sportiness) can be determined. The trajectory can then be selected from the multitude of possible trajectories.

[0018] Determining a possible trajectory for a driving maneuver can involve determining initial values ​​for a multitude of vehicle state variables at an initial point in time of the possible trajectory. These state variables can include the vehicle's position, velocity, acceleration, and / or jerk. The initial values ​​can be derived from the vehicle's current state. Furthermore, final values ​​can be determined for these state variables at an end point in time of the possible trajectory. These final values ​​can be at least partially predetermined by the driving maneuver. The possible trajectory can also be determined based on the initial values, the final values, the end point, and a polynomial of order 5, 6, 7, or higher. To account for jerk in the initial and final values, at least a 7th-order polynomial is required.

[0019] Order is required. The position of the vehicle along the possible trajectory can be determined using the polynomial. The coefficients of the polynomial can be calculated based on the initial and final values.

[0020] Furthermore, values ​​for a selection parameter can be determined for one or more of the multitude of possible trajectories. The selection parameter can depend on a target state to be achieved, a target time, and / or the acceleration or jerk profile during the maneuver. The trajectory can then be selected based on the selection parameter. This ensures that the selected trajectory fulfills predefined objectives (e.g., a predetermined target state).

[0021] According to another aspect, a device for determining a trajectory for a vehicle maneuver is described. The device is configured to determine an approximate end time for the end of the maneuver. Furthermore, the device is configured to define a search space for determining the trajectory based on this approximate end time. Finally, the device is configured to determine the trajectory using this defined search space.

[0022] According to another aspect, a vehicle (in particular a road motor vehicle such as a passenger car, a truck or a motorcycle) is described that includes the device described in this document for determining a trajectory for a driving maneuver of the vehicle.

[0023] Another aspect described is a software (SW) program. The SW program can be configured to run on a processor (e.g., on a vehicle's control unit) and thereby execute the procedure described in this document.

[0024] Another aspect describes a storage medium. This storage medium can include a software program configured to run on a processor and thereby execute the procedure described in this document.

[0025] It should be noted that the methods, devices, and systems described in this document can be used both alone and in combination with other methods, devices, and systems described in this document. Furthermore, any aspect of the methods, devices, and systems described in this document can be combined with one another in a variety of ways. In particular, the features of the claims can be combined with one another in a variety of ways.

[0026] The invention will now be described in more detail using exemplary embodiments. Fig. 1 an exemplary traffic situation that requires the planning of a trajectory to carry out a driving maneuver; Fig. 2. A flowchart of an exemplary procedure for determining a trajectory; Fig. 3 exemplary coordinates for trajectory planning; and Fig. 4. A flowchart of an exemplary procedure for determining a trajectory with reduced computational effort.

[0027] As stated at the outset, this document addresses the technical task of reducing the computational effort required to determine the trajectory of a vehicle (also referred to as an ego-vehicle). In this context, it shows Fig. 1. An exemplary traffic situation. The ego-vehicle 100 is driving on a multi-lane road 101. A vehicle 103 in the same lane of road 101 ahead of the ego-vehicle 100 may be traveling at a relatively low speed. The ego-vehicle 100 then has the option, for example, of performing an overtaking maneuver and changing lanes along a trajectory 112 to overtake vehicle 102. A collision with other vehicles 102 must be avoided.

[0028] To carry out the in Fig. In the overtaking maneuver shown in Figure 1, a control unit of the ego vehicle 100 can determine a trajectory 112 that satisfies one or more boundary conditions. When determining a trajectory 112, vehicle dynamics aspects can be taken into account. In particular, depending on one or more vehicle parameters and / or depending on the current driving situation, a trajectory 112 can be determined that can realistically be driven by the vehicle 100. For example, the Kamm circle for the vehicle 100 can be considered in the current driving situation. Furthermore, a curvature that can be implemented by the vehicle 100 can be taken into account. Other examples of vehicle parameters that can be considered are acceleration or deceleration of the vehicle 100 (implementable in the current driving situation).

[0029] Furthermore, a trajectory 112 is typically determined in such a way that a collision with the detected objects 102 in the vicinity of the ego-vehicle 100 can be avoided. For example, a collision probability can be determined for a multitude of possible trajectories 112, and the possible trajectory 112 with the lowest collision probability can be selected as the trajectory 112 with which the driving maneuver is carried out.

[0030] The trajectory 112 thus determined can then be transferred to one or more controllers for the lateral / longitudinal guidance of the vehicle 100. In particular, a path control controller can be used to ensure that the vehicle 100 travels along the determined trajectory 112. Furthermore, a vehicle control controller can ensure that the necessary braking / acceleration / steering torques are applied. Separating the longitudinal / lateral guidance control into a path control controller and a vehicle control controller is advantageous because, due to this separation, a relatively simple model of the vehicle 100 can be used within the path control controller, thus making the control of the vehicle 100's guidance along the determined trajectory 112 more robust and stable.

[0031] Fig. Figure 2 shows a flowchart of an exemplary method 200 for determining a trajectory 112 for a vehicle 100. The determination of a trajectory 112 is preferably carried out in a straightened coordinate system, relative to a road alignment. The method 200 can therefore include the step of transforming state data or values ​​of state variables of the vehicle 100 (such as the position of the vehicle 100, a yaw angle of the vehicle 100 and / or a steering angle of the vehicle 100) from a Cartesian coordinate system into a (straightened) Frenet coordinate system.

[0032] The straightening is exemplified in Fig. Figure 3 illustrates this. For the curvature correction, measurement signals regarding the state of vehicle 100 are transformed into a lane coordinate system. The trajectory planning itself therefore does not take place in a Cartesian coordinate system 301, but in a Frenet coordinate system. The Frenet coordinate system is described with respect to a reference curve 300 (e.g., the center of a lane of a road). The vehicle position is thus described by the variables s(t) 303 in the longitudinal direction and d(t) 302 in the lateral direction. ṡ(t) and d(t) describe the longitudinal and lateral velocities, and s̈(t) and s̈(t) describe the accelerations. Both the vehicle's own motion and the other road users to be considered are taken into account in the Frenet coordinate system. Intuitively, this transformation corresponds to the curvature correction of the coordinate system 301 and thus allows the separate optimization of the longitudinal and lateral motion of vehicle 100.

[0033] Determining a trajectory 112 while considering physical, technical, and comfort-related boundary conditions results in an optimization problem with constraints. Due to strict boundary conditions (such as vehicle dynamics limitations, actuator limitations, and collision avoidance), the resulting optimization problem exhibits both equational and inequalities. This makes solving the optimization problem complex, especially when the number and nature of the constraints change. This can occur particularly due to the varying requirements of different driver assistance functions.

[0034] To ensure the convergence of the optimization and to determine the global optimum, the convexity of the optimization problem typically needs to be proven, which is usually not possible due to the existing constraints. Therefore, the optimization would have to be performed with different initial conditions to ultimately achieve the best result. Furthermore, when applying an optimization algorithm, the maximum number of iterations and thus the required computation time is difficult to estimate, which can lead to substantial problems for a control unit (i.e., a control system) of a vehicle 100, which is supposed to calculate trajectories 112 in real time.

[0035] For the reasons mentioned above, an alternative solution to the optimization problem is used below, which exploits the structure of the entire optimization problem and the knowledge about the limited number of possible solutions. This allows for a significant reduction in computational effort.

[0036] The lateral and longitudinal motion of a vehicle 100 can be described as an optimal control problem with output s(t) = x1(t) (in the case of longitudinal planning) or d(t) = x1(t) (in the case of lateral planning) of an integrator system (i.e., a vehicle model). Here, x1(t) is a first state variable of the vehicle 100, which describes the position of the vehicle 100 (in the longitudinal or lateral direction). The jerk can serve as the input of the integrator system. x1(3) (t) (i.e. the 3 te The derivative of the state variable x1(t) is defined. However, in this document, the derivative of the jerk is used as the input. x1(4) (t) (i.e. the 4 te The derivative of the state variable x1(t) is used. This allows, as shown below, the use of 7th-order polynomials as an approach. In particular, this increases the number of degrees of freedom (e.g., the number of boundary conditions), which is especially advantageous with regard to the lateral guidance of vehicle 100.

[0037] The integrator system can be defined as follows: x˙=[0100001000010000]x+

[0001] u where the input variable u is the derivative of the jerk x1(4)(t) This corresponds to the state of a vehicle100 at a specific time t, which can be described by the state vector x. T = [x1, x z , x3, x4] where x2(t) = ẋ1(t), x3(t) = ẋ2(t) and x4(t) = ẋ3(t) .

[0038] It can be shown that the state vector x(t) is given by x(t)=[1tt2t3012t3t20026t0006]︸=:M1(t)c0123+[t4t5t6t74t35t46t57t612t220t330t442t524t60t2120t3210t4]︸=:M2(t)c4567

[0039] The above equations describe a 7th order polynomial with respect to the spatial course x1 (t).

[0040] The following performance functional can be used to solve the optimization problem based on a 7th order polynomial: J=12∫0tf(x(4)(t))2dt+k1(xref−x1)2+k2tf

[0041] The parameters c 0123 T = [c0, c1, c2, c3] are calculated from the initial conditions x(0) = x0 of trajectory 112 at time t = 0 as c0123=M1−1(0)x0

[0042] The parameters c 4567 T = [c4, c5, c6, c7] are calculated from the final conditions x(t f ) of trajectory 112 at time t = t f as c4567=M2−1(tf)(x(tf)−M1(tf)c0123)

[0043] The end conditions can be specified, as in the formula above. Alternatively, a reference curve can be described by x. ref = [x 1,ref , x 2,ref , x 3,ref , x 4,ref ] T The optimization goal in this case is to get as close as possible to this reference curve. In this case, the parameters c 4367 T as follows: c4567=M3(tf)−1(xref−M1(tf)c0123) with M3(tf)=M2(tf)−(0005040k2000000000000).

[0044] The optimization problem now consists of determining both the end time or the end point t. f as well as, if applicable, the final state x(t f ) to determine an optimal trajectory 112. In particular, the optimization problem aims to determine the final time t. f and the position of vehicle 100 at the end time t f , i.e., x1(t f), or the speed of the vehicle 100 at the final time t f , dh ẋ1(t f ). will be determined.

[0045] To calculate a transverse trajectory, 7th-order polynomials can be chosen to specify the 3rd derivative of trajectory 112 at its beginning and end. In particular, this allows for a much more precise specification of the steering angle at the beginning and end of trajectory 112. The desired endpoint of trajectory 112 can be a target area d. ziel a specified range, for example, indicating an area on an adjacent lane (as in Fig. 1 shown). This target area can, for example, be the desired final position of the final state x(t). f ) be determined with x1(t f ) = d ziel .

[0046] The following function can be used as a selection criterion or as a quality criterion for determining a trajectory 112 for the lateral guidance of the vehicle 100: Jquer=12∫0tf(d(4)(t))2dt+kq1(dtarget−d(tf))2+kq2tf

[0047] The first expression evaluates the development of the derivative of the jerk along trajectory 112. The second expression evaluates the deviation of the final position d(t). f ) from the target position d ziel Furthermore, the third expression evaluates the time length of trajectory 112. This is determined using the weighting factors k. q1 and k q2 The characteristics of trajectory 112 can be weighted.

[0048] Longitudinal planning can be carried out in a similar manner. However, it has been shown that a 4th or 5th order polynomial is sufficient for longitudinal planning. Furthermore, combined longitudinal and transverse planning can be achieved by combining (e.g., summing) the selection parameters for transverse and longitudinal guidance. For longitudinal planning, the following selection parameter or quality parameter, for example, can be used. Jlong=12∫0tf(s(4)(t))2dt+kl1(sziel−s(tf))2+kl2tf, especially if a specific target position s ziel The desired outcome is to be achieved. Alternatively, the selection criterion or quality criterion can be used. Jlong=12∫0tf(s(4)(t))2dt+kl1(s˙ziel−s˙(tf))2+kl2tf, especially when a certain target speed ṡ ziel to be achieved.

[0049] To determine an optimal trajectory 112, the selection measure J can be used for different values ​​of t. f and / or for different final states x(t f The above formulas can be used for this calculation. This results in a curve for the selection measure J, where a minimum value of the selection measure J represents the optimal value for time t. f and / or for the final state x(t f ). In a further step, one or more constraints can then be taken into account.

[0050] The constraints can therefore be considered after the optimization process. To do this, the best trajectory 112, as defined by the cost functional J (i.e., the selection measure), can be chosen and checked for compliance with the constraints. If the constraints are met, trajectory 112 is implemented. Otherwise, the next best trajectory 112 is selected and checked for compliance with the constraints. This procedure is repeated until an optimal solution is found that satisfies the constraints.

[0051] Constraints such as actuator and vehicle dynamics limitations can be considered. Furthermore, collision avoidance with predicted object trajectories of other objects / vehicles can be taken into account.

[0052] The Fig. The two illustrated methods 200 for determining a trajectory 112 for the longitudinal and / or lateral guidance of a vehicle 100 thus comprise the determination 201 of initial values ​​or initial conditions x(0) = x0 for a plurality of state variables x of the vehicle 100. The plurality of state variables includes a position x1(t) of the vehicle 100, a velocity ẋ1(t) of the vehicle 100, an acceleration ẍ1(t) of the vehicle 100, and a jerk. x1(3)(t) of the vehicle 100. This includes x1(3)(t) the third derivative of the position x1(t) of vehicle 100.

[0053] Procedure 200 also includes determining 202 final values ​​x(t). f ) at a final time t f for the multitude of state variables x of the vehicle 100. In addition, the procedure 200 includes the determination 203 of a trajectory 112 based on the initial values ​​x(0) = x0, the final values ​​x(t) f ), the end time t fand based on a polynomial of 5th, 7th, or higher / lower order. The polynomial of 5th, 7th, or higher / lower order can determine the position x1(t) of vehicle 100 as a function of time t between the initial position x1(0) and the final position x1(t). f ) of trajectory 112. To calculate the (state) trajectory x(t) 112, the formulas for c given above can be used. 0123 T , c 4567 T and x(t) are used. In particular, the formula for x(t) describes the position x1(t) of vehicle 100 by a 7th-order polynomial.

[0054] To determine an optimal trajectory 112 (in the sense of a selection measure J), ​​the values ​​of the selection measure J for trajectories 112 with different end times t can be used. f and / or with different final values ​​x(t fThe number of state variables can be determined. The (state) trajectory 112 that optimizes the selection measure J can then be selected. Furthermore, it can be checked whether one or more constraints are met (as explained above).

[0055] The determined trajectory 112 can then be transformed from the Frenet coordinate system back into a Cartesian coordinate system. Furthermore, the determined trajectory 112 can be used to guide the vehicle (e.g., for an evasive maneuver or a parking maneuver).

[0056] As explained above, determining an optimal trajectory 112 requires considering a large number of possible trajectories 112 for different end times t. f and final states x(t f ) can be calculated. This is particularly relevant when determining trajectories 112 with a relatively long planning horizon (i.e., with possible end times t). f, which lie relatively far in the future) result in a high computational effort. It is therefore advantageous, as a first step, to narrow down the possible search space for determining possible trajectories 112.

[0057] The search space can be narrowed down, in particular, by specifying requirements regarding the acceleration ẍ1(t) of vehicle 100. For example, it can be specified that the average acceleration of vehicle 100 during trajectory 112 should not exceed a certain acceleration threshold, or that the average acceleration of vehicle 100 during trajectory 112 should be at a specific acceleration value. With this specification, a requirement for the final time t can be established. f or an approximate end time t̂ f to be determined.

[0058] For example, an approximate end time t̂ f as follows t^f=2|dziel−d(0)|d¨m, where d̈ m the mean lateral acceleration of vehicle 100 along the trajectory 112 to be determined, and where d(0) is the lateral displacement of vehicle 100 at the starting point of trajectory 112 and d ziel This corresponds to the transverse positioning of vehicle 100 at the endpoint of trajectory 112.

[0059] For longitudinal motion, a velocity adjustment from an initial velocity ṡ(0) to a target velocity ṡ can be achieved. ziel a mean longitudinal acceleration s̈ m can be specified. From this, an approximate final time t̂ can then be calculated. f the acceleration maneuver will be determined, t^f=|s˙ziel−s˙(0)|s¨m. It is therefore possible to easily approximate the final time t̂ f can be determined. Furthermore, a final state x(t), e.g., specified by a driver assistance system, can be determined. f ) (especially an end position x1(t) f) and / or a final velocity ẋ1(t f )) as approximate final state or as target final state x̂(t f The trajectory 112 to be determined can then be considered in a search space around the approximate end time t̂. f and around the approximate final state or around the target final state x̂(t f ) around. This is exemplified in Fig. 1 shown. Fig. Figure 1 shows a search area 121 for cross-deposits around an approximate end-deposit d̂ ziel around. Furthermore, it shows Fig. 1. A search range 122 for the end time t f around the approximate end time t̂ faround. It should be noted that the determination of a limited search space described in this document is particularly advantageous when planning a trajectory 112 that has a relatively long planning horizon. This is typically the case when a trajectory 112 is to be determined for a lane change across a large number of lanes.

[0060] Search areas 121 and 122 define a reduced search space in which possible trajectories 112 are searched. This reduces the computational effort required to determine a trajectory 112, especially for trajectories 112 with a relatively long planning horizon.

[0061] Fig.Figure 4 shows a flowchart of an exemplary procedure 400 for determining a trajectory 112 for a driving maneuver of a vehicle 100. The procedure 400 includes determining 401 an approximate end time for the end of the driving maneuver. Furthermore, the procedure 400 includes limiting 402 a search space 121, 122 for determining the trajectory 112 as a function of the approximate end time. Finally, the procedure 400 includes determining 403 the trajectory 112 using the limited search space 121, 122.

[0062] The approximate final time can be determined by using a preliminary polynomial for a preliminary trajectory, where the preliminary polynomial has an order lower than that of the polynomial used for the trajectory 112 to be determined. For example, specifying an average acceleration corresponds to using a second-order polynomial for the preliminary trajectory. Alternatively, the approximate final time can be determined by using a different representation of a preliminary trajectory. This representation has a lower complexity than the representation of the trajectory 112 to be determined.

[0063] The trajectory 112 for the driving maneuver can be determined within the limited search space 121, 122. For this purpose, discrete end times from the limited search space 121, 122 can be considered to determine possible trajectories 112.

[0064] In summary, this substantially reduces the computational effort required to determine a trajectory 112 for a driving maneuver, without substantially compromising the optimality of the determined trajectory 112. This is particularly true for driving maneuvers with a long time horizon (e.g., lane changes across multiple lanes). The reduction in computational effort described in this document enables the timely determination of trajectories on a vehicle control unit 100.

[0065] The present invention is not limited to the embodiments shown. In particular, it should be noted that the description and the figures are intended only to illustrate the principle of the proposed methods, devices, and systems.

Claims

[1] Method (400) for determining a trajectory (112) for a driving maneuver of a vehicle (100), the method (400) comprising - determining (401) an approximate end time for an end of the driving maneuver, wherein, to determine the approximate end time, a preliminary trajectory is determined which is based on a trajectory shape which has a reduced complexity compared to a trajectory shape of the trajectory to be determined; - determining a target end state of the vehicle (100), wherein the target end state comprises a transverse offset of the vehicle (100) at the end of the driving maneuver; - limiting (402) a search space (121, 122) for determining the trajectory (112) as a function of the approximated end time and the target end state; - determining (403) the trajectory (112) using the limited search space (121, 122); and - controlling and / or regulating a transverse and / or longitudinal guidance of the vehicle (100) as a function of the determined trajectory (112). [2] Method (400) according to claim 1, wherein, to determine the approximate end time, a preliminary trajectory is determined which is described by a preliminary polynomial with an order which is smaller than the order of a polynomial which is used to describe the trajectory to be determined. [3] Method (400) according to one of the preceding claims, wherein the target end state further comprises a speed of the vehicle (100) at the end of the driving maneuver. [4] Method (400) according to one of the preceding claims, wherein determining (401) an approximate end time comprises - determining a desired state variable of the vehicle (100) for the driving maneuver, in particular an average desired state variable; and - Determination of the approximate end time depending on the target state variable. [5] Method (400) according to claim 4, wherein the desired state variable comprises a desired acceleration of the vehicle (100) for the driving maneuver, in particular an average desired acceleration of the vehicle (100) during the driving maneuver. [6] Method (400) according to one of the preceding claims, wherein - the driving maneuver comprises an acceleration or deceleration of the vehicle (100) in the longitudinal direction; and - the approximate end time depends on an initial speed at the beginning of the driving manoeuvre and on a final speed at the end of the driving manoeuvre; and / or - the driving maneuver comprises a transverse storage of the vehicle (100); and - the approximate end time depends on an initial offset at the beginning of the driving maneuver and on an end offset at the end of the driving maneuver. [7] Method (400) according to one of the preceding claims, wherein determining (403) the trajectory (112) comprises - determining a plurality of possible trajectories (112) for different end times from the limited search space (121, 122); - determining a selection measure for the plurality of possible trajectories (112); and - selecting a trajectory (112) from the plurality of possible trajectories (112) depending on the selection measure. [8] Method (400) according to claim 7, wherein determining a possible trajectory (112) for the driving maneuver comprises - determining (301) initial values ​​for a plurality of state variables of the vehicle (100); wherein the plurality of state variables include a position (x1(t)) of the vehicle (100), a speed (ẋ1(t)) of the vehicle (100), an acceleration (ẍ1(t)) of the vehicle (100) and / or a jerk (x1(3)(t)) of the vehicle (100); - determining (302) final values ​​at an end time for the plurality of state variables of the vehicle (100); and - Determining (303) the possible trajectory (112) based on the initial values, the final values, the final time and based on a 5th order or higher polynomial. [9] Method (400) according to one of the preceding claims, further comprising determining a steering specification for a power steering system of the vehicle (100) and / or a deceleration specification for a braking system of the vehicle (100) and / or an acceleration specification for a drive of the vehicle (100) as a function of the trajectory (112). [10] Device for determining a trajectory (112) for a driving maneuver which comprises the transverse and / or longitudinal guidance of a vehicle (100), the device being designed - to determine an approximate end time for the end of the driving maneuver, wherein, to determine the approximate end time, a preliminary trajectory is determined which is based on a trajectory shape which has a reduced complexity compared to a trajectory shape of the trajectory to be determined; - to determine a target end state of the vehicle (100), wherein the target end state comprises a transverse offset of the vehicle (100) at the end of the driving maneuver; - to limit a search space (121, 122) for determining the trajectory (112) as a function of the approximated end time and the target end state; - to determine the trajectory (112) using the limited search space (121, 122), and - to control and / or regulate a transverse and / or longitudinal guidance of the vehicle (100) depending on the determined trajectory (112).

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