DE102018204101A1 - Method and device for planning a trajectory for the longitudinal and / or transverse guidance of a vehicle - Google Patents

Abstract

A method (600) for planning a trajectory (112) for a vehicle (100) is described. The method (600) comprises dividing (601) a region for a trajectory (112) into a plurality of partial regions (411, 412, 413) such that in each partial region (411, 412, 413) of the plurality of partial regions (411 , 412, 413) in each case a constant within the respective sub-area (411, 412, 413) amount of secondary conditions with respect to obstacles (101, 102, 103) in an environment of the vehicle (100) applies. In addition, the method (600) includes determining (602) a plurality of different possible length records (420); wherein a length record (420) indicates possible lengths (422) of the subregions (411, 412, 413) of the plurality of subregions (411, 412, 413) along the trajectory (112). The method (600) further comprises determining (603) a trajectory (112) based on the plurality of possible length data sets (420) and considering a quality measure.

Description

The invention relates to a method and a corresponding device with which a trajectory for the at least partially automated longitudinal and / or transverse guidance of a vehicle can be planned.

A central aspect of a partially or highly automated driving operation of a vehicle is the planning of an optimal trajectory of the vehicle by which collisions with other road users are avoided. The determination of such a trajectory (for example, an evasion trajectory, a trajectory for a subsequent journey and / or a trajectory for a lane change) is associated with a high level of computation, which can typically or not be provided by control devices in a vehicle.

One possibility for reducing the computational effort is the separate determination of a longitudinal trajectory for the longitudinal guidance and a transverse trajectory for the transverse guidance. In this case, however, a relatively high computational effort may be required to select a longitudinal and a transverse trajectory for a driving maneuver, which can be driven in collision-free combination by a vehicle.

Among other things, the present document deals with the technical problem of efficiently determining a vehicle-driven, collision-free trajectory for a (possibly combined) longitudinal and / or lateral maneuver. Optionally, safety distances to one or more obstacles should also be defined and taken into account when determining a trajectory.

The object is solved by the independent claims. Advantageous embodiments are described i.a. in the dependent claims. It should be noted that additional features of a claim dependent on an independent claim without the features of the independent claim or only in combination with a subset of the features of the independent claim may form an independent invention independent of the combination of all features of the independent claim, the subject of an independent claim, a divisional application or a subsequent application. This applies equally to technical teachings described in the specification, which may form an independent invention of the features of the independent claims.

In one aspect, a method for determining a trajectory for a vehicle is described. The determined trajectory may be used to provide a driving function (e.g., automated longitudinal and / or lateral guidance of the vehicle). The trajectory determined in the context of the method can be or include a longitudinal trajectory along a direction of travel of the vehicle.

The method comprises dividing the trajectory to be determined into a plurality, in particular into a sequence, of partial regions. In other words, the (temporal and / or local) area or planning horizon for the trajectory to be determined can be subdivided into a plurality of partial areas. The trajectory to be determined typically has a certain planning horizon. The planning horizon can then be divided into different, directly adjacent, subregions (e.g., in 2, 3, 4, 5, or more subregions). In this case, the subdivision into subregions can be carried out in such a way that in each subarea of the plurality of subareas a respective amount of subordinate conditions with respect to obstacles in an environment of the vehicle prevails within the respective subarea. In other words, each of the subareas may be assigned a certain amount of constraints, with zero, one or more constraints to be considered in the particular subarea for determining the trajectory. The one or more obstacles around the vehicle may be other road users (e.g., other vehicles). An obstacle can be fixed or movable.

The vehicle may include one or more environmental sensors (e.g., an image camera, a radar sensor, a LIDAR sensor, an ultrasonic sensor, etc.). Based on the sensor data of the one or more environment sensors, one or more obstacles in the environment of the vehicle can be detected. In particular, the one or more obstacles around the vehicle can be detected, which are to be taken into account when determining the trajectory (for example because the vehicle at least temporarily travels on a lane on which an obstacle is located in the course of the implementation of the trajectory).

It can then be formulated for each detected obstacle one or more constraints that are taken into account in the determination of the trajectory. In particular, for the trajectory to be determined, a total amount of V constraints with respect to corresponding V obstacles can be determined, with V> 0, in particular V = 2, 3, 4 or more. In a lane change, for example, secondary conditions in relation to a front vehicle in front of the vehicle and / or to a rear vehicle behind the vehicle on the starting vehicle may be used. Lane and / or on the destination lane.

The subdivision into subareas can then take place in such a way that a constant subset of the subconditions applies for each subarea, wherein the subset preferably has less than V secondary conditions. The entire trajectory to be determined can thus be subdivided into its sequence of subregions, wherein a constant (each minimally large) subset of subconditions must be taken into account in each subarea. A (partial) set of constraints may include zero, one or more constraints. The zero, one or more secondary conditions for a partial area are typically to be considered for all times or points of the respective partial area. By dividing the planning area for a trajectory into different subareas in such a way, an overall non-convex optimization problem for determining the overall trajectory can be subdivided into a plurality of convex sub-optimization problems for determining trajectory sections in the individual subareas.

The method further comprises determining a plurality of different possible length data sets for the trajectory to be determined. In this case, a length record indicates possible (temporal or possibly local) lengths of the subregions of the plurality of subregions along the trajectory to be determined. The different length data sets can thus have different sequences of subregions, the (temporal or local) lengths of the subregions in the different length data sets being at least partially different. The (temporal or spatial) total length of the different length data sets is typically the same for all length data sets (and may, for example, correspond to the planning horizon of the trajectory to be determined). By considering different possible length data sets of the sequence of partial regions, it is possible to ensure that an optimal trajectory for a driving maneuver can be determined on the basis of the described method.

A length data set can also be regarded as a "coding" for the lengths of the different subregions of the trajectory to be determined. For this reason, this document also uses the operation "coding" for a length record. In this case, the lengths of the subregions may be defined by a specific code, e.g. represented by one or more binary variables. Such a representation of a length data set or a coding of the lengths of the subarea enables a particularly efficient implementation of the described method.

In addition, the method comprises determining a trajectory on the basis of the multiplicity of possible codings or the plurality of possible length data records and taking into account a quality function or a quality measure. In particular, a trajectory can be determined which improves the quality function or the quality measure, in particular optimizes it. The quality function or the quality measure can e.g. have or be a cost function. In this case, the costs can increase with increasing deviation of the determined trajectory from a target position of the trajectory. Alternatively or additionally, the costs may increase with decreasing ride comfort of the determined trajectory (e.g., with increasing jerk). By taking into account a quality function or a quality measure, it can thus be ensured that an (optimized) trajectory is determined with which the vehicle is guided (preferably in the most comfortable manner possible) to a specific target position.

Checking different possible encodings or length records of the subregions, i. the checking of different possible combinations of (temporal or local) lengths of the subregions, for the trajectory to be determined is preferably carried out iteratively. For this purpose, the method may include adjusting a possible coding or length record (e.g., by changing the lengths of at least two sub-ranges). It is then possible to determine a trajectory for the adapted possible coding or for the adapted length data set. The adaptation of the possible length data set and the determination of an (optimized) trajectory for the respectively adapted length data set can be repeated iteratively so that the quality measure is improved. In this case, the iterative adaptation of a possible length data set preferably takes place using a branch-and-bound method and / or a cutting plan method or a branch-and-cut method or a combination of these methods to determine the number of items to be checked to reduce possible encodings or possible length data sets and / or to exclude a subset of possible encodings or length records as suboptimal. Due to the iterative execution of the method, an optimized trajectory for a driving maneuver can be determined in a particularly efficient manner.

A possible coding or a possible length record for the sequence of partial areas can be determined or adapted as a function of one or more restrictions. The one or more constraints may include a limitation on an order of the portions. Alternatively or additionally, the one or more Restrictions include a limitation with respect to a minimum and / or a maximum length of at least one subarea. By taking into account one or more restrictions, the number of possible codings or length data sets to be checked and thus the computational effort for determining an (optimized) trajectory can be further reduced.

As already explained above, the trajectory can include a longitudinal trajectory along a roadway traveled by the vehicle. In other words, the method may be designed to determine a longitudinal trajectory. The transverse offset of the vehicle can be described separately from a longitudinal trajectory using a transverse trajectory. For this purpose, the method may further comprise determining a transverse trajectory transverse to the roadway. By superimposing the longitudinal trajectory and the transverse trajectory, a combined longitudinal transverse trajectory can then be determined. On the basis of the combined longitudinal transverse trajectory, an (automated) driving function of the vehicle can then be provided.

The longitudinal trajectory can be determined in such a way that the determined longitudinal trajectory makes it possible to determine a transverse trajectory transverse to the roadway, which results in a combined longitudinal-transverse trajectory that can be traveled by the vehicle. For this purpose, information relating to the transverse trajectory to be determined (for example, a transverse offset to be effected) may be taken into account in the determination of the longitudinal trajectory, in particular in the division of the longitudinal trajectory into a sequence of partial regions. The longitudinal trajectory can thus be determined in such a way that the planned longitudinal trajectory makes it possible to plan a drivable transverse trajectory in order to solve a specific driving task (for example a lane change) so that the combined longitudinal-transverse trajectory is mobile.

In particular, the (longitudinal) trajectory to be determined can be subdivided into subareas in such a way that a specific transverse offset of the vehicle across the roadway is effected in a specific subarea of the plurality of subareas (in the context of a transverse trajectory to be determined separately). In other words, it is possible (at least or precisely) to define a specific subarea in which the transverse offset of the vehicle takes place. Such a subarea typically has a relatively high number of constraints because one or more obstacles on multiple lanes are to be considered.

The method may include determining a minimum length of the particular portion (in which a particular lateral offset is to be effected) in dependence on the determined lateral offset (and typically in response to a possible lateral acceleration of the vehicle). The minimum length of the particular partition may then be taken into account in determining the plurality of possible encodings or length records (as a constraint).

In order to determine the minimum length of the specific subarea, the longitudinal acceleration a _{x of} the vehicle for the longitudinal trajectory in the specific subarea can be determined. The longitudinal acceleration a _{x of} the vehicle can be determined, for example, on the basis of a state (in particular of a state vector) of the vehicle within the specific subarea, the state of the vehicle being determined from the trajectory to be determined (eg from the trajectory determined in the context of the preceding iteration) can.

ermittelt werden.On the basis of the longitudinal acceleration a _x and on the basis of a (typically known) maximum acceleration a _{max of} the vehicle, it is then possible to determine a possible transverse acceleration a _{y of} the vehicle in the specific subarea. In particular, on the basis of a maximum longitudinal acceleration (for example a maximum possible longitudinal acceleration) in the specific subarea, a possible transverse acceleration a _{y of} the vehicle in the specific subarea can be determined. The (possibly maximum) longitudinal acceleration a _{x is} preferably smaller than the maximum acceleration a _max . To calculate the (possibly maximum) possible lateral acceleration a _y , the comb circle of the vehicle can be taken into account. In particular, the possible lateral acceleration based on ${\alpha }_y=\sqrt{{\alpha }_{max}^2-{\alpha }_x^2}$

be determined.

ermittelt werden, wobei d_y der bestimmte Querversatz ist, und wobei δ_steer eine Reaktionszeit einer Lenkung des Fahrzeugs ist, und wobei tmin eine zeitliche Mindestlänge des bestimmten Teilbereichs ist.The minimum length of the specific subarea can then be based on the lateral acceleration a _y , in particular based on $t_{min}=\sqrt{\frac{2d_y}{{\alpha }_y}}+{\delta }_{steer}.$

where d _{y is} the determined _{lateral offset} , and where δ _{steer is} a reaction time of a steering of the vehicle, and where t min is a minimum time length of the particular subrange.

It is thus possible on the basis of one or more driving dynamics parameters of a vehicle to determine one or more restrictions with respect to the length of one or more subregions. Thus, the number of possible codings or length records can be reduced and the efficiency of the method can be further increased. Furthermore, it can be guaranteed by the minimum length of the specific subarea, that overlaying the planned transverse and longitudinal trajectory to a movable transverse-longitudinal trajectory leads. This can be attributed to the fact that the physical maximum accelerations and the accelerations necessary for the driving task can be maintained or called up at any time.

The one or more constraints to be considered may each include at least one safety distance to an obstacle in the vicinity of the vehicle. The safety distance to be maintained typically depends on the driving speed of the vehicle. In particular, the safety distance to be maintained may increase in a non-linear manner (in particular, quadratically) with increasing vehicle speed. By taking into account a driving speed-dependent safety margin, the reliability and safety of a determined trajectory and the trajectory using the trajectory can be increased.

wobei v_obj die Geschwindigkeit des Hindernisses ist, wobei δ_brake eine Reaktionszeit einer Bremsung des Fahrzeugs ist, und wobei a_max,obj und a_max,ego die Maximalbeschleunigung des Hindernisses bzw. des Fahrzeugs sind. Die abschnittsweise lineare Funktion für den Sicherheitsabstand kann dann für alle betrachteten Fahrgeschwindigkeiten v_ego einen Wert des Sicherheitsabstands liefern, der gleich wie oder größer als d_safe,2 ist. Durch das Berücksichtigen einer abschnittsweise linearen Approximation einer nicht-linearen Sicherheitsabstandsfunktion kann die Konvexität des Optimierungsproblems beibehalten werden, was die effiziente Ermittlung einer optimalen Trajektorie ermöglicht. Dabei wird bei der abschnittsweise linearen Approximation bevorzugt die Konvexität der nicht-linearen Sicherheitsabstandsfunktion ausgenutzt, so dass die abschnittsweise lineare Approximation niemals Werte zulässt, die den durch die nicht-linearen Sicherheitsabstandsfunktion gegebenen Mindest-Sicherheitsabstand nicht einhalten.The safety distance can be defined by a section-wise linear function of the driving speed v _{ego of} the vehicle. The section-wise linear function may (exclusively) have values that are equal to or greater than the underlying non-linear function for the safety distance. For example, the safety margin can be described by the following non-linear function, as $$d_{\text{safe}2}=\frac{{\mathrm{\nu }}_{\text{obj}}^2}{-2\left|{\alpha }_{\text{Max}\text{, obj}}\right|}-\frac{{\mathrm{\nu }}_{\text{ego}}^2}{-2\left|{\alpha }_{\text{Max}\text{,ego}}\right|}+{\nu }_{\text{ego}}{\delta }_{\text{brake}}$$

where v _{obj is} the speed of the obstacle, where δ _{brake is} a reaction time of braking the vehicle, and where a _{max, obj} and a _{max, ego are} the maximum acceleration of the obstacle or the vehicle, respectively. The piecewise linear function for the safety distance can then provide a value of the safety distance for all considered speeds v _ego which is equal to or greater than d _{safe, 2.} By taking into account a sectionally linear approximation of a non-linear safety distance function, the convexity of the optimization problem can be maintained, which enables the efficient determination of an optimal trajectory. In this case, the convexity of the non-linear safety distance function is preferably utilized in the section-wise linear approximation, so that the section-wise linear approximation never allows values that do not comply with the minimum safety distance given by the non-linear safety distance function.

The (longitudinal) trajectory to be determined or determined can include a state sequence x (k) of a state vector x at a sequence of times k = 1,..., N _lon , where N _lon the (temporal) planning horizon for the trajectory. The state vector x may include a position of the vehicle, a speed of the vehicle, an acceleration of the vehicle and / or a jolt of the vehicle. The trajectory can thus indicate the state of the vehicle at the sequence of times k.

The one or more possible length data sets or codes can then indicate the subarea of the trajectory for each time of the sequence of times. This can be done in a particularly efficient way by a binary coding. As already stated above, for the trajectory to be determined, a total of V constraints with respect to corresponding V obstacles may be taken into account. A possible coding can then comprise a certain number of binary vectors, each with N _lon , vector elements, by which in combination at each of the times k = 1, ...., N _lon , is indicated: the respective subarea; and / or the subset of constraints to be applied in each subarea. The number of binary vectors of the possible codings can be equal to or greater than the rounded value of log ₂ V. By coding and / or by a length data set can thus be displayed, which subset of the total amount of V constraints must be taken into account in the different sub-areas for the planning of the trajectory.

The provision of a binary coding for the subareas allows a particularly efficient consideration of the secondary conditions within the method described. In particular, a possible (binary) coding may take into account the V constraints such that each of the V constraints is activated or deactivated depending on a value of the one or more binary vectors, for example using a Big-M method.

The determination of a trajectory for a particular possible coding or for a particular possible length record may include determining a state sequence x (k) in dependence on a state model of the vehicle. The state model can indicate how a state vector x is converted at a first time into a state vector x at a subsequent second point in time. In this case, a linear state model is preferably used. It is thus possible to determine a state sequence x (k) which is compatible with a state model of the vehicle and thus can in principle be implemented as a trajectory by the vehicle.

It can then be checked whether the determined state sequence x (k) determines the particular possible Coding or the particular possible length record (and thus the respective subsets of constraints in the respective sub-areas) met. Furthermore, the value of the quality function or the quality measure for the determined state sequence x (k) can be determined.

In order to determine an (optimal) trajectory or an (optimal) state sequence x (k) for a specific possible coding or for a particular possible length dataset, an iterative adaptation of the state sequence x (k) can take place, so that the value of the quality function or the quality measure is improved (in particular optimized), and as long as (or so) the state sequence x (k) fulfills the specific possible coding or the specific possible length data set. This can e.g. be done efficiently by a gradient-descent method.

The method may include transforming one or more state variables of the vehicle from a first coordinate system to a second coordinate system relative to a roadway of the vehicle. The trajectory can then be determined in the second coordinate system. Subsequently, data relating to the determined trajectory from the second coordinate system can be transformed back into the first coordinate system in order to determine control data for controlling one or more actuators of the vehicle, and to provide a driving function of the vehicle as a function of the determined trajectory. Through a transformation into a second coordinate system relative to the roadway of the vehicle, a separate planning of longitudinal and transverse trajectories for a vehicle can be carried out efficiently.

According to a further aspect, a (further) method for determining or planning a trajectory for a vehicle is described. The aspects described in this document also apply to this procedure. The method may be performed by a device or by a control unit of a vehicle.

The method includes determining at least one constraint with respect to at least one obstacle in an environment of the vehicle. In this case, the secondary condition includes a safety distance to the obstacle in the vicinity of the vehicle, wherein the safety distance depends on the driving speed of the vehicle. Typically, the (required) safety margin is a non-linear function of vehicle speed. However, in the context of the constraint, the safety margin may be determined by a sectional linear function of the vehicle's vehicle speed (e.g., with 2, 3, 4, 5, or more subsections). The method further comprises determining a trajectory on the basis of a quality measure and as a function of the at least one secondary condition (with the sectionally linearized safety distance). Thus, an efficient and optimal determination of a trajectory can be made possible.

In another aspect, an apparatus for planning a trajectory for a vehicle is described. The device is set up to divide a (planning) area for a trajectory to be determined for the vehicle into a plurality of partial areas, so that in each partial area of the plurality of partial areas a constant amount of secondary conditions with respect to obstacles in the respective partial area an environment of the vehicle applies. In addition, the device is set up to determine a multiplicity of possible length data records, wherein a possible length data record indicates possible lengths of the subregions of the plurality of subregions along the trajectory. The device is further configured to determine a trajectory based on the plurality of different possible length data sets and taking into account a quality measure.

According to a further aspect, a road vehicle (in particular a passenger car or a truck or a bus or a motorcycle) is described, which comprises the device described in this document.

In another aspect, a software (SW) program is described. The SW program may be set up to be executed on a processor (e.g., on a controller of a vehicle) and thereby perform the method described in this document.

In another aspect, a storage medium is described. The storage medium may include a SW program that is set up to run on a processor and thereby perform the method described in this document.

It should be understood that the methods, devices and systems described herein may be used alone as well as in combination with other methods, devices and systems described in this document. Furthermore, any aspects of the methods, devices, and systems described herein may be combined in a variety of ways. In particular, the features of the claims can be combined in a variety of ways.

• 1 eine beispielhafte Verkehrssituation;
• 2a ein Ablaufdiagramm eines beispielhaften Verfahrens zur Ermittlung einer Trajektorie;
• 2b ein Ablaufdiagramm eines beispielhaften Verfahrens zur Ermittlung einer Trajektorie für eine bestimmte mögliche Kodierung von Teilbereichen;
• 3 eine beispielhafte Transformation in ein Koordinatensystem relativ zu einer Referenzlinie eines Fahrzeugs;
• 4a beispielhafte Teilbereiche für eine Trajektorie;
• 4b eine beispielhafte Kodierung einer Sequenz von Teilbereichen;
• 5 eine beispielhafte abschnittsweise lineare Approximation einer Sicherheitsabstands-Funktion; und
• 6 ein Ablaufdiagramm eines beispielhaften Verfahrens zur Ermittlung einer Trajektorie für eine Fahrfunktion eines Fahrzeugs.

Furthermore, the invention will be described in more detail with reference to exemplary embodiments. Show

• 1 an exemplary traffic situation;
• 2a a flowchart of an exemplary method for determining a trajectory;
• 2 B a flowchart of an exemplary method for determining a trajectory for a particular possible coding of partial areas;
• 3 an exemplary transformation into a coordinate system relative to a reference line of a vehicle;
• 4a exemplary subregions for a trajectory;
• 4b an exemplary coding of a sequence of partial areas;
• 5 an exemplary sectional linear approximation of a safety distance function; and
• 6 a flowchart of an exemplary method for determining a trajectory for a driving function of a vehicle.

As stated above, the present document deals with the technical task of efficiently determining a safe longitudinal and / or transverse trajectory for a vehicle (which is also referred to as an ego vehicle). In this context shows 1 an exemplary traffic situation. The ego vehicle 100 drives on a multi-lane road 105 , A vehicle 101 on the same lane of the roadway 101 in front of the ego vehicle 100 (ie a vehicle 101 on the ego lane) can have a relatively low driving speed. The ego vehicle 100 has, for example, the opportunity to perform an overtaking maneuver and along a trajectory 112 to change the lane to the vehicle 101 to overtake. There is a collision with other vehicles 102 . 103 to avoid.

To carry out the in 1 Maneuver shown, a control unit or a device of the ego vehicle 100 a trajectory 112 determine one or more constraints. In the determination of a trajectory 112 Among other things, driving dynamics aspects can be taken into account. In particular, depending on one or more vehicle parameters and / or depending on a current driving situation, a trajectory 112 be determined with the vehicle 100 can be driven realistically. It can be one of the vehicle 100 feasible curvature be considered. Further examples of vehicle parameters that can be taken into account are a lateral and / or longitudinal acceleration or deceleration of the vehicle (which can be implemented in the current driving situation) 100 ,

Furthermore, it becomes a trajectory 112 typically determined such that with the trajectory 112 a collision with the detected objects or obstacles 101 . 102 . 103 around the ego vehicle 100 can be avoided. The trajectory thus determined 112 may then be to one or more controllers for the transverse guidance and / or the longitudinal guidance of the vehicle 100 be handed over.

The determination of a trajectory 112 preferably takes place in a curved coordinate system, relative to a roadway course. The method for determining a trajectory described in this document may therefore include the step, 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 (curved) Frenet coordinate system.

The decurling of the road course (by a curved coordinate system) is exemplary in 3 shown. For the decurling measurement signals are regarding the condition of the vehicle 100 transformed into a lane coordinate system. The trajectory planning itself does not find itself in a Cartesian coordinate system 301 instead, but in a Frenet coordinate system. The Frenet coordinate system is relative to a reference curve 300 (eg the lane center of a lane course). The vehicle position is thus replaced by the variables s (t) 303 in the longitudinal direction and d (t) 302 described in the transverse direction. s (t) and d (t) describe the longitudinal or lateral velocity and s̈ (t) and d̈ (t) describe the longitudinal or lateral acceleration.

Both the vehicle's own movement and the road users or objects to be considered 101 . 102 . 103 can be considered in the Frenet coordinate system. Clearly, this transformation corresponds to the warping of the coordinate system 301 and thus allows the separate optimization of the longitudinal and transverse movement of the vehicle 100 ,

(d.h. die 3^te Ableitung der Zustandsgröße x₁(t)) und/oder die Ableitung des Rucks $x_1^{\left(4\right)}\left(t\right)$

(d.h. die 4^te Ableitung der Zustandsgröße x₁(t)) definiert werden.The transverse and longitudinal movement of a vehicle 100 can be used as an optimal control problem with output s (t) = x ₁ (t) (in the case of longitudinal planning) or d (t) = x ₁ (t) (in the case of cross-planning) of an integrator system (ie a model of the dynamics of a vehicle 100 ). In this case, x ₁ (t) is a first state variable of the vehicle 100 indicating the position of the vehicle 100 (in the longitudinal direction or in the transverse direction) describes. As input of the integrator system can the jerk $x_1^{\left(3\right)}\left(t\right)$

(ie, 3 ^th derivative of the state variable x ₁ (t)) and / or the derivative of the jerk $x_1^{\left(4\right)}\left(t\right)$

(ie the 4 ^th derivative of the state variable x ₁ (t)) are defined.

wobei die Eingangsgröße u der Ableitung des Rucks $x_1^{\left(4\right)}\left(t\right)$

entspricht. Der Zustand eines Fahrzeugs 100 zu einem bestimmten Zeitpunkt t kann durch den Zustandsvektor x^T = [x₁, x₂, x₃, x₄] beschrieben werden, wobei x₂(t) = ẋ₁(t), x₃(t) = x₂(t) und x₄(t) = ẋ₃(t) ist.An exemplary integrator system or state model of a vehicle 100 can be defined as follows: $$\dot{\text{x}}=\left[\begin{array}{llll}0\hfill & 1\hfill & 0\hfill & 0\hfill \\ 0\hfill & 0\hfill & 1\hfill & 0\hfill \\ 0\hfill & 0\hfill & 0\hfill & 1\hfill \\ 0\hfill & 0\hfill & 0\hfill & 0\hfill \end{array}\right]\text{x}+\left[\begin{array}{c}0\\ 0\\ 0\\ 1\end{array}\right]u$$

where the input u is the derivative of the jerk $x_1^{\left(4\right)}\left(t\right)$

equivalent. The condition of a vehicle 100 at a certain point in time t, the state vector can be used to describe x ^T = [x ₁ , x ₂ , x ₃ , x ₄ ], where x ₂ (t) = ẋ ₁ (t), x ₃ (t) = x ₂ ( t) and x ₄ (t) = ẋ ₃ (t).

It is now possible to determine a trajectory, ie a temporal sequence of states x (t) or in the time-discrete region x (k), where k = 1, ...., N _lon , where N _{lon is} the planning horizon. In this case, the state sequence x (k) can be determined by which a cost or quality function is reduced, in particular minimized. It can be specified in the cost function that the vehicle 100 has a specific target position at the end of the planning horizon. Alternatively or additionally, it can be specified that the state sequence fulfills one or more comfort criteria (eg with regard to the jerk).

For calculating a transverse trajectory, a target area d _target can be specified as a desired end point of a trajectory, for example of an area on an adjacent lane indicates (as in 1 shown). This target range can be defined, for example, as the desired end position of the final state x (t _f ) or x (N _lon ), if necessary with x ₁ (t _f ) = x ₁ (N _lon ) = d _target . The planning horizon for the planning of a transverse trajectory and the planning horizon for the planning of a longitudinal trajectory can differ from each other. Typically, the planning horizon for a transverse trajectory is shorter than for a longitudinal trajectory (eg 6s vs. 10s).

As a cross-selection measure or as a cross-quality measure for the determination of a trajectory for the lateral guidance of the vehicle 100 For example, the following function can be used: $$J_{quer}=\frac{1}{2}{\displaystyle {\int }_0^{t_f}{\left(d^{\left(4\right)}\left(t\right)\right)}^{2}dt+k_{q1}}{\left(d_{ziel}-d\left(t_f\right)\right)}^2+k_{q2}{t}_f$$

The first expression evaluates the evolution of the derivative of the jerk along the trajectory 112 (and thus the comfort). The second term evaluates the deviation of the final position d (t _f ) from the target position d _target . Furthermore, the third term evaluates the time length of the trajectory 112 , The expression of the trajectory can be determined by the weighting factors k _q1 and k _q2 112 to be influenced.

insbesondere wenn eine bestimmte Zielposition s_ziel erreicht werden soll. Alternativ kann das folgende Längs-Auswahlmaß bzw. Längs-Gütefunktional verwendet werden $$J_{längs}=\frac{1}{2}{\displaystyle {\int }_0^{t_f}{\left(s^{\left(4\right)}\left(t\right)\right)}^{2}dt+k_{l1}}{\left({\dot{s}}_{ziel}-\dot{s}\left(t_f\right)\right)}^2+k_{l2}{t}_f,$$

insbesondere wenn eine bestimmte Zielgeschwindigkeit ṡ_ziel erreicht werden soll.The longitudinal planning can be done in a similar way. For longitudinal planning, for example, the following longitudinal selection dimension or longitudinal quality function can be used $$J_{länGs}=\frac{1}{2}{\displaystyle {\int }_0^{t_f}{\left(s^{\left(4\right)}\left(t\right)\right)}^{2}dt+k_{l1}}{\left(s_{ziel}-s\left(t_f\right)\right)}^2+k_{l2}{t}_f.$$

especially if a specific target position s _{goal is to be} achieved. Alternatively, the following longitudinal selection measure or longitudinal quality function can be used $$J_{länGs}=\frac{1}{2}{\displaystyle {\int }_0^{t_f}{\left(s^{\left(4\right)}\left(t\right)\right)}^{2}dt+k_{l1}}{\left({\dot{s}}_{ziel}-\dot{s}\left(t_f\right)\right)}^2+k_{l2}{t}_f.$$

especially if a certain target speed ṡ _{goal is to be} achieved.

Thus, a longitudinal trajectory can be determined, wherein a longitudinal trajectory is the state x of the vehicle 100 , in particular the position s (k) of the vehicle 100 , at a plurality of sampling times k, with k = 1, ...., N _lon , where N _{lon is} the planning horizon. It is then necessary to check which of the plurality of longitudinal trajectories has one or more constraints with respect to obstacles, in particular with respect to other vehicles 101 . 102 . 103 , Fulfills. It typically does not have all the obstacles 101 . 102 . 103 be taken into account during the entire driving maneuver. Adding or dropping constraints when planning a trajectory 112 However, for a driving maneuver leads to non-linearities and / or non-convex driving tubes, which makes finding an optimal solution difficult.

wobei s_ego die Position des Fahrzeugs 100 in Längsrichtung ist und wobei s_i(k), i = 1, ...,3, die prädizierten Positionen der anderen Fahrzeuge 101, 102, 103 an dem k^ten Abtastzeitpunkt der geplanten Trajektorie sind. Des Weiteren sind d_safe,i, i = 1, ...,3, Sicherheitsabstände 401, 402, 403 zu den anderen Fahrzeugen 101, 102, 103.It is therefore proposed to determine the trajectory to be determined for a driving maneuver in several subregions or subregions 411 . 412 . 413 to divide (see 4a) , each subsection 411 . 412 . 413 has a fixed amount of side conditions. For example, in the 1 and 4a shown lane change in a first subarea 411 (when driving in the ego lane), in a second subarea 412 (when changing to the neighboring lane) and in a third subarea 413 (when driving in the neighboring lane) are divided. The first section 411 can also be used as a pre-, the second subarea 412 can be used as a peri- and third part 413 can be referred to as a post-region. In the in 4a Example shown arise for the subarea 411 . 412 . 413 the following constraints for the planning of the longitudinal trajectory $$\begin{array}{c}{\text{Pre}}^k=\left\{{\text{s}}_{\text{ego}}\in ℝ|{\text{s}}_{\text{ego}}<{\text{s}}_1\left(k\right)-d_{\text{safe}\mathrm{,1}}\right\}\\ {\text{Peri}}^k=\{{\text{s}}_{\text{ego}}\in ℝ|{\text{s}}_{\text{ego}}<{\text{s}}_1\left(k\right)-d_{\text{safe}\mathrm{,1}}\wedge \\ {\text{s}}_{\text{ego}}<{\text{s}}_2\left(k\right)-d_{\text{safe}2}\wedge \\ {\text{s}}_{\text{ego}}{\text{> s}}_3\left(k\right)+d{}_{\text{safe}3}\}\\ {\text{post}}^{\text{k}}=\left\{{\text{s}}_{\text{ego}}\in ℝ|{\text{s}}_{\text{ego}}<{\text{s}}_2\left(k\right)-d_{safe2}\right\}.\end{array}$$

where _{ego is} the position of the vehicle 100 in the longitudinal direction and where s _i (k), i = 1, ..., 3, the predicted positions of the other vehicles 101 . 102 . 103 at the k ^th sampling time of the planned trajectory are. Furthermore, d _{safe, i} , i = 1, ..., 3, safety distances 401 . 402 . 403 to the other vehicles 101 . 102 . 103 ,

wobei δ₁ und δ₂ Vektoren mit der Dimension N_lon sind, durch die in Kombination angezeigt werden kann, in welchem Teilbereich 411, 412, 413 sich das Fahrzeug 100 befindet. Anhand der binären Kodierung können die o.g. Nebenbedingungen in linearer Form für das gesamte Fahrmanöver bzw. für den gesamten Planungshorizont der Trajektorie geschrieben werden, als: $$\begin{array}{l}{\text{s}}_{\text{ego}}\le {\text{s}}_{O_1}-d_{\text{safe}\text{,1}}+{\delta }_2{M}_{\text{big}}\hfill \\ {\text{s}}_{\text{ego}}\le {\text{s}}_{O_2}-d_{\text{safe}\text{,2}}+\left({\delta }_1-{\delta }_2\right)M_{\text{big}}\hfill \\ {\text{s}}_{\text{ego}}\ge {\text{s}}_{O_3}-d_{\text{safe}\text{,3}}+{\delta }_1{M}_{\text{big}}.\hfill \end{array}$$

The points on a longitudinal trajectory can now each one of the different sections 411 . 412 . 413 be assigned to. For this purpose, a binary coding can be used, for example as follows $$\left[{\delta }_1\left(k\right){\delta }_2\left(k\right)\right]=\{\begin{array}{c}\left[1\text{0}\right]{\text{s}}_{\text{ego}}\left(k\right)\in {\text{Pre}}^k\\ \left[\text{0 0}\right]{\text{s}}_{\text{ego}}\left(k\right)\in {\text{Peri}}^k\\ \left[1\text{1}\right]{\text{s}}_{\text{ego}}\left(k\right)\in {\text{post}}^k\end{array}$$

where δ ₁ and δ ₂ are vectors with the dimension N _lon , which can be used to indicate in combination in which subarea 411 . 412 . 413 the vehicle 100 located. Based on the binary coding, the above-mentioned secondary conditions can be written in a linear form for the entire driving maneuver or for the entire planning horizon of the trajectory, as: $$\begin{array}{l}{\text{s}}_{\text{ego}}\le {\text{s}}_{O_1}-d_{\text{safe}\text{,1}}+{\delta }_2{M}_{\text{big}}\hfill \\ {\text{s}}_{\text{ego}}\le {\text{s}}_{O_2}-d_{\text{safe}\text{2}}+\left({\delta }_1-{\delta }_2\right)M_{\text{big}}\hfill \\ {\text{s}}_{\text{ego}}\ge {\text{s}}_{O_3}-d_{\text{safe}\text{3}}+{\delta }_1{M}_{\text{big}},\hfill \end{array}$$

Here are s _Or , r = 1, ..., 3, the above-mentioned predicted positions s _r (k), r = 1, ..., 3, of the other vehicles 101 . 102 . 103 , M _big is a sufficiently large constant that ensures that the respective constraint becomes irrelevant due to the size of M _big , if δ ₁ , δ ₂ or δ ₁ -δ _{2 are} zero.

To ensure that a planned combined longitudinal and transverse trajectory by a vehicle 100 can actually be driven when determining the subregions 411 . 412 . 413 a driving maneuver that takes into account a subarea 412 in which a significant lateral acceleration of the vehicle 100 takes place (such as in the second subarea 412 ), a (temporal) minimum length n _min ∈ {0, ..., N _lon }.

wobei a_x die (maximale) Längsbeschleunigung und a_max die Maximalbeschleunigung des Fahrzeugs 100 ist. Um einen bestimmten Querversatz d_y zu erreichen, wird eine bestimmte Mindestzeit $t_{min}=\sqrt{\frac{2d_y}{{\alpha }_y}}+{\delta }_{steer},$

benötigt, wobei δ_steer eine Reaktionszeit der Lenkung des Fahrzeugs 100 ist. Die Mindestzeit tmin kann über die Schrittweite Δt_lon der Zeitschritte (d.h. über die Abtastrate) in eine (zeitliche) Mindestlänge n_min des zweiten Teilbereichs 412 umgerechnet werden, als $n_{min}=\frac{t_{min}}{\Delta t_{lon}}\cdot n_{min}$

gibt somit eine Mindestzahl an Abtastzeitpunkten für den zweiten Teilbereich 412 an.From the Kamm circle results for the lateral acceleration ${\alpha }_y=\sqrt{{\alpha }_{max}^2-{\alpha }_x^2}.$

where a _{x is} the (maximum) longitudinal acceleration and a _{max is} the maximum acceleration of the vehicle 100 is. In order to achieve a certain transverse offset d _y , a certain minimum time $t_{min}=\sqrt{\frac{2d_y}{{\alpha }_y}}+{\delta }_{steer}.$

required, where δ _steer a reaction time of the steering of the vehicle 100 is. The minimum time tmin can be achieved over the step size Δt _{lon of} the time steps (ie via the sampling rate) into a (time-related) minimum length n _{min of} the second partial area 412 be converted as $n_{min}=\frac{t_{min}}{\Delta t_{lOn}}\cdot n_{min}$

Thus, there is a minimum number of sampling times for the second subarea 412 at.

• • δ₂ wechselt nur maximal einmal von Null auf Eins;
• • δ₂ wechselt den Wert nicht vor δ₁;
• • nach Durchlaufen des zweiten Teilbereichs 411 wechseln δ₁ und δ₂ gleichzeitig; und
• • der zweite Teilbereich 412 weist eine Mindestlänge n_min auf, und folglich muss die Kodierung für eine Längstrajektorie einen entsprechend kodierten zusammenhängenden Block mit der Mindestlänge n_min aufweisen.

When selecting a suitable longitudinal trajectory, the following boundary conditions or restrictions for the binary vectors δ ₁ and δ ₂ can now be taken into account:

• • δ ₂ changes only once from zero to one;
• • δ ₂ does not change the value before δ ₁ ;
• • after passing through the second subarea 411 change δ ₁ and δ ₂ simultaneously; and
• • the second subarea 412 has a minimum length n _min , and thus the coding for a longitudinal trajectory must have a correspondingly coded contiguous block with the minimum length n _min .

4b shows exemplary binary vectors δ ₁ and δ _{2 of} a coding 420 for the subareas 411 . 412 . 413 out 4a , The length of time 422 of the second subarea 412 (ie, the number of sampling times within the second subarea 412 ) corresponds to at least n _min .

wobei δ_brake die Reaktionszeit einer Bremsung des Ego-Fahrzeugs 100 ist. The constraints defined in this document include safety margins 401 . 402 . 403 d _{safe, r} , r = 1, ..., 3, to one or more other vehicles 101 . 102 . 103 , Assuming that the ego vehicle 100 has a greater maximum acceleration a _{max, ego} than another vehicle 101 . 102 . 103 (a _{max, obj} ), can provide a sufficient safety margin 401 . 402 . 403 as a function of the speed _{ego of} the ego vehicle 100 be defined as follows $$\begin{array}{c}{d}_{\text{safe}\text{,1}}=\frac{{\left({\nu }_{\text{obj}}-\left|{\alpha }_{\text{Max}\text{, obj}}\right|{\delta }_{\text{brake}}-{\nu }_{\text{ego}}\right)}^2}{-2\left(\left|{\alpha }_{\text{Max}\text{, obj}}\right|-\left|{\alpha }_{\text{Max}\text{,ego}}\right|\right)}-{\nu }_{\text{obj}}{\delta }_{\text{brake}}\\ +\frac{1}{2}\left|{\alpha }_{\text{Max}\text{, obj}}\right|{\delta }_{\text{brake}}^2+{\nu }_{\text{ego}}{\delta }_{\text{brake}}\end{array}$$

where δ _{brake is} the reaction time of a braking of the ego vehicle 100 is.

Typically, however, it is assumed that the maximum acceleration a _{max, ego of} the ego vehicle 100 less than the maximum acceleration a _{max, obj of} the other vehicle 101 . 102 . 103 is. In this case, the safety distance 401 . 402 . 403 be defined as $$d_{\text{safe}\text{2}}=\frac{{\nu }_{\text{obj}}^2}{-2\left|{\alpha }_{\text{Max}\text{, obj}}\right|}-\frac{{\nu }_{\text{ego}}^2}{-2\left|{\alpha }_{\text{Max}\text{,ego}}\right|}+{\nu }_{\text{ego}}{\delta }_{\text{brake}}$$

definiert werden, wobei v_max eine Maximalgeschwindigkeit des Ego-Fahrzeugs 100 ist und v_min eine Minimalgeschwindigkeit des Ego-Fahrzeugs 100 ist. v_i ist ein Grenzgeschwindigkeit zwischen zwei direkt benachbarten Teilabschnitten 503 mit i = 0, ..., p - 1. Der Sicherheitsabstand 401, 402, 403 ergibt sich dann in abschnittsweise linearisierter Form als $${\tilde{d}}_{safe}\left({\nu }_{\text{ego}}\right)=\{\begin{array}{l}{g}_1\left({\nu }_{\text{ego}}\right),{\nu }_0\le {\nu }_{\text{ego}}<{\nu }_1,\hfill \\ g_1\left({\nu }_{\text{ego}}\right),{\nu }_1\le {\nu }_{\text{ego}}<{\nu }_2,\hfill \\ ⋮\hfill \\ g_p\left({\nu }_{\text{ego}}\right),{\nu }_{\text{ego}}\ge {\nu }_{p-1.}\hfill \end{array}$$

5 shows an exemplary course 501 the safety margin 401 . 402 . 403 as a function of the driving speed v _ego 502 of the ego vehicle 100 , To take into account the safety distance 401 . 402 . 403 within the constraints would have the non-linearity of the safety margin 401 . 402 . 403 in relation to the driving speed v _ego 502 of the ego vehicle 100 which would lead to a non-linearity of the constraints. In order to continue to be able to take into account linear constraints, the velocity profile 501 the safety margin 401 . 402 . 403 through linear sections 503 g ₁ , g ₂ , ..., g _{p are} described, the linear sections 503 one safety distance each 401 . 402 . 403 deliver that (at least slightly) above the exact speed gradient 501 the safety margin 401 . 402 . 403 lies. The individual sections 503 can for different speed ranges $${\nu }_i=\left({\nu }_{\text{Max}}-{\nu }_{\text{min}}\right)\frac{i}{p}+{\nu }_{\text{min}}$$

be defined, where v _{max is} a maximum speed of the ego vehicle 100 and v _{min is} a minimum speed of the ego vehicle 100 is. v _i is a limit speed between two directly adjacent sections 503 with i = 0, ..., p - 1. The safety distance 401 . 402 . 403 then results in sections linearized form as $${\tilde{d}}_{safe}\left({\nu }_{\text{ego}}\right)=\{\begin{array}{l}{G}_1\left({\nu }_{\text{ego}}\right).{\mathrm{<figure-callout\; id="0"\; label="\nu "\; filenames="DE102018204101A1\_0026.png"\; state="\{\{state\}\}">\nu </figure-callout>}}_0\le {\nu }_{\text{ego}}<{\mathrm{<figure-callout\; id="1"\; label="\nu "\; filenames="DE102018204101A1\_0026.png"\; state="\{\{state\}\}">\nu </figure-callout>}}_1.\hfill \\ G_1\left({\nu }_{\text{ego}}\right).{\mathrm{<figure-callout\; id="1"\; label="\nu "\; filenames="DE102018204101A1\_0026.png"\; state="\{\{state\}\}">\nu </figure-callout>}}_1\le {\nu }_{\text{ego}}<{\nu }_2.\hfill \\ ⋮\hfill \\ G_p\left({\nu }_{\text{ego}}\right).{\nu }_{\text{ego}}\ge {\nu }_{p-1.}\hfill \end{array}$$

This formulation of the safety margin 401 . 402 . 403 can be taken into account under the linear constraints. In this case, it can be taken into account that each linear subfunction for the individual subsections 503 in the form g _i (v _ego ) = m _i v _ego + Δ _i let write, ie with a slope m _i and an offset Δ _i . In the above-mentioned secondary conditions for the different subareas 411 . 412 . 413 thus can the safety distances 401 . 402 . 403 d _{aafe, r} , r = 1, ..., 3 are replaced by g _i (v _ego ) = m _i v _ego + Δ _i , eg for the first subrange 411 $${\text{s}}_{\text{ego}}\le {\text{s}}_{O1}-\left(m_i{\nu }_{\text{ego}}+{\Delta }_i\right)+{\delta }_2{M}_{\text{big}\text{,}}$$

When checking the one or more secondary conditions, the relevant speed-dependent subsection can then be used for a trajectory and for a specific sampling instant k 503 and thus values for m _i and Δ _{i are} determined. It can then be efficiently checked whether the trajectory satisfies the constraint or not.

2a shows a flowchart of an exemplary method 200 for determining a (longitudinal) trajectory for a vehicle 100 , In a first step 201 can be a coding 420 for one or more constraints. In doing so, the set of possible codings 420 due to certain boundary conditions or restrictions, in particular due to restrictions with regard to the minimum length of at least one subarea 412 the trajectory, be limited. The selected encoding 420 then describes a possible division of the trajectory into a plurality of subregions 411 . 412 . 413 , where within each subarea 411 . 412 . 413 a lot of consistent constraints (in terms of a consistent amount of obstacles or other vehicles 101 . 102 . 103 ) applies.

It can then be used for the selected encoding 420 a state sequence s (k) is determined, which reduces the quality function J _{longitudinally} , in particular minimized, while just the selected coding 420 (ie just the one or more constraints) met. The determination of an optimal state sequence s (k) for a specific coding 420 can by the method 210 out 2 B respectively.

It can then be a different encoding 420 be selected (step 202 ) and again it may be the optimal state sequence s (k) for this encoding 420 be determined. This process can be used for a variety of different (possibly for all possible encodings 420 ) be repeated. Finally, the state sequence s (k) can be selected as the optimal trajectory for all possible encodings 420 minimizes the quality functional (step 203 ).

Due to the above limitations, the number of possible encodings 420 typically much smaller (by the factor 10 . 50 . 100 or more) than the set of all possible combinations of constraints. In particular, by considering the lateral dynamics of the vehicle 100 be significantly reduced in determining the longitudinal trajectory of the computational effort. In particular, it is ensured by the measures described that the superimposed longitudinal transverse trajectory can be moved straight away. Otherwise, several different trajectories would have to be planned and checked for drivability, which would be associated with an increased computational effort. Furthermore, a search method can be used, for example a branch-and-bound method, for the number of encodings to be checked 420 continue to reduce.

For a specific encoding 420 the optimal state sequence s (k) can be determined on the basis of in 2 B illustrated method 210 be determined. This is a convex optimization problem that can be solved more efficiently and optimally, for example, by means of a gradient method. In a first step 211 For example, a state sequence s (k) can be determined which corresponds to the state model of the vehicle 100 is compatible. You can also check (step 212 ), whether the determined state sequence s (k) by the coding 420 displayed one or more constraints met. If this is the case, then the value of the quality function for the determined state sequence s (k) can be determined (step 213 ).

The procedure 210 will then be determined by 211 a new state sequence s (k). If the new state sequence s (k) continues to fulfill the one or more constraints and further reduces the quality function, then the method can 210 be iteratively continued until a state sequence s (k) is found, which indeed reduces the quality function, but no longer fulfills the one or more constraints. The optimal state sequence s (k) is then the last-found state sequence s (k) which still satisfies the one or more (in particular all) constraints to be met by a state sequence (step 214 ). In this case, the search method for an optimal state sequence can be accelerated if the optimization algorithm starts directly at the limit of permitted and forbidden solutions, wherein prohibited solutions at least partially do not fulfill the one or more constraints to be met. In this case, for example, the inside-points method can be used.

Furthermore, a transverse trajectory can be determined (eg following the determination of the longitudinal trajectory, wherein a determined longitudinal trajectory can be taken into account in the determination of a transverse trajectory). By superposition of the longitudinal and transverse trajectories (and possibly by back transformation into the Cartesian coordinate system 301 ) can then be a combined longitudinal-transverse trajectory 112 for driving the vehicle 100 to be provided.

6 shows a flowchart of an exemplary method 600 for the determination or planning of a trajectory 112 for a vehicle 100 , The procedure 600 In particular, it may be designed to provide a longitudinal trajectory for the vehicle 100 along a reference curve 300 to investigate. The procedure 600 can by a control unit or by a control unit of the vehicle 100 be executed.

The procedure 600 includes splitting 601 (a planning area or planning horizon) of the trajectory to be determined 112 into a plurality of subareas 411 . 412 . 413 (In particular, in a sequence of each directly consecutive sections 411 . 412 . 413 ), so that in each subarea 411 . 412 . 413 the majority of subareas 411 . 412 . 413 one each within the respective subarea 411 . 412 . 413 consistent amount of constraints on obstacles 101 . 102 . 103 in an environment of the vehicle 100 applies.

In the context of the entire trajectory to be planned, it is possible for V constraints with respect to V different obstacles 101 . 102 . 103 to be considered. The division into subareas 411 . 412 . 413 can be done such that in each subarea 411 . 412 . 413 a different subset of the V constraints is taken into account. In this case, a subset preferably contains less than V secondary conditions. By dividing into different subareas 411 . 412 . 413 may be the optimization problem for finding a trajectory 112 in a convex subproblem for the individual subareas 411 . 412 . 413 be divided. Thus, an optimal solution of the optimization problem can be determined in an efficient manner.

In addition, the process includes 600 the determining 602 a variety of different possible encodings 420 (also referred to as possible length records in this document). This shows a coding or a length record 420 possible lengths 422 of the subareas 411 . 412 . 413 the majority of subareas 411 . 412 . 413 along the trajectory 112 at. In particular, for each subarea 411 . 412 . 413 the majority of subareas 411 . 412 . 413 the length 422 of the respective subarea 411 . 412 . 413 are displayed. The different possible codings 420 thus describe different trajectories 112 with at least partially different lengths of subareas 411 . 412 . 413 , The total length of the sequence of subregions 411 . 412 . 413 is typically constant (and may correspond to the planning horizon N _lon ).

Furthermore, the method comprises 600 , the determining 603 an (optimal) trajectory 112 based on the multitude of possible codings 420 and on the basis of a quality function or a quality measure. The quality function or the quality measure can be designed to have one or more optimization criteria for the trajectory to be determined 112 set. For example, the quality function or the quality measure can have at least one term with which a target position of the trajectory 112 is determined. Alternatively or additionally, the quality function or the quality measure can have at least one term with which the ride comfort (eg the jerk and / or a derivative of the jerk) of the trajectory 112 is described.

Determining 602 the multitude of possible codings or length data sets 420 and determining 603 an (optimal) trajectory 112 can be iterative. In particular, a coding 420 be adjusted iteratively (see step 201 from proceedings 200 ). It can then be the (optimal) trajectory 112 for the adapted coding 420 be determined (see step 202 from proceedings 200 ). Thus, in a particularly efficient manner (in particular using a branch-and-bound method) an overall optimal trajectory 112 be determined.

The procedure 600 can be repeated at a sequence of times to each updated trajectory 112 to investigate. It can at any time an updated distribution of the trajectory to be determined 112 into a sequence of subregions 411 . 412 . 413 respectively. Furthermore, based on the updated distribution of the trajectory to be determined 112 into different subareas 411 . 412 . 413 an updated trajectory 112 be determined. Thus, in a continuous manner, a driving function using a planned trajectory 112 (eg a lane change assistant, an automated longitudinal and / or transverse guidance, etc.) are provided.

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

Claims (20)

A method (600) for planning a trajectory (112) for a vehicle (100); the method comprising (600) Dividing (601) a region for a trajectory (112) into a plurality of subregions (411, 412, 413) so that in each subregion (411, 412, 413) of the plurality of subregions (411, 412, 413) respectively a constant amount of constraints (101, 102, 103) within the respective subarea (411, 412, 413) in an environment of the vehicle (100); - determining (602) a plurality of different possible length records (420); wherein a length record (420) indicates possible lengths (422) of the portions (411, 412, 413) of the plurality of portions (411, 412, 413) along the trajectory (112); and - Determining (603) a trajectory (112) based on the plurality of possible length data sets (420) taking into account a quality measure. Method (600) according to Claim 1 wherein - a possible length record (420) is determined (602) in response to one or more constraints; and - comprising one or more constraints - a restriction on an order of the subregions (411, 412, 413); and / or a restriction with respect to a minimum and / or a maximum length of at least one partial area (411, 412, 413). Method (600) according to one of the preceding claims, wherein - The trajectory (112) comprises a longitudinal trajectory along a road (105) traveled by the vehicle (100); and - The longitudinal trajectory is determined such that the determined longitudinal trajectory allows the determination of a transverse trajectory transverse to the roadway (105) through which a combined longitudinal-transverse trajectory, by the vehicle (100) movable is. Method (600) according to one of the preceding claims, wherein - the trajectory (112) comprises a longitudinal trajectory along a roadway (105) traveled by the vehicle (100); - The trajectory (112) is divided such that in a certain portion (412) of the plurality of sub-areas (411, 412, 413) a certain Transverse displacement of the vehicle (100) is effected transversely to the roadway (105); - the method (600) comprises, determining a minimum length of the particular portion (412) in dependence on the determined transverse offset; and - the minimum length of the particular subarea (412) is taken into account in determining (602) the plurality of possible length data sets (420). Method (600) according to Claim 4 wherein the determining comprises a minimum length of the specific subarea (412), - determining a longitudinal acceleration a _{x of} the vehicle (100) for the longitudinal trajectory in the determined subarea (412); Determining, on the basis of the longitudinal acceleration a _x and on the basis of a maximum acceleration a _{max of} the vehicle (100), a possible lateral acceleration a _{y of} the vehicle (100) in the specific subarea (412), in particular based on ${\alpha }_y=\sqrt{{\alpha }_{max}^2-{\alpha }_x^2};$

and determining the minimum length of the specific subarea (412) on the basis of the lateral acceleration a _y , in particular based on $t_{min}=\sqrt{\frac{2d_y}{{\alpha }_y}}+{\delta }_{steer}.$

where d _{y is} the determined _{lateral offset} , and where δ _{steer is} a reaction time of a steering of the vehicle (100), and where t min is a minimum time length of the particular subarea (412). Method (600) according to one of the preceding claims, wherein a secondary condition comprises a safety distance (401, 402, 403) to an obstacle (101, 102, 103) in the vicinity of the vehicle (100); and - The safety distance (401, 402, 403) from a travel speed (502) of the vehicle (100) depends. Method (600) according to Claim 6 in which - the safety distance (401, 402, 403) is determined by a section-wise linear function (503) of the driving speed v _ego (502) of the vehicle (100); - The sectionwise linear function (503) for all considered driving speeds v _ego (502) provides in particular a value of the safety distance (401, 402, 403), which is equal to or greater than d _{safe, 2} , with $$d_{\text{safe}\text{2}}=\frac{{\nu }_{\text{obj}}^2}{-2\left|{\alpha }_{\text{Max}\text{, obj}}\right|}-\frac{{\nu }_{\text{ego}}^2}{-2\left|{\alpha }_{\text{Max}\text{,ego}}\right|}+{\nu }_{\text{ego}}{\delta }_{\text{brake}}$$

- v _{obj is} a speed of the obstacle (101, 102, 103); - δ _{brake is} a reaction time of a braking of the vehicle (100); and - a _{max, obj} and a _{max, ego are} a maximum acceleration of the obstacle (101, 102, 103) and the vehicle (100), respectively. Method (600) according to one of the preceding claims, wherein - the trajectory (112) comprises a state sequence x (k) of a state vector x at a sequence of times k = 1, ...., N _lon ; the state vector x comprises a position of the vehicle (100), a speed of the vehicle (100), an acceleration of the vehicle (100) and / or a jolt of the vehicle (100); and - a possible length record (420) for each point in time of the sequence of times indicates the portion (411, 412, 413) of the trajectory (112). Method (600) according to Claim 8 in which - for the trajectory (112) a total of V constraints with respect to corresponding V obstacles (101, 102, 103) are to be considered; - V>0; a possible length record (420) comprises a number of binary vectors each having N _lon vector elements, by which in combination at each of the times k = 1,..., N _lon , the respective subregion (411, 412, 413) is displayed; and - the subset of constraints to be applied in each subarea (411, 412, 413) is displayed; and - the number of binary vectors is equal to or larger than the rounded value of log ₂ V. Method (600) according to Claim 9 wherein - a possible length record (420) comprises encoding the V constraints; the coding takes into account the V constraints such that each of the V constraints is activated or deactivated depending on a value of the one or more binary vectors, in particular using a Big-M method. The method (600) according to one of the preceding claims, wherein the method comprises (600) adapting (201) a possible length data set (420), and determining (202) a trajectory (112) for the adapted possible length data set (420 ), iteratively, so that the quality measure is improved. Method (600) according to Claim 11 wherein the iterative fitting (201) of a possible length record (420) is performed using a branch-and-bound method to reduce a number of possible length records (420) to be checked. Method (600) according to one of the preceding claims, wherein - the trajectory (112) comprises a state sequence x (k) of a state vector x at a sequence of times k = 1, ...., N _lon ; - determining (603) a trajectory (112) for a particular possible length record (420), determining (211) a state sequence x (k) in dependence on a state model of the vehicle (100); the state model indicates how a state vector x is transferred at a first time into a state vector x at a subsequent second point in time; the state model is in particular linear; - detecting (603) a trajectory (112), checking (212) whether the determined state sequence x (k) satisfies the particular possible length record (420); and - determining (603) a trajectory (112), determining (213) a value of the quality measure for the determined state sequence x (k). Method (600) according to Claim 13 wherein the method (600) comprises iteratively adjusting the state sequence x (k) so that the value of the measure of merit is improved and as long as the state sequence x (k) satisfies the determined possible length record (420) , Method (600) according to one of the preceding claims, wherein - The trajectory (112) is a longitudinal trajectory along a road (105) traveled by the vehicle (100); the method (600) further comprises determining a transverse trajectory transverse to the roadway (105); and - the method (600) further comprises superimposing the longitudinal trajectory and the transverse trajectory to determine a combined longitudinal-transverse trajectory. Method (600) according to one of the preceding claims, wherein the method (600) comprises transforming one or more state variables of the vehicle (100) from a first coordinate system (301) into a second coordinate system relative to a roadway (105) of the vehicle (100); the trajectory (112) in the second coordinate system is determined (603); and - The method (600) comprises transforming data with respect to the determined trajectory (112) from the second coordinate system in the first coordinate system (301) to determine drive data for driving one or more actuators of the vehicle (100). The method (600) according to one of the preceding claims, wherein the method (600) comprises providing a driving function of the vehicle (100) in dependence on the determined trajectory (112). Method for planning a trajectory (112) for a vehicle (100); the method comprises - determining at least one constraint with respect to at least one obstacle (101, 102, 103) in an environment of the vehicle (100); wherein the constraint includes a safety margin (401, 402, 403) to the obstacle (101, 102, 103) around the vehicle (100); and wherein the safety distance (401, 402, 403) depends on a vehicle speed (502) of the vehicle (100); wherein the safety margin (401, 402, 403) is determined by a sectional linear function (503) of the vehicle speed (502) of the vehicle (100); and - Determining a trajectory (112) taking into account a quality measure and in dependence on the at least one constraint. Device for planning a trajectory (112) for a vehicle (100); wherein the device is set up, to divide an area for a trajectory (112) to be determined for the vehicle (100) into a plurality of partial areas (411, 412, 413), such that in each partial area (411, 412, 413) of the plurality of partial areas (411, 412, 413) in each case a constant within the respective sub-area (411, 412, 413) amount of secondary conditions with respect to obstacles (101, 102, 103) in an environment of the vehicle (100) applies; determining a plurality of possible length data sets (420), wherein one possible length data set (420) includes possible lengths (422) of the subregions (411, 412, 413) of the plurality of subregions (411, 412, 413) along the Trajectory (112) indicates; and - Based on the large number of different possible length records (420) and taking into account a quality measure to determine a trajectory (112). Device for planning a trajectory (112) for a vehicle (100); wherein the device is arranged to: - determine at least one constraint with respect to at least one obstacle (101, 102, 103) in an environment of the vehicle (100); wherein the constraint includes a safety margin (401, 402, 403) to the obstacle (101, 102, 103) around the vehicle (100); and wherein the safety distance (401, 402, 403) depends on a vehicle speed (502) of the vehicle (100); wherein the safety margin (401, 402, 403) is determined by a sectional linear function (503) of the vehicle speed (502) of the vehicle (100); and - taking into account a quality measure and depending on the at least one constraint to determine a trajectory (112).

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