Determining dynamically possible driving maneuvers

Abstract

The invention relates to a computer-implemented method (100) for computing a trajectory of a mobile platform. The method computes an exact or an approximate solution of an optimization problem that minimizes a travel time from a given initial state to a given final state, wherein vibrations of the mobile platform are limited in amount to a maximum vibration, and wherein an acceleration of the mobile platform is limited, wherein the limit of the acceleration can depend on a velocity of the mobile platform.

Description

TECHNICAL FIELD

[0001] The present invention relates to a computer-implemented method for computing a trajectory of a mobile platform, a data processing system for performing the method, a computer program and a computer-readable storage medium. BACKGROUND

[0002] In the coming years, vehicles will be provided more and more with partially automated, highly automated or fully automated driving functions. Thereby, the burden of the driver can be reduced and the risk of accidents can be decreased. Adaptive cruise control and lane keeping assistants are already available, for example. It is expected that highly and fully automated driving functions will be added, for example autopilots for motorways.

[0003] These functions require the computation of an environment model based on sensor data, for example camera data, radar data, lidar data and / or ultrasound data. Based on the environment model and taking into account locally applicable traffic rules, a vehicle trajectory describing the motion of the ego vehicle can be computed. The vehicle trajectory can be computed by solving an optimization problem. The optimization problem can usually only be solved numerically if static and dynamic objects detected in the environment of the ego vehicle, traffic rules and limitations on the ego vehicle dynamics should be taken into account.

[0004] In the article "On the computation of switching surfaces in optimal control: A Gröbner basis approach" by U. Walther, T. Georgiou and A. Tannenbaum, IEEE Trans. on Automatic Control, Vol. 46, No. 4, 2001, hereinafter referred to as [Walther et al.], the solution of the following optimal control problem is described:

[0005] min t f

[0006] s.t. x(t) = [x 1 (t), x 2 (t), x 3 (t)] T

[0007] dx(t) / dt = [x 2 (t), x 3 (t), u(t)] T

[0008] x(t = 0) = [s 10 , x 20 , x 30 ] T

[0009] x(t = t f ) = [x 1f , x 2f , x 3f ] T

[0010] |u(t)| ≤ 1

[0011] Here, the optimization variable is a scalar function. x 1 (t) , x 2 (t) , x 3 (t) and u(t) and from the initial state [x 1f , x 2f , x 3f ] T Departure to final state [x 1f , x 2f , x 3f ] T Required time t f The initial state and the final state are fixed, pre-given parameters of the optimal control problem. Specifically, it is shown in [Walther et al.] that the solution is a function... u (t) Its absolute value is in the interval 0 ≤ t ≤ t f The constant is 1, and its sign changes at most twice. u(t) Points with discontinuities are referred to as switching points in the following text.

[0012] Numerical solutions of optimization problems for computing trajectories of vehicles usually require high computational effort and long computation times. However, there are often situations in which it should be determined within a short time whether a driving maneuver of the ego vehicle or of another vehicle is dynamically feasible. For example, it can be necessary to determine for a vehicle on an acceleration lane whether it can merge into the traffic on the main lane. Furthermore, it can be necessary to determine whether the vehicle can be completely braked before the end of the acceleration lane. In other situations, it can be necessary to determine whether another traffic participant can be overtaken. In many other situations, it can be necessary to determine within a short time whether a driving maneuver of a vehicle is dynamically feasible. SUMMARY

[0013] It is therefore the task of the present invention to determine whether a driving maneuver of a vehicle is dynamically feasible with small waiting times.

[0014] A first aspect of the present invention relates to a computer-implemented method for computing a trajectory of a mobile platform, wherein the method comprises solving exactly or approximately an optimization problem taking into account a Ruck auxiliary condition of the optimization problem and taking into account an acceleration auxiliary condition of the optimization problem. Herein, a cost function of the optimization problem has a travel time of the mobile platform from an initial state to a final state. Furthermore, the Ruck auxiliary condition limits a jerk of the mobile platform numerically to a maximum jerk. In addition, the acceleration auxiliary condition has a limit for an acceleration of the mobile platform.

[0015] The mobile platform is preferably a vehicle, i.e. a moving transportation means for transporting people or goods. However, the mobile platform can also be an automated or partially automated mobile robot which is not necessarily for transporting people or goods. Although the present invention is generally applicable to mobile platforms, a vehicle is described in the following for the sake of clarity.

[0016] By minimizing the travel time of the vehicle from the initial state to the final state, a trajectory can be computed in which the dynamic possibilities are utilized to the greatest extent. Thus, by computing a trajectory according to the present invention, it can also be implicitly determined which driving maneuvers are feasible under given dynamic auxiliary conditions.

[0017] The computer-implemented method for computing a trajectory of a vehicle can essentially comprise an exact or approximate solution of an optimization problem, wherein the optimization problem can be represented as follows:

[0018] min t f

[0019] s.t. x(t) = [x 1 (t), x 2 (t), x3 (t)] T

[0020] dx(t) / dt = [x 2 (t), x 3 (t), u(t)] T

[0021] x(t = 0) = [s 0 , v 0 , a 0 ] T

[0022] x(t = t f ) = [s f , v f , a f ] T

[0023] |u(t)| ≤ u 0

[0024] g min ≤ x 3 (t) ≤ g max

[0025] Here, x 1 (t) Describing the position of the vehicle as a function of time t, x 2 (t) Describing the speed of the vehicle, x 3 (t) Describing the acceleration of the vehicle, u(t) Describing the vibration of the vehicle. Optimization variable x 1 (t) , x 2 (t) , x 3 (t) and u(t) ​is preferably a scalar function of time t. Thus, the method for calculating a vehicle trajectory is preferably a method for calculating a one-dimensional vehicle trajectory. The restriction to one dimension enables to reduce the computational complexity and the computation time for determining an approximate or exact solution of the shown optimization problem. Here, the dimension can in particular correspond to the longitudinal direction of the vehicle.

[0026] Furthermore, in the optimization problem, dx(t) / dt denotes a vector x(t) derivative with respect to time. For example, the velocity is the derivative of the position with respect to time, thus dx 1 (t) / dt = x 2 (t) .

[0027] Furthermore, [s0, v0, a0] T describes a pre-given initial state of the vehicle, i.e. at time t = 0. The initial state has an initial position s0, an initial velocity v0and an initial acceleration a0.

[0028] In addition, t f describes the travel time from the initial state to a final state, which is in turn fixedly pre-given. As shown above, the final state can have a final position s f , a final velocity v f and a final acceleration a f . However, the final state does not necessarily have to have a final position, a final velocity and a final acceleration. For example, if a trajectory should be determined such that the vehicle stops as quickly as possible within a pre-given distance, the final state can only have a final position and a final velocity. On the other hand, if the vehicle should reach a final velocity as quickly as possible, the final state can only have a final velocity. In other cases, it can be necessary to determine a trajectory such that the vehicle drives as quickly as possible over a pre-given distance. In this case, the final state can only have a final position. By leaving the final position, the final velocity and / or the final acceleration indeterminate, the allowed number of the optimization problem can be increased and the travel time t f to reach the final state can be reduced. Thus, the flexible determination of the final state can enable the optimization problem to better adapt to traffic conditions, so that a better vehicle trajectory can be calculated with a shorter travel time t f .

[0029] vibration auxiliary condition |u(t)| ≤ u 0 limits the vibration of the vehicle numerically to a maximum vibration u0.

[0030] Furthermore, the optimization problem has an acceleration auxiliary condition gmin ≤ x 3 (t) ≤ g max wherein g min denotes a lower limit of the acceleration, while g max denotes an upper limit of the acceleration. Alternatively, the optimization problem can have only an upper limit g max of the acceleration. Alternatively, the optimization problem can have only a lower limit g min of the acceleration. The upper limit and / or the lower limit can depend on the speed of the vehicle. Thus, in particular, it can apply that g max = g max (x 2 (t)) and / or g min = g min (x 2 (t)) Here, the upper limit and / or the lower limit can be a polynomial function of the speed of the vehicle. In particular, the upper limit and / or the lower limit can be a zeroth, first, second or third polynomial of the speed of the vehicle.

[0031] In particular, the vibration auxiliary condition and the acceleration auxiliary condition can be implemented to take into account dynamic capabilities of different vehicle types, e.g. passenger cars or trucks. Furthermore, the vibration auxiliary condition and the acceleration auxiliary condition can be implemented to take into account different driving styles, e.g. cautious or sporty. Furthermore, the vibration auxiliary condition and the acceleration auxiliary condition can be implemented to take into account different vehicle states, e.g. new, old or tuned. Furthermore, the vibration auxiliary condition and the acceleration auxiliary condition can be implemented to take into account road conditions, e.g. dry, wet, snow or icy. For example, an icy lane can be taken into account by a corresponding low value of the maximum vibration and a corresponding low value of the upper limit of the acceleration.

[0032] The optimization problem shown above can not take into account various parameters of an environmental model determined based on sensor data, e.g. positions of static and / or dynamic objects in the environment of the vehicle. Thus, the shown optimization problem represents a simplification of a more general optimization problem in which additional parameters, e.g. positions of static and / or dynamic objects, are taken into account. Due to this simplification, the method for calculating a trajectory of a vehicle according to the present application is relevant in particular when the dynamic capabilities of the vehicle are most important. At the same time, by simplifying the optimization problem the computational complexity can be reduced and, thereby, the waiting time for calculating an exact or approximate solution.

[0033] According to one implementation, the limitation on the acceleration of a vehicle depends on the speed of the vehicle.

[0034] According to another embodiment, the limitation on the acceleration of the vehicle is a polynomial function of the vehicle's speed.

[0035] According to another embodiment, the method includes calculating a first switching point, wherein at the first switching point a first state curve contacts a second state curve, wherein the first state curve depends on the initial state, wherein the vibration-assisted condition is valid during the first state curve, and wherein the acceleration-assisted condition is valid during the second state curve.

[0036] The first and second state curves are preferably three-dimensional curves, which have vehicle position, vehicle speed and vehicle acceleration with respect to time, respectively.

[0037] Therefore, the magnitude of the vibration during the first state curve is equal to the maximum vibration u0. In particular, the vibration of the vehicle during the first state curve is preferably constant. Hereinafter, the vibration of the vehicle during the first state curve will be referred to as u1. The sign of u1 can be determined as in [Walther et al.], where the acceleration auxiliary condition is not considered.

[0038] [Walther et al.] disclosed a solution to the optimization problem based on the method according to the invention without considering the aforementioned acceleration auxiliary condition, wherein the solution is obtained by means of variables. x 1 (t),x 2 (t),x 3 (t) and u(t) The corresponding proportional transformation can consider values ​​where u0≠1. Compared to this known optimal control problem, the introduction of acceleration auxiliary conditions allows for better and, in particular, more accurate modeling of vehicle dynamics.

[0039] Even without considering the acceleration auxiliary condition in [Walther et al.], the solution to the simple control problem described in [Walther et al.] can satisfy this auxiliary condition. Therefore, the solution described in [Walther et al.] can represent an exact solution to the optimization problem upon which the method for calculating vehicle trajectory according to the present invention is based. Therefore, the method for calculating vehicle trajectory according to the present invention can include solving the simple control problem according to [Walther et al.] without considering the acceleration auxiliary condition.

[0040] The method for calculating a vehicle trajectory according to the present invention involves solving an optimization problem with vibration and acceleration auxiliary conditions, either precisely or approximately. Here, solving the optimization problem precisely or approximately should be understood as taking into account at least the vibration and acceleration auxiliary conditions. Therefore, the term "approximately solving the optimization problem" should not be interpreted in particular as completely disregarding the vibration or acceleration auxiliary conditions. The vibration and acceleration auxiliary conditions can be considered in different ways. For example, it can be checked whether the acceleration auxiliary condition is satisfied at a point on the trajectory. The acceleration auxiliary condition can also be considered in different forms, for example, as part of the Lagrangian function of a dual optimization problem.

[0041] The solution proposed by [Walther et al.] has at most three constant solutions. u(t) The section, of which u(t) The sign changes at the switching point. Therefore, if the solution of [Walther et al.] satisfies the acceleration auxiliary condition, the vehicle trajectory calculated according to the invention also has at most three segments with constant vibration. Conversely, if the solution of [Walther et al.] does not satisfy the acceleration auxiliary condition, the vehicle trajectory calculated according to the invention has an additional segment. This additional segment can be connected to the first segment of the vehicle trajectory and corresponds to the second state curve. The vibration can vary during the second state curve.

[0042] Therefore, the vehicle trajectory calculated according to the present invention can have a first state curve and a second state curve, wherein the second state curve immediately follows the first state curve. In other words, the vehicle trajectory can have a first segment and a second segment, which correspond to the first state curve and the second state curve, respectively. However, the second state curve is not necessarily a segment of the vehicle trajectory calculated according to the present invention. In particular, if the solution of [Walther et al.] does not satisfy the acceleration auxiliary condition, then the second state curve is a segment of the vehicle trajectory calculated according to the present invention. Furthermore, the vehicle trajectory calculated according to the present invention can have a third state curve, which can be connected to the second state curve. Furthermore, the vehicle trajectory calculated according to the present invention can have a fourth state curve, which is connected to the third state curve.

[0043] The vibration-assisted condition can be effective during the first, third, and fourth state curves. Furthermore, the vibration can be constant during the first, third, and fourth state curves, wherein the sign sequence of the vibration is the same as the corresponding sign sequence of the solution described in [Walther et al.] under the condition without considering acceleration assistance.

[0044] The first state curve preferably runs through an initial state of the vehicle trajectory. In particular, the first state curve preferably starts from the initial state, so that the course of change of the first state curve follows:

[0045] x 11 (t) = s 0 + v 0 t + a 0 t 2 / 2 + u 1 t 3 / 6

[0046] x 21 (t) = v 0 + a 0 t + u 1 t 2 / 2

[0047] x 31 (t) = a 0 + u 1 t .

[0048] Herein, x 11 (t) Description x 1 (t) of the first section, x 21 (t) Description x 2 (t) of the first section, x 31 (t) Description x 3 (t) of the first section.

[0049] The acceleration auxiliary condition is valid during the second state curve. If the acceleration auxiliary condition has both an upper limit of acceleration and a lower limit of acceleration, the upper limit of acceleration can be valid when ui is positive, while the lower limit of acceleration can be valid when ui is negative. To show an exemplary assumption that the upper limit of acceleration is valid, i.e. x 32 (t) = g max where x 32 (t) The vehicle acceleration during the second state curve is described. The upper limit g max may be a function of velocity, so that the differential equation

[0050] x 32 (t) = dx 22 (t) / dt = g max (x 22 (t)) is valid,

[0051] where x 22 (t) The vehicle velocity during the second state curve is described.

[0052] At the first switching point, the first state curve and the second state curve touch, so that

[0053] x 21 (t 1 ) = x 22 (t 1 ) , and

[0054] x 31 (t 1 ) = x 32 (t 1 ) ,

[0055] where ti is the time of the first switching point. This can also be rewritten as

[0056] v 0 + a 0 t 1+ u 1 (t 1 ) 2 / 2 = x 22 (t 1 ) , and

[0057] a 0 + u 1 t 1 =g max (x 22 (t 1 )) .

[0058] Thus, we have two equations with two unknowns, t1 and t2 x 22 (t 1 ) a system of equations.

[0059] By solving the second equation for t1 we obtain

[0060] t 1 = (g max (x 22 (t 1 )) - a 0 ) / u 1 .

[0061] Substituting into the first equation we obtain

[0062] v 0 + a 0 (g max (x 22 (t 1 )) - a 0 ) / u 1 + u 1 ((g max (x 22(t 1 )) - a 0 ) / u 1 ) 2 / 2 = x 22 (t 1 ) ,

[0063] where only x 22 (t 1 ) is unknown. It can also be solved numerically or according to the upper bound g max (x 22 (t)) This equation can be solved analytically. Moreover, it is clear that the first switching point can be solved by solving a univariate equation. Moreover, it is clear that if g max (x 22 (t)) is a polynomial function of x 22 (t) then the first switching point can be solved by solving a univariate polynomial equation.

[0064] For example, if the upper bound of the acceleration is an affine function of the vehicle speed, i.e. if

[0065] g max (x 22 (t)) = m x 22 (t) + b ,

[0066] then it follows that

[0067] v 0 + a 0 (m x 22 (t 1 ) + b - a 0 ) / u 1 + u 1 ((m x 22 (t 1 ) + b - a 0) / u 1 ) 2 / 2 = x 22 (t 1 ) ,

[0068] Thus, in this case, the first switching point at which the first state curve and the second state curve touch each other can be calculated by solving a quadratic equation.

[0069] After having determined x 22 (t 1 ) Further parameters of the first switching point can then be calculated directly. The time of the first switching point is obtained from

[0070] t 1 = (g max (x 22 (t 1 )) - a 0 ) / u 1 .

[0071] The position and the acceleration at the first switching point are obtained by substituting x 11 (t) and x 31 (t) into the differential equation dx 22 (t) / dt = g max (x 22 (t)) follows the course of the second state curve.

[0072] According to another embodiment, the method further comprises calculating a second switching point at which the second state curve touches a third state curve and a third switching point at which the third state curve touches a fourth state curve, wherein the vibration auxiliary condition is valid with different signs during the third and fourth state curve, and wherein the fourth state curve depends on the final state.

[0073] The vibration of the vehicle is preferably constant during the third state curve and equal in magnitude to the maximum vibration u0. The vibration of the vehicle during the third state curve is hereinafter referred to as u3. The sign of u3 is preferably opposite to the sign of ui. Since the vibration of the vehicle during the third state curve is known, the change process of the third state curve can be expressed as follows:

[0074] x 13 (t) = s 3 + v 3 t + a 3 t 2 / 2 + u 3 t 3 / 6

[0075] x 23 (t) = v 3 + a 3 t + u 3 t 2 / 2

[0076] x 33 (t) = a 3 + u 3 t ,

[0077] wherein x 13 (t) The position of the vehicle during the third state curve is described, x 23 (t) The speed of the vehicle during the third state curve is described, x 33 (t) The acceleration of the vehicle during the third state curve is described, whereas s3, v3 and a3 are first unknown.

[0078] Furthermore, the vibration of the vehicle during the fourth state curve is preferably constant and equal in magnitude to the maximum vibration u0. The vibration of the vehicle during the fourth state curve is hereinafter referred to as u4. The sign of u4 is preferably opposite to the sign of u3. Thus, the change process of the fourth state curve can be expressed as follows:

[0079] x 14 (t) = s 4 + v 4 t + a 4 t 2 / 2 + u 4 t 3 / 6

[0080] x 24 (t) = v 4 + a 4 t + u 4 t 2 / 2

[0081] x 34 (t) = a 4 + u 4 t ,

[0082] wherein x 14 (t) a position of the vehicle during the fourth state curve is described, x 24 (t) a velocity of the vehicle during the fourth state curve is described, x 34 (t) an acceleration of the vehicle during the fourth state curve is described, while s4, v4 and a4 are first unknown.

[0083] The fourth state curve preferably runs through the final state. The fourth state curve preferably ends at the final state. Thus:

[0084] x 14 (t f ) = s 4 + v 4 t f + a 4 t f2 / 2 + u 4 t f 3 / 6 = s f

[0085] x 24 (t f ) = v 4 + a 4 t f + u 4 t f 2 / 2 = v f

[0086] x 34 (t f ) = a 4 + u 4 t f = a f .

[0087] Thus, the three unknowns s4, v4 and a4 can be expressed as a function of the unknown travel time t f Thus, the number of unknowns for the fourth state curve is reduced from three to one.

[0088] The following applies for the second switching point:

[0089] x 12 (t 2 ) = x 13 (t 2 )

[0090] x 22 (t 2 ) = x 23 (t 2 )

[0091] x32 (t 2 ) = x 33 (t 2 ) ,

[0092] where t2 is the time of the second switching point, and s3, v3 and a3 are unknown, except for t2. Furthermore, the following applies to the third switching point:

[0093] x 13 (t 3 ) = x 14 (t 3 )

[0094] x 23 (t 3 ) = x 24 (t 3 )

[0095] x 33 (t 3 ) = x 34 (t 3 ) ,

[0096] where t3 is the time of the third switching point, and s3, v3, a3 and t f are unknown, except for t3. Thus, in total, a system of equations with six unknowns t2, t3, s3, v3, a3 and t f is obtained. This system of equations can be combined into a system of equations with four unknowns, wherein, in particular, the fact that the functions x 33 (t) and x 34 (t) are affine is utilized. Here, different forms of the system of equations are possible.

[0097] Thus, by solving the system of equations, the second and third switching points can be calculated efficiently, i.e. with a lower computational complexity and thus also with a shorter computation time.

[0098] According to another embodiment, the second and third switching points are calculated by solving a system of equations.

[0099] According to another embodiment, the initial state has an initial position, an initial velocity and an initial acceleration of the vehicle.

[0100] According to another embodiment, the final state has a final position, a final velocity and / or a final acceleration of the moving platform.

[0101] According to another embodiment, the calculated trajectory is a one-dimensional trajectory.

[0102] According to another embodiment, control signals for actuating a drive system and / or a brake system of the vehicle and / or warning signals for warning an occupant of the vehicle are provided based on the calculated trajectory.

[0103] In order to travel along the calculated trajectory, in particular the drive system and / or the brake system of the own vehicle can be actuated.

[0104] A second aspect of the present application relates to a data processing system comprising means for carrying out the method according to the present application.

[0105] The data processing system is for example a control device. The data processing system has at least one processor and a storage unit. The processor can be for example a microprocessor, a microcontroller or a special purpose processor. The storage unit has preferably a non-volatile storage unit on which a computer program is stored which is written to carry out the method according to the present application. The data processing system can have a number of other components, for example a communication unit via which the data processing system can communicate with a server so that parts of the computer program according to the present application can be stored and / or executed on the server.

[0106] A third aspect of the present application therefore relates to a computer program, wherein the computer program comprises instructions which, when executed by a data processing system, cause the data processing system to carry out the method according to the present application.

[0107] A fourth aspect of the present application relates to a computer readable storage medium on which the computer program according to the present application is stored. BRIEF DESCRIPTION OF DRAWINGS

[0108] Further explanations and a description of preferred embodiments of the present application are shown in detail below on the basis of the drawings.

[0109] Figure 1 A method for calculating a trajectory of a vehicle according to an embodiment of the present application is shown. DETAILED DESCRIPTION

[0110] Figure 1 A method 100 for calculating a trajectory of a vehicle according to an embodiment of the present application is shown. In a first step S1, a sequence of signs of oscillations is calculated, for which the method described in [Walther et al.] can be used. Thus, in addition to the solution in a constant section, it can be implicitly determined how many switching points the solution without taking the acceleration auxiliary condition into account has. The sequence of signs can be calculated without taking the acceleration auxiliary condition into account. The sign of oscillation in the first section of the vehicle trajectory calculated according to the present application taking the acceleration auxiliary condition into account is preferably the same as the sign of oscillation in the first section of the solution without taking the acceleration auxiliary condition into account. u(t)

[0111] In a second step S2, the first switching point is calculated according to the method described in [Walther et al.]. Thus, the acceleration auxiliary condition is not taken into account, and the first switching point is calculated at which the function u(t) first changes its sign. The time of the first switching point without taking the acceleration auxiliary condition into account will be referred to as τ 12 .

[0112] In a third step S3, the first switching point is calculated taking the acceleration auxiliary condition into account. For this purpose, the switching point is calculated at which the first state curve touches the second state curve, wherein the starting point of the first state curve is given by the initial state [s 0 , v 0 , a 0 ] T is given, wherein the oscillation during the first state curve u(t) is equal in amount to the maximum oscillation, wherein the sign of oscillation during the first state curve is the same as the sign calculated in step S1, and wherein the acceleration auxiliary condition is valid during the second state curve. The time of the first switching point taking the acceleration auxiliary condition into account is t1.

[0113] In a fourth step S4, it is checked whether τ1 is less than or equal to t1. Thus, it is checked whether the first switching point without taking the acceleration auxiliary condition into account is before the first switching point taking the acceleration auxiliary condition into account.

[0114] If τ1 is less than or equal to t1, the vehicle trajectory calculated according to the present application is preferably the same as the trajectory calculated according to [Walther et al.] without taking the acceleration auxiliary condition into account. Further parameters of this trajectory can be determined in step S5a. ​

[0115] If t1 is greater than t1, the vehicle trajectory calculated according to the present application has a first and a second section, wherein the first section of the vehicle trajectory is given by the first state curve as described above, and wherein the second state curve is given by a second state curve.

[0116] If the solution calculated according to [Walther et al.] without considering the acceleration auxiliary condition has a switching point, the vehicle trajectory calculated according to the present application preferably has a third section. Furthermore, if the solution without considering the acceleration auxiliary condition has a second switching point, the vehicle trajectory calculated according to the present application preferably has a fourth section. The number of switching points of the solution without considering the acceleration auxiliary condition is directly derived from the sequence of signs determined in step S1. Thus, in step S5b, the second and third switching points can be calculated, wherein at the second switching point the second state curve touches the third state curve, and at the third switching point the third state curve touches the fourth state curve, wherein the vibration auxiliary condition is valid with different signs during the third and fourth state curve, and wherein the fourth state curve ends in a final state [s f , v f , a f ] T the fourth state curve. In particular, the sequence of vibration signs during the first, third and fourth state curve is identical to the sequence of vibration signs of the corresponding solution according to [Walther et al.] without considering the acceleration auxiliary condition. The second and third switching points can be calculated by solving a system of equations with four unknowns of four equations.

[0117] In step S6, the vehicle trajectory according to the present application can be generated.

[0118] After calculating a trajectory that makes the most of the dynamic possibilities, it can be determined, for example, whether it is possible to merge into a traffic flow, whether it is possible to brake completely before an obstacle or an acceleration band ends, or whether it is possible to overtake a traffic participant. Depending on this, in particular, the drive system, the brake system and / or the steering system can be manipulated in order to follow the trajectory calculated according to the present application. However, the trajectory calculated according to the present application can also be disadvantageous, because, for example, it is no longer possible to brake completely before an obstacle. In this case, the trajectory calculated according to the present application can be modified, for example, to avoid the obstacle.

[0119] The described embodiments equally relate to a computer-implemented method for computing a vehicle trajectory, a data processing system for performing the method, a computer program and a computer readable storage medium. In other words, features that have been described with reference to the computer-implemented method can also be implemented in the data processing system, the computer program and / or the storage medium, and vice versa.

[0120] Synergistic effects can be obtained from different combinations of embodiments, even if these combinations have not been described in detail.

Claims

1. A computer-implemented method (100) for calculating the trajectory of a mobile platform to determine whether a vehicle's driving maneuver is dynamically feasible, the method comprising: The optimization problem is solved accurately or approximately by considering both the vibration-assisted conditions and the acceleration-assisted conditions of the optimization problem. The cost function of the optimization problem includes the travel time of the mobile platform from the initial state to the final state. The vibration-assisted condition hereby limits the vibration of the mobile platform to a maximum in terms of quantity. The acceleration assistance condition described herein has limitations on the acceleration of the mobile platform. The method includes calculating a first switching point. At the first switching point, the first state curve contacts the second state curve. The first state curve depends on the initial state. The vibration-assisted condition is effective during the first state curve. The acceleration auxiliary condition is valid during the second state curve. The first switching point is calculated by solving a polynomial equation, and The vibration-assisted condition and the acceleration-assisted condition can be implemented as follows: -Considering the dynamic capabilities of different vehicle types -Consider different driving styles, and / or - Consider road conditions.

2. The method (100) according to claim 1. The limitation on the acceleration of the mobile platform depends on the speed of the mobile platform.

3. The method (100) according to claim 2. The limitation on the acceleration of the mobile platform is a polynomial function of the speed of the mobile platform.

4. The method (100) according to claim 1 The method includes calculating a second switching point and a third switching point. At the second switching point, the second state curve contacts the third state curve, and at the third switching point, the third state curve contacts the fourth state curve. The vibration-assisted condition is effective with different signs during the third and fourth state curves, and The fourth state curve depends on the final state.

5. The method (100) according to claim 4. The second switching point and the third switching point are calculated by solving a system of equations.

6. The method (100) according to any one of claims 1-5. The initial state includes the initial position, initial velocity, and initial acceleration of the mobile platform.

7. The method (100) according to any one of claims 1-5. The final state includes the final position, final velocity, and / or final acceleration of the mobile platform.

8. The method (100) according to any one of claims 1-5. The trajectory mentioned therein is a one-dimensional trajectory.

9. The method (100) according to any one of claims 1-5. The calculated trajectory provides control signals for manipulating the drive and / or braking systems of the mobile platform, and / or provides warning signals for alerting the occupants of the mobile platform.

10. A data processing system comprising a memory and a processor, wherein a computer program comprising instructions is stored in the memory, wherein when the computer program is executed by the data processing system, the instructions cause the data processing system to perform the method (100) according to any one of claims 1-9.

11. A computer program product having a computer program including instructions that, when executed by a data processing system, cause the data processing system to perform the method (100) according to any one of claims 1 to 9.

12. A computer-readable storage medium having a computer program thereon containing instructions that, when executed by a data processing system, cause the data processing system to perform the method (100) according to any one of claims 1-9.

Images