Determining the trajectory of a first vehicle in consideration of the driving behavior of a second vehicle

Abstract

The invention relates to determining a trajectory of a first vehicle (1) taking into account the driving behavior of a second vehicle (18), wherein the second vehicle (18) drives in front of the first vehicle (1). Herein, a processor unit (3) is configured to access speed data of the second vehicle (18), wherein the speed data has been generated by sensors of the first vehicle (1). In addition, the processor unit is configured to establish a driving behavior pattern of the second vehicle (18) based on the speed data and to predict a future driving behavior of the second vehicle (18) based on the driving behavior pattern of the second vehicle (18). Furthermore, the processor unit is configured to determine the trajectory of the first vehicle (1) by executing an MPC algorithm comprising a longitudinal dynamics model of the first vehicle and a cost function to be minimized, such that the cost function is minimized, wherein the prediction of the future driving behavior of the second vehicle (18) is considered as a constraint when determining the trajectory.

Description

Technical Field

[0001] The present invention relates to determining a trajectory of a first vehicle taking into account the driving behavior of a second vehicle, where the second vehicle is driving in front of the first vehicle. In this context, the present invention particularly relates to a processor unit, a driver assistance system, a vehicle, a method and a computer program product. Background Art

[0002] It is well known that in an adaptive cruise control system (ACC), efficiency criteria are also taken into account when planning a speed trajectory. Here, a rapidly developing method is trajectory planning by means of a so-called MPC solver. When using this method, a large number of possible trajectories can be evaluated on a virtual domain with respect to their overall efficiency. Here, other traffic participants may also affect the overall efficiency of the finally selected trajectory. For example, when a vehicle in front introduces a braking process or drives more slowly and thus reduces the solution space of the MPC solver of this vehicle, this vehicle is forced to adopt a less optimal trajectory. A fundamental problem here is that this vehicle generally does not know how the vehicle driving in front will behave.

[0003] ZHOU BINGYU et al. disclose a method for joint behavior estimation and trajectory planning in "Joint Multi-Policy Behavior Estimation and Receding-Horizon Trajectory Planning for Automated Urban Driving", 2018 IEEE INTERNATIONAL CONFERENCE ON ROBOTICS AND AUTOMATION (ICRA 2018), IEEE, May 21, 2018, pages 2388 - 2394, XP033403553, DOI: 10.1109 / ICRA.2018.8461138. This method models interaction and multi-policy decision-making. This method uses a partially observable Markov decision process to estimate the behavior of other traffic participants with respect to the planned trajectory of this vehicle, and uses receding horizon control to generate a safe trajectory for this vehicle. To achieve safe navigation, stochastic constraints for multiple motion strategies are introduced in the receding horizon planner. These constraints take into account the uncertainty of the behavior of other traffic participants.

[0004] LIU CHANG et al., in "Path planning for autonomous vehicles using model predictive control", 2017 IEEE INTELLIGENT VEHICLES SYMPOSIUM (IV), IEEE, June 11, 2017, pp. 174-179, XP033133751, DOI: 10.1109 / IVS.2017.7995716, further taught: As an alternative to explicit rules, a unified path planning method is used with model predictive control (MPC), which automatically determines the motion mode. To ensure safety, surrounding vehicles are modeled as polygons, and certain restrictions are made in MPC to enforce collision avoidance between the vehicle and surrounding vehicles. In order to achieve comfortable and natural operation, the potential field associated with the trajectory is introduced into the objective function of MPC.

[0005] Furthermore, DE 10 2011 002275 A1 discloses a method for predicting the driving behavior of a vehicle traveling ahead by means of a motor vehicle control device of a vehicle traveling behind the vehicle traveling ahead. Here, first, the corresponding current position of the vehicle traveling ahead is determined by means of the motor vehicle control device of the vehicle traveling behind the vehicle traveling ahead from the corresponding current position of the vehicle traveling behind the vehicle traveling ahead and the corresponding current distance to the vehicle traveling ahead. The motor vehicle control device of the vehicle traveling behind the vehicle traveling ahead determines matching driving segment data from the current position of the vehicle traveling ahead and determines characteristic values ​​of the vehicle traveling ahead from driving dynamics data of the vehicle traveling ahead determined for the corresponding current position of the vehicle traveling ahead. Then, the driving behavior of the vehicle traveling ahead is predicted by means of the motor vehicle control device of the vehicle traveling behind the vehicle traveling ahead from the characteristic values ​​of the vehicle traveling ahead and from driving segment data of the driving segment ahead of the vehicle traveling ahead. Summary of the invention

[0006] The object of the present invention may be seen as providing an MPC control of a first vehicle, wherein the behavior of a second motor vehicle travelling ahead of the first vehicle is taken into account.

[0007] This object is achieved by the subject matter of the independent patent claims. Advantageous embodiments are the subject matter of the dependent claims, the following description and the drawings.

[0008] The present invention proposes to model the driving behavior of a vehicle moving ahead and then use a driver model to implement driver assistance functions for the vehicle moving ahead. Such a modeling logic for a vehicle moving ahead can be combined with an MPC-based driving strategy. Here, the vehicle moving ahead can be modeled based on radar data, and then the driver model can be used to optimize longitudinal automated driving assistance functions. The present invention thus enables anticipation of the behavior of a vehicle moving ahead.

[0009] In this sense, according to a first aspect of the present invention, a processor unit is provided for a first vehicle. The processor unit is configured to determine the trajectory of the first vehicle taking into account the driving behavior of a second vehicle, wherein the second vehicle is moving ahead of the first vehicle (this vehicle). Thus, the second vehicle is a vehicle moving ahead relative to the first vehicle. The feature "trajectory of the first vehicle" can be understood as the path that the first vehicle should follow in the future, for example, within the next few seconds. Here, a speed profile can be assigned to the path, wherein the speed profile can specify the target speed of the first vehicle for each point along the path. From this association of the path and the speed, the speed trajectory of the first vehicle is obtained.

[0010] The processor unit is configured to access speed data of the second vehicle, wherein the speed data has been generated by a sensor of the first vehicle. The speed data describes at least one speed at which the second vehicle is moving. The speed can be a time profile of the speed at which the second vehicle is moving within a determinable time period. The sensor of the first vehicle is in particular configured to detect the speed of the second vehicle. For example, the sensor can be a radar sensor.

[0011] Using the information collected, a driving behavior model of the second vehicle can be established. For example, a vehicle that consistently maintains an average speed well below the legally permitted maximum speed can be described as a less aggressive traffic participant. In this sense, the processor unit is configured to establish a driving behavior model of the second vehicle based on the speed data.

[0012] According to the present invention, the driving behavior model of the second vehicle is used to obtain the driving anticipation of the modeled vehicle. In this sense, the processor unit is configured to anticipate the future driving behavior of the second vehicle based on the driving behavior model of the second vehicle.

[0013] The resulting advance information can be forwarded to the MPC logic for planning an optimal driving trajectory for the first vehicle. The MPC logic plans an optimal speed trajectory for the first vehicle for a forward section taking into account route topology, traffic, and other environmental information. The speed trajectory can now be refined and thus improved taking into account the advance information about the vehicle driving ahead. In this way, an integrated optimization of different degrees of freedom is also possible, which results in an overall optimal driving behavior. The prediction about the vehicle driving ahead can be used as a hard auxiliary condition for the MPC logic. A hard auxiliary condition can be understood as an auxiliary condition that must be compulsorily observed when determining the trajectory of the first vehicle. In this sense, the processor unit is also configured to determine the trajectory of the first vehicle by executing an MPC algorithm that includes a longitudinal dynamics model of the first vehicle and a cost function to be minimized, such that the cost function is minimized, wherein the advance information about the future driving behavior of the second vehicle is considered as an auxiliary condition when determining the trajectory.

[0014] The method of model-based predictive control (MPC) enables finding an optimal solution for a so-called "driving efficiency" driving function in each situation under given boundary conditions and restrictions, which provides an efficient driving manner. The MPC method is based on a system model that describes the behavior of the system, in the present invention based on a longitudinal dynamics model of the first vehicle. In addition, the MPC method is based on an objective function or cost function that describes the optimization problem and determines which state variables should be minimized.

[0015] The longitudinal dynamics model can depict the powertrain of the vehicle and can include a vehicle model with vehicle parameters and powertrain losses (sometimes approximate characteristic curves). Information about the topology of the forward section of the road (such as curves and slopes) can also be incorporated into the longitudinal dynamics model of the powertrain. In addition, information about the speed limit of the forward section of the road can also be incorporated into the dynamics model of the powertrain. The MPC algorithm can include an MPC solver in the form of a software module. The MPC solver can contain instructions or program code that instruct the processor unit to determine the trajectory of the first vehicle according to the longitudinal dynamics model of the first vehicle such that the cost function is minimized.

[0016] The processor unit can forward the optimized trajectory of the first vehicle to a software module ("target generator"). With the help of this software module, the processor unit can convert the mathematical optimal planning of all available degrees of freedom into practically exploitable component signals. For example, the speed trajectory of the first vehicle can be optimally planned for the next 5000 m by means of MPC control. In this case, the target generator "converts" the first (= currently required) speed value of this trajectory into the required torque of, for example, the electric motor of the first vehicle (as an efficiency-related component). The component software can then use this value to operate and regulate the desired speed.

[0017] According to another embodiment, the first term of the cost function comprises electrical energy weighted with a first weighting factor and predicted according to a dynamic model, which electrical energy is provided by the battery of the powertrain of the first vehicle within the prediction horizon to drive the electric motor. In addition, the cost function can comprise the travel time weighted with a second weighting factor and predicted according to a longitudinal dynamics model as the second term, which travel time the first vehicle requires to cover the entire predicted section within the prediction horizon. The processor unit can be set to determine the input parameters of the electric motor depending on the first term and depending on the second term by executing an MPC algorithm, such that the cost function is minimized.

[0018] The state variables for the driving efficiency driving function can thus be, for example, the vehicle speed or kinetic energy, the remaining energy in the battery, and the travel time. The optimization of the energy consumption and the travel time can be carried out, for example, based on the gradient of the road ahead and the limitations on speed and driving force, and based on the current system state. With the objective function or cost function of the driving efficiency driving strategy, in addition to the overall losses or energy consumption, the travel time can also be minimized. This results in: depending on the choice of the weighting factor, a low speed is not always evaluated as optimal and thus the problem no longer occurs that the resulting speed always lies at the lower limit of the permitted speed. It is possible to achieve that the driver influence is no longer related to the energy consumption and the travel time of the first vehicle, since the electric motor can be controlled by the processor unit based on the input parameters, which are determined by executing an MPC algorithm. In particular, the optimal motor operating point of the electric motor can be adjusted with the help of the input parameters. Thereby, the optimal speed of the first vehicle can be directly regulated.

[0019] In particular, the cost function can have only linear terms and quadratic terms. As a result, the entire problem has a quadratic optimization form with linear auxiliary conditions and manifests itself as a convex problem that can be solved well and quickly. The objective function or cost function can be provided with weights (weighting factors), wherein in particular energy efficiency, driving time and driving comfort are calculated and weighted. The energy-optimal speed trajectory can be calculated online for the front boundary on a processor unit, which can in particular form a component of the central controller of the first vehicle. By using the MPC method, the target speed of the first vehicle can also be periodically recalculated based on the current driving state and the information about the road section ahead.

[0020] The current state parameters can be measured, the corresponding data can be recorded and provided to the MPC algorithm. Therefore, the section data from the electronic map for the forward-looking boundary or predicted boundary (e.g. 400m) in front of the first vehicle can be upgraded or updated, especially periodically upgraded or updated. The section data can include, for example, slope information, curve information and information about speed limits. In addition, the curve curvature can be converted into the speed limit of the first vehicle by the maximum lateral acceleration allowed. In addition, the first vehicle can be oriented, especially accurately positioned on the electronic map by GNSS signals.

[0021] The speed data of the second vehicle include the time curve of the actual speed of the second vehicle determined by the sensor of the first vehicle. The function can calculate the average value of the relative deviation or percentage deviation from the speed limit (taking into account the driving situation). This average deviation can be applied to the maximum speed ahead of the second vehicle.

[0022] According to the present invention, the processor unit is configured to access a first speed limit value, which is applicable to a first road section on which a second vehicle is traveling, and to access a second speed limit value, which is applicable to a second road section on which the second vehicle will travel in the future. For example, the speed limit value specified in km / h (kilometers / hour) is the maximum speed of a vehicle legally permitted or allowed on a road section. The speed limit value is a binding limit on the speed of the vehicle, which is not allowed to be exceeded. In layman's terms, the term "speed limit" is also used in this case. The speed limit value can generally be set by regulations and indicated by traffic signs, and is applicable to specific vehicles, the transportation of specific goods or specific sections of roads, railways or waterways, and is sometimes also applicable to airspace.

[0023] Furthermore, the processor unit is configured to generate a time function of the relative speed deviation of the actual speed of the second vehicle from the first speed limit value from the time curve of the actual speed of the second vehicle. A "time function" may be understood as a mathematical function that describes the curve of the relative speed deviation of the actual speed of the second vehicle from the first speed limit value over time.

[0024] The processor unit is further configured to determine an average relative speed deviation from the time function of the relative speed deviation, establish a driving behavior pattern of the second vehicle based on the average relative speed deviation, and predict the future driving behavior of the second vehicle based on the driving behavior pattern of the second vehicle, such that the future speed of the second vehicle on the second section is determined depending on the average relative speed deviation and the second speed limit value.

[0025] In a simple example, there may be a constant first speed limit of 100 km / h on the first section, where the observed second vehicle moves in front of the first vehicle at a speed of 80 km / h on the first section, for example, during the entire observation period, for example, 30 seconds. In this case, there is also an average deviation of -20% from the first speed limit. If a new second speed limit (e.g., 50 km / h) now appears within the forward driving range, the predicted speed of the second vehicle (after the speed adjustment process is completed) can be predicted to be 40 km / h (50 km / h * (100% - 20%) = 40 km / h).

[0026] In another embodiment, the processor unit is configured to store the time-discrete relative speed deviation of the actual speed of the second vehicle from the first speed limit value in chronological order in a data set for a determined time period, and generate a time function of the relative speed deviation of the actual speed of the second vehicle from the first speed limit value from the time-discrete, chronologically stored relative speed deviations.

[0027] For example, the actual speed v of the second vehicle driving ahead can be determined with the aid of available radar information detected . Then the actual speed v of the second vehicle driving ahead can be obtained detected and the relative deviation Δv limit1 from the first speed limit value v rel . The relative speed deviation can be calculated by the following formula: Δv rel =(v limit1 -v detected ) / v limit1 or Δv rel =(v detected -v limit1 ) / v limit1 . The calculated relative deviation or percentage deviation can be stored in the data set, particularly in a first-in-first-out (FIFO) vector, where the data set can have a preset storage duration, for example, 30 s. The data set, particularly the FIFO vector, can be described as a data array as follows:

[0028]

[0029] Here, a single value Δv rel (t1) to Δv rel (t n ) is the calculated percentage deviation at the corresponding time points t1 to t n , where t1 is the first time point during a preset storage duration (e.g., 30 s; "determined time period"), and where t n is the last time point during the preset storage duration. Storage within the data set, especially storage within a FIFO vector, enables the curve description of the percentage deviation of the actual speed of the second vehicle traveling ahead from the first speed limit value. For this purpose, Δv rel (t1) to Δv rel (t n ) is stored in chronological order in the data set, especially in a FIFO vector. Based on the time-discrete values Δv rel (t1) to Δv rel (t n ) a function of the relative speed difference over time can be generated. This function can be differentiated twice, where the first derivative describes the time curve of the acceleration of the second vehicle, and where the second derivative describes the time curve of the jerk of the second vehicle.

[0030] In another embodiment, the processor unit is configured to determine the average acceleration of the second vehicle from the first derivative of the time function of the speed deviation with respect to time, and to establish a driving behavior pattern of the second vehicle based on the average acceleration of the second vehicle. For example, a vehicle with only a small average acceleration can be modeled as a less aggressive traffic participant.

[0031] Information about the average acceleration can be applied to the acceleration operation and the braking operation of the second vehicle. The acceleration operation and the braking operation are performed especially when the maximum allowed speed change occurs, in front of a traffic light or in front of an intersection. Similar to the prediction of the speed of the second vehicle described above, the average (=characteristic) value of the acceleration is also calculated here, for example, during the speed limit transition. In this sense, the processor unit can be configured to predict the future driving behavior of the second vehicle based on the driving behavior pattern of the second vehicle, such that the future acceleration of the second vehicle, especially on the first section, is determined depending on the average acceleration, the average relative speed deviation, and the second speed limit value.

[0032] For example, an average acceleration value of -1 m / s is calculated 2, that is to say, the second vehicle brakes (braking operation) on average with this negative acceleration value. If now the speed limit value changes in the boundary region (for example, changes from 100 km / h as the first speed limit value to 50 km / h as the second speed limit value), then the average acceleration or the representative acceleration can be used for prediction. Here, in particular, it can be assumed that the second vehicle reaches its target speed at the start of the new second speed limit value, and the target speed can be determined as described above depending on the average relative speed deviation and the second speed limit value. Then, starting from this road point (the transition between the first section where the first speed limit value applies and the second section where the second speed limit value applies), it can be calculated backwards when and where the braking operation starts.

[0033] The representative jerk of the second vehicle can be used for predicting the acceleration transition of the second vehicle in a similar manner. In this sense, the processor unit can be set to determine the average jerk of the second vehicle from the second derivative of the time function of the speed deviation with respect to time, and to establish a driving behavior pattern of the second vehicle based on the average jerk of the second vehicle. For example, a vehicle with an average small jerk can be modeled as a less aggressive traffic participant. The processor unit can also be set to predict the future driving behavior of the second vehicle based on the driving behavior pattern of the second vehicle, such that the future jerk of the second vehicle, especially on the first section, is determined depending on the average jerk, average acceleration, average relative speed deviation, and the second speed limit value. For example, a value of -1 m / s 3 can be determined for the average jerk. In this case, during the further braking operation described above, for example, the transition of the acceleration from 0 m / s 2 to -1 m / s 2 takes one second. From this, the duration of the transition between the non-braking pedal position and the representative braking pedal position can be predicted. For the length of this transition, the jerk remains constant.

[0034] The maximum jerk and the maximum acceleration can also be used to detect the possibility of emergency braking. In this sense, the processor unit can be set to determine the maximum acceleration of the second vehicle from the first derivative of the time function of the speed deviation with respect to time, and to determine the maximum jerk of the second vehicle from the second derivative of the time function of the speed deviation with respect to time, and to establish a driving behavior pattern of the second vehicle based on the maximum acceleration and maximum jerk of the second vehicle. In addition, the processor unit can be set to predict the future driving behavior of the second vehicle based on the driving behavior pattern of the second vehicle, such that the emergency braking of the second vehicle is detected depending on the maximum acceleration and maximum jerk.

[0035] Within the scope of the MPC method, the above functions or steps can be performed in each calculation step (usually 10 ms). In this sense, the processor unit can be set to: anticipate the future driving behavior of the second vehicle every time the MPC algorithm is executed to determine the trajectory of the first vehicle.

[0036] According to a second aspect of the invention, there is provided a driver assistance system for performing a driver assistance function of a first vehicle taking into account the driving behavior of a second vehicle, wherein the second vehicle is traveling in front of the first vehicle. The driver assistance system is set to access, in particular by means of a communication interface, the trajectory of the first vehicle determined by the processor unit according to the first aspect of the invention, and to perform, in particular by means of the processor unit, the driver assistance function of the first vehicle using the trajectory of the first vehicle.

[0037] The driver assistance function includes autonomous or semi-autonomous driving functions. The autonomous driving function allows the vehicle to drive itself, i.e., without the vehicle occupant controlling the vehicle. The driver has handed over the control of the vehicle to the driver assistance system. Thus, the autonomous driving function includes: the vehicle is set, in particular by means of a processor unit for determining the trajectory of the vehicle or the processor unit of the driver assistance system, to perform, for example, steering, lighting indication, acceleration and braking operations without human intervention, and in particular to control external lighting and signal indication, such as the indicator lights of the vehicle. The semi-autonomous driving function can be understood as a driving function that supports the vehicle driver in controlling the vehicle, especially during steering, lighting indication, acceleration and braking operations, wherein the driver still has control of the vehicle.

[0038] According to a third aspect of the invention, there is provided a first vehicle. The first vehicle includes sensors, in particular radar sensors. The sensors are set to generate speed data of a second vehicle traveling in front of the first vehicle. In addition, the first vehicle includes a processor unit according to the first aspect of the invention and a driver assistance system according to the second aspect of the invention.

[0039] The first vehicle is in particular a motor vehicle, such as a car (e.g., a passenger car with a weight of less than 3.5 t), a motorcycle, a moped, a scooter, a bicycle, an electric bicycle, a bus or a goods vehicle (e.g., with a weight of more than 3.5 t), or a rail vehicle, a ship, an aircraft, such as a helicopter or an airplane. The invention can also be used in small and light electric motor vehicles for micro-mobility, where these motor vehicles are in particular used for the first and last mile of traffic in urban areas and rural areas. The first and last mile of traffic can be understood as all sections and routes in the first and last links of the mobility chain. This is, for example, the route from home to the train station or the section from the train station to the workplace. In other words, the invention can be used in the fields of all modes of transport, such as motor vehicles, aviation, navigation, spaceflight, etc.

[0040] According to a fourth aspect of the invention, there is provided a method for determining the trajectory of a first vehicle taking into account the driving behavior of a second vehicle, wherein the second vehicle is driving in front of the first vehicle. The method comprises the following steps:

[0041] - Generating speed data of the second vehicle,

[0042] - Establishing a driving behavior pattern of the second vehicle based on the speed data,

[0043] - Predicting the future driving behavior of the second vehicle based on the driving behavior pattern of the second vehicle,

[0044] - Determining the trajectory of the first vehicle by executing an MPC algorithm comprising a longitudinal dynamics model of the first vehicle and a cost function to be minimized, thereby minimizing the cost function, wherein the prediction of the future driving behavior of the second vehicle is considered as an auxiliary condition when determining the trajectory, and wherein the speed data comprises the time curve of the actual speed of the second vehicle determined by a sensor of the first vehicle,

[0045] - Accessing a first speed limit value applicable to a first section on which the second vehicle is driving,

[0046] - Accessing a second speed limit value applicable to a second section on which the second vehicle will drive in the future,

[0047] - Generating a time function of the relative speed deviation between the actual speed of the second vehicle and the first speed limit value from the time curve of the actual speed of the second vehicle,

[0048] - Determining an average relative speed deviation from the time function of the relative speed deviation,

[0049] - Establishing a driving behavior pattern of the second vehicle based on the average relative speed deviation, and

[0050] Predict the future driving behavior of the second vehicle based on the driving behavior pattern of the second vehicle, such that the future speed of the second vehicle on the second section is determined depending on the average relative speed deviation and the second speed limit value.

[0051] According to a fifth aspect of the present invention, there is provided a computer program product for determining the trajectory of a first vehicle while taking into account the driving behavior of a second vehicle, wherein the second vehicle is traveling in front of the first vehicle. When executed on a processor unit, the computer program product instructs the processor unit to:

[0052] - Access speed data of the second vehicle, wherein the speed data has been generated by a sensor of the first vehicle,

[0053] - Establish a driving behavior pattern of the second vehicle based on the speed data,

[0054] - Predict the future driving behavior of the second vehicle based on the driving behavior pattern of the second vehicle,

[0055] - Determine the trajectory of the first vehicle by executing a MPC algorithm that includes a longitudinal dynamics model of the first vehicle and a cost function to be minimized, thereby minimizing the cost function, wherein the prediction of the future driving behavior of the second vehicle is considered as an auxiliary condition when determining the trajectory. The MPC algorithm may form part of the computer program product as software code, wherein the speed data includes a time curve of the actual speed of the second vehicle determined by a sensor of the first vehicle,

[0056] - Access a first speed limit value that applies to a first section on which the second vehicle is traveling,

[0057] - Access a second speed limit value that applies to a second section on which the second vehicle will be traveling in the future,

[0058] - Generate a time function of the relative speed deviation between the actual speed of the second vehicle and the first speed limit value from the time curve of the actual speed of the second vehicle,

[0059] - Determine the average relative speed deviation from the time function of the relative speed deviation,

[0060] - Establish a driving behavior pattern of the second vehicle based on the average relative speed deviation, and

[0061] - Predict the future driving behavior of the second vehicle based on the driving behavior pattern of the second vehicle, such that the future speed of the second vehicle on the second section is determined depending on the average relative speed deviation and the second speed limit value.

[0062] Embodiments related to the processor unit according to the first aspect of the present invention are similarly applicable to the driver assistance system according to the second aspect of the present invention, the first vehicle according to the third aspect of the present invention, the method according to the fourth aspect of the present invention, and the computer program product according to the fifth aspect of the present invention. Description of the Drawings

[0063] Embodiments of the present invention are explained in detail below with reference to schematic diagrams, wherein identical or similar elements are provided with the same reference numerals. Among them:

[0064] Figure 1 A schematic diagram showing a first vehicle, and

[0065] Figure 2 Showing a second vehicle that is traveling in front of the first vehicle on a first section of a road according to Figure 2 the first vehicle shown. Detailed Description of the Invention

[0066] Figure 1 A first vehicle 1 is shown. In the illustrated embodiment, the first vehicle is a motor vehicle, such as a passenger car. The motor vehicle 1 includes an MPC system 2 for determining the trajectory of the first motor vehicle 1 taking into account the driving behavior of the second vehicle 18 shown by Figure 2 wherein the second vehicle 18 is traveling in front of the first motor vehicle 1. In the illustrated embodiment, the second vehicle 18 is also a motor vehicle, such as also a passenger car. The first motor vehicle 1 further includes a driver assistance system 16 having a processor unit and a communication interface 20.

[0067] In the illustrated embodiment, the MPC system 2 includes a processor unit 3, a memory unit 4, a communication interface 5, and a detection unit 6, which is especially for determining the speed of the vehicle traveling in front (the second motor vehicle 18 in the embodiment shown by Figure 2 and for detecting other environmental data and status data related to the motor vehicle 1. The motor vehicle 1 further includes a powertrain 7, which may include, for example, an electric machine 8 that can operate as a motor and as a generator, a battery 9, and a transmission 10. During motor operation, the electric machine 8 can drive the wheels of the motor vehicle 1 through the transmission 10, which may have a constant transmission ratio, for example. The battery 9 can provide the required electrical energy. When the electric machine 8 operates in generator operation (regeneration), the battery 9 can be charged by the electric machine 8. The battery 9 can also optionally be charged at an external charging station. The powertrain of the motor vehicle 1 can also optionally have an internal combustion engine 17, which can drive the motor vehicle 1 as an alternative or supplement to the electric machine 8. The internal combustion engine 17 can also drive the electric machine 8 to charge the battery 9.

[0068] The computer program product 11 can be stored in the memory unit 4. The computer program product 11 can be executed on the processor unit 3. For this purpose, the processor unit 3 and the memory unit 4 are interconnected via a communication interface 5. When the computer program product 11 is executed on the processor unit 3, the computer program product 11 guides the processor unit 3 to implement the functions described in connection with the accompanying drawings or to execute the method steps.

[0069] The computer program product 11 includes the MPC algorithm 13. The MPC algorithm 13 in turn includes the longitudinal dynamics model 14 of the powertrain 7 of the motor vehicle 1. The MPC algorithm 13 also includes the cost function 15 to be minimized. The processor unit 3 executes the MPC algorithm 13 and, based on the longitudinal dynamics model 14, determines the optimal speed trajectory of the first motor vehicle 1 to minimize the cost function 15.

[0070] For the calculation points within the prediction horizon, the optimal rotational speed and the optimal torque of the electric machine 8 can also be obtained as the output optimized by the MPC algorithm 13. For this purpose, the processor unit 3 can determine the input parameters for the electric machine 8 to generate the optimal rotational speed and the optimal torque. The processor unit 3 can control the electric machine 8 based on the determined input parameters. However, this can also be achieved by the driver assistance system 16.

[0071] The detection unit 6 can measure the current state parameters of the first motor vehicle 1, record the corresponding data and transmit it to the MPC algorithm 13. In addition, the route data for the forward-looking or prediction horizon (e.g., 400 m) in front of the motor vehicle 1 from the electronic map can also be updated or renewed periodically in particular. The route data can include, for example, slope information, bend information and information on speed limits. In addition, the bend curvature can be converted into the speed limit of the motor vehicle 1 by the maximum allowable lateral acceleration. In addition, the detection unit 6 can perform orientation of the first motor vehicle 1, in particular precise positioning on the electronic map by means of the signal generated by the GNSS sensor 12. In addition, the detection unit 6 has a radar sensor 24 for determining the speed ( Figure 2 ) of the vehicle 18 traveling ahead. The processor unit 3 can access the information of the mentioned elements, for example, via the communication interface 5. This information can flow into the longitudinal model 14 of the motor vehicle 1, in particular as constraints or auxiliary conditions.

[0072] According to Figure 2An apparently simplified example shows a first motor vehicle 1 on a first section 22 of a road 21. The first motor vehicle 1 autonomously travels at a first speed v1 in a first travel direction x1 with the support of the aforementioned driver assistance functions. A second motor vehicle 18 is located in front of the first motor vehicle 1 and is also on the first section 22 of the road 21. The second motor vehicle 1 travels in a second travel direction x2 in front of the first motor vehicle 1 at a second speed v2. In the illustrated embodiment, the first section 22 extends straight, and the first travel direction x1 of the first motor vehicle 1 is the same as the second travel direction x2 of the second motor vehicle 18. However, this is only exemplary and not mandatory. The first speed v1 of the first motor vehicle 1 may be equal to the second speed v2 of the second motor vehicle 18 (v1 = v2), but this is also only exemplary and not mandatory. The first speed v1 of the first motor vehicle 1 may also be different from the second speed v2 of the second motor vehicle 18 (v1 ≠ v2).

[0073] A first legal speed limit applies to the first section 22, which may for example be set to a first speed limit value v limit1 = 100 km / h. The second motor vehicle 18 travels in front of the first motor vehicle in the direction of a second section 23, and the second motor vehicle 2 is expected to travel on said second section 23. The first motor vehicle 1 follows the second motor vehicle 18 in the direction of the second section 23. A second legal speed limit applies to the second section 23, which may for example be set to a second speed limit value v limit2 = 50 km / h.

[0074] For example, the first speed limit value v limit1 and the second speed limit value v limit2 may be stored in the map of the navigation system of the first motor vehicle 1. The processor unit 3 of the MPC system 2 may access the first speed limit value v limit1 and the second speed limit value v limit2 via a communication interface 5.

[0075] A radar sensor 24 generates speed data of the second motor vehicle 18. The processor unit 3 of the MPC system 2 may access the speed data via a communication interface 5. In the illustrated embodiment, the radar sensor 24 determines the actual speed v n of the second motor vehicle 18 at discrete time points t1 to t detected (t1) to v detected (t n ), from which the time curve of the speed v1 of the second motor vehicle 18 can be described.

[0076] Based on the determined actual speed v detected (t1) to v detected (t n) and the first speed limit value v limit1 , the processor unit 3 determines the actual speed v detected (t1) to v detected (t n ) and the first speed limit value v limit1 of the time-discrete relative speed deviation Δv rel (t1) to Δv rel (t n ). The relative speed deviation Δv rel (t1) to Δv rel (t n ) can be calculated, for example, as follows:

[0077] For all i from 1 to n,

[0078] the relative speed deviation Δv rel (t1) to Δv rel (t n ) can be stored in a data group, which is a first-in-first-out (FIFO) vector in the example shown, where the FIFO vector can have a preset storage time, for example 30 s. The FIFO vector can be the data array described as follows:

[0079]

[0080] Here, the individual values Δv rel (t1) to Δv rel (t n ) are the percentage deviations calculated at the corresponding time points t1 to t n , where t1 is the first time point during the preset storage time (for example 30 s), and where t n is the last time point during the preset storage time. The storage within the FIFO vector enables: depicting the curve of the percentage deviation of the actual speed of the second vehicle 18 traveling ahead from the first speed limit value v limitl . For this purpose, the values Δv rel (t1) to Δv rel (t n ) are stored in the FIFO vector in chronological order. Based on the time-discrete values Δv rel (t1) to Δv rel (t n ), the processor unit 3 can generate the function Δv rel (t), which describes the speed difference Δv rel with respect to time. This function can be differentiated twice by the processor unit 3, where the first derivative Δv′ rel(t) describes the time curve of the acceleration a of the second vehicle 18, and wherein the second derivative Δv″ rel (t) describes the time curve of the jerk j of the second vehicle 18.

[0081] The processor unit 3 determines the following values:

[0082] - The average relative speed deviation Δv of the second vehicle 18 determined from the function Δv rel of the relative speed difference Δv with respect to time t rel (t) relaverage ,

[0083] - The average acceleration a of the second vehicle 18 determined from the first time derivative Δv′ rel of the function Δv rel (t) of the relative speed difference Δv with respect to time t rel (t) average ,

[0084] - The maximum acceleration a of the second vehicle 18 determined from the first time derivative Δv′ rel of the function Δv rel (t) of the relative speed difference Δv with respect to time t rel (t) max ,

[0085] - The average jerk j of the second vehicle 18 determined from the second time derivative Δv″ rel of the function Δv rel (t) of the relative speed difference Δv with respect to time t rel (t) average , and

[0086] - The maximum jerk j of the second vehicle 18 determined from the second time derivative Δv″ rel of the function Δv rel (t) of the relative speed difference Δv with respect to time t rel (t) max .

[0087] Based on at least one of these values Δv relaverage , a average , a max , j average , j max The processor unit 3 constructs a pattern describing the driving behavior of the second motor vehicle 18 ("driving behavior pattern"). If the second motor vehicle 18, for example, maintains an average speed well below the maximum speed v limit1And if it has on average only a small acceleration a and a jerk j, the second motor vehicle 18 can, for example, be modeled as a less aggressive traffic participant. Based on the driving behavior pattern of the second vehicle 18, the processor unit 3 anticipates the future driving behavior of the second vehicle 18.

[0088] As already mentioned, the speed limit value v limit1 = 100 km / h applies to the first section 22. For example, the second vehicle 18 can move in front of the first vehicle 1 on the first section 22 at an actual speed v detected of 80 km / h over a complete observation time of, for example, 30 seconds. In this case, an average relative speed deviation Δv limit1 from the first speed limit value v rel average results as -20%. On the predicted driving horizon, a second speed limit value of 50 km / h results for the second section 23. In this case, the processor unit 3 anticipates (after the speed adjustment process has been completed) that the second vehicle 18 will move at a speed of 40 km / h on the second section 23 (50 km / h * (100% - 20%) = 40 km / h).

[0089] For example, a value of -1 m / s 2 can be calculated for the average acceleration, that is to say the second vehicle 18 brakes on average with this negative acceleration value (braking operation). If now on the horizon a change in the speed limit value from 100 km / h to 50 km / h results, the average acceleration a average can be used to anticipate the driving behavior of the second motor vehicle 18. Here, in particular, it can be assumed that the second vehicle 18 will already have reached its target speed (40 km / h) at the start of the second speed limit value v limit2 which, as described above, can depend on the average relative speed deviation Δv rel average and the second speed limit value v limit2 to be determined. Subsequently, based on this road point (transition between the first section 22 and the second section 23), it can be calculated backwards when and where the braking operation of the second motor vehicle 18 begins.

[0090] The average jerk j average of the second vehicle 18 can be used in a similar way to anticipate the acceleration transition of the second vehicle 18. For example, a value of -1 m / s average can be determined for the average jerk j 3 . In this case, in the case of the braking operation described above, the acceleration, for example, changes from 0 m / s 2 to -1 m / s 2The transition takes one second. From this, the transition time between the non-braking pedal position and the represented braking pedal position can be predicted. During this transition, the jerk j remains constant. The maximum value of the acceleration a max and the maximum value of the jerk j max can also be used to detect the possibility of emergency braking.

[0091] The processor unit 3 determines the trajectory of the first motor vehicle 1 by executing the MPC algorithm 13, thereby minimizing the cost function 15, where the prediction of the future driving behavior of the second vehicle 18 is considered as a side condition when determining the trajectory. In addition, in particular, together with considering the route terrain, traffic, and other environmental information, to determine the optimal speed trajectory of the first vehicle 1 for the forward section.

[0092] The processor unit 19 of the driver assistance system 16 accesses the trajectory of the first motor vehicle 1 determined by the processor unit 3 of the MPC system 2 via the communication interface 20, and executes the autonomous driving function of the first motor vehicle 1 using the trajectory of the first motor vehicle 1. Alternatively, the processor unit 3 of the MPC system 2 can also execute the autonomous driving function of the first motor vehicle 1 using the trajectory of the first motor vehicle 1. In this case, the driver assistance system 16 is integrated into the MPC system 2, or the MPC system 2 forms the driver assistance system 16.

[0093] Possible embodiments of the longitudinal dynamics model 14 and the cost function 15, which are components of the MPC algorithm 13 for determining the trajectory of the first motor vehicle 1, are described in more detail below.

[0094] Thus, the longitudinal dynamics model 14 of the motor vehicle 1 can be mathematically represented as follows:

[0095]

[0096] Here:

[0097] v is the speed of the motor vehicle,

[0098] F trac is the traction force applied to the wheels of the motor vehicle by the motor or the brake,

[0099] F r is the rolling resistance, which is the effect of the deformation of the tire during rolling and depends on the load on the wheel (the normal force between the wheel and the road) and thus on the inclination angle of the road,

[0100] F gr is the slope resistance, which describes the longitudinal component of the gravitational force acting on the motor vehicle during uphill or downhill driving, and the slope resistance depends on the gradient of the lane,

[0101] F d the air resistance of the motor vehicle, and

[0102] m eq The equivalent mass of the motor vehicle, the equivalent mass includes in particular the inertia of the rotating parts of the drive train (motor, transmission drive shaft, wheels) which are subject to the accelerations of the motor vehicle.

[0103] By switching from talking about time to talking about distance and to eliminate the square of the velocity in the air resistance, The coordinate transformation is:

[0104]

[0105] In order to enable the problem to be solved quickly and simply by the MPC algorithm 13, the dynamic equations of the longitudinal dynamic model 14 can be linearized as follows: the velocity is converted from the kinetic energy de by a coordinate transformation kin To express it. From this, it is used to calculate the air resistance F d The squared terms of are replaced by linear terms and at the same time the longitudinal dynamics model 14 of the motor vehicle 1 is no longer described in terms of time as usual, but in terms of distance. In this respect this is well suited for optimization problems, since the forward-looking information of the electrical domain is based on distance.

[0106] In addition to the kinetic energy, there are two other state variables, which can also be described in a linear and distance-dependent manner in the sense of a simple optimization problem. On the one hand, the electrical energy consumption of the powertrain 7 is usually described in the form of a characteristic curve as a function of the torque and the motor speed. In the illustrated embodiment, the motor vehicle 1 has a fixed transmission ratio between the electric motor 8 and the road on which the motor vehicle 1 moves. As a result, the rotational speed of the electric motor 8 can be directly converted into the speed of the motor vehicle 1 or the kinetic energy of the motor vehicle 1. In addition, the electrical power of the electric motor 8 can be converted by dividing the energy consumption per meter by the corresponding speed. In order to be able to use the corresponding characteristic curve for optimization, a linear approximation is performed: for all i, Energy perMeter ≥a i *e kin +b i *F trac ,(Energy perMeter :energy 每米 ).

[0107] The cost function 15 to be minimized can be expressed mathematically, for example, as follows:

[0108]

[0109] Here:

[0110] w Bat Weighting factor for the energy consumption of the battery

[0111] E Bat Energy consumption of the battery

[0112] S Distance

[0113] S E-1 Distance at the time step before the end of the prediction horizon

[0114] F A Driving force provided by the electric machine, which is constantly converted by the transmission and applied to the wheels of the motor vehicle

[0115] W Tem Weighting factor for the torque gradient

[0116] W TemStart Weighting factor for the torque mutation

[0117] T Time required for the vehicle to travel the entire predicted distance within the prediction horizon

[0118] w Time Weighting factor for time T

[0119] S E Distance at the end of the horizon

[0120] w Slack Weighting factor for the slack variable

[0121] Var Slack Slack variable.

[0122] In the illustrated embodiment, the cost function 15 has only linear and quadratic terms. Thus, the entire problem has the form of a quadratic optimization with linear auxiliary conditions and results in a convex problem that can be solved well and quickly.

[0123] The cost function 15 includes the electrical energy E Bat weighted by the first weighting factor w and predicted according to the longitudinal dynamics model Bat as the first term, which is provided by the battery 9 of the powertrain 7 within the prediction horizon for driving the electric machine 8.

[0124] The cost function 15 includes the second weighting factor W TimeThe weighted travel time T predicted according to the longitudinal dynamics model 14 as an additional term, which is the time required for the motor vehicle 1 to travel the predicted distance. This results in: Depending on the choice of the weighting factor, a low speed is not always evaluated as optimal, and thus there is no longer a problem that the resulting speed is always at the lower limit of the permitted speed.

[0125] The energy consumption and the travel time can be evaluated and weighted respectively at the end of the horizon. Thus, these terms are only valid for the last point of the horizon.

[0126] An excessive torque gradient within the horizon is disadvantageous. Therefore, the torque gradient has been penalized in the cost function 15, i.e., by the term is penalized. The square of the driving force deviation per meter is weighted with the weighting factor W Tem and minimized in the cost function. As an alternative to the driving force F A per meter, the torque M provided by the electric motor 8 can also be used EM and weighted with the weighting factor W Tem to obtain the alternative term Due to the constant transmission ratio of the transmission 10, the driving force and the torque are directly proportional to each other.

[0127] To ensure a comfortable drive, another term for penalizing torque jerks has been introduced into the cost function 15, i.e., w TemStart ·(F A (s1) - F A (s0)) 2 . As an alternative to the driving force F A , the torque M provided by the electric motor 8 can also be used here EM to obtain the alternative term w TemStart ·(M EM (s1) - M EM (s0)) 2 . For the first point within the prediction horizon, the deviation from the previously set torque is evaluated negatively and weighted with the weighting factor W Temstart to ensure a seamless and jerk-free transition when switching between the old and new trajectories.

[0128] The speed limit is a hard limit for optimization that is not allowed to be exceeded. In practice, it is always allowed to slightly exceed the speed limit, and this is especially normal when transitioning from the first speed zone to the second speed zone. In a dynamic environment where the speed limit transfers from one calculation cycle to the next, no valid solution for the speed curve can be found in the case of a complete hard limit. To increase the stability of the calculation algorithm, a limit ("soft constraint") is introduced into the cost function 15. Here, with the weighting factor W SlackWeighted slack variable Var Slack Becomes effective within a predetermined narrow range before reaching the hard speed limit. Solutions that are very close to the hard speed limit, i.e., solutions whose speed trajectories maintain a certain distance from the hard limit, are evaluated worse.

[0129] List of reference numerals

[0130] v1 Speed of the first motor vehicle

[0131] x1 Driving direction of the first motor vehicle

[0132] v2 Speed of the second motor vehicle

[0133] x2 Driving direction of the second motor vehicle

[0134] 1 First motor vehicle

[0135] 2 MPC system

[0136] 3 Processor unit

[0137] 4 Memory unit

[0138] 5 Communication interface

[0139] 6 Detection unit

[0140] 7 Powertrain

[0141] 8 Electric motor

[0142] 9 Battery

[0143] 10 Transmission

[0144] 11 Computer program product

[0145] 12 GNSS sensor

[0146] 13 MPC algorithm

[0147] 14 Longitudinal dynamics model

[0148] 15 Cost function

[0149] 16 Driver assistance system

[0150] 17 Internal combustion engine

[0151] 18 Second motor vehicle

[0152] 19 Processor unit of the driver assistance system

[0153] 20 Communication interface of the driver assistance system

[0154] 21 Road

[0155] 22 First section

[0156] 23 Second section

[0157] 24 Radar sensor

Claims

1. A processor unit (3) for determining a trajectory of a first vehicle (1) taking into account a driving behavior of a second vehicle (18), wherein, The second vehicle (18) travels in front of the first vehicle (1), and wherein the processor unit (3) is configured to: - Access speed data of the second vehicle (18), wherein the speed data has been generated by a sensor (24) of the first vehicle (1), - Establish a driving behavior pattern of the second vehicle (18) based on the speed data, - Predict a future driving behavior of the second vehicle (18) based on the driving behavior pattern of the second vehicle (18), - Determine a trajectory of the first vehicle (1) by executing a MPC algorithm (13) that includes a longitudinal dynamics model (14) of the first vehicle (1) and a cost function (15) to be minimized, so as to minimize the cost function (15), wherein the prediction of the future driving behavior of the second vehicle (18) is considered as a secondary condition when determining the trajectory, wherein the speed data includes a time curve of the actual speed of the second vehicle (18) determined by a sensor (24) of the first vehicle (1), and wherein the processor unit (3) is configured to: - Access a first speed limit value that applies to a first section (22) on which the second vehicle (18) travels, - Access a second speed limit value that applies to a second section (23) on which the second vehicle (18) will travel in the future, - Generate a time function of a relative speed deviation between the actual speed of the second vehicle (18) and the first speed limit value from the time curve of the actual speed of the second vehicle (18), - Determine an average relative speed deviation from the time function of the relative speed deviation, - Establish a driving behavior pattern of the second vehicle (18) based on the average relative speed deviation, and - Predict a future driving behavior of the second vehicle (18) based on the driving behavior pattern of the second vehicle (18), such that the future speed of the second vehicle (18) on the second section (23) is determined depending on the average relative speed deviation and the second speed limit value.

2. The processor unit (3) according to claim 1, wherein, The processor unit (3) is configured to: - Store the time-discrete relative speed deviation between the actual speed of the second vehicle (18) and the first speed limit value in a data set in chronological order for a determined time period, and - Generate a time function of the relative speed deviation between the actual speed of the second vehicle (18) and the first speed limit value from the time-discrete, chronologically stored relative speed deviations.

3. The processor unit (3) according to claim 1, wherein, The processor unit (3) is configured to: - Determine an average acceleration of the second vehicle (18) from a first derivative of the time function of the relative speed deviation with respect to time, - Establish a driving behavior pattern of the second vehicle (18) based on the average acceleration of the second vehicle (18), and Predict the future driving behavior of the second vehicle (18) based on the driving behavior pattern of the second vehicle (18), such that the future acceleration of the second vehicle (18) on the first section (22) is determined depending on the average acceleration, the average relative speed deviation, and the second speed limit value.

4. The processor unit (3) according to claim 3, wherein, The processor unit (3) is configured to: - Determine the average jerk of the second vehicle (18) from the second derivative of the time function of the relative speed deviation with respect to time, - Establish a driving behavior pattern of the second vehicle (18) based on the average jerk of the second vehicle (18), and - Predict the future driving behavior of the second vehicle (18) based on the driving behavior pattern of the second vehicle (18), such that the future jerk of the second vehicle (18) on the first section (22) is determined depending on the average jerk, the average acceleration, the average relative speed deviation, and the second speed limit value.

5. The processor unit (3) according to any one of claims 2 to 4, wherein, The processor unit (3) is configured to: - Determine the maximum acceleration of the second vehicle (18) from the first derivative of the time function of the relative speed deviation with respect to time, - Determine the maximum jerk of the second vehicle (18) from the second derivative of the time function of the relative speed deviation with respect to time, - Establish a driving behavior pattern of the second vehicle (18) based on the maximum acceleration and maximum jerk of the second vehicle (18), and - Predict the future driving behavior of the second vehicle (18) based on the driving behavior pattern of the second vehicle (18), such that an emergency braking of the second vehicle (18) is detected depending on the maximum acceleration and the maximum jerk.

6. The processor unit (3) according to any one of claims 1 to 4, wherein, The processor unit (3) is configured to: Predict the future driving behavior of the second vehicle (18) each time the MPC algorithm (13) is executed to determine the trajectory of the first vehicle (1).

7. A driver assistance system (16) for performing a driver assistance function of a first vehicle (1) taking into account the driving behavior of a second vehicle (18), wherein, The second vehicle (18) travels in front of the first vehicle (1), and wherein the driver assistance system (16) is configured to: - Access the trajectory of the first vehicle (1) determined by the processor unit (3) according to any one of claims 1 to 6, and - Execute the driver assistance function of the first vehicle (1) using the trajectory of the first vehicle (1).

8. The first vehicle (1), the first vehicle comprising: A sensor (24), the sensor being configured to generate speed data of a second vehicle (18) traveling in front of the first vehicle (1); The processor unit (3) according to any one of claims 1 to 6; and the driver assistance system (16) according to claim 7.

9. A method for determining the trajectory of a first vehicle (1) taking into account the driving behavior of a second vehicle (18), wherein, The second vehicle (18) travels in front of the first vehicle (1), the method comprising the steps of: - Generate speed data of the second vehicle (18), - Establish a driving behavior pattern of the second vehicle (18) based on the speed data, - Predict the future driving behavior of the second vehicle (18) based on the driving behavior pattern of the second vehicle (18), - Determine the trajectory of the first vehicle (1) by executing an MPC algorithm (13) that includes the longitudinal dynamics model (14) of the first vehicle (1) and a cost function (15) to be minimized, thereby minimizing the cost function (15), wherein the prediction of the future driving behavior of the second vehicle (18) is considered as an auxiliary condition when determining the trajectory, and wherein the speed data includes the time curve of the actual speed of the second vehicle (18) determined by the sensor (24) of the first vehicle (1), - Access a first speed limit value that applies to a first section (22) on which the second vehicle (18) travels, - Access a second speed limit value that applies to a second section (23) on which the second vehicle (18) will travel in the future, - Generate a time function of the relative speed deviation between the actual speed of the second vehicle (18) and the first speed limit value from the time curve of the actual speed of the second vehicle (18), - Determine the average relative speed deviation from the time function of the relative speed deviation, - Establish a driving behavior pattern of the second vehicle (18) based on the average relative speed deviation, and - Predict the future driving behavior of the second vehicle (18) based on the driving behavior pattern of the second vehicle (18), such that the future speed of the second vehicle (18) on the second section (23) is determined depending on the average relative speed deviation and the second speed limit value.

10. A computer program product (11) for determining the trajectory of a first vehicle (1) taking into account the driving behavior of a second vehicle (18), wherein, The second vehicle (18) travels in front of the first vehicle (1), wherein the computer program product (11), when executed on the processor unit (3), instructs the processor unit (3): - Access the speed data of the second vehicle (18), wherein the speed data has been generated by the sensor (24) of the first vehicle (1), - Establish a driving behavior pattern of the second vehicle (18) based on the speed data, - Predict the future driving behavior of the second vehicle (18) based on the driving behavior pattern of the second vehicle (18), - Determine the trajectory of the first vehicle (1) by executing an MPC algorithm (13) that includes the longitudinal dynamics model (14) of the first vehicle (1) and a cost function (15) to be minimized, thereby minimizing the cost function (15), wherein the prediction of the future driving behavior of the second vehicle (18) is considered as an auxiliary condition when determining the trajectory, and wherein the speed data includes the time curve of the actual speed of the second vehicle (18) determined by the sensor (24) of the first vehicle (1), - Access a first speed limit value that applies to a first section (22) on which the second vehicle (18) travels, - Access a second speed limit value that applies to a second section (23) on which the second vehicle (18) will travel in the future, - Generate a time function of the relative speed deviation between the actual speed of the second vehicle (18) and the first speed limit value from the time curve of the actual speed of the second vehicle (18), - Determine an average relative speed deviation from the time function of the relative speed deviation, - Establish a driving behavior pattern of the second vehicle (18) based on the average relative speed deviation, and - Predict the future driving behavior of the second vehicle (18) based on the driving behavior pattern of the second vehicle (18), such that the future speed of the second vehicle (18) on the second section (23) is determined depending on the average relative speed deviation and the second speed limit value.

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