DE102018125250B4 - Method and control unit for guiding a vehicle - Google Patents

Abstract

Method (700) for automated longitudinal and / or lateral guidance of a vehicle (100) based on a system model of the vehicle (100); wherein the method (700) comprises - determining (701) a value of a first state component (601) as a deviation of an actual value of a state variable of the vehicle (100) from a planned value of the state variable that is dependent on a target trajectory (103); wherein the state variable of the vehicle (100) is dependent on a manipulated variable (602) via the system model; - determination (702) of time-variable restrictions (503) of the first state component (601) and / or the manipulated variable (602) for N points in time the time k, with N> 1; - determining (703) values (611, 612, 613, 614) of one or more second state components (603) of a constraint model at the time k in such a way that the determined, time-variable constraints ( 503) of the first state component (601) and / or of the manipulated variable (602) are approximated by values of at least one second state component (603) at the N times from time k; - determining (704) a value of the manipulated variable (602) the time k, based on the value of the first state component (601) and based on the values (611, 612, 613, 614) of the one or more second state components (603) at the time k and based on a predefined function (300) , the egg n is directed to assign a value of the manipulated variable (602) to different value combinations of the first state component (601) and the one or more second state components (603); and- operating (705) a vehicle guidance system (206) for automated longitudinal and / or lateral guidance of the vehicle (100) as a function of the determined value of the manipulated variable (602).

Description

The invention relates to methods and corresponding control units for the automated guidance of a vehicle.

For automated guidance, in particular transverse and / or longitudinal guidance, of a vehicle, trajectory planning is typically carried out, taking into account temporally variable restrictions from an environment model of the surroundings of the vehicle (e.g. a maximum permissible lateral distance), and taking into account physical vehicle restrictions (e.g. a maximum permissible change in curvature that can be implemented by the vehicle). As part of the trajectory planning, a finite, planned target trajectory for the longitudinal and / or the transverse guidance can be provided.

Furthermore, a trajectory follower can be provided for the longitudinal and / or lateral guidance, which is intended to cause the vehicle to follow a planned target trajectory. For this purpose, the input of a trajectory follower is considered to be the difference between the target state of the vehicle (given by the planned target trajectory) and the measured actual state of the vehicle, and the output of the trajectory follower is an acceleration to be provided by the vehicle (for the longitudinal guide) or curvature (for the transverse guide) is determined as a manipulated variable.

In addition, to provide automated longitudinal and / or lateral guidance, a vehicle guidance system (also referred to in this document as CVM (Central Vehicle Management) module) is typically used, which provides the required curvature (for lateral guidance) or acceleration (for longitudinal guidance). to the respective vehicle inputs (e.g. drive, brake, steering angle, etc.) and dynamic and / or effects of vehicle behavior caused by a change in the coefficient of friction of the road are largely compensated for with an internal curvature and / or acceleration control.

Due to the separation between trajectory planning and trajectory follow-up control, it cannot always be ensured that the curvature or acceleration determined within the scope of the trajectory follow-up control can actually be implemented by the vehicle without collision.

This document deals with the technical task of providing a trajectory sequence control for a vehicle through which a reliable and collision-free implementation of curvature and acceleration specifications is ensured in a resource-efficient manner.

For the state of the art, see the publications DE 10 2017 010 180 B3 , DE 10 2015 015 302 A1 , DE 10 2012 001 405 A1 and DE 102 18 010 A1 referenced.

The problem is solved by each of the independent claims. Advantageous embodiments are i.a. described in the dependent claims. It is pointed out that additional features of a patent claim dependent on an independent patent claim without the features of the independent patent claim or only in combination with a subset of the features of the independent patent claim can form a separate invention independent of the combination of all features of the independent patent claim, which can be made the subject of an independent claim, a divisional application or a subsequent application. This applies equally to the technical teachings described in the description, which can form an invention that is independent of the features of the independent patent claims.

In the context of the document, the term “automated driving” can be understood to mean driving with automated longitudinal or lateral guidance or autonomous driving with automated longitudinal and lateral guidance. The automated driving can be, for example, driving on the motorway for a longer period of time or driving for a limited time as part of parking or maneuvering. The term “automated driving” includes automated driving with any degree of automation. Exemplary degrees of automation are assisted, partially automated, highly automated or fully automated driving. These degrees of automation were defined by the Federal Highway Research Institute (BASt) (see BASt publication “Research compact”, edition 11/2012). With assisted driving, the driver continuously performs longitudinal or lateral guidance, while the system takes on the other function within certain limits. With partially automated driving (TAF), the system takes over the longitudinal and lateral guidance for a certain period of time and / or in specific situations, whereby the driver has to continuously monitor the system as with assisted driving. In highly automated driving (HAF), the system takes over the longitudinal and lateral guidance for a certain period of time without this the driver must constantly monitor the system; however, the driver must be able to take over driving the vehicle within a certain period of time. With fully automated driving (VAF), the system can automatically cope with driving in all situations for a specific application; a driver is no longer required for this application. The four degrees of automation mentioned above correspond to SAE levels 1 to 4 of the SAE J3016 standard (SAE - Society of Automotive Engineering). For example, highly automated driving (HAF) Level 3 corresponds to the SAE J3016 standard. In addition, SAE J3016 provides SAE level 5 as the highest level of automation, which is not included in the definition of BASt. SAE level 5 corresponds to driverless driving in which the system can automatically handle all situations like a human driver during the entire journey; a driver is generally no longer required. The aspects described in this document can be used for an “assisted driving” automation level and higher.

According to one aspect, a method for automated longitudinal and / or lateral guidance of a vehicle (in particular a motor vehicle) based on a system model of the vehicle is described. The system model is preferably invariant over time and / or linear in order to enable the method to be carried out in a resource-efficient manner. The system model can enable a certain number of state variables or state components of the system to be predicted over a certain time interval (the so-called planning horizon). In particular, the system model can make it possible, starting from an initial state, to recursively enable the prediction of the state variables or state components at successive points in time or time steps. Such a system model is also referred to in this document from a recursive system model.

The system model of the vehicle can include a first partial model that represents an approximation of the behavior of the vehicle guidance system of the vehicle with which the automated longitudinal and / or lateral guidance of the vehicle is implemented. The vehicle guidance system can e.g. comprise an automated steering device, an automated drive and / or an automated braking device. Furthermore, the system model can include a second partial model that describes the movement and / or the kinematics of the vehicle.

In particular, the system model can include a system matrix that describes a relationship between different state variables at a point in time k and a subsequent point in time k + 1. Furthermore, the system model can include an input vector that describes an influence of a manipulated variable of the system on the different state variables. Furthermore, the system model can comprise an output matrix or an output vector which makes it possible to determine an output variable of the system from the state variables at a specific point in time k.

The method can include (at a point in time k) the determination of a deviation of an actual value of a state variable of the vehicle from a planned value of the state variable that is dependent on a target trajectory (planned within the scope of trajectory planning) as a first state component. In other words, a value of a first state component can be determined as a deviation of an actual value of a state variable of the vehicle from a planned value of the state variable that is dependent on a target trajectory. The first status component can be viewed as a control error or as part of a control error. As already explained above, the system model can be set up or have the property, based on the first status component at time k (using the system matrix) and based on a manipulated variable at time k (using the input vector), the first status component a subsequent point in time k + 1 (by using the system matrix and / or the input vector). In other words, the state variable of the vehicle can be dependent on a manipulated variable via the system model.

In addition, the method includes determining temporally variable restrictions of the first state component and / or the manipulated variable for N points in time from the point in time k, with N> 1 (typically N = 5, 8, 10 or more). In particular, a restriction can be provided for the times k, k + 1, k + 2, .., k + N − 1. Directly consecutive points in time can be spaced apart in time according to a sampling rate (e.g. by 100 ms, 50 ms, 20 ms or less).

The first state component and / or the manipulated variable can thus each have a restriction that can change over time. For example, the deviation of the lateral storage of the vehicle from the planned lateral storage can vary depending on the current situation in the surroundings of the vehicle. The time-variable limitation of the first state component can thus be based on sensor data from one or more environmental sensors (e.g. a camera, a radar sensor, an ultrasonic sensor, a LIDAR sensor, etc.) of the vehicle. The sensor data can describe the surroundings of the vehicle.

The method further includes approximating the temporally variable limitation of the first state component (or, if applicable, the manipulated variable) by means of a (recursive) limitation model with one or more second state components. The restriction model can be set up to determine the one or more second state components at the subsequent point in time k + 1 on the basis of the one or more second state components at the point in time k. Furthermore, at least one second state component can display the approximated restriction of the first state component. The constraint model is preferably linear and time-invariant. In particular, the constraint model can preferably be described by a time-invariant constraint matrix. It can thus be made possible, by defining one or more additional (second) state components, to approximate a time-variable restriction in a linear and time-invariant manner. Starting from an initial state, the time-variable restriction can be described recursively by means of the restriction model (in particular by means of a restriction matrix). Limitations of a state variable and / or a manipulated variable can thus be taken into account in a resource-efficient manner within the framework of a trajectory sequence control.

In other words, values of one or more second state components of a restriction model can be determined at point in time k in such a way that the determined, temporally variable restrictions of the first state component and / or the manipulated variable are derived from values of at least one second state component at the N points in time the point in time k can be approximated. A linear and time-invariant constraint model can be used for this purpose. The constraint model can have a time-invariant constraint matrix.

In particular, a system model of the vehicle can be supplemented by a restriction model of a time-variable restriction. A (recursive) overall model can thus be provided which includes both the system model of the vehicle and a restriction model of the restriction of the first state component (and / or the manipulated variable). In this way, a particularly resource-efficient automated longitudinal and / or lateral guidance of a vehicle (taking into account environmental conditions and / or technical restrictions) can be made possible.

The approximated restriction of the first state component (and / or the manipulated variable) brought about by the restriction model preferably represents an equal or stronger restriction at each of the N times than the temporally variable restriction of the first state component (and / or the manipulated variable). In other words, the approximated restriction is preferably at no point in time more generous than the original time-variable restriction. Reliable, automated longitudinal and / or lateral guidance of a vehicle can thus be made possible.

In a preferred example, the approximated constraint brought about by the constraint model is a linear approximation of the temporally variable constraint. The use of a linear approximation enables a particularly resource-efficient, automated longitudinal and / or lateral guidance of a vehicle.

The method further comprises determining a value of the manipulated variable at time k, based on the value of the first state component and the value of the one or more second state components at time k, and based on a predefined function. The predefined one is set up to assign different value combinations of the first state component and the one or more second state components each with a (possibly different) value of the manipulated variable. The predefined function can e.g. in the form of a look-up table. Alternatively or in addition, the predefined function can be provided as a piecewise affine function.

The predefined function can e.g. for a value combination of the first state component and the one or more second state components, coefficients or weights with which the first state component at time k and the one or more second state components at time k are to be multiplied in order to obtain the To determine the value of the manipulated variable at time k.

The predefined function can enable an explicit model predictive control (with a planning horizon of the time length N). Furthermore, the predefined function can be derived from the (recursive) System model and / or be dependent on the (recursive) constraint model. Furthermore, the predefined function can be dependent on a cost-functional which comprises a term relating to the first state component at the N times from time k.

The predefined function can have been determined in advance by means of an optimization process. A cost functional may have been used, e.g. is designed to determine the sequence of values of the manipulated variable at the N times from time k, by means of which the cost-functional is optimized. The cost functional can e.g. be designed to reduce, in particular to minimize, the (quadratic or absolute) sum of the values of the first state component at the N times from time k. The approximated restriction of the first state component (and / or the manipulated variable) can be taken into account as a secondary condition within the framework of the optimization method. The use of a constraint model to describe the approximated constraint enables multiparametric programming to be used to determine the predefined function, and thus to determine an optimal value of the manipulated variable.

The predefined function can thus be determined in advance of the execution of the method that the value of the manipulated variable displayed for the value combination of the first state component and the one or more second state components at the point in time k for the point in time k takes into account a certain cost-functional the time-variable limitation of the first state component and / or the manipulated variable is optimized, in particular minimized. The cost functional can be a cost functional in the sense of the model predictive regulation.

The method also includes the operation of the vehicle guidance system for automated longitudinal and / or lateral guidance of the vehicle as a function of the determined value of the manipulated variable. In particular, the determined value of the manipulated variable, which can be viewed as a control component of the manipulated variable, can be combined with a precontrol component of the manipulated variable in order to determine an overall value of the manipulated variable. The total value of the manipulated variable can then be used as an input variable of the vehicle guidance system of the vehicle.

The described method thus makes it possible to take into account temporally variable restrictions of a state component of a state vector of the vehicle within the framework of the trajectory sequence control. A reliable, executable and collision-free automated longitudinal and / or lateral guidance can thus be made possible in an efficient manner.

The method is typically repeated at a sequence of times k in order to determine the manipulated variable at the sequence of times k and to operate the vehicle guidance system at the sequence of times k. A trajectory sequence control that lasts over time can thus be effected.

The state variable and / or the manipulated variable can display values relative to a reference curve or to a reference profile. The reference curve can in particular run along a roadway on which the vehicle is traveling (e.g. along the middle of a lane). The method can in particular be carried out in a de-curved coordinate system or in a Frenet coordinate system (in particular for the automated lateral guidance of the vehicle). In this way, the resource efficiency and the accuracy of the method can be further increased.

The method can include the determination of time-variable restrictions of the manipulated variable for N points in time from time k, with N> 1. The time-variable restriction of the manipulated variable can be based on the current (longitudinal) driving speed of the vehicle (at time k ) be determined. Alternatively or additionally, the time-variable limitation of the manipulated variable can be determined on the basis of a technical limitation of the steering device, the drive device and / or the braking device of the vehicle.

In addition, the method can include approximating the time-variable restriction of the manipulated variable by means of a further (recursive) restriction model with one or more third state components. The further restriction model can be set up to determine the one or more third state components at the subsequent point in time k + 1 on the basis of the one or more third state components at point in time k, with at least one third state component indicating the approximate restriction of the manipulated variable. An (approximated) time-variable limitation of the manipulated variable can thus (alternatively or additionally) be included in the overall model. In this way it can be ensured in an efficient manner that a manipulated variable provided by the trajectory sequence control also can actually be implemented by the vehicle. Reliable trajectory sequencing is thus made possible.

The manipulated variable at time k can also be determined on the basis of the one or more third state components, the predefined function being able to be set up for this purpose, different value combinations of the first state component, the one or more second state components and the one or more third state components, respectively to assign a different value to the manipulated variable.

For the automated lateral guidance of the vehicle, the state variable can include the quotient of the lateral deviation of the vehicle relative to the reference curve or to a reference profile and the driving speed of the vehicle. As an alternative or in addition, the manipulated variable for the automated transverse guidance of the vehicle can comprise the product of the curvature of the trajectory to be driven by the vehicle and the driving speed of the vehicle. In this way, a linear, time-invariant system model can be provided in an efficient and precise manner. This in turn enables a resource-efficient and reliable trajectory sequence control of a vehicle.

The method can include determining a deviation of an actual value of a further state variable of the vehicle from a planned value of the further state variable that is dependent on the target trajectory as a further state component. The further state variable can include a direction of travel angle of the vehicle (e.g. relative to the reference curve). The system model can be set up to predict the first status component at a subsequent time k + 1 on the basis of the further status component at time k. By taking several state variables into account, the quality of the trajectory sequence control can be further increased.

For the automated longitudinal guidance of the vehicle, the state variable can include a position of the vehicle along the longitudinal direction of the vehicle. Furthermore, the manipulated variable for the automated longitudinal guidance can include an acceleration of the vehicle in the longitudinal direction.

It should be noted that the numbering of the different state variables or state components (i.e. the "first", the "second" and the "third" state components) is only used to identify different state variables or state components and, in particular, should not indicate any sequence. The different state components can e.g. can be combined in any order or arrangement in a state vector.

According to a further aspect, a control unit for automated longitudinal and / or lateral guidance of a vehicle based on a (recursive) system model of the vehicle is described. The control unit can be set up (at a point in time k) to determine a deviation of an actual value of a state variable of the vehicle from a planned value of the state variable that is dependent on a target trajectory as the value of a first state component. The system model can be set up or have the property of predicting the first status component at a subsequent time k + 1 on the basis of the first status component at time k and on the basis of a manipulated variable at time k. In other words, the state variable of the vehicle can be dependent on a manipulated variable via the system model.

The control unit is also set up to determine a time-variable restriction or time-variable restriction of the first state component and / or the manipulated variable for N points in time from point in time k, with N> 1.

In addition, the control unit is set up to approximate the temporally variable limitation of the first state component and / or the manipulated variable by means of a (recursive) limitation model with one or more second state components. The restriction model can be set up to determine the one or more second state components at the subsequent point in time k + 1 on the basis of the one or more second state components at the point in time k. At least one second state component shows the approximated limitation of the first state component and / or the manipulated variable. In other words, the control unit can be set up to determine values of one or more second state components of a constraint model at point in time k in such a way that the temporally variable constraints of the first state component and / or the manipulated variable by values of at least one second state component at the N. Points in time from the point in time k are approximated.

Furthermore, the control unit is set up, based on the value of the first state component and the value of the one or more second state components at time k and based on a predefined function that is set up, different value combinations of the first state component and the one or more second state components to assign a (possibly different) value to the manipulated variable in each case, to determine a value of the manipulated variable at time k. A vehicle guidance system of the vehicle can then be operated as a function of the determined value of the manipulated variable in order to bring about an automated longitudinal and / or lateral guidance along the planned target trajectory.

According to a further aspect, a method for automated lateral guidance of a vehicle based on a (recursive) system model of the vehicle is described. The aspects described in this document are also applicable to this method.

The method comprises (at a point in time k) the determination of a deviation of an actual value of a state variable of the vehicle from a planned value of the state variable that is dependent on a target trajectory as a first state component. In other words, a value of a first state component can be determined as the deviation of an actual value of a state variable of the vehicle from a planned value of the state variable that is dependent on a target trajectory. The system model can be set up or have the property of predicting the first status component at a subsequent time k + 1 based on the first status component at time k and based on a manipulated variable at time k. In other words, the state variable of the vehicle can be dependent on a manipulated variable via the system model.

The state variable can include a basic state variable (e.g. the lateral deviation of the vehicle) modulated with the (longitudinal) driving speed of the vehicle. As an alternative or in addition, the manipulated variable can include a basic manipulated variable modulated with the driving speed of the vehicle (e.g. the curvature of a trajectory to be driven by the vehicle). The modulation can be done by multiplication and / or by division.

In particular, the state variable can include or correspond to the quotient of the (relative) transverse deviation of the vehicle relative to a reference curve or to a reference profile and the driving speed of the vehicle (in the longitudinal direction). Furthermore, the manipulated variable can include or correspond to the product of the (relative) curvature of a trajectory to be driven by the vehicle and the driving speed of the vehicle (in the longitudinal direction).

By choosing a state variable and / or manipulated variable that is modulated with the driving speed, it is possible to formulate a time-invariant and linear system model, which in turn enables resource-efficient, automated lateral guidance of a vehicle.

The method further includes determining a value of the manipulated variable at point in time k, based on the value of the first state component at point in time k and based on a predefined function that is set up, different values of the first state component each have a (possibly different) value to assign the manipulated variable. The vehicle guidance system of the vehicle can then be operated for automated lateral guidance of the vehicle as a function of the determined value of the manipulated variable in order to guide the vehicle along the target trajectory.

According to a further aspect, a control unit for automated lateral guidance of a vehicle based on a (recursive) system model of the vehicle is described. The control unit can be set up (at a point in time k) to determine a deviation of an actual value of a state variable of the vehicle from a planned value of the state variable that is dependent on a target trajectory as values of a first state component. In this case, the system model can be set up to predict the first status component at a subsequent time k + 1 on the basis of the first status component at time k and on the basis of a manipulated variable at time k. In other words, the state variable of the vehicle can be dependent on a manipulated variable via the system model.

The state variable can comprise a base state variable modulated with the driving speed of the vehicle and / or the manipulated variable can comprise a base manipulated variable modulated with the driving speed of the vehicle. The state variable preferably comprises the quotient of a transverse deviation of the vehicle relative to a reference curve or to a reference profile and a driving speed of the vehicle. Furthermore, the manipulated variable preferably comprises the product of a curvature of a trajectory to be driven by the vehicle and the driving speed of the vehicle.

Furthermore, the control unit can be set up to assign a (possibly different) value of the manipulated variable to different values of the first state component, based on the first status component at time k and on the basis of a predefined function, a value of the manipulated variable to determine the point in time k. In addition, the control unit can be set up to operate a vehicle guidance system of the vehicle for automated lateral guidance of the vehicle as a function of the determined value of the manipulated variable.

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

According to a further aspect, a software (SW) program is described. The software program can be set up to be executed on a processor (e.g. on a control unit of a vehicle) and thereby to execute one of the methods described in this document.

According to a further aspect, a storage medium is described. The storage medium can comprise a software program which is set up to be executed on a processor and thereby to execute one of the methods described in this document.

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

• 1 eine beispielhafte geplante Trajektorie für einen Spurwechsel;
• 2a ein beispielhaftes Blockdiagramm einer Trajektorienfolgeregelung;
• 2b einen beispielhaften Signalflussplan der Regelstrecke;
• 3 eine beispielhafte vordefinierte Funktion zur Ermittlung des Wertes einer Stellgröße;
• 4a einen beispielhaften Regelkreis;
• 4b einen beispielhaften Regelkreis mit modifizierten Zustands- und Stellgrößen;
• 5 eine beispielhafte lineare Approximation einer zeitlich variablen Beschränkung;
• 6 ein Blockdiagramm einer beispielhaften Trajektorienfolgeregelung unter Verwendung von zusätzlichen Zustandskomponenten für zeitlich variable Beschränkungen;
• 7a ein Ablaufdiagramm eines beispielhaften Verfahrens zur automatisierten Längs- und/oder Querführung eines Fahrzeugs; und
• 7b ein Ablaufdiagramm eines beispielhaften Verfahrens zur automatisierten Querführung eines Fahrzeugs.

The invention is described in more detail below on the basis of exemplary embodiments. Show it

• 1 an exemplary planned trajectory for a lane change;
• 2a an exemplary block diagram of a trajectory sequence control;
• 2 B an exemplary signal flow diagram of the controlled system;
• 3 an exemplary predefined function for determining the value of a manipulated variable;
• 4a an exemplary control loop;
• 4b an exemplary control loop with modified state and manipulated variables;
• 5 an exemplary linear approximation of a time-varying constraint;
• 6 a block diagram of an exemplary trajectory sequence control using additional state components for time-variable restrictions;
• 7a a flowchart of an exemplary method for automated longitudinal and / or lateral guidance of a vehicle; and
• 7b a flowchart of an exemplary method for automated lateral guidance of a vehicle.

As stated at the beginning, the present document is concerned with the provision of a reliable trajectory sequence control, through which manipulated or setpoint values for controlling a vehicle are specified, which can actually be implemented by the vehicle and which can reliably prevent collisions with surrounding objects. A trajectory sequence control for lateral guidance of a vehicle is described below. The aspects described here can be used in a corresponding manner for the longitudinal guidance.

1 shows a vehicle 100 (represented by a rectangle), which is on a (uncurved) roadway 101 moves. To guide the vehicle 100 can be a reference or. Target trajectory 103 (relative to a specific reference curve 102 , roughly the middle of the adjacent lane). The reference or target trajectory 103 can in this way depending on sensor data from one or more environment sensors 111 of the vehicle 100 can be determined that by driving the vehicle 100 along the reference or target trajectory 103 Collisions with one or more detected objects in the vicinity (e.g. other Road users, lane edges, etc.) are avoided. The target trajectory 103 can be determined as part of a trajectory planning.

und/oder eine geplante relative Querabweichung $d_r^{*}$

relativ zu der Referenzkurve 102 ermittelt werden. Das Fahrzeug 100 kann abweichend dazu einen tatsächlichen bzw. aktuellen Fahrrichtungswinkel θ_r und/oder eine tatsächliche bzw. aktuelle relative Querabweichung d_r aufweisen. Aufgabe der Trajektorienfolgeregelung ist es, die Abweichung zwischen der geplanten Zieltrajektorie 103 und der tatsächlich gefahrenen Trajektorie zu reduzieren, insbesondere zu minimieren. Zu diesem Zweck können im Rahmen der Trajektorienfolgeregelung der Regelfehler Δθ = ${\theta }_r^{*}-{\theta }_r$

des relativen Fahrtrichtungswinkels und/oder der Regelfehler $\Delta d=d_r^{*}-$

$d_r$

der relativen Querabweichung reduziert, insbesondere minimiert, werden.Out 1 it can be seen that through the reference or target trajectory 103 a certain planned curvature κ * is given while that of the vehicle 100 actually driven trajectory has a certain driven actual curvature κ _ist . Furthermore, a planned relative angle of travel can be used as part of the trajectory planning ${\theta }_r^{*}$

and / or a planned relative lateral deviation $d_r^{*}$

relative to the reference curve 102 be determined. The vehicle 100 can differ from this have an actual or current direction of travel angle θ _r and / or an actual or current relative transverse deviation d _r . The task of the trajectory sequence control is to determine the deviation between the planned target trajectory 103 and to reduce the trajectory actually driven, in particular to minimize it. For this purpose, the control error Δθ = ${\theta }_r^{*}-{\theta }_r$

the relative travel direction angle and / or the control error $\Delta d=d_r^{*}-$

$d_r$

the relative transverse deviation reduced, in particular minimized.

The vehicle 100 typically comprises at least one control unit 110 that is set up based on the sensor data of the one or more environment sensors 111 a target trajectory 103 to determine. Furthermore, based on the sensor data of the one or more environment sensors 111 and / or on the basis of the sensor data from one or more vehicle sensors (e.g. a speed sensor, a yaw rate sensor, an inertial sensor, etc.) the actual values of the one or more state variables (e.g. the actual or current driving direction angle θ _r and / or the actual or current relative transverse deviation d _r ) can be determined. In addition, on the basis of the control error within the trajectory tracking κ a value of a control variable (for example the curvature _to that of the vehicle 100 to be driven trajectory) can be determined. A control device 112 (for example a drive device, a braking device and / or a steering device) of the vehicle 100 can then be controlled as a function of the determined value of the manipulated variable to provide automated longitudinal and / or lateral guidance of the vehicle 100 to enable.

und/oder eine geplante Querabweichung $d_r^{*},$

ermittelt werden. In einer Vorsteuereinheit 203 kann eine Kompensation des zu regelnden Fahrzeugführungssystems 206 erfolgen. Zu diesem Zweck ist eine Inversion der Übertragungsstrecke G_csm(s) des zu regelnden Fahrzeugführungssystems 206 erforderlich. Das Fahrzeugführungssystem 206 kann typischerweise durch ein PDT4-Übertragungsglied und mit ausreichender Genauigkeit durch ein Modell 3^ter Ordnung modelliert und/oder approximiert werden. Um die Inversion eines solchen Modells zu ermöglichen, kann durch Verwendung eines Doppelintegrators die Nennerordnung des Modells erhöht, und das Modell dadurch invertierbar gemacht werden. Als Eingangsgröße der Vorsteuerreinheit 203 kann dann die zweite Ableitung der geplanten Krümmung κ*, d.h. der geplante Querruck κ̈*, betrachtet werden. Die Vorsteuereinheit 203 kann dann als Übertragungsfunktion eine Kombination aus einem Doppelintegrator und dem invertierten Modell (3^ter Ordnung) von G_csm(s) aufweisen. Durch die Vorsteuereinheit 203 wird ein Vorsteueranteil κ_ν, der zu fahrenden (Soll-) Krümmung κ_soll (d.h. der Stellgröße) bereitgestellt. Die Soll-Krümmung κ_soll ergibt sich dabei aus dem Vorsteueranteil κ_ν, und dem Regelungsanteil κ_r. 2a FIG. 10 shows a block diagram of an exemplary trajectory follower 200 . In the planning unit 202 can taking into account the current reference 201 , 102 a planned target trajectory 103 , in particular a planned curvature κ *, a planned travel direction angle ${\theta }_r^{*}$

and / or a planned transverse deviation $d_r^{*},$

be determined. In a pilot control unit 203 can compensate the vehicle control system to be controlled 206 respectively. For this purpose, an inversion of the transmission path G _csm (s) of the vehicle _{guidance system to be controlled is required} 206 required. The vehicle guidance system 206 may typically through a pDT4-transmitting member and are modeled with sufficient accuracy by a model ^of order 3 and / or approximated. In order to enable the inversion of such a model, the denominator order of the model can be increased by using a double integrator, and the model can thereby be made invertible. As an input variable for the pilot control unit 203 the second derivative of the planned curvature κ *, ie the planned transverse jerk κ̈ *, can then be considered. The pilot control unit 203 may then have a transfer function of a combination of a double integrator, and the inverted model (3 ^th order) of _csm G (s). Through the pilot control unit 203 a pre-control component κ _ν , the (target) curvature κ _{to be driven} (ie the manipulated variable) is provided. _To the desired curvature κ there results from the pilot portion _κ ν, and the control portion κ _r.

The target curvature κ target _is determined by the vehicle guidance system 206 (e.g. an electric power steering as a control device 112 includes) implemented. As already explained above, the vehicle guidance system 206 can be described by a CVM model G _csm (s). Disturbances z _κ (typically unknown) can act on the curvature (such as a cross wind, for example). It results as the output of the vehicle guidance system 206 those of the vehicle 100 actually traveled actual curvature _is κ. Using a kinematic model 207 can describing the vehicle transverse movement _kin G (s) from the actual curvature κ _is the actual driving direction angle θ _r and / or the actual lateral deviation d _r are determined. The direction of travel angle θ and / or the transverse deviation d can each be used as a state variable of the system model of the vehicle 100 to be viewed as.

ein (einfacher) Integrator und sin die Sinus-Funktion. Das CVM-Modell G_csm(s) kann dabei in einen Anteil G_eps(s) für die elektrische Servolenkung und einen Anteil G_fzg(s) für die Querdynamik des Fahrzeugs 100 aufgeteilt werden.The kinematic model 207 is exemplary in 2 B shown. Here, κ _{ref are} the curvature of the reference curve 102 , θ _{ref is} the driving direction angle of the reference curve 102 , ν is the driving speed of the vehicle 100 , $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

a (simple) integrator and sin is the sine function. The CVM model G _csm (s) can be used in a part G _eps (s) for the electric power steering and a part G _fzg (s) for the transverse dynamics of the vehicle 100 be divided.

On the basis of the control errors Δθ and Δd, a controller 204 , 205 the control component κ _{r of} the target curvature (ie the manipulated variable) can be determined. This can be done in the control unit 204 an explicit model predictive control (EMPC) takes place. The states or state _components x _{Δcvm of} the system to be controlled that are required to carry out such a state control 206 can use a parallel model unit 205 can be determined from the control component κ _r . The states or state _components x _Δcvm correspond to the state _component caused by the control _component κ _{r of} the target curvature (which is to be indicated by the Δ symbol). Furthermore, in the control unit 204 the input control component κ _ν , the target curvature must be taken into account.

The transfer function G _csm (s) of the CVM model (ie the model of the vehicle _{guidance system} 206 ) Can be prepared by a pDT4 gate, ie ^ter by a model order 4 will be described. It can be shown that even a reduced model ^of order 3 further provides a relatively good approximation of the transfer function. This transfer function for the order l = 3 can be given as follows: $$G_{cvm}^{l=3}\left(s\right)=\frac{\frac{c_1}{a_0}\mathrm{S.}+\frac{c_0}{a_0}}{\frac{a_3}{a_0}{\mathrm{S.}}^3+\frac{a_2}{a_0}{\mathrm{S.}}^2+\frac{a_1}{a_0}\mathrm{S.}+1}.$$

The values of the different parameters of the model can be based on measurements on a specific vehicle 100 or vehicle type can be determined. A model description in the (continuous) state space results from the above transfer function: $$\begin{array}{l}{\dot{x}}_{\Delta cvm}\left(t\right)=\underset{{\mathrm{A.}}_{cvm}^{l=3}}{\underbrace{\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ -a_0& -a_1& -a_2\end{array}\right]}}{x}_{\Delta cvm}\left(t\right)\underset{{\mathrm{B.}}_{cvm}^{l=3}}{\underbrace{\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right]}}{\kappa }_r\left(t\right),\\ {\kappa }_{\Delta ist}\left(t\right)=\underset{{\mathrm{C.}}_{cvm}^{l=3}}{\underbrace{\left[\begin{array}{ccc}{c}_0& c_1& c_2\end{array}\right]}}{x}_{\Delta cvm}\left(t\right).\end{array}$$

stellt die Systemmatrix des Systemmodells des Fahrzeugführungssystems 206 dar, der Vektor $B_{cvm}^{l=3}$

stellt den Eingangsvektor des Systemmodells des Fahrzeugführungssystems 206 dar, und der Vektor $C_{cvm}^{l=3}$

stellt den Ausgangsvektor des Systemmodells des Fahrzeugführungssystems 206 dar. Bei der o.g. Darstellung des Systemmodells handelt es sich um eine kontinuierliche Zustandsdarstellung, die durch bekannte Verfahren der Diskretisierung in eine zeitdiskrete (rekursive) Zustandsdarstellung überführt werden kann.Here, κ _Δist by the control portion κ _{r is} the desired curvature caused proportion of the actual _curvature κ. The matrix ${\mathrm{A.}}_{cvm}^{l=3}$

represents the system matrix of the system model of the vehicle guidance system 206 represent, the vector ${\mathrm{B.}}_{cvm}^{l=3}$

represents the input vector of the system model of the vehicle guidance system 206 represent, and the vector ${\mathrm{C.}}_{cvm}^{l=3}$

represents the output vector of the system model of the vehicle guidance system 206 The above representation of the system model is a continuous state representation which can be converted into a time-discrete (recursive) state representation using known discretization methods.

Using the above-mentioned system model (in particular using a time-discrete version of the system model), within the parallel model unit 205 the states x _{Δcvm of} the system to be controlled 206 can be determined at a sequence of points in time.

The control unit 204 can be set up to carry out a model predictive control (MPC). The model predictive control is a digital control algorithm in which a time course of the manipulated variable (eg the control component κ _{r of} the target curvature) is determined by solving an optimization problem. The optimization is based on a system model that describes the system dynamics so that the time course of the one or more system states or state components can be predicted as a function of a time course of the manipulated variables.

Which state curves are optimal is generally defined using a linear or quadratic quality criterion and recorded in a cost function. To the optimal To calculate the sequence of manipulated variables, the formulated cost-functional for a finite prediction horizon (of N time steps) is minimized using numerical optimization methods. The system is transferred from an initial state to a desired final state (which is derived from the reference or target trajectory, for example 103 ) results.

The idea of model predictive control is to solve the optimization problem cyclically on a progressive horizon. In each time step k, only the first interval of the manipulated variable sequence is typically used as the manipulated variable for controlling the system. The manipulated variable in the subsequent time step k + 1 is recalculated taking into account the measured state feedback (initial state). The continuous optimization during runtime offers the possibility of reacting to parameter fluctuations or to a non-linear time-variant behavior of the controlled system by adapting the prediction model.

Another advantage of the MPC is the ability to take physical and / or performance-related restrictions of the controlled system into account. On the one hand, a limitation of the manipulated variable can be included in the control task. On the other hand, by restricting one or more system states or state components, it is possible to prevent undesired overshoots and / or to avoid safety-critical states.

Due to the fact that in a model predictive control the manipulated variable is determined via an optimization, a relatively high computational effort arises at runtime. In order to reduce this computational effort, the control unit 204 preferably an explicit model predictive control is used.

wobei U ein Vektor der zu ermittelnden Stellgrößenfolge u(k) für k = 0, ... , N - 1, ist, wobei x(k) der Systemzustand zum Zeitpunkt k ist, und wobei x(0) der Anfangszustand ist, und wobei Q und R eine Wichtungsmatrix bzw. ein Wichtungsskalar sind. Der Systemzustand x(k) umfasst typischerweise eine Vielzahl von Zustandskomponenten. Die Systemdynamik des Gesamtmodells und der Anfangszustand können durch eine zeitdiskrete Zustandsdarstellung wie folgt beschrieben werden $$\begin{array}{l}\begin{array}{cc}\text{x}\left(k+1\right)=\text{Ax}\left(k\right))+\text{B}u\left(k\right),& \text{A }\in {ℝ}^{n\times n}\end{array},\text{B }\in {ℝ}^n,\\ \text{x}\left(0\right)={\text{x}}_0,\end{array}$$

und das Kostenfunktional kann in Abhängigkeit von Beschränkungen für die Stellgröße und/oder für die einzelnen Zustandskomponenten optimiert, insbesondere minimiert, werden, $$\begin{array}{cc}{u}_{min}\le u\left(k\right)\le u_{max},& k=\mathrm{0,}\dots ,N-1\\ x_{min}\le x\left(k\right)\le x_{max},& k=\mathrm{1,}\dots ,N.\end{array}$$

An exemplary cost functional for a model predictive control is $$J\left(\text{x}\left(0\right),\text{U}\right)={\displaystyle \sum _{k=0}^N\text{x}{\left(k\right)}^T\text{Qx}}\left(k\right)+{\displaystyle \sum _{k=0}^{N-1}u}{\left(k\right)}^T\mathrm{R.}u\left(k\right)$$

where U is a vector of the manipulated variable sequence u (k) to be determined for k = 0, ..., N - 1, where x (k) is the system state at time k, and where x (0) is the initial state, and where Q and R are a weighting matrix and a weighting scalar, respectively. The system state x (k) typically comprises a large number of state components. The system dynamics of the overall model and the initial state can be described using a discrete-time state representation as follows $$\begin{array}{l}\begin{array}{cc}\text{x}\left(k+1\right)=\text{Ax}\left(k\right))+\text{B.}u\left(k\right),& \text{A.}\in {ℝ}^{n\times n}\end{array},\text{B.}\in {ℝ}^n,\\ \text{x}\left(0\right)={\text{x}}_0,\end{array}$$

and the cost-functional can be optimized, in particular minimized, depending on restrictions for the manipulated variable and / or for the individual state components, $$\begin{array}{cc}{u}_{min}\le u\left(k\right)\le u_{max},& k=\mathrm{0,}...,N-1\\ x_{min}\le x\left(k\right)\le x_{max},& k=\mathrm{1,}...,N.\end{array}$$

With model predictive control, the above-mentioned linear-quadratic optimization problem can be solved online in order to determine an optimal manipulated variable sequence U and in particular an optimal value u (0) of the manipulated variable to be used based on a measured initial state x (0). Due to the relatively high computing effort during runtime, it is used in particular for regulating a vehicle guidance system 206 , in which the solution has to be determined in a relatively short time (e.g. in a few milliseconds).

For the control of linear time-invariant systems with (time) constant restrictions, the computational effort during the operation of a vehicle can be reduced by an explicit design of the model predictive control 100 can be significantly reduced without having to forego the positive properties of model predictive control. The main idea of the explicit model predictive control is to formulate the quadratic program as a multiparametric quadratic program in order to solve this offline in advance using methods of multiparametric (MP) optimization. If it is assumed that the possible initial states x (0) lie in a specified range of values, then these can be defined as free parametric variables in an MP optimization problem. As a result, will The optimization precalculates the minimum of the quadratic cost function or the optimal manipulated variable u (0) depending on the specified range of values of the initial states x (0).

With the help of the so-called KKT (Karush-Kuhn-Tucker) optimality conditions, a piecewise affine function is developed, which is defined by polyhedral partitions of the permissible state space. The computational effort that arises during runtime is reduced to a quantity affiliation test, similar to a lookup table, so that control is carried out on control units 110 of a vehicle 100 can be executed in real time.

The complexity of the explicit MPC or the affine function depends on the system order used in the system model and the optimization horizon N. The dimensionality of the polyhedra increases with every system order, while the number of partitions usually increases exponentially with the length of the optimization horizon N.

Dabei repräsentiert z die oben genannte stückweise affine Funktion, die im Zuge der Optimierung über polyhedrische Partitionen definiert wird. „uBv.“ steht für „unter der Bedingung von“. Insbesondere gilt $$\begin{array}{ccc}\text{z}\widehat{=}\text{U}+{\text{H}}^{-1}{\text{F}}^T\text{x}\left(0\right)& \text{und}& \text{S}\widehat{=}\text{E}+{\text{GH}}^{-1}{\text{F}}^T\end{array}$$

mit $$\begin{array}{ccc}\text{H}=B^{T}QB,& \text{F}=A^{T}QB,& \text{Y}=A^T\end{array}QA$$

sowie $$\begin{array}{rrr}\hfill \text{G}=\left[\begin{array}{r}\hfill {\text{I}}_{nN}B\\ \hfill -{\text{I}}_{nN}B\\ \hfill {\text{I}}_N\\ \hfill -{\text{I}}_N\end{array}\right],& \hfill \text{W=}\left[\begin{array}{r}\hfill {\text{X}}_{max}\\ \hfill -{\text{X}}_{min}\\ \hfill {\text{U}}_{max}\\ \hfill -{\text{U}}_{min}\end{array}\right],& \hfill \text{E=}\left[\begin{array}{r}\hfill -{\text{I}}_{nN}A\\ \hfill {\text{I}}_{nN}A\\ \hfill 0\\ \hfill 0\end{array}\right]\end{array}.$$

It can be shown that the above mentioned optimization problem can be converted into the following multiparametric optimization problem, $$\begin{array}{l}J*\left(\text{x}\left(0\right)\right)=\underset{z}{\text{<figure-callout id="1" label="min z" filenames="DE102018125250B4\_0061.png,DE102018125250B4\_0062.png" state="{{state}}">min</figure-callout>}}\frac{1}{2}{z}^T\text{Hz}\\ \text{uBv}\text{. Gz}\le \text{W.}+\text{Sx}\left(0\right).\end{array}$$

Here, z represents the piecewise affine function mentioned above, which is defined in the course of the optimization using polyhedral partitions. "UBv." Stands for "on condition of". In particular, $$\begin{array}{ccc}\text{z}\widehat{=}\text{U}+{\text{H}}^{-1}{\text{F.}}^T\text{x}\left(0\right)& \text{and}& \text{S.}\widehat{=}\text{E.}+{\text{GH}}^{-1}{\text{F.}}^T\end{array}$$

With $$\begin{array}{ccc}\text{H}={\mathrm{B.}}^{T}Q\mathrm{B.},& \text{F.}={\mathrm{A.}}^{T}Q\mathrm{B.},& \text{Y}={\mathrm{A.}}^T\end{array}Q\mathrm{A.}$$

as $$\begin{array}{rrr}\hfill \text{G}=\left[\begin{array}{r}\hfill {\text{I.}}_{nN}\mathrm{B.}\\ \hfill -{\text{I.}}_{nN}\mathrm{B.}\\ \hfill {\text{I.}}_N\\ \hfill -{\text{I.}}_N\end{array}\right],& \hfill \text{W =}\left[\begin{array}{r}\hfill {\text{X}}_{max}\\ \hfill -{\text{X}}_{min}\\ \hfill {\text{U}}_{max}\\ \hfill -{\text{U}}_{min}\end{array}\right],& \hfill \text{E =}\left[\begin{array}{r}\hfill -{\text{I.}}_{nN}\mathrm{A.}\\ \hfill {\text{I.}}_{nN}\mathrm{A.}\\ \hfill 0\\ \hfill 0\end{array}\right]\end{array}.$$

und für die Beschränkungen der Stellgröße $${\text{U}}_{min}={\left[u_{min}\left(0\right),\dots ,u_{min}\left(N-1\right)\right]}^T,{\text{U}}_{max}={\left[u_{max}\left(0\right),\dots ,u_{max}\left(N-1\right)\right]}^T$$

sowie für die Beschränkungen der einzelnen Zustandskomponenten $$\begin{array}{cc}{\text{X}}_{min}={\left[{\text{x}}_{min}\left(1\right),\dots ,{\text{x}}_{min}\left(N\right)\right]}^T,& {\text{X}}_{max}={\left[{\text{x}}_{max}\left(1\right),\dots ,{\text{x}}_{max}\left(N\right)\right]}^T\end{array}$$

Des Weiteren sind I_N und I_nN Einheitsmatrizen der Größe N bzw. nN, wobei n die Systemordnung des Gesamtmodells (d.h. die Anzahl der Zustandskomponenten) ist.Furthermore applies $$\underset{\text{X}}{\underbrace{\left[\begin{array}{c}\text{x}\left(1\right)\\ \text{x}\left(2\right)\\ ⋮\\ \text{x}\left(N\right)\end{array}\right]}}=\underset{\mathrm{A.}}{\underbrace{\left[\begin{array}{c}\text{A.}\\ {\text{A.}}^2\\ ⋮\\ {\text{A.}}^N\end{array}\right]}}\text{x}\left(0\right)+\underset{\mathrm{B.}}{\underbrace{\left[\begin{array}{cccc}\text{B.}& 0& ...& 0\\ \text{FROM}& \text{B.}& ...& 0\\ ⋮& \ddots & \ddots & ⋮\\ {\text{A.}}^{N-1}\text{B.}& ...& \text{FROM}& \text{B.}\end{array}\right]}}\underset{\text{U}}{\underbrace{\left[\begin{array}{c}u\left(0\right)\\ u\left(1\right)\\ ⋮\\ u\left(N-1\right)\end{array}\right]}}$$

and for the restrictions of the manipulated variable $${\text{U}}_{min}={\left[u_{min}\left(0\right),...,u_{min}\left(N-1\right)\right]}^T,{\text{U}}_{max}={\left[u_{max}\left(0\right),...,u_{max}\left(N-1\right)\right]}^T$$

as well as for the limitations of the individual state components $$\begin{array}{cc}{\text{X}}_{min}={\left[{\text{x}}_{min}\left(1\right),...,{\text{x}}_{min}\left(N\right)\right]}^T,& {\text{X}}_{max}={\left[{\text{x}}_{max}\left(1\right),...,{\text{x}}_{max}\left(N\right)\right]}^T\end{array}$$

Furthermore, I _N and I _{nN are} unit _matrices of size N and nN, respectively, where n is the system order of the overall model (ie the number of state components).

Provided that the overall model under consideration and the constraints are time-invariant, the above-mentioned multiparametric optimization problem for different initial states x (0) can be solved in order to determine a piece-wise affine function, which shows a value of the manipulated variable u (0) for different initial states x (0).

For a simplified overall model with the states or state components lateral deviation Δd and course angle error Δθ, the in 3 shown piecewise affine function 300 be determined. How out 3 As can be seen, the curvature κ (“kappa”) can be determined directly as a functional value from the initial state x (0) in relation to the lateral deviation Δd and course angle error Δθ (“theta”).

Unter Berücksichtigung der Linearisierung der Sinus-Funktion für relativ kleine Werte von Δθ(t) ergibt sich daraus das lineare zeitvariante System $$\left[\begin{array}{c}\Delta \dot{d}\left(t\right)\\ \Delta \dot{\theta }\left(t\right)\end{array}\right]=\underset{{\text{A}}_{kin}\left(t\right)}{\underbrace{\left[\begin{array}{cc}0& v\left(t\right)\\ 0& 0\end{array}\right]}}\underset{x_{\Delta kin}\left(t\right)}{\underbrace{\left[\begin{array}{c}\Delta d\left(t\right)\\ \Delta \theta \left(t\right)\end{array}\right]}}+\underset{{\text{B}}_{kin}\left(t\right)}{\underbrace{\left[\begin{array}{c}0\\ v\left(t\right)\end{array}\right]}}{\kappa }_{\Delta ist}\left(t\right)$$

und zusammengefasst für das Gesamtsystem bzw. für das Gesamtmodell (in kontinuierlicher Zustandsdarstellung) $$\left[\begin{array}{c}{\dot{\text{x}}}_{\Delta kin}\left(t\right)\\ {\dot{\text{x}}}_{\Delta cvm}\left(t\right)\end{array}\right]=\underset{{\text{A}}_{ges}\left(t\right)}{\underbrace{\left[\begin{array}{cc}{\text{A}}_{kin}\left(t\right)& B_{kin}\left(t\right){\text{C}}_{cvm}\\ 0& {\text{ A}}_{cvm}\end{array}\right]}}\underset{{\text{x}}_{\Delta ges}\left(t\right)}{\underbrace{\left[\begin{array}{c}{\text{x}}_{\Delta kin}\left(t\right)\\ {\text{x}}_{\Delta cvm}\left(t\right)\end{array}\right]}}+\underset{{\text{B}}_{ges}\left(t\right)}{\underbrace{\left[\begin{array}{c}0\\ {\text{B}}_{cvm}\end{array}\right]}}{\kappa }_r\left(t\right)$$

Dieses Gesamtmodell ist aufgrund der Abhängigkeit von der (typischerweise nicht konstanten) Fahrgeschwindigkeit ν(t) zeitvariant. Um ein zeitinvariantes Gesamtsystem bereitzustellen, kann anstelle der Krümmung κ_r(t) die mit der Fahrgeschwindigkeit ν(t) multiplizierte Krümmung κ_r(t), d.h. $${\tilde{\kappa }}_r\left(t\right)={\kappa }_r\left(t\right)v\left(t\right)$$

betrachtet werden. Die modifizierte Stellgröße κ̃_r(t) des modifizierten Reglers kann als (zeitlicher Verlauf der) Gierrate betrachtet werden. Außerhalb der Regelung kann dann durch Rücksubstitution auf Basis der ermittelten modifizierten Stellgröße κ̃_r(t) und auf Basis der Fahrgeschwindigkeit ν(t) der Regelungsanteil κ_r(t) der Soll-Krümmung κ_soll(t) ermittelt werden.A description of the CVM model in the state space has already been given above. To predict the relative vehicle movement along a given trajectory, the CVM model with the states or state _components x _{Δcvm can be} expanded to include the states or state components of the lateral deviation Δd (t) and the heading angle error Δθ (t). The following applies here (as in 2 B visible) $$\begin{array}{ccc}\Delta \dot{d}\left(t\right)=v\left(t\right)sin\left(\Delta \theta \left(t\right)\right),& \text{and}& \Delta \dot{\theta }\left(t\right)=v\left(t\right){\kappa }_{\Delta ist}\end{array}\left(t\right).$$

Taking into account the linearization of the sine function for relatively small values of Δθ (t), the linear time-variant system results $$\left[\begin{array}{c}\Delta \dot{d}\left(t\right)\\ \Delta \dot{\theta }\left(t\right)\end{array}\right]=\underset{{\text{A.}}_{kin}\left(t\right)}{\underbrace{\left[\begin{array}{cc}0& v\left(t\right)\\ 0& 0\end{array}\right]}}\underset{x_{\Delta kin}\left(t\right)}{\underbrace{\left[\begin{array}{c}\Delta d\left(t\right)\\ \Delta \theta \left(t\right)\end{array}\right]}}+\underset{{\text{B.}}_{kin}\left(t\right)}{\underbrace{\left[\begin{array}{c}0\\ v\left(t\right)\end{array}\right]}}{\kappa }_{\Delta ist}\left(t\right)$$

and summarized for the overall system or for the overall model (in continuous status display) $$\left[\begin{array}{c}{\dot{\text{x}}}_{\Delta kin}\left(t\right)\\ {\dot{\text{x}}}_{\Delta cvm}\left(t\right)\end{array}\right]=\underset{{\text{A.}}_{Ges}\left(t\right)}{\underbrace{\left[\begin{array}{cc}{\text{A.}}_{kin}\left(t\right)& {\mathrm{B.}}_{kin}\left(t\right){\text{C.}}_{\mathrm{<figure-callout\; id="0"\; label="c\; v\; m"\; filenames="DE102018125250B4\_0064.png"\; state="\{\{state\}\}">c</figure-callout>}vm}\\ 0& {\text{A.}}_{cvm}\end{array}\right]}}\underset{{\text{x}}_{\Delta Ges}\left(t\right)}{\underbrace{\left[\begin{array}{c}{\text{x}}_{\Delta kin}\left(t\right)\\ {\text{x}}_{\Delta cvm}\left(t\right)\end{array}\right]}}+\underset{{\text{B.}}_{Ges}\left(t\right)}{\underbrace{\left[\begin{array}{c}0\\ {\text{B.}}_{cvm}\end{array}\right]}}{\kappa }_r\left(t\right)$$

This overall model is time-variant due to the dependence on the (typically not constant) driving speed ν (t). In order to provide a time-invariant overall system, instead of the curvature κ _r (t), the curvature κ _r (t) multiplied by the driving speed ν (t), ie $${\tilde{\kappa }}_r\left(t\right)={\kappa }_r\left(t\right)v\left(t\right)$$

to be viewed as. The modified manipulated variable κ̃ _r (t) of the modified controller can be viewed as the (time course of) yaw rate. Outside the control can then be back-substitution based on the determined modified manipulated variable κ _r (t) and on the basis of the vehicle speed ν (t) of the control portion κ _r (t) of the target curvature _to κ (t) are determined.

betrachtet werden. Es ergibt sich dann das zeitinvariante modifizierte Gesamtmodell (in kontinuierlicher Zustandsdarstellung) $$\left[\begin{array}{c}\Delta \dot{\tilde{d}}\left(t\right)\\ \Delta \dot{\theta }\left(t\right)\\ {\dot{\text{x}}}_{\Delta cvm}\left(t\right)\end{array}\right]=\underset{{\overline{\text{A}}}_{ges}}{\underbrace{\left[\begin{array}{cc}\left[\begin{array}{cc}0& 1\\ 0& 0\end{array}\right]& \left[\begin{array}{c}0\\ 1\end{array}\right]{\text{C}}_{cvm}^l\\ \begin{array}{cc}0& 0\end{array}& {\text{A}}_{cvm}^l\end{array}\right]}}\underset{{\overline{\text{x}}}_{\Delta ges}\left(t\right)}{\underbrace{\left[\begin{array}{c}\Delta \tilde{d}\left(t\right)\\ \Delta \theta \left(t\right)\\ {\text{x}}_{\Delta cvm}\left(t\right)\end{array}\right]}}+\underset{{\text{B}}_{ges}}{\underbrace{\left[\begin{array}{c}0\\ 0\\ {\text{B}}_{cvm}^l\end{array}\right]}}{\tilde{\kappa }}_r\left(t\right)$$

Furthermore, instead of the transverse deviation Δd (t), the modified state or the modified state component Δd̃ (t), with $$\Delta \tilde{d}\left(t\right)=\Delta d\left(t\right)\text{/}v\left(t\right)$$

to be viewed as. The result is the time-invariant modified overall model (in a continuous representation of the state) $$\left[\begin{array}{c}\Delta \dot{\tilde{d}}\left(t\right)\\ \Delta \dot{\theta }\left(t\right)\\ {\dot{\text{x}}}_{\Delta cvm}\left(t\right)\end{array}\right]=\underset{{\overline{\text{A.}}}_{Ges}}{\underbrace{\left[\begin{array}{cc}\left[\begin{array}{cc}0& 1\\ 0& 0\end{array}\right]& \left[\begin{array}{c}0\\ 1\end{array}\right]{\text{C.}}_{c\mathrm{<figure-callout\; id="0"\; label="v\; m\; l"\; filenames="DE102018125250B4\_0064.png"\; state="\{\{state\}\}">v</figure-callout>}m}^l\\ \begin{array}{cc}0& 0\end{array}& {\text{A.}}_{cvm}^l\end{array}\right]}}\underset{{\overline{\text{x}}}_{\Delta Ges}\left(t\right)}{\underbrace{\left[\begin{array}{c}\Delta \tilde{d}\left(t\right)\\ \Delta \theta \left(t\right)\\ {\text{x}}_{\Delta cvm}\left(t\right)\end{array}\right]}}+\underset{{\text{B.}}_{Ges}}{\underbrace{\left[\begin{array}{c}0\\ 0\\ {\text{B.}}_{cvm}^l\end{array}\right]}}{\tilde{\kappa }}_r\left(t\right)$$

As already explained above, the o.g. The overall model can be converted into a (recursive) time-discrete overall model through discretization.

The 4a and 4b show the original controller (with a time-variant overall model) and the modified controller (with a time-invariant overall model).

Dabei sind ${\kappa }_{soll}^{max}\left(t\right)\text{bzw}\text{.}{\kappa }_{soll}^{min}\left(t\right)$

Grenzwerte für die zulässige (gesamte) Soll-Krümmung.The one from a vehicle 100 convertible curvature typically depends on a limited steering angle range of the vehicle 100 and the maximum realizable transverse acceleration of the vehicle 100 from. The maximum transverse acceleration that can be achieved depends in turn on the driving speed v (k) of the vehicle 100 at a point in time k. For the maximum or minimum permissible control component of the set curvature (i.e. the manipulated variable to be determined), the following applies: $$\begin{array}{ccc}{\kappa }_r^{max}\left(k\right)={\kappa }_{sOll}^{max}\left(k\right)-{\kappa }_v\left(k\right)& \text{or}\text{.}& {\kappa }_r^{min}\left(k\right)={\kappa }_{sOll}^{min}\left(k\right)-{\kappa }_v\left(k\right)\end{array}.$$

Are there ${\kappa }_{sOll}^{max}\left(t\right)\text{or}\text{.}{\kappa }_{sOll}^{min}\left(t\right)$

Limit values for the permissible (total) nominal curvature.

Für die oben definierten modifizierten Größen ergibt sich $${\tilde{\kappa }}_r^{max}\left(k\right)={\kappa }_r^{max}\left(k\right)\nu \left(k\right)\text{ bzw}\text{. }{\tilde{\kappa }}_r^{min}\left(k\right)={\kappa }_r^{min}\left(k\right)\nu \left(k\right)$$

$$\begin{array}{cc}{\widetilde{\mathrm{\Delta }d}}_{max}\left(k\right)=\mathrm{\Delta }{d}_{max}\left(k\right)\text{/}\nu \left(k\right),& {\widetilde{\mathrm{\Delta }d}}_{min}\left(k\right)=\mathrm{\Delta }{d}_{min}\left(k\right)\text{/}\nu \left(k\right)\end{array}$$

Somit ergibt sich für die zu berücksichtigenden Nebenbedingungen bzw. Beschränkungen $$\begin{array}{cc}{\tilde{\kappa }}_{min}\left(k\right)\le {\tilde{\kappa }}_r\left(k\right)\le {\tilde{\kappa }}_{max}\left(k\right),& k=0\end{array},\dots ,N-\mathrm{1,}$$

$${\mathbf{w}}_{min}^{\mathrm{\Delta }cvm}\le {\mathbf{x}}_{\mathrm{\Delta }cvm}\left(k\right)\le {\mathbf{w}}_{max}^{\mathrm{\Delta }cvm},$$

$$\mathrm{\Delta }{\theta }_{min}\le \mathrm{\Delta }\theta \left(k\right)\le \mathrm{\Delta }{\theta }_{max},$$

$$\begin{array}{cc}{\widetilde{\mathrm{\Delta }d}}_{min}\left(k\right)\le \widetilde{\mathrm{\Delta }d}\left(k\right)\le {\widetilde{\mathrm{\Delta }d}}_{max}\left(k\right),& k=\mathrm{0,}\dots ,N.\end{array}$$

Dabei beschreiben die konstanten Vektoren $${\mathbf{w}}_{max}^{\mathrm{\Delta }cvm}\in {ℝ}^l\text{ und }{\mathbf{w}}_{min}^{\mathrm{\Delta }cvm}\in {ℝ}^l$$

(zeitlich konstante) Beschränkungen für die Zustände bzw. Zustandskomponenten x_Δcvm des CVM-Modells.On the status side, there is typically the permissible maximum (ie left-hand) transverse deviation or minimum (ie right-hand) transverse deviation due to changing situations in the vicinity of the vehicle 100 variable over time, ie $$\mathrm{\Delta }{d}_{max}\left(k\right)\text{or}\text{.}\mathrm{\Delta }{d}_{min}\left(k\right)$$

For the modified quantities defined above, this results $${\tilde{\kappa }}_r^{max}\left(k\right)={\kappa }_r^{max}\left(k\right)\nu \left(k\right)\text{or}\text{.}{\tilde{\kappa }}_r^{min}\left(k\right)={\kappa }_r^{min}\left(k\right)\nu \left(k\right)$$

$$\begin{array}{cc}{\widetilde{\mathrm{\Delta }d}}_{max}\left(k\right)=\mathrm{\Delta }{d}_{max}\left(k\right)\text{/}\nu \left(k\right),& {\widetilde{\mathrm{\Delta }d}}_{min}\left(k\right)=\mathrm{\Delta }{d}_{min}\left(k\right)\text{/}\nu \left(k\right)\end{array}$$

This results in the secondary conditions or restrictions to be taken into account $$\begin{array}{cc}{\tilde{\kappa }}_{min}\left(k\right)\le {\tilde{\kappa }}_r\left(k\right)\le {\tilde{\kappa }}_{max}\left(k\right),& k=0\end{array},...,N-\mathrm{1,}$$

$${\mathbf{w}}_{min}^{\mathrm{\Delta }cvm}\le {\mathbf{x}}_{\mathrm{\Delta }cvm}\left(k\right)\le {\mathbf{w}}_{max}^{\mathrm{\Delta }cvm},$$

$$\mathrm{\Delta }{\theta }_{min}\le \mathrm{\Delta }\theta \left(k\right)\le \mathrm{\Delta }{\theta }_{max},$$

$$\begin{array}{cc}{\widetilde{\mathrm{\Delta }d}}_{min}\left(k\right)\le \widetilde{\mathrm{\Delta }d}\left(k\right)\le {\widetilde{\mathrm{\Delta }d}}_{max}\left(k\right),& k=\mathrm{0,}...,N.\end{array}$$

Describe the constant vectors $${\mathbf{w}}_{max}^{\mathrm{\Delta }cvm}\in {ℝ}^l\text{and}{\mathbf{w}}_{min}^{\mathrm{\Delta }cvm}\in {ℝ}^l$$

Restrictions (constant over time) for the states or state _components x _{Δcvm of} the CVM model.

The time-varying restrictions can be approximated by a function with one or more function parameters. In particular, the time-varying restrictions can each be approximated by a linear function. The approximation can take place in such a way that the approximation is always more restrictive and / or at least not less restrictive than the original time-variable restriction.

5 shows the time course of the restriction 503 a variable 502 (e.g. a manipulated variable or a status component) as a function of time 501 . Furthermore shows 5 the approximation 504 the restriction 503 by a linear function.

$$\begin{array}{cc}{\tilde{\kappa }}_{min}\left(k\right)\approx {\tilde{\kappa }}_{min}^0+{\tilde{\kappa }}_{min}^m\cdot k,& {\tilde{\kappa }}_{max}\left(k\right)\approx {\tilde{\kappa }}_{max}^0+{\tilde{\kappa }}_{max}^m\cdot k,\end{array}$$

mit $$\begin{array}{cc}{\tilde{\kappa }}_{min}^0={\tilde{\kappa }}_{min}\left(0\right)& {\tilde{\kappa }}_{max}^0={\tilde{\kappa }}_{max}\left(0\right),\end{array}$$

$$\begin{array}{cc}{\widetilde{\mathrm{\Delta }d}}_{min}^0={\widetilde{\mathrm{\Delta }d}}_{min}\left(0\right)& {\widetilde{\mathrm{\Delta }d}}_{max}^0={\widetilde{\mathrm{\Delta }d}}_{max}\left(0\right).\end{array}$$

Für die Steigungen ergibt sich $${\tilde{\kappa }}_{min}^m=max\left(\left\{\frac{{\tilde{\kappa }}_{min}\left(1\right)-{\tilde{\kappa }}_{min}^0}{1},\frac{{\tilde{\kappa }}_{min}\left(2\right)-{\tilde{\kappa }}_{min}^0}{2},\dots ,\frac{{\tilde{\kappa }}_{min}\left(N-1\right)-{\tilde{\kappa }}_{min}^0}{N-1}\right\}\right),$$

$${\tilde{\kappa }}_{max}^m=min\left(\left\{\frac{{\tilde{\kappa }}_{max}\left(1\right)-{\tilde{\kappa }}_{max}^0}{1},\frac{{\tilde{\kappa }}_{max}\left(2\right)-{\tilde{\kappa }}_{max}^0}{2},\dots ,\frac{{\tilde{\kappa }}_{max}\left(N-1\right)-{\widetilde{\mathrm{\Delta }d}}_{max}^0}{N-1}\right\}\right)$$

sowie $${\widetilde{\mathrm{\Delta }d}}_{min}^m=max\left(\left\{\frac{{\widetilde{\mathrm{\Delta }d}}_{min}\left(1\right)-{\widetilde{\mathrm{\Delta }d}}_{min}^0}{1},\frac{{\widetilde{\mathrm{\Delta }d}}_{min}\left(2\right)-{\widetilde{\mathrm{\Delta }d}}_{min}^0}{2},\dots ,\frac{{\widetilde{\mathrm{\Delta }d}}_{min}\left(N\right)-{\widetilde{\mathrm{\Delta }d}}_{min}^0}{N}\right\}\right),$$

$${\widetilde{\mathrm{\Delta }d}}_{max}^m=min\left(\left\{\frac{{\widetilde{\mathrm{\Delta }d}}_{max}\left(1\right)-{\widetilde{\mathrm{\Delta }d}}_{max}^0}{1},\frac{{\widetilde{\mathrm{\Delta }d}}_{max}\left(2\right)-{\widetilde{\mathrm{\Delta }d}}_{max}^0}{2},\dots ,\frac{{\widetilde{\mathrm{\Delta }d}}_{max}\left(N\right)-{\widetilde{\mathrm{\Delta }d}}_{max}^0}{N}\right\}\right).$$

Die approximierten, zeitlich veränderlichen Beschränkungen können in Zustandsform beschrieben und dadurch in dem Gesamt-Zustandsmodell berücksichtigt werden, $$\left[\begin{array}{rrrr}\hfill \underset{x_a\left(k+1\right)}{\underbrace{\left[\begin{array}{r}\hfill {\widetilde{\mathrm{\Delta }d}}_{max}\left(k+1\right)\\ \hfill {\widetilde{md}}_{max}\left(k+1\right)\\ \hfill {\widetilde{\mathrm{\Delta }d}}_{min}\left(k+1\right)\\ \hfill {\widetilde{md}}_{min}\left(k+1\right)\\ \hfill {\tilde{\kappa }}_{max}\left(k+1\right)\\ \hfill {\widetilde{m\kappa }}_{max}\left(k+1\right)\\ \hfill {\tilde{\kappa }}_{min}\left(k+1\right)\\ \hfill {\widetilde{m\kappa }}_{min}\left(k+1\right)\end{array}\right]}}& \hfill =& \hfill \underset{A_a}{\underbrace{\left[\begin{array}{llllllll}1\hfill & 1\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill \\ 0\hfill & 1\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill \\ 0\hfill & 0\hfill & 1\hfill & 1\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill \\ 0\hfill & 0\hfill & 0\hfill & 1\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill \\ 0\hfill & 0\hfill & 0\hfill & 0\hfill & 1\hfill & 1\hfill & 0\hfill & 0\hfill \\ 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 1\hfill & 0\hfill & 0\hfill \\ 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 1\hfill & 1\hfill \\ 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 1\hfill \end{array}\right]}}& \hfill \underset{x_a\left(k\right)}{\underbrace{\left[\begin{array}{r}\hfill {\widetilde{\mathrm{\Delta }d}}_{max}\left(k\right)\\ \hfill {\widetilde{md}}_{max}\left(k\right)\\ \hfill {\widetilde{\mathrm{\Delta }d}}_{min}\left(k\right)\\ \hfill {\widetilde{md}}_{min}\left(k\right)\\ \hfill {\tilde{\kappa }}_{max}\left(k\right)\\ \hfill {\widetilde{m\kappa }}_{max}\left(k\right)\\ \hfill {\tilde{\kappa }}_{min}\left(k\right)\\ \hfill {\widetilde{m\kappa }}_{min}\left(k\right)\end{array}\right]}}\end{array}\right]$$

If a linear approximation is used, this results in 502 (ie for the modified state component and for the modified manipulated variable) $$\begin{array}{cc}{\widetilde{\mathrm{\Delta }d}}_{min}\left(k\right)\approx {\widetilde{\mathrm{\Delta }d}}_{min}^0+{\widetilde{\mathrm{\Delta }d}}_{min}^m\cdot k,& {\widetilde{\mathrm{\Delta }d}}_{max}\left(k\right)\approx {\widetilde{\mathrm{\Delta }d}}_{max}^0+{\widetilde{\mathrm{\Delta }d}}_{max}^m\cdot k,\end{array}$$

$$\begin{array}{cc}{\tilde{\kappa }}_{min}\left(k\right)\approx {\tilde{\kappa }}_{min}^0+{\tilde{\kappa }}_{min}^m\cdot k,& {\tilde{\kappa }}_{max}\left(k\right)\approx {\tilde{\kappa }}_{max}^0+{\tilde{\kappa }}_{max}^m\cdot k,\end{array}$$

With $$\begin{array}{cc}{\tilde{\kappa }}_{min}^0={\tilde{\kappa }}_{min}\left(0\right)& {\tilde{\kappa }}_{max}^0={\tilde{\kappa }}_{max}\left(0\right),\end{array}$$

$$\begin{array}{cc}{\widetilde{\mathrm{\Delta }d}}_{min}^0={\widetilde{\mathrm{\Delta }d}}_{min}\left(0\right)& {\widetilde{\mathrm{\Delta }d}}_{max}^0={\widetilde{\mathrm{\Delta }d}}_{max}\left(0\right).\end{array}$$

For the slopes results $${\tilde{\kappa }}_{min}^m=max\left(\left\{\frac{{\tilde{\kappa }}_{min}\left(1\right)-{\tilde{\kappa }}_{min}^0}{1},\frac{{\tilde{\kappa }}_{min}\left(2\right)-{\tilde{\kappa }}_{min}^0}{2},...,\frac{{\tilde{\kappa }}_{min}\left(N-1\right)-{\tilde{\kappa }}_{min}^0}{N-1}\right\}\right),$$

$${\tilde{\kappa }}_{max}^m=min\left(\left\{\frac{{\tilde{\kappa }}_{max}\left(1\right)-{\tilde{\kappa }}_{max}^0}{1},\frac{{\tilde{\kappa }}_{max}\left(2\right)-{\tilde{\kappa }}_{max}^0}{2},...,\frac{{\tilde{\kappa }}_{max}\left(N-1\right)-{\widetilde{\mathrm{\Delta }d}}_{max}^0}{N-1}\right\}\right)$$

as $${\widetilde{\mathrm{\Delta }d}}_{min}^m=max\left(\left\{\frac{{\widetilde{\mathrm{\Delta }d}}_{min}\left(1\right)-{\widetilde{\mathrm{\Delta }d}}_{min}^0}{1},\frac{{\widetilde{\mathrm{\Delta }d}}_{min}\left(2\right)-{\widetilde{\mathrm{\Delta }d}}_{min}^0}{2},...,\frac{{\widetilde{\mathrm{\Delta }d}}_{min}\left(N\right)-{\widetilde{\mathrm{\Delta }d}}_{min}^0}{N}\right\}\right),$$

$${\widetilde{\mathrm{\Delta }d}}_{max}^m=min\left(\left\{\frac{{\widetilde{\mathrm{\Delta }d}}_{max}\left(1\right)-{\widetilde{\mathrm{\Delta }d}}_{max}^0}{1},\frac{{\widetilde{\mathrm{\Delta }d}}_{max}\left(2\right)-{\widetilde{\mathrm{\Delta }d}}_{max}^0}{2},...,\frac{{\widetilde{\mathrm{\Delta }d}}_{max}\left(N\right)-{\widetilde{\mathrm{\Delta }d}}_{max}^0}{N}\right\}\right).$$

The approximated, temporally variable restrictions can be described in state form and thus taken into account in the overall state model, $$\left[\begin{array}{rrrr}\hfill \underset{x_a\left(k+1\right)}{\underbrace{\left[\begin{array}{r}\hfill {\widetilde{\mathrm{\Delta }d}}_{max}\left(k+1\right)\\ \hfill {\widetilde{md}}_{max}\left(k+1\right)\\ \hfill {\widetilde{\mathrm{\Delta }d}}_{min}\left(k+1\right)\\ \hfill {\widetilde{md}}_{min}\left(k+1\right)\\ \hfill {\tilde{\kappa }}_{max}\left(k+1\right)\\ \hfill {\widetilde{m\kappa }}_{max}\left(k+1\right)\\ \hfill {\tilde{\kappa }}_{min}\left(k+1\right)\\ \hfill {\widetilde{m\kappa }}_{min}\left(k+1\right)\end{array}\right]}}& \hfill =& \hfill \underset{{\mathrm{A.}}_a}{\underbrace{\left[\begin{array}{llllllll}1\hfill & 1\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill \\ 0\hfill & 1\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill \\ 0\hfill & 0\hfill & 1\hfill & 1\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill \\ 0\hfill & 0\hfill & 0\hfill & 1\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill \\ 0\hfill & 0\hfill & 0\hfill & 0\hfill & 1\hfill & 1\hfill & 0\hfill & 0\hfill \\ 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 1\hfill & 0\hfill & 0\hfill \\ 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 1\hfill & 1\hfill \\ 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 0\hfill & 1\hfill \end{array}\right]}}& \hfill \underset{x_a\left(k\right)}{\underbrace{\left[\begin{array}{r}\hfill {\widetilde{\mathrm{\Delta }d}}_{max}\left(k\right)\\ \hfill {\widetilde{md}}_{max}\left(k\right)\\ \hfill {\widetilde{\mathrm{\Delta }d}}_{min}\left(k\right)\\ \hfill {\widetilde{md}}_{min}\left(k\right)\\ \hfill {\tilde{\kappa }}_{max}\left(k\right)\\ \hfill {\widetilde{m\kappa }}_{max}\left(k\right)\\ \hfill {\tilde{\kappa }}_{min}\left(k\right)\\ \hfill {\widetilde{m\kappa }}_{min}\left(k\right)\end{array}\right]}}\end{array}\right]$$

The matrix A _{a can be} referred to as a (time-invariant) constraint matrix, by means of which a (recursive) constraint model for describing the one or more constraints is provided. It is thus possible to describe a time-invariant limitation of a manipulated variable and / or a state component by means of a linear and time-invariant limitation model.

Dabei ist ${\tilde{A}}_{ges}^D$

die zeitdiskretisierte Version der Matrix ${\tilde{A}}_{ges}.{\tilde{B}}_{ges}^D$

ist die zeitdiskretisierte Version von B_ges.The overall model including the approximated time-variant restrictions then results (in a time-discrete state representation) $$\begin{array}{llllll}\left[\begin{array}{c}{\tilde{X}}_{\mathrm{\Delta }Ges}\left(k+1\right)\\ {\mathbf{X}}_a\left(k+1\right)\end{array}\right]\hfill & =\hfill & \left[\begin{array}{cc}{\widetilde{\mathrm{A.}}}_{Ges}^{\mathrm{D.}}& 0\\ 0& {\mathbf{A.}}_a\end{array}\right]\hfill & \left[\begin{array}{c}{\tilde{X}}_{\mathrm{\Delta }Ges}\left(k\right)\\ {\mathbf{X}}_a\left(k\right)\end{array}\right]\hfill & +\hfill & \left[{}_0^{{\widetilde{\mathrm{B.}}}_{Ges}^{\mathrm{D.}}}\right].\hfill \end{array}$$

It is ${\widetilde{\mathrm{A.}}}_{Ges}^{\mathrm{D.}}$

the time-discretized version of the matrix ${\widetilde{\mathrm{A.}}}_{Ges}.{\widetilde{\mathrm{B.}}}_{Ges}^{\mathrm{D.}}$

is the time-discretized version of B _tot .

sowie der geplanten Querabweichung $d_r^{*},$

der modifizierte Fahrdynamik-Zustandsvektor $${\tilde{x}}_{\mathrm{\Delta }kin}\left(k\right)=\left[\begin{array}{c}\widetilde{\mathrm{\Delta }d}\left(k\right)\\ \mathrm{\Delta }\theta \left(k\right)\end{array}\right]$$

mit zwei Zustandsgrößen bzw. zwei (ersten) Zustandskomponenten 601. Außerdem können die zeitabhängigen Beschränkungen für die (modifizierte) Stellgröße und/oder für die (modifizierte) Querabweichung durch acht zusätzliche (zweite) Zustandskomponenten 603 x_a(k) geschrieben werden. Es ergibt sich somit ein Gesamtzustandsvektor x(k) mit 14 Zustandskomponenten. Die Werte 611, 612, 613, 614 der (zweiten) Zustandskomponenten 603 x_a(k) an einem bestimmten Anfangszeitpunkt können durch Approximation der zeitabhängigen Beschränkungen ermittelt werden. 6 represents the control loop resulting from the use of the explicit model predictive control 600 About the CVM parallel model unit 205 become the states or state components 604 x _Δcvm (k) of the CVM model provided at a specific point in time k. If a CVM model of order l = 3 is used, the state vector x _Δcvm (k) has four state _components 604 on. Furthermore, the measurement of the actual transverse deviation d _r (k) and the measurement of the actual direction of travel angle θ _r (k), taking into account the speed v (k) and the planned angle of travel direction ${\theta }_r^{*}$

as well as the planned transverse deviation $d_r^{*},$

the modified driving dynamics state vector $${\tilde{x}}_{\mathrm{\Delta }kin}\left(k\right)=\left[\begin{array}{c}\widetilde{\mathrm{\Delta }d}\left(k\right)\\ \mathrm{\Delta }\theta \left(k\right)\end{array}\right]$$

with two state variables or two (first) state components 601 . In addition, the time-dependent restrictions for the (modified) manipulated variable and / or for the (modified) lateral deviation can be set by eight additional (second) state components 603 x _a (k) can be written. This results in an overall state vector x (k) with 14 state components. The values 611 , 612 , 613 , 614 the (second) state components 603 x _a (k) at a certain starting point in time can be determined by approximating the time-dependent restrictions.

Within the control unit 204 the initial state x (0), ie the current state at a specific point in time k, can be determined. The initial state shows the values (ie a combination of values) of the different state components 601 , 603 at the specific point in time k (ie at the start point in time). On the basis of the piecewise affine function determined in advance 300 (eg in the form of a look-up table) can then be a corresponding value for the modified manipulated variable 602 κ̃ _r (0) can be determined at the point in time k, which can be divided by the current driving speed v (0) in order to determine the control component κ _r (0) of the desired curvature κ _soll (0).

The above process can be repeated iteratively for a sequence of points in time k in order to provide a trajectory sequence control.

In a corresponding manner, a trajectory sequence control can be provided for the longitudinal guidance. The longitudinal acceleration ν̇ (k) serves as the manipulated variable, the limitations of which depend on the current driving speed v (k). The state model includes the position deviation in the longitudinal direction as a state component, which is subject to environment-dependent restrictions. The time-dependent restrictions can be taken into account as state components by the approximation described in this document and / or the consideration of the functional parameters. In the case of longitudinal guidance, the model of the driving dynamics is typically already time-invariant, so that a modified state component and / or a modified manipulated variable is typically not required.

7a shows a flow diagram of an exemplary method 700 for the automated longitudinal and / or lateral guidance of a vehicle 100 based on a (recursive) system model of the vehicle 100 . The procedure 700 can through a control unit 110 of the vehicle 100 are executed.

und durch die Eingangsmatrix ${\tilde{B}}_{ges}^D$

beschrieben werden.The procedure 700 comprises, at a point in time k, the determination 701 a deviation of an actual value of a state variable (for example the relative transverse deviation d _r ) of the vehicle 100 from one of the target trajectory 103 dependent planned value of the state variable as the value of a first state component 601 (in particular as the initial value of the first state component 601 ). The (discrete-time) system model can be set up or have the property based on the value of the first state component 601 at time k and based on the value of a manipulated variable 602 (for example the control component κ _{r of} the curvature) at the point in time k the value of the first state component 601 to predict k + 1 at a subsequent point in time. The system model can be, for example, through the system matrix ${\widetilde{\mathrm{A.}}}_{Ges}^{\mathrm{D.}}$

and through the input matrix ${\widetilde{\mathrm{B.}}}_{Ges}^{\mathrm{D.}}$

to be discribed.

The procedure also includes 700 determining 702 of time-variable restrictions 503 the first state component 601 and / or the manipulated variable 602 for N times from time k, with N> 1 (typically N = 5, 8, 10 or more). The time-variable restrictions 503 can be based on the sensor data of the one or more environment sensors 111 of the vehicle 100 be determined. Alternatively or in addition, the variable restrictions 503 based on the (predicted) driving speed v of the vehicle 100 and / or based on a technical limitation of the steering and / or drive and / or braking device 112 of the vehicle 100 be determined.

The procedure 700 further comprises approximating 703 the time-variable restrictions 503 the first state component 601 and / or the manipulated variable 602 by a recursive (time-discrete) constraint model (eg with the system or constraint matrix A _a ) with one or more second state components 603 . The restriction model can be set up or have the property of a value of the one or more second state components 603 at the subsequent point in time k + 1 on the basis of the values of the one or more second state components 603 to be determined at time k. It shows at least a second state component 603 the approximated constraint 504 the first state component 601 and / or the manipulated variable 602 on. The constraint model is preferably linear and time-invariant. The use of a linear and time-invariant (recursive) constraint model thus enables a (possibly non-linear) time-variant constraint 503 to describe.

In other words, the procedure 700 may include determining 703 of values 611 , 612 , 613 , 614 of one or more second state components 603 of a restriction model at the point in time k such that the determined, time-variable restrictions 503 the first state component 601 and / or the manipulated variable 602 by values of at least one second state component 603 can be approximated at the N times from time k.

The method also includes 700 determining 704 a value of the manipulated variable 602 at time k, based on the value of the first state component 601 and the values of the one or more second state components 603 at time k and on the basis of a predefined function 300 that is set up, different value combinations of the first state component 601 and the one or more second state components 603 each one (possibly different) value of the manipulated variable 602 assign. The procedure 700 also includes operating 705 of the vehicle guidance system 206 of the vehicle 100 (in particular operating the steering and / or drive and / or braking device 112 of the vehicle 100 ) depending on the determined value of the manipulated variable. In this way, a robust and precise trajectory sequencing control along the planned target trajectory can be carried out in a resource-efficient manner 103 are made possible.

7b shows a flow diagram of an exemplary method 710 for automated lateral guidance of a vehicle 100 based on a (time-discrete) system model of the vehicle 100 . The procedure 710 can through a control unit 110 of the vehicle 100 are executed.

und durch die Eingangsmatrix ${\tilde{B}}_{ges}^D$

beschrieben werden.The procedure 710 comprises (at a point in time k) the determining 711 a deviation of an actual value of a state variable of the vehicle 100 from one of a target trajectory 103 dependent planned value of the state variable as the value of a first state component 601 . The system model can be set up or have the property on the basis of a value of the first state component 601 at time k and based on a value of a manipulated variable 602 at the point in time k the value of the first state component 601 to predict k + 1 at a subsequent point in time. The system model can be, for example, through the system matrix ${\widetilde{\mathrm{A.}}}_{Ges}^{\mathrm{D.}}$

and through the input matrix ${\widetilde{\mathrm{B.}}}_{Ges}^{\mathrm{D.}}$

to be discribed.

The state variable can be related to the (longitudinal) driving speed of the vehicle 100 modulated basic state variable (eg the transverse deviation d _r (k) of the vehicle 100 ) include. The manipulated variable 602 can one with the driving speed of the vehicle 100 modulated basic manipulated variable (eg the curvature κ _r (k)). The modulation can include multiplying and / or dividing.

The state variable is preferably the quotient from the transverse deviation d _r (k) of the vehicle 100 relative to a reference curve 102 and the driving speed v (k) of the vehicle 100 (In particular, the first state component is preferably Δd̃ (k)). Furthermore, the manipulated variable is 602 preferably the product of the curvature κ _r (k) of a trajectory to be driven by the vehicle and the driving speed v (k) of the vehicle (in particular the manipulated variable is 602 preferably κ̃ _r (k)). This enables the use of a linear and time-invariant system model for the control. This in turn enables the use of a resource-efficient explicit model predictive control.

The procedure 710 may further include determining 712 a value of the manipulated variable 602 at the point in time k based on the value of the first state component 601 at time k and on the basis of a predefined function 300 , which is set up, different values of the first state component 601 each one (possibly different) value of the manipulated variable 602 assign. The predefined function 300 can be determined in advance by multiparametric programming.

The method also includes operating 713 of the vehicle guidance system 206 of the vehicle 100 (in particular operating the steering and / or drive and / or braking device 112 of the vehicle 100 ) depending on the determined value of the manipulated variable 602 . For this purpose, the value of the manipulated variable 602 at the point in time k based on the vehicle speed v (k) 100 be modified at the point in time k to the control component κ _r (k) of the manipulated variable 602 to determine. The control component can then be combined with an advance component to form the total value of the manipulated variable 602 to determine. The vehicle guidance system 206 can then be based on the total value of the manipulated variable 602 operate.

In this way, a robust and precise trajectory sequencing control along the planned target trajectory can be carried out in a resource-efficient manner 103 are made possible.

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

Claims (16)

Method (700) for automated longitudinal and / or lateral guidance of a vehicle (100) based on a system model of the vehicle (100); wherein the method (700) comprises - determining (701) a value of a first state component (601) as a deviation of an actual value of a state variable of the vehicle (100) from a planned value of the state variable that is dependent on a target trajectory (103); wherein the state variable of the vehicle (100) is dependent on a manipulated variable (602) via the system model; - Determination (702) of temporally variable restrictions (503) of the first state component (601) and / or the manipulated variable (602) for N times from time k, with N>1; - Determination (703) of values (611, 612, 613, 614) of one or more second state components (603) of a constraint model at the point in time k such that the determined, time-variable constraints (503) of the first state component (601) and / or the manipulated variable (602) are approximated by values of at least one second state component (603) at the N times from time k; - Determination (704) of a value of the manipulated variable (602) at the point in time k, based on the value of the first state component (601) and based on the values (611, 612, 613, 614) of the one or more second state components (603) at time k and on the basis of a predefined function (300) which is set up to assign different value combinations of the first state component (601) and the one or more second state components (603) each with a value of the manipulated variable (602); and - operating (705) a vehicle guidance system (206) for automated longitudinal and / or lateral guidance of the vehicle (100) as a function of the determined value of the manipulated variable (602). Method (700) according to Claim 1 , wherein the predefined function (300) - enables an explicit model predictive control; and / or - is dependent on the system model and on the restriction model; and / or - is dependent on a cost-functional which comprises a term relating to the first state component at the N times from the time k. Method (700) according to one of the preceding claims, wherein - the system model is invariant over time and / or linear; and or - The system model is set up and / or has the property, based on the value of the first state component (601) at time k and based on the value of the manipulated variable (602) at time k, a value of the first state component (601) at a subsequent point in time k + 1 to be predicted. Method (700) according to one of the preceding claims, wherein - approximated restrictions (504) of the first state component (601) brought about by the restriction model represent an equal or greater restriction than the temporally variable restrictions (503) of the first state component (601) at each of the N times; and or - The approximated restrictions (504) brought about by the restriction model represent a linear approximation of the temporally variable restrictions (503) of the first state component (601). The method (700) according to any one of the preceding claims, wherein the method (700) is repeated at a sequence of times k in order to determine values of the manipulated variable (602) at the sequence of times k, and the vehicle guidance system (206) at the To operate sequence of times k. The method (700) according to any one of the preceding claims, wherein the system model of the vehicle (100) comprises - A first partial model that represents an approximation of a behavior of the vehicle guidance system (206); and or - A second partial model that describes a movement and / or kinematics of the vehicle (100). Method (700) according to one of the preceding claims, wherein - the state variable and the manipulated variable display values relative to a reference curve (102); and - The reference curve (102) runs in particular along a roadway (101) on which the vehicle (100) is traveling. Method (700) according to one of the preceding claims, wherein - The temporally variable restrictions (503) of the first state component (601) are determined on the basis of sensor data from one or more environment sensors (111) of the vehicle (100); and - the sensor data indicate an environment of the vehicle (100); and or - The temporally variable restrictions (503) of the manipulated variable (602) are determined on the basis of a current driving speed of the vehicle (100), and / or on the basis of a technical restriction of a steering device (112), a drive device (112) and / or a Braking device (112) of the vehicle (100). Method (700) according to one of the preceding claims, wherein for lateral guidance of the vehicle (100), - the state variable comprises the quotient of a lateral deviation of the vehicle (100) relative to a reference curve (102) and a travel speed of the vehicle (100); and or - the manipulated variable (602) comprises the product of a curvature of a trajectory to be driven by the vehicle (100) and the driving speed of the vehicle (100). Method (700) according to Claim 9 - The method (700) comprises determining a deviation of an actual value of a further state variable of the vehicle (100) from a planned value of the further state variable that is dependent on the target trajectory (103) as a further state component; wherein the system model is set up and / or has the property of predicting the first status component (601) at a subsequent time k + 1 on the basis of the further status component at time k; and - the further state variable comprises an angle of travel direction of the vehicle (100). Method (700) according to one of the preceding claims, wherein for a longitudinal guidance of the vehicle (100) - The state variable comprises a position of the vehicle (100) along a longitudinal direction of the vehicle (100); and or - The manipulated variable (602 includes an acceleration of the vehicle (100) in the longitudinal direction. Method (700) according to one of the preceding claims, wherein - the restriction model is set up and / or has the property of determining values of the one or more second state components (603) at the subsequent point in time k + 1 on the basis of the values of the one or more second state components (603) at the point in time k; and or - the constraint model is time-invariant and linear. Control unit (110) for automated longitudinal and / or lateral guidance of a vehicle (100) based on a system model of the vehicle (100); wherein the control unit (110) is set up, - to determine a value of a first state component (601) as a deviation of an actual value of a state variable of the vehicle (100) from a planned value of the state variable that is dependent on a target trajectory (103); wherein the state variable of the vehicle (100) is dependent on a manipulated variable (602) via the system model; - to determine temporally variable restrictions (503) of the first state component (601) and / or of the manipulated variable (602) for N points in time from point in time k, with N> 1; - to determine values (611, 612, 613, 614) of one or more second state components (603) of a restriction model at time k in such a way that the temporally variable restrictions (503) of the first state component (601) and / or the manipulated variable ( 602) are approximated by values of at least one second state component (603) at the N times from the time k; - On the basis of the value of the first state component (601) and the value of the one or more second state components (603) at the time k and on the basis of a predefined function (300) which is set up, different value combinations of the first state component (601) and to assign a value of the manipulated variable (602) to the one or more second state components (603), to determine a value of the manipulated variable (602) at time k, and - To operate a vehicle guidance system (206) for automated longitudinal and / or lateral guidance of the vehicle (100) as a function of the determined value of the manipulated variable (602). Method (710) for automated lateral guidance of a vehicle (100) based on a system model of the vehicle (100); the method comprising (710), - determining (711) a value of a first state component (601) as a deviation of an actual value of a state variable of the vehicle (100) from a planned value of the state variable that is dependent on a target trajectory (103); wherein the state variable of the vehicle (100) is dependent on a manipulated variable (602) via the system model; wherein the state variable comprises a base state variable modulated with a driving speed of the vehicle (100) and / or the manipulated variable (602) comprises a base manipulated variable modulated with the driving speed of the vehicle (100); - Determination (712) of a value of the manipulated variable (602) at the point in time k on the basis of the value of the first state component (601) at the point in time k and on the basis of a predefined function (300) which is set up to different values of the first state component ( 601) assign a value to the manipulated variable (602) in each case; and - Operation (713) of a vehicle guidance system (206) for automated lateral guidance of the vehicle (100) as a function of the determined value of the manipulated variable (602). Method (710) according to Claim 14 , in which - the state variable comprises the quotient of a lateral deviation of the vehicle (100) relative to a reference curve (102) and a driving speed of the vehicle (100); and / or - the manipulated variable (602) comprises the product of a curvature of a trajectory to be driven by the vehicle (100) and the driving speed of the vehicle (100). Control unit (110) for automated lateral guidance of a vehicle (100) based on a system model of the vehicle (100); wherein the control unit (110) is set up, - to determine a value of a first state component (601) as a deviation of an actual value of a state variable of the vehicle (100) from a planned value of the state variable that is dependent on a target trajectory (103); wherein the state variable of the vehicle (100) is dependent on a manipulated variable (602) via the system model; wherein the state variable comprises a base state variable modulated with a driving speed of the vehicle (100) and / or wherein the manipulated variable (602) comprises a base manipulated variable modulated with the driving speed of the vehicle (100); - On the basis of the value of the first state component (601) at the point in time k and on the basis of a predefined function (300) which is set up to assign a value of the manipulated variable (602) to different values of the first state component (601), a value of the Determine manipulated variable (602) at time k; and - to operate a vehicle guidance system (206) for automated lateral guidance of the vehicle (100) of the vehicle (100) as a function of the determined value of the manipulated variable (602).

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