Limiting a steering rate of a motor vehicle

Abstract

For limiting a steering rate of a motor vehicle (1), a driven path (8), which has been driven by the motor vehicle (1) up to a current time instance, is determined. An expected position (Pex), which is expected to be reached by the motor vehicle (1) at a target time instance, which lies after the current time instance by a predefined time interval, is determined depending on the driven path (8) and depending on a current velocity of the motor vehicle (1) and / or depending on a target velocity for the motor vehicle (1). A lateral position range, which includes the expected position (Pex), is determined depending on a predefined lateral position offset (D, D'). At least one limit value for the steering rate is determined depending on the lateral position range.

Description

[0001]2023PF00526 1 Limiting a steering rate of a motor vehicle The present invention is directed to a method for limiting a steering rate of a motor vehicle and to a method for guiding a motor vehicle at least in part automatically, wherein such a method for limiting a steering rate of the motor vehicle is carried out. The invention is further directed to a data processing apparatus for carrying out such a method for limiting a steering rate of the motor vehicle, to an electronic vehicle guidance system comprising such a data processing apparatus, and to a corresponding computer program product. When guiding a motor vehicle at least in part automatically, for example at least the steering of the motor vehicle may be carried out automatically, in particular by an electronic vehicle guidance system of the motor vehicle. This may include cases of fully autonomous cars but also cases where the automatic steering is carried out as a support for a driver or only temporarily. Other operations of the motor vehicle like deceleration and acceleration may be carried out manually, automatically or in part automatically. Due to various reasons, it may happen that there is a request to change a lateral position of the motor vehicle. This may be due to errors in the decision or control process or due to discontinuities of sensor data, for example positioning jumps data from a GNSS (global navigation satellite system) receiver, et cetera. When such a request is served by the electronic vehicle guidance system, it may lead to an abrupt or harsh steering maneuver, which may be problematic in view of passenger safety and / or comfort. It is possible to restrict the steering parameters, in particular a maximum steering angle and / or a maximum steering rate, that is the temporal change of the steering angle, based on look-up tables or the like. This suffers, however, from a low level of flexibility of the restriction and, for example, for a too pessimistic restriction or a too high safety risk on the other hand. It is an objective of the present invention to provide an improved concept for limiting a steering rate of a motor vehicle, which overcomes said drawbacks at least partially. This objective is achieved by the subject matter of the independent claim. Further implementations and preferred embodiments are subject matter of the dependent claims. 2023PF00526 2 The invention is based on the idea to provide a predefined time interval and a predefined lateral position offset. An expected position of the motor vehicle after the time interval has passed is estimated and a limit value for the steering rate is determined depending on a lateral position range, which is given by the lateral position offset at the expected position. According to an aspect of the invention, a method for limiting a steering rate of a motor vehicle is provided. Therein, a driven path, which has been driven by the motor vehicle up to a current time instance, is determined. An expected position, which is expected to be reached by the motor vehicle at a target time instance, which lies after the current time instance by a predefined time interval, is determined depending on the driven path and depending on a current velocity of the motor vehicle at the current time instance and / or depending on a predefined target velocity for the motor vehicle. A lateral position range, which includes the expected position, is determined depending on a predefined lateral position offset. At least one limit value for the steering rate is determined depending on the lateral position range and, in particular, set in force for guiding the motor vehicle at least in part automatically. In some embodiments, the method for limiting a steering rate of a motor vehicle is purely computer implemented. Unless stated otherwise, all steps of a computer-implemented method may be performed by a data processing apparatus, which comprises at least one computing unit, in particular a data processing apparatus of the motor vehicle. In particular, the at least one computing unit is configured or adapted to perform the steps of the computer-implemented method. For this purpose, the at least one computing unit may for example store a computer program comprising instructions which, when executed by the at least one computing unit, cause the at least one computing unit to execute the computer-implemented method. All computing units of the at least one computing unit may be comprised by the motor vehicle. However, it is also possible that all computing units of the at least one computing unit are part of an external computing system external to the motor vehicle, for example a backend server or a cloud computing system. It is also possible that the at least one computing unit comprises at least one vehicle computing unit of the motor vehicle as well as at least one external computing unit comprised by the external computing system. The at least one vehicle computing unit may for example be comprised by one or more electronic control units, ECUs, and / or one or more zone control units, ZCUs, and / or one or more domain control units, DCUs, of the motor vehicle. 2023PF00526 3 For example, the motor vehicle may be steered automatically such that the steering rate of the motor vehicle is limited by the determined at least one limit value. For example, the at least one limit value may comprise a maximum steering rate. The motor vehicle may then be steered automatically such that the steering rate of the motor vehicle is equal to or less than the maximum steering rate. For example, the at least one limit value may comprise a minimum steering rate. The motor vehicle may then be steered automatically such that the steering rate of the motor vehicle is equal to or greater than the minimum steering rate. Both cases can be combined in some embodiments, such that the motor vehicle may be steered automatically such that the steering rate of the motor vehicle is equal to or greater than the minimum steering rate and equal to or less than the maximum steering rate. Unless stated otherwise, here and in the following, a steering angle of the motor vehicle may be understood as a steering angle of a steerable wheel of the motor vehicle or as an effective steering angle of steerable wheels of the motor vehicle according to a predefined vehicle model, such as a bicycle model, for example. In general, a steering wheel angle of a steering wheel inside the cockpit of the motor vehicle differs from the steering angle of the motor vehicle according to this understanding. Unless stated otherwise, here and in the following, a velocity of the motor vehicle corresponds to a longitudinal velocity of the motor vehicle. Unless stated otherwise, here and in the following, a position of the motor vehicle may be understood as a position in a predefined reference coordinate system, for example a map coordinate system of a digital map. The driven path may be received for example from a storage device of the motor vehicle or at least one computing unit or from a data bus of the motor vehicle. The driven path may also be computed based on sensor data received from respective sensors of the motor vehicle, including for example inertial measurement units, IMUs, GNSS-receivers, cameras or other environmental sensor systems, et cetera. For example, odometric methods including classical odometry and / or visual odometry, SLAM (simultaneous localization and mapping) methods, and so forth may be used for this purpose. The expected position may for example be determined by extrapolating the driven path over the time interval, assuming that the velocity remains constant, or the like. Depending on 2023PF00526 4 the actual embodiment, the extrapolated path may assume a constant steering angle. Then the extrapolated path is a straight line or a circular arc segment. The extrapolated path may, however, also take into account a change in the steering angle. Then the extrapolated path may then for example be a polynomial or another smooth curve. The lateral position range may correspond to a range of lateral positions, where the corresponding longitudinal position is given by the expected position. For example, a line perpendicular to a longitudinal direction at the expected position may be constructed and the lateral position range may be defined as a range along the perpendicular line, wherein the expected position lies in the center of the range. The limits of the lateral position range may be given by the lateral position offset in either direction from the expected position along the perpendicular line. However, in general, also different offsets may be provided for the two different directions. For example, the longitudinal direction at the expected position may be given by a tangent to the extrapolated path at the expected position. The target velocity may for example be given by a single predefined target value for the target time instance. The target velocity may for example be determined by a system of the motor vehicle for longitudinal control of the motor vehicle, for example an adaptive cruise control system or the like. Using the target velocity may further increase the accuracy, in particular in case the predefined time interval is relatively long. The target velocity may also be given by a target velocity profile. According to the invention, it is therefore achieved to limit the steering rate in a flexible manner taking into account both, predefined parameters such as the lateral position offset and the time interval, the historic motion of the motor vehicle in terms of the driven path and the current velocity. According to several embodiments, the least one limit value for the steering rate is determined depending on the lateral position range, such that, for the velocity of the motor vehicle being constant and the steering rate being equal to any of the at least one limit value between the current time instance and the target time instance, a position of the motor vehicle according to the target time instance lies in the lateral position range. In other words, if the motor vehicle is driven with the velocity being constantly the current velocity, the steering angle starting at the current steering angle at the current time instance and the steering angle being changed with a steering rate given by any of the at least one limit value, the position of the motor vehicle according to the target time instance 2023PF00526 5 lies in the lateral position range. For example, the at least one limit value may comprise a first limit value and a second limit value corresponding to the minimum steering rate and the maximum steering rate, respectively. If the steering rate is given by the first limit value, then the position of the motor vehicle according to the target time instance corresponds to a first limiting position of the lateral position range. If the steering rate is given by the second limit value, then the position of the motor vehicle according to the target time instance corresponds to a second limiting position of the lateral position range. In particular, the boundaries of the lateral position range, given by the first and the second limiting positions of the lateral position range, are considered to lie in the lateral position range. Consequently, the lateral deviation of the motor vehicle from the expected position is limited by the lateral position range, in particular by the lateral position offset. According to several embodiments, a request to change a lateral position of the motor vehicle is detected. The motor vehicle is steered automatically such that the steering rate of the motor vehicle is limited by the determined at least one limit value in response to the request. In particular, the motor vehicle may be steered automatically according to a predefined trajectory for the motor vehicle, wherein the steering rate of the motor vehicle is limited by the determined at least one limit value. The predefined trajectory may for example be obtained from a path planning or a route planning or a navigational system of the motor vehicle and may be given in terms of a curve or a set of waypoints, for example. The request may for example be generated by the at least one computing unit depending on sensor data from one or more sensors of the motor vehicle and / or as a result of a path planning, et cetera. Some or all steps of determining the driven path, the expected position, the lateral position range and the at least one limit value may be carried out only if the request is detected. In other embodiments, said steps may be carried out repeatedly and / or continuously independent of such request preventively. According to several embodiments, a plurality of positions of the motor vehicle between a predefined previous time instance, which lies before the current time instance, and the current time instance is determined. At least one fitted curve parameter is determined by 2023PF00526 6 fitting a predefined curve to the plurality of positions. The driven path is determined as the curve with the at least one fitted curve parameter between a position according to the previous time instance and a current position of the motor vehicle according to the current time instance. The previous time instance may for example be defined by defining a further time interval prior to the current time instance. For example, odometric methods including classical odometry and / or visual odometry, SLAM (simultaneous localization and mapping) methods, and so forth may be used for determining the plurality of positions. The curve is predefined in the sense that the type of the curve is predefined depending on the at least one curve parameter. Different values of the at least one curve parameter lead to different shapes of the curve. The at least one fitted curve parameter is obtained by a known fitting method. For example, the curve may be defined as a straight line. Then the at least one curve parameter comprises for example an inclination of the straight line. For example, the curve may be defined as a circle. Then the at least one curve parameter comprises for example a radius and a center position of the circle. For example, the curve may be defined as a polynomial of d-th degree. Then the at least one curve parameter comprises for example the d+1 polynomial coefficients. Further curve types may also be used. According to several embodiments, the extrapolated path ending at the expected position and, in particular, beginning at the current position of the motor vehicle at the current time instance, is determined by extrapolating the driven path depending on the current velocity of the motor vehicle, in particular assuming the velocity being constant. The time interval may be relatively short, for example it duration may lie in the range [0.2 s, 5 s] or in the range [0.8 s, 2 s]. Consequently, the resulting lateral position range may be constructed in an accurate manner by means of the extrapolated path. According to several embodiments, an extrapolated path is determined as the curve with the at least one fitted curve parameter between the position according to the current position of the motor vehicle and the position of the motor vehicle according to the target time instance. The expected position is given by the position according to the target time instance. 2023PF00526 7 In other words, it is assumed for determining the expected position that the motor vehicle follows the same curve, which also approximates the driven path. The length of the extrapolated path is given by the current velocity and the time interval. For example, if the curve is a straight line, the extrapolated path is a straight line as well with a length given by the current velocity multiplied with the time interval. For example, if the curve is a circle or a circular arc segment, the extrapolated path is a circular arc segment as well with an arc length given by the current velocity multiplied with the time interval. Also other curves can be parametrized with the time and the velocity accordingly. In this way, a realistic estimation of the expected position is achieved. According to several embodiments, the predefined curve is a circle or a circular arc section or a straight line. In this way, a simple construction of the extrapolated path and the driven path is possible, while the achievable accuracy is still high, in particular considering said ranges for the duration of the time interval. According to several embodiments, the predefined curve is a polynomial curve, in particular a polynomial of d-th degree with d ≥ 3. The accuracy and flexibility of the method can be further increased in this way. According to several embodiments, the driven path is determined as the curve with the at least one fitted curve parameter as described above and the predefined curve is a circle or a circular arc section. If the radius of the circle or circular arc section is less than a predefined minimum radius, an extrapolated path is determined as the curve with the at least one fitted curve parameter between the current position of the motor vehicle and the position according to the target time instance, wherein the expected position is given by the position according to the target time instance. If the radius of the circle or circular arc section is greater than the minimum radius, the extrapolated path is determined as a straight line between the current position of the motor vehicle and the position according to the target time instance, wherein a direction of the straight line is given by a tangent to the circle or circular arc section at the current position of the motor vehicle and the expected position is given by the position according to the target time instance In particular, in the first case, the extrapolated path is a circular arc segment with an arc length given by the current velocity multiplied with the time interval. In the second case, 2023PF00526 8 the extrapolated path is a straight line with a length given by the current velocity multiplied with the time interval. In case the radius of the circle or circular arc section is equal to or greater than to the minimum radius, the extrapolated path is determined as said straight line in some embodiments and as the curve with the at least one fitted curve parameter in other embodiments. The minimum radius may for example lie in the order of thousands of meters, for example in the range [5000 m, 15000 m] or in the range [8000 m, 12000 m]. In such embodiments, the construction of the expected position is further simplified for very low curvatures of the driven path while the accuracy is still high, in particular for larger curvatures of the driven path. According to several embodiments, a lateral offset of a lane boundary from the expected position is determined and, if the lateral offset of the lane boundary is greater than the lateral position offset, the motor vehicle is automatically decelerated. In other words, the velocity of the motor vehicle is reduced from the current velocity to a reduced velocity to decelerate the motor vehicle. For example, the reduced velocity may be given by subtracting a predefined decrement from the current velocity or by multiplying the current velocity with a predefined reduction factor, which is greater than zero and less than one. The decrement or the reduction factor may have fixed values or may be determined depending on the current velocity and / or the current steering angle according to a predefined rule. In particular, the motor vehicle is automatically decelerated if the lane boundary lies outside of the lateral position range. Consequently, it can be achieved that the limitation of the steering according to the at least one limit value is sufficient not only to avoid abrupt changes in the lateral position of the motor vehicle but also for guiding the motor vehicle safely on the current lane. For example, the described may be repeated iteratively after the automatic deceleration of the motor vehicle until the lateral offset of the lane boundary is equal to or less than the lateral position offset. 2023PF00526 9 According to several embodiments, a further extrapolated path is determined by extrapolating the driven path depending on the current velocity of the motor vehicle, wherein an end point of the further extrapolated path has a longitudinal position corresponding to a longitudinal position of a predefined waypoint for the motor vehicle, in particular a future waypoint for the motor vehicle. A further lateral position range, which includes the end point, is determined depending on the end point of the further extrapolated path and the lateral position offset. If a lateral position of the end point of the further extrapolated path lies outside the further lateral position range, the motor vehicle is automatically decelerated. The explanations regarding the extrapolated path and the lateral position range carry over analogously to the further extrapolated path and the further lateral position range, respectively. In other words, the velocity of the motor vehicle is reduced from the current velocity to a reduced velocity to decelerate the motor vehicle. For example, the reduced velocity may be given by subtracting a predefined decrement from the current velocity or by multiplying the current velocity with a predefined reduction factor, which is greater than zero and less than one. The decrement or the reduction factor may have fixed values or may be determined depending on the current velocity and / or the current steering angle according to a predefined rule. In particular, the motor vehicle is automatically decelerated if the waypoint lies outside of the further lateral position range. Consequently, it can be achieved that the limitation of the steering according to the at least one limit value is sufficient not only to avoid abrupt changes in the lateral position of the motor vehicle but also for guiding the motor vehicle safely to the waypoint. For example, the described may be repeated iteratively after the automatic deceleration of the motor vehicle until the lateral offset of the end point of the further extrapolated path is equal to or less than the further lateral position offset. According to several embodiments, a first limiting curve between the current position of the motor vehicle and a first limiting position of the lateral position range is determined depending on the current velocity of the motor vehicle and a current steering angle of the motor vehicle at the current time instance. A first limit value of the at least one limit value 2023PF00526 10 for the steering rate is determined depending on a curvature of the first limiting curve at the first limiting position and, for example, depending on the current steering angle. For example, the first limiting position has a lateral distance from the expected position, which is given by the lateral position offset. The first limiting position lies, in particular, in a first direction with respect to the expected position. In particular, the curvature of the first limiting curve is proportional to a tangent of the steering angle. Consequently, the difference between the steering angle at the first limiting position and the current steering angle may be used to define the first limit value for the steering rate, in particular by dividing the difference by the time interval. For determining the first limiting curve, a curve of a predefined type, for example a straight line, a circular arc or a polynomial, may be provided and respective curve parameters, for example an inclination of the straight line, a radius and center point of the circular arc or polynomial coefficients, respectively, may be determined depending on the current velocity, the current steering angle, the current position and the first limiting position. In this way, a particularly suitable and realistic first limit value is obtained. According to several embodiments, a second limiting curve between the current position of the motor vehicle and a second limiting position of the lateral position range is determined depending on the current velocity of the motor vehicle and the current steering angle of the motor vehicle at the current time instance. A second limit value of the at least one limit value for the steering rate is determined depending on a curvature of the second limiting curve at the second limiting position. For example, the second limiting position has a lateral distance from the expected position, which is given by the lateral position offset. The second limiting position lies, in particular, in a second direction with respect to the expected position, which is opposite to the first direction. For example, the difference between the steering angle at the second limiting position and the current steering angle may be used to define the second limit value for the steering rate, in particular by dividing the difference by the time interval. 2023PF00526 11 For determining the second limiting curve, a curve of a predefined type, for example a straight line, a circular arc or a polynomial, may be provided and respective curve parameters, for example an inclination of the straight line, a radius and center point of the circular arc or polynomial coefficients, respectively, may be determined depending on the current velocity, the current steering angle, the current position and the second limiting position. In this way, a particularly suitable and realistic second limit value is obtained. In particular, the second limit value may be the maximum steering rate and the first limit value may be the minimum steering rate or vice versa. According to several embodiments, the first limiting curve is determined as a polynomial of n-th degree, wherein n is at least two, and / or the second limiting curve is determined as a polynomial of m-th degree, wherein m is at least two. Consequently, a particularly accurate first limiting curve and / or second limiting curve is obtained. According to several embodiments, the first limiting curve is determined as a curve with constant curvature or with monotonically increasing curvature or with monotonically decreasing curvature between the current position of the motor vehicle and the first limiting position. According to several embodiments, the second limiting curve is determined as a curve with constant curvature or with monotonically increasing curvature or with monotonically decreasing curvature between the current position of the motor vehicle and the second limiting position. According to several embodiments, the first limiting curve is determined as a polynomial of 3rd degree, that is n=3, and / or the second limiting curve is determined as a polynomial of 3rd degree, that is m=3. An advantage of 3rd order polynomials compared to higher order polynomials is that the third derivative of a 3rd order polynomial is a constant. Consequently, the curvature of a third order polynomial is monotonic, that is monotonically increasing or decreasing. Therefore, the curvature of the first limiting curve at the first limiting position or the second limiting curve at the second limiting, respectively, is a maximum curvature or a minimum 2023PF00526 12 curvature between the current position and the first limiting position or the second limiting position, respectively. Thus, also the steering angle at the first limiting position or the second limiting position, respectively, is a maximum steering angle or a minimum steering angle, respectively. The same holds analogously for other curves with monotonic curvature. The 3rd order polynomial is a particularly simple curve with this property, which still offers a high degree of flexibility due to the number of its polynomial coefficients. According to several embodiments, a steering angle at the first limiting position is computed depending on the curvature of the first limiting curve at the first limiting position using a predefined vehicle model, for example a bicycle model. A first angle difference between the steering angle at the first limiting position and the current steering angle is computed. The first limit value for the steering rate is determined as the first angle difference divided by the predefined time interval. In this way, a reliable first limit value is obtained. According to several embodiments, a steering angle at the second limiting position is computed depending on the curvature of the second limiting curve at the second limiting position using the predefined vehicle model. A second angle difference between the steering angle at the second limiting position and the current steering angle is computed. The second limit value for the steering rate is determined as the second angle difference divided by the predefined time interval. In this way, a reliable second limit value is obtained. According to several embodiments, the steering angle at the first limiting position is computed according to the vehicle model, in particular the bicycle model, as ^^^ = atan (^^^(^ + ^ ∗ ^^^^ , wherein V denotes the current velocity, W denotes a wheelbase of the motor vehicle, cL1 denotes the curvature of the first limiting curve at the first limiting position, and K is a predefined constant depending on mechanical properties of the motor vehicle, in particular only mechanical properties of the motor vehicle. According to several embodiments, the steering angle at the second limiting position is computed according to the vehicle model, in particular the bicycle model, as 2023PF00526 13 ^^^ = atan (^^^(^ + ^ ∗ ^^^^ , wherein cL2 denotes the curvature of the second limiting curve at the second limiting position. According to the bicycle model, it is for example assumed that the front wheels of the motor vehicle are steerable and are represented by a single effective front wheel and that the rear wheels of the motor vehicle are not steerable and are represented by a single effective rear wheel. The mechanical properties of the motor vehicle may for example comprise or consist of the wheelbase, a mass of the motor vehicle, distance between the center of gravity of the motor vehicle and a front wheel axis of the motor vehicle, a distance between the center of gravity of the motor vehicle and a rear wheel axis of the motor vehicle, a cornering stiffness of the front tires of the motor vehicle, and a cornering stiffness of the rear tires of the motor vehicle. In particular, K may be given by wherein m denotes the mass, LR and LF denote the distances between the center of gravity and the rear wheel axis and the front wheel axis, respectively, and CR and CF denote the cornering stiffness of the rear tires and the front tires, respectively. In this way, a particularly accurate estimation of the steering angles is achieved. In alternative embodiments, above equation with K=0 may be used. This may reduce the computational effort, in particular in use cases where W is much greater than K*V2. For use cases or use situations which may arise in a method according to the invention and which are not explicitly described herein, it may be provided that, in accordance with the method, an error message and / or a prompt for user feedback is output and / or a default setting and / or a predetermined initial state is set. 2023PF00526 14 According to a further aspect of the invention, a method for guiding a motor vehicle at least in part automatically. is provided. Therein, a method for limiting a steering rate of the motor vehicle according to the invention is carried out. At least one control signal for guiding the motor vehicle at least in part automatically is generated depending on the at least one limit value for the steering angle, wherein the at least one control signal comprises at least one steering control signal for steering the motor vehicle automatically according to the limit value for the steering angle. In particular, the at least one steering control signal for steering the motor vehicle automatically is generated depending on the at least one limit value for the steering angle. The at least one control signal may for example be provided to one or more actuators of the motor vehicle, including for example one or more braking actuators and / or one or more steering actuators and / or one or more propulsion motors of the motor vehicle. The one or more actuators may affect a longitudinal and / or lateral control of the motor vehicle in order to guide the motor vehicle at least in part automatically. In particular, the at least one steering control signal may be provided to the one or more steering actuators. The one or more steering actuators may affect the lateral control of the motor vehicle in order to steer the motor vehicle at least in part automatically. According to a further aspect of the invention, a data processing apparatus comprising at least one computing unit is provided. The at least one computing unit is adapted to carry out a method for limiting a steering rate of the motor vehicle according to the invention. In the present disclosure, a computing unit may for example be understood as a data processing device with processing circuitry. A computing unit can therefore perform computing operations in order to process data. The computing operations may also include indexed accesses to a data structure, for example a look-up table, LUT. In particular, a computing unit may include one or more computers, one or more microcontrollers, and / or one or more integrated circuits, for example, one or more application-specific integrated circuits, ASIC, one or more field-programmable gate arrays, FPGA, and / or one or more systems on a chip, SoC. The computing unit may also include one or more processors, for example one or more microprocessors, one or more central processing units, CPU, one or more graphics processing units, GPU, and / or one or more signal processors, in particular one or more digital signal processors, DSP. The computing unit may also include a physical or a virtual cluster of computers or other of said units. 2023PF00526 15 A computing unit may also comprise one or more hardware and / or software interfaces and / or one or more memory units. Therein, a memory unit may be implemented as a volatile data memory, for example a dynamic random access memory, DRAM, or a static random access memory, SRAM, or as a non-volatile data memory, for example a read- only memory, ROM, a programmable read-only memory, PROM, an erasable programmable read-only memory, EPROM, an electrically erasable programmable read- only memory, EEPROM, a flash memory or flash EEPROM, a ferroelectric random access memory, FRAM, a magnetoresistive random access memory, MRAM, or a phase-change random access memory, PCRAM. According to a further aspect of the invention, an electronic vehicle guidance system for a motor vehicle is provided. The electronic vehicle guidance system comprises a data processing apparatus according to the invention. The at least one computing unit is configured to carry out a method for guiding a motor vehicle at least in part automatically according to the invention. An electronic vehicle guidance system may be understood as an electronic system, configured to guide a vehicle in a fully automated or a fully autonomous manner and, in particular, without a manual intervention or control by a driver or user of the vehicle being necessary. The vehicle carries out all required functions, such as steering maneuvers, deceleration maneuvers and / or acceleration maneuvers as well as monitoring and recording the road traffic and corresponding reactions automatically. In particular, the electronic vehicle guidance system may implement a fully automatic or fully autonomous driving mode according to level 5 of the SAE J3016 classification. An electronic vehicle guidance system may also be implemented as an advanced driver assistance system, ADAS, assisting a driver for partially automatic or partially autonomous driving. In particular, the electronic vehicle guidance system may implement a partly automatic or partly autonomous driving mode according to levels 1 to 4 of the SAE J3016 classification. Here and in the following, SAE J3016 refers to the respective standard dated April 2021. Guiding the vehicle at least in part automatically may therefore comprise guiding the vehicle according to a fully automatic or fully autonomous driving mode according to level 5 of the SAE J3016 classification. Guiding the vehicle at least in part automatically may also comprise guiding the vehicle according to a partly automatic or partly autonomous driving mode according to levels 1 to 4 of the SAE J3016 classification. 2023PF00526 16 Further implementations of the electronic vehicle guidance system according to the invention follow directly from the various embodiments of the methods according to the invention and vice versa. In particular, individual features and corresponding explanations as well as advantages relating to the various implementations of the methods according to the invention can be transferred analogously to corresponding implementations of the electronic vehicle guidance system according to the invention. In particular, the electronic vehicle guidance system according to the invention is designed or programmed to carry out a method according to the invention. In particular, the electronic vehicle guidance system according to the invention carries out a method according to the invention. According to a further aspect of the invention, a computer program comprising instructions is provided. When the instructions are executed by at least one computing unit, the instructions cause the at least one computing unit to carry out a method for limiting a steering rate of the motor vehicle according to the invention and / or a method for guiding a motor vehicle at least in part automatically according to the invention. The instructions may be provided as program code, for example. The program code can for example be provided as binary code or assembler and / or as source code of a programming language, for example C, and / or as program script, for example Python. According to a further aspect of the invention, a computer-readable storage medium storing a computer program according to the invention is provided. The computer program and the computer-readable storage medium are respective computer program products comprising the instructions. Further features of the invention are apparent from the claims, the figures and the figure description. The features and combinations of features mentioned above in the description as well as the features and combinations of features mentioned below in the description of figures and / or shown in the figures may be comprised by the invention not only in the respective combination stated, but also in other combinations. In particular, embodiments and combinations of features, which do not have all the features of an originally formulated claim, may also be comprised by the invention. Moreover, embodiments and combinations of features, which go beyond or deviate from the combinations of features set forth in the recitations of the claims may be comprised by the invention. 2023PF00526 17 In the following, the invention will be explained in detail with reference to specific exemplary implementations and respective schematic drawings. In the drawings, identical or functionally identical elements may be denoted by the same reference signs. The description of identical or functionally identical elements is not necessarily repeated with respect to different figures. In the figures, Fig.1 shows schematically a motor vehicle with an exemplary implementation of an electronic vehicle guidance system according to the invention; Fig.2 shows schematically aspects for determining a driving path of a motor vehicle according to an exemplary implementation of a method for limiting a steering rate of a motor vehicle according to the invention; Fig.3 shows schematically aspects for determining an expected position according to a further exemplary implementation of a method for limiting a steering rate of a motor vehicle according to the invention; Fig.4 shows schematically aspects for determining a lateral position range according to a further exemplary implementation of a method for limiting a steering rate of a motor vehicle according to the invention; Fig.5 shows schematically aspects for determining a lateral position range according to a further exemplary implementation of a method for limiting a steering rate of a motor vehicle according to the invention; Fig.6 shows schematically aspects for determining a lateral position range according to a further exemplary implementation of a method for limiting a steering rate of a motor vehicle according to the invention; Fig.7 shows schematically aspects for determining a limiting curve according to a further exemplary implementation of a method for limiting a steering rate of a motor vehicle according to the invention; 2023PF00526 18 Fig.8 shows a schematic illustration of a vehicle model for use in a further exemplary implementation of a method for limiting a steering rate of a motor vehicle according to the invention; Fig.9 shows a schematic illustration of use case for a further exemplary implementation of a method for limiting a steering rate of a motor vehicle according to the invention; and Fig.10 shows a schematic illustration of use case for a further exemplary implementation of a method for limiting a steering rate of a motor vehicle according to the invention. Fig.1 shows schematically a motor vehicle 1 with an exemplary implementation of an electronic vehicle guidance system 2 according to the invention. The electronic vehicle guidance system 2 comprises at least one computing unit 3. In some embodiments, the electronic vehicle guidance system 2 may comprise one or more sensor systems for the motor vehicle 1 including, for example and without a restriction, one or more steering angle sensors 4, one or more environmental sensor systems 6, such as a camera, a lidar system, a radar system, and / or an ultrasonic sensor system et cetera, one or more inertial sensors 5, such as one or more inertial measurement units, IMUs, one or more acceleration sensors and / or one or more yaw rate sensors. The electronic vehicle guidance system 2 may also include other sensors, such as a wheel rotation speed sensor, a GNNS-receiver, and so forth. W denotes a wheelbase of the motor vehicle 1, which is a distance between a front wheel axis and a rear wheel axis of the motor vehicle 1. The at least one computing unit 3 is configured to carry out a method for limiting a steering rate of the motor vehicle 1 according to the invention. As a result, the at least one computing unit generates at least one limit value for the steering rate of the motor vehicle 1. The at least one computing unit 3 generates at least one control signal for guiding the motor vehicle 1 at least in part automatically depending on the limit value for the steering rate, wherein the at least one control signal comprises at least one steering control signal for steering the motor vehicle 1 automatically according to the at least one limit value for the steering rate. 2023PF00526 19 Several aspects of the method for limiting the steering rate of the motor vehicle 1 are explained for exemplary embodiments of the method in the following and, in particular, with reference to Fig.2 to Fig.8 To carry out the method for limiting a steering rate of the motor vehicle 1, the at least one computing unit 3 determines a driven path 8, which has been driven by the motor vehicle 1 up to a current time instance. For example, a plurality of positions 7, P1, P2, P3 of the motor vehicle 1 between a predefined previous time instance and the current time instance is determined. At least one fitted curve parameter is determined by fitting a predefined curve to the plurality of positions 7, P1, P2, P3, also denoted as historical positions. The driven path 8 is determined as the curve with the at least one fitted curve parameter between a position according to the previous time instance and a current position of the motor vehicle 1 according to the current time instance. This is illustrated for the exemplary case of a circle as the predefined curve in Fig.2 and Fig.3. Referring to Fig.2, the circle can, in principle, be defined based only three historical positions P1 = (XP1, YP1), P2 = (XP2, YP2), P3 = (XP3, YP3). To this end, the inclination m12 of the line connecting P1 to P2 may be computed as m12 = (YP2 – YP1) / (XP2 – XP1), and the inclination m23 of the line connecting P2 to P3 may be computed as m23 = (YP3 – YP2) / (XP3 – XP2). The X-coordinate of the center position C = (XC, YC) of the circle may be calculated as XC = (m12*m23*(YP3-YP1) + m12*(XP2+XP3) – m23*(XP1+XP2)) / (2*(m12-m23)). The Y-coordinate of the center position C = (XC, YC) may also be computed, since m12 and m23 are not both equal to zero. For example for non-zero m23: YC = (-1 / m23)*(XC – (XP2+XP3) / 2) + (YP2+YP3) / 2, or for m23 = 0 and non-zero m12 2023PF00526 20 YC = (-1 / m12)*(XC – (XP1+XP2) / 2) + (YP1+YP2) / 2. The radius of the circle is then for example given by R = ((XP1-XC)2+ (YP1-YC)2)1 / 2. The at least one computing unit 3 determines an expected position Pex, which is expected to be reached by the motor vehicle 1 at a target time instance, which lies after the current time instance by a predefined time interval, depending on the driven path 8 and depending on a current velocity of the motor vehicle 1 at the current time instance. Following the example of Fig.2, the expected position Pex may for example be determined by extending the circle by an extrapolated path 9, which is a circular arc with an arc length d = V*T, wherein V is the current velocity and T is the time interval, as shown in Fig.3. The end point of the extrapolated path 9 is the expected position Pex. The at least one computing unit 3 determines a lateral position range, which includes the expected position Pex, depending on a predefined lateral position offset D, D’. In particular, a straight line is constructed, which is perpendicular to the tangent to the extrapolated path 9 at the expected position Pex. In case of a circle, this line passes through the center position C. A first limiting point A lies on said line in a distance D from the expected position Pex and a second limiting point B lies on said line in a distance D’ from the expected position Pex in an opposite direction compared to A. For example, D=D’. The lateral position range is then given by the straight line connecting the limiting points A and B to each other. It is also possible that the extrapolated path 9 does not lie on the same circle as the driven path 8. For example, if the radius R is greater than a predefined minimum radius, for example 10,000 m, then the extrapolated path 9 may be given by a straight line of length d = V*T, as shown in Fig.5 and Fig.6. In the example of Fig.5, the extrapolated path 9 is parallel to a tangent to the driven path 8 at the current position, while this is not the case in Fig.6. The situation of Fig.6 is not possible if the motor vehicle’s 1 only steerable wheels are the front wheels. If the rear wheels are steerable as well, the situation of Fig.6 is possible. 2023PF00526 21 The at least one computing unit 3 determines at least one limit value for the steering rate depending on the lateral position range. To this end, the at least one computing unit 3 may for example determine a first limiting curve 10 between the current position of the motor vehicle 1 and the first limiting position A of the lateral position range and a second limiting curve 11 between the current position of the motor vehicle 1 and the second limiting position B of the lateral position range depending on the current velocity and a current steering angle of the motor vehicle 1 at the current time instance. A first limit value of the at least one limit value for the steering rate is determined depending on a curvature of the first limiting curve 10 at the first limiting position A and a second limit value of the at least one limit value for the steering rate is determined depending on a curvature of second first limiting curve 11 at the second limiting position B. The limiting curves 10, 11 may for example be constructed as polynomials of third degree. Using the Ackermann law based on the bicycle model illustrated in Fig.8, the curvature c relates to the steering angle θ via the velocity V and a constant K given by wherein m denotes the mass of the motor vehicle 1, LRand LFdenote the distances between the center of gravity G and the rear wheel axis and the front wheel axis of the motor vehicle 1, respectively, and CRand CFdenote the cornering stiffness of the rear tires 17 and the front tires 16, respectively. The first limiting curve 10 may be denoted as Y1(X) = a1*X + a2*X2+ a3*X3, wherein, with the current steering angle ω and the coordinates of the first limiting position A being (XA, YA): 2023PF00526 22 ^1 = tan (^^,^2 =^ !("^ / ^ $%&∗'(, and The steering angle at the first limiting position A is then given by ^^^ = atan (^^^(^ + ^ ∗ ^^^^ , wherein cL1 denotes the curvature of the first limiting curve 10 at the first limiting position A. The first limit value for the steering rate may then, for example, be computed as ^^^ − ^. / The second limiting curve 11 may be denoted as Y2(X) = b1*X + b2*X2+ b3*X3, wherein, with the coordinates of the second limiting position B being (XB, YB): 01 = ^1 = tan (^^, The steering angle at the first second limiting position B is then given by ^^^ = atan (^^^(^ + ^ ∗ ^^^^ , wherein cL2 denotes the curvature of the second limiting curve 11 at the second limiting position B. The second limit value for the steering rate may then, for example, be computed as 2023PF00526 23 As illustrated in Fig.9, upon an abrupt request for change of the lateral position of the motor vehicle 1, for example from a lane 12 to an adjacent lane 13, the steering rate may be limited according to the first and the second limit value. As schematically illustrated in Fig.10, in some embodiments, a lateral offset of a lane boundary 14, 15 from the expected position Pexis determined and, if the lateral offset of the lane boundary 14, 15 is greater than the lateral position offset D, D’, the motor vehicle 1 is automatically decelerated. As described, in particular with reference to the figures, the invention overcomes drawbacks of conventional approached to limit steering parameters when steering a motor vehicle automatically at least in part. According to several embodiments, an acceptable vehicle path distance deviation in a fixed time delay is predefined. For example, it may be defined that the motor vehicle shall not deviate more than 1 m from the current motor vehicle path during the next 1 second. The limit value for the steering rate may be determined to reach said positions deviation limit after the time delay. Said deviation limits may also be used to define the acceptable speed in a scenario with varying lane curvature. According to several embodiments, the steering rate is limited in case of lane detection jump. If a safety driver is present, they may for example be informed of the limitation such that the driver can react accordingly. In case of a fully autonomous vehicle, the time interval may for example be used to analyze the issue causing the lane detection jump and determine, for example, a minimum risk maneuver. According to several embodiments, a velocity limit to pass a lane curvature variation may be determined. Knowing the future path, for example in terms of waypoints, for each waypoint the admissible velocity to comply with the steering rate limitation may be estimated. For each waypoint, it is possible to trace an estimate the forward path deviation based on the previous waypoints. If the next waypoint is not between the maximum lateral left and right deviation, the velocity can be reduced.

Claims

2023PF00526 24 Claims 1. Method for limiting a steering rate of a motor vehicle (1), wherein - a driven path (8), which has been driven by the motor vehicle (1) up to a current time instance, is determined; - an expected position (Pex), which is expected to be reached by the motor vehicle (1) at a target time instance, which lies after the current time instance by a predefined time interval, is determined depending on the driven path (8) and depending on a current velocity of the motor vehicle (1) and / or is determined depending on the driven path (8) and depending on a predefined target velocity for the motor vehicle (1); - a lateral position range, which includes the expected position (Pex), is determined depending on a predefined lateral position offset (D, D’); - at least one limit value for the steering rate is determined depending on the lateral position range.

2. Method according to claim 1, wherein the at least one limit value for the steering rate is determined depending on the lateral position range, such that, for the velocity of the motor vehicle (1) being constant and the steering rate being equal to any of the at least one limit value between the current time instance and the target time instance, a position of the motor vehicle (1) according to the target time instance lies in the lateral position range.

3. Method according to one of the preceding claims, wherein - a request to change a lateral position of the motor vehicle (1) is detected; and - the motor vehicle (1) is steered automatically such that the steering rate of the motor vehicle (1) is limited by the determined at least one limit value in response to the request.

4. Method according to one of the preceding claims, wherein - a plurality of positions (7, P1, P2, P3) of the motor vehicle (1) between a predefined previous time instance and the current time instance is determined;2023PF00526 25 - at least one fitted curve parameter is determined by fitting a predefined curve to the plurality of positions (7, P1, P2, P3); and - the driven path (8) is determined as the curve with the at least one fitted curve parameter between a position according to the previous time instance and a current position of the motor vehicle (1) according to the current time instance.

5. Method according to claim 4, wherein an extrapolated path (9) is determined as the curve with the at least one fitted curve parameter between the current position of the motor vehicle (1) and the position of the motor vehicle (1) according to the target time instance, wherein the expected position (Pex) is given by the position according to the target time instance.

6. Method according to one of claims 4 or 5, wherein the predefined curve is a circle or a circular arc section or a straight line or a polynomial curve.

7. Method according to claim 4, wherein the predefined curve is a circle or a circular arc section, and - if a radius (R) of the circle or circular arc section is less than a predefined minimum radius (R), an extrapolated path (9) is determined as the curve with the at least one fitted curve parameter between the current position of the motor vehicle (1) and a position according to the target time instance, wherein the expected position (Pex) is given by the position according to the target time instance; and - if the radius (R) of the circle or circular arc section is greater than the minimum radius (R), the extrapolated path (9) is determined as a straight line between the current position of the motor vehicle (1) and the position according to the target time instance, wherein a direction of the straight line is given by a tangent to the circle or circular arc section at the current position of the motor vehicle (1) and the expected position (Pex) is given by the position according to the target time instance.

8. Method according to one of claims 1 to 3, wherein an extrapolated path (9) ending at the expected position (Pex) is determined by extrapolating the driven path (8) depending on the current velocity of the motor vehicle (1) and / or depending on the target velocity.2023PF00526 26 9. Method according to one of the preceding claims, wherein a lateral offset of a lane boundary (14, 15) from the expected position (Pex) is determined and, if the lateral offset of the lane boundary (14, 15) is greater than the lateral position offset (D, D’), the motor vehicle (1) is automatically decelerated.

10. Method according to one of the preceding claims, wherein - a further extrapolated path (9) is determined by extrapolating the driven path (8) depending on the current velocity of the motor vehicle (1) and / or depending on the target velocity, wherein an end point of the further extrapolated path (9) has a longitudinal position corresponding to a longitudinal position of a predefined waypoint for the motor vehicle (1); - a further lateral position range, which includes the end point, is determined depending on the lateral position offset (D, D’); and - if a lateral position of the end point of the further extrapolated path (9) lies outside the further lateral position range, the motor vehicle (1) is automatically decelerated.

11. Method according to one of the preceding claims, wherein - a first limiting curve (10, 11) between the current position of the motor vehicle (1) and a first limiting position (A, B) of the lateral position range is determined depending on the current velocity of the motor vehicle (1) and / or the target velocity, and depending on a current steering angle of the motor vehicle (1) at the current time instance; and - a first limit value of the at least one limit value for the steering rate is determined depending on a curvature of the first limiting curve (10, 11) at the first limiting position (A, B).

12. Method according to claim 11, wherein - the first limiting curve (10, 11) is determined as a polynomial of n-th degree, wherein n is at least two; or - the first limiting curve (10, 11) is determined as a polynomial of 3rd degree.

13. Method according to one of claims 11 or 12, wherein the first limiting curve (10, 11) is determined as a curve with constant curvature or with monotonically increasing curvature or with monotonically decreasing curvature between the current position of the motor vehicle (1) and the first limiting position (A, B).2023PF00526 27 14. Method according to claim one of claims 11 to 13, wherein - a steering angle at the first limiting position (A, B) is computed depending on the curvature of the first limiting curve (10, 11) at the first limiting position (A, B) using a predefined vehicle model; and - an angle difference between the steering angle at the first limiting position (A, B) and the current steering angle is computed; and - the first limit value is determined as the angle difference divided by the time interval.

15. Method according to claim 14, wherein the steering angle at the first limiting position (A, B) is computed according to the vehicle model as ^^^ = atan (^^^(^ + ^ ∗ ^^^^ , wherein V denotes the current velocity, W denotes a wheelbase of the motor vehicle (1), cL1denotes the curvature of the first limiting curve (10, 11) at the first limiting position (A, B), and K is a predefined constant depending on mechanical properties of the motor vehicle (1).

16. Method according to one of the preceding claims, wherein - a second limiting curve (10, 11) between the current position of the motor vehicle (1) and a second limiting position (A, B) of the lateral position range is determined depending on the current velocity of the motor vehicle (1) and the current steering angle of the motor vehicle (1) at the current time instance; and - a second limit value of the at least one limit value for the steering rate is determined depending on a curvature of the second limiting curve (10, 11) at the second limiting position (A, B).

17. Method for guiding a motor vehicle (1) at least in part automatically, wherein - a method for limiting a steering rate of the motor vehicle (1) according to one of the preceding claims is carried out; and - at least one control signal for guiding the motor vehicle (1) at least in part automatically is generated depending on the limit value for the steering rate, wherein the at least one control signal comprises at least one steering control signal for2023PF00526 28 steering the motor vehicle (1) automatically according to the at least one limit value for the steering rate.

18. Data processing apparatus comprising at least one computing unit (3), which is adapted to carry out a method according to one of claims 1 to 16.

19. Electronic vehicle guidance system (2) for a motor vehicle (1), which comprises a data processing apparatus according to claim 18, wherein the at least one computing unit (3) is configured to carry out a method according to claim 17.

20. Computer program product comprising instructions, which, when executed by a data processing apparatus, cause the data processing apparatus to carry out a method according to one of claims 1 to 17.

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