DE102024200004A1 - Estimation of a friction coefficient for a means of transport - Google Patents

Abstract

The present invention relates to a method, a computer program with instructions, and a device for estimating a friction coefficient for a means of transport, as well as to a means of transport with sensors that uses a method or a device according to the invention. The invention also relates to a method, a computer program with instructions, and a device for training a machine learning algorithm for estimating a friction coefficient for a means of transport, as well as a correspondingly trained algorithm. In a first step, measurement data originating from sensors of the means of transport are received (10). The measurement data indicate at least a lateral acceleration of the means of transport and forces occurring in the steering system of the means of transport. By applying a machine learning algorithm to the measurement data, a friction coefficient is estimated (11). The estimated friction coefficient is output (12) for further use in the means of transport.

Description

The present invention relates to a method, a computer program with instructions, and a device for estimating a friction coefficient for a means of transport, as well as to a means of transport with sensors that uses a method or device according to the invention. The invention also relates to a method, a computer program with instructions, and a device for training a machine learning algorithm for estimating a friction coefficient for a means of transport, as well as to a correspondingly trained algorithm.

In the following description, some English terms are used, as German-language technical terms have not been established in the field of machine learning. The English terms used are familiar to those skilled in the art.

For the safe driving of a motor vehicle, knowledge of the coefficient of friction, or the maximum possible achievable longitudinal and lateral acceleration, is critical. This information becomes even more important for automated vehicles. If such a vehicle were to always assume the coefficient of friction of a dry, grippy road surface due to a lack of information about the current coefficient of friction, the occupants would be at high risk when cornering. If, on the other hand, the vehicle were to assume the extreme case of a low coefficient of friction, such as on a snow-covered road, the vehicle would be met with little acceptance due to the excessively low or overly cautious speeds and the resulting long driving times.

Known approaches for determining the coefficient of friction can be divided into vehicle-external and vehicle-internal approaches. Vehicle-external approaches are based, for example, on weather data, image data, or information from stationary measuring points. Vehicle-internal approaches use, for example, information generated during stabilizing braking interventions by the anti-lock braking system (ABS) or the electronic stability control (ESC), the difference in longitudinal slip between a driven and a non-driven axle, the maximum lateral acceleration achieved, or special sensors in the tire carcass. A fusion of several approaches is usually useful here, as their information areas, i.e., the area of horizontal acceleration, complement rather than overlap.

Due to the external information sources, the vehicle-external approaches are difficult to transfer to the specific vehicle, resulting in a significant degree of inaccuracy. Furthermore, both the vehicle-external and the vehicle-internal approaches are sometimes not very informative for small horizontal accelerations, or, like the tire sensor, they involve additional costs.

Another approach involves using a vehicle dynamics model, e.g., a Kalman filter, to determine and evaluate the tire aligning torque occurring during cornering. The physical effect of the tire aligning torque makes it possible to evaluate the friction coefficient at approximately half the maximum lateral acceleration. However, the required vehicle dynamics model is complex, and tuning a Kalman filter is time-consuming.

It is an object of the invention to provide improved solutions for estimating a friction coefficient for a means of transport.

This object is achieved by a method having the features of claim 1 or 7, by a device having the features of claim 5 or 9, by a means of transport according to claim 6, by an algorithm according to claim 10, and by a computer program with instructions according to claim 11. Preferred embodiments of the invention are the subject of the dependent claims.

• - Empfangen von Messdaten von Sensoren des Fortbewegungsmittels, wobei die Messdaten zumindest eine Querbeschleunigung des Fortbewegungsmittels und im Lenksystem des Fortbewegungsmittels auftretende Kräfte angeben;
• - Schätzen eines Reibwertes durch Anwenden eines Algorithmus des maschinellen Lernens auf die Messdaten; und
• - Ausgeben des geschätzten Reibwertes.

According to a first aspect of the invention, a method for estimating a coefficient of friction for a means of transport comprises the steps:

• - receiving measurement data from sensors of the means of transport, the measurement data indicating at least a lateral acceleration of the means of transport and forces occurring in the steering system of the means of transport;
• - Estimating a friction coefficient by applying a machine learning algorithm to the measured data; and
• - Output the estimated friction coefficient.

• - Empfangen von Messdaten von Sensoren des Fortbewegungsmittels, wobei die Messdaten zumindest eine Querbeschleunigung des Fortbewegungsmittels und im Lenksystem des Fortbewegungsmittels auftretende Kräfte angeben;
• - Schätzen eines Reibwertes durch Anwenden eines Algorithmus des maschinellen Lernens auf die Messdaten; und
• - Ausgeben des geschätzten Reibwertes.

According to a further aspect of the invention, a computer program contains instructions which, when executed by a computer, cause the computer to perform the following steps for estimating a coefficient of friction for a means of transport:

• - receiving measurement data from sensors of the means of transport, the measurement data indicating at least a lateral acceleration of the means of transport and forces occurring in the steering system of the means of transport;
• - Estimating a friction coefficient by applying a machine learning algorithm to the measured data; and
• - Output the estimated friction coefficient.

The term "computer" should be understood broadly. In particular, it also includes control units, embedded systems, and other processor-based data processing devices.

The computer program may, for example, be made available for electronic retrieval or stored on a computer-readable storage medium.

• - ein Empfangsmodul, das eingerichtet ist, Messdaten von Sensoren des Fortbewegungsmittels zu empfangen, wobei die Messdaten zumindest eine Querbeschleunigung des Fortbewegungsmittels und im Lenksystem des Fortbewegungsmittels auftretende Kräfte angeben;
• - einen Reibwertschätzer, der eingerichtet ist, einen Reibwert durch Anwenden eines Algorithmus des maschinellen Lernens auf die Messdaten zu schätzen; und
• - ein Ausgabemodul, das eingerichtet ist, den geschätzten Reibwert auszugeben.

According to a further aspect of the invention, a device for estimating a coefficient of friction for a means of transport comprises:

• - a receiving module configured to receive measurement data from sensors of the means of transport, the measurement data indicating at least a lateral acceleration of the means of transport and forces occurring in the steering system of the means of transport;
• - a friction coefficient estimator configured to estimate a friction coefficient by applying a machine learning algorithm to the measurement data; and
• - an output module configured to output the estimated friction coefficient.

The inventive solution utilizes the physical effect of the tire aligning torque. The lateral force behaves linearly with the slip angle. For small slip angle values, the tire aligning torque also behaves linearly with the slip angle. The progression of the tire aligning torque to zero at larger slip angles depends on the coefficient of friction and can therefore be used to determine the coefficient of friction. However, in production vehicles, neither the tire aligning torque nor the slip angle are available as measured variables. Therefore, other measured variables are used in the inventive solution. Instead of the slip angle, lateral acceleration is used here. Instead of the tire aligning torque, forces occurring in the steering system of the vehicle are used. For example, the sum of the tie rod forces on the steered front axle can be used. These can be measured using strain gauges on the tie rods. If the tie rod forces are not available, which may be the case in production vehicles, the sum of the steering pinion torque and the servo pinion torque can be used instead. Other advantageous variables are the steering wheel angle, the rack position, the driving speed, the yaw rate, the sideslip angle and the wheel speeds or the resulting driving speed. The received measurement data is fed to a trained machine learning algorithm, which estimates the friction coefficient based on the measurement data. Depending on the design of the algorithm, the algorithm receives only the measurement data from the current point in time or the measurement data from a sliding time window, i.e., the measurement data for a number of time steps in a predetermined time interval are fed into the friction coefficient estimator. One advantage of the solution according to the invention is that the friction coefficient can be determined even at small lateral accelerations, typically starting from half the maximum lateral acceleration at all driving speeds. No additional sensor technology is required; only the measurement data from sensors available in the production vehicle is used.

According to one aspect of the invention, the estimated friction coefficient is output as a continuous value or as a decision class. The estimate of the friction coefficient can be output in the form of a decision for a friction coefficient class. For example, the friction coefficient classes 0.1, 0.4, 0.7, and 1.0 can be used. This simplifies subsequent processing of the friction coefficient by assistance systems of the means of transport and is generally sufficiently accurate. Alternatively, the friction coefficient can also be output as a continuous value, where "continuous" here is understood in the context of the data resolution.

According to one aspect of the invention, an estimated coefficient of friction is only output if the lateral acceleration or the magnitude of the lateral acceleration is sufficiently large, or a minimum value of the coefficient of friction is output if the lateral acceleration or the magnitude of the lateral acceleration is not sufficiently large. The maximum lateral acceleration is approximately 8 m/s ² , so that an estimate of the coefficient of friction is possible from approximately 4 m/s ² . If the lateral acceleration is too small, the tire aligning torque is in the linear range. In this case, no coefficient of friction can be determined and none of the above-mentioned friction coefficient classes is output. If necessary, a characteristic value can be output, such as -1, to clarify that no estimation is possible. However, at least a minimum value for the coefficient of friction can be output for the linear range of the tire aligning torque. This is calculated from a currently measured lateral acceleration multiplied by a factor greater than 1. When the lateral acceleration or the magnitude of the lateral acceleration is sufficiently large depends on the behavior of the trained estimator and the existing friction coefficient. A reserve for the coefficient of friction or a minimum reserve for the minimum value of the coefficient of friction can be issued.

According to one aspect of the invention, the machine learning algorithm uses a neural network. In principle, the algorithm can be implemented as a classifier from the field of machine learning. Classic approaches such as decision trees, k-nearest neighbors (KNN), support vector machines (SVMs), random forests, etc. are certainly acceptable. However, a neural network, such as a convolutional neural network (CNN), a recurrent neural network (RNN), or a long-short-term memory (LSTM), is preferred.

Advantageously, a means of transport equipped with sensors comprises a device according to the invention or is configured to carry out a method according to the invention for estimating a friction coefficient. The means of transport can be, in particular, a passenger car, a bus, or a commercial vehicle, e.g., a truck, an agricultural machine, or a construction machine.

• - Vorgeben von Reibwerten;
• - Erzeugen von simulierten Messdaten mittels eines Fahrzeugmodells für die vorgegebenen Reibwerte, wobei die simulierten Messdaten zumindest eine Querbeschleunigung des Fortbewegungsmittels und im Lenksystem des Fortbewegungsmittels auftretende Kräfte angeben; und
• - Trainieren des Algorithmus des maschinellen Lernens mit den vorgegebenen Reibwerten und den simulierten Messdaten.

According to a further aspect of the invention, a method for training a machine learning algorithm for estimating a friction coefficient for a means of transport comprises the steps:

• - Specifying friction values;
• - generating simulated measurement data using a vehicle model for the specified friction values, wherein the simulated measurement data indicate at least a lateral acceleration of the means of transport and forces occurring in the steering system of the means of transport; and
• - Training the machine learning algorithm with the specified friction values and the simulated measurement data.

• - Vorgeben von Reibwerten;
• - Erzeugen von simulierten Messdaten mittels eines Fahrzeugmodells für die vorgegebenen Reibwerte, wobei die simulierten Messdaten zumindest eine Querbeschleunigung des Fortbewegungsmittels und im Lenksystem des Fortbewegungsmittels auftretende Kräfte angeben; und
• - Trainieren des Algorithmus des maschinellen Lernens mit den vorgegebenen Reibwerten und den simulierten Messdaten.

According to a further aspect of the invention, a computer program includes instructions which, when executed by a computer, cause the computer to perform the following for training a machine learning algorithm for estimating a coefficient of friction for a means of transport:

• - Specifying friction values;
• - generating simulated measurement data using a vehicle model for the specified friction values, wherein the simulated measurement data indicate at least a lateral acceleration of the means of transport and forces occurring in the steering system of the means of transport; and
• - Training the machine learning algorithm with the specified friction values and the simulated measurement data.

The term "computer" should be understood broadly. It specifically includes workstations, distributed systems, and other processor-based data processing devices.

The computer program may, for example, be made available for electronic retrieval or stored on a computer-readable storage medium.

• - ein Vorgabemodul, das eingerichtet ist, Reibwerte vorzugeben;
• - ein Simulationsmodul, das eingerichtet ist, simulierte Messdaten mittels eines Fahrzeugmodells für die vorgegebenen Reibwerte zu erzeugen, wobei die simulierten Messdaten zumindest eine Querbeschleunigung des Fortbewegungsmittels und im Lenksystem des Fortbewegungsmittels auftretende Kräfte angeben; und
• - ein Trainingsmodul, das eingerichtet ist, den Algorithmus des maschinellen Lernens mit den vorgegebenen Reibwerten und den simulierten Messdaten zu trainieren.

According to a further aspect of the invention, a device for training a machine learning algorithm for estimating a friction coefficient for a means of transport comprises:

• - a specification module designed to specify friction values;
• - a simulation module configured to generate simulated measurement data using a vehicle model for the specified friction values, the simulated measurement data indicating at least a lateral acceleration of the means of transport and forces occurring in the steering system of the means of transport; and
• - a training module configured to train the machine learning algorithm with the specified friction values and the simulated measurement data.

In the solution according to the invention, a machine learning algorithm is used to estimate a coefficient of friction. To train such an algorithm, measurement data from the system is usually used as training data. If the algorithm is to output friction coefficient classes, for example, this would mean that the measurement data would be recorded during test runs with the vehicle. The test runs for each individual friction coefficient class would have to be carried out on a road surface with exactly the specified friction coefficient. Furthermore, all driving situations that occur during driving must be experienced. This is not possible in practice. According to the invention, the training data is therefore essentially obtained by simulating a corresponding vehicle model. Different values are specified for the variable "coefficient of friction", and training data is generated for each of these values. The values for the coefficient of friction correspond to the friction coefficient classes or, in the case of continuous output, are distributed across the value range. For the simulation, corresponding input time delays Simulations are provided, e.g., time courses for the steering wheel angle as well as braking and acceleration inputs. The algorithm is then trained with the simulated measurement data generated in this way. In addition to the simulated training data, real measurement data can be added to account for complex, non-modelable effects.

According to one aspect of the invention, input time profiles for the vehicle model are generated using random generators. Advantageously, the input time profiles do not merely represent simulations of typical driving situations, but rather time profiles generated using random generators are used. This approach is based on the assumption that the friction coefficient estimator trained in this way will find the correct friction coefficient or be able to generalize sufficiently well even in a driving situation not included in the training data.

Advantageously, a machine learning algorithm for estimating a friction coefficient for a means of transport is trained using a method according to the invention. Such an algorithm is capable of determining the friction coefficient at all driving speeds, even at low lateral accelerations, typically starting at half the maximum lateral acceleration.

• 1 zeigt schematisch ein Verfahren zum Schätzen eines Reibwertes für ein Fortbewegungsmittel;
• 2 zeigt eine erste Ausführungsform einer Vorrichtung zum Schätzen eines Reibwertes für ein Fortbewegungsmittel;
• 3 zeigt eine zweite Ausführungsform einer Vorrichtung zum Schätzen eines Reibwertes für ein Fortbewegungsmittel;
• 4 stellt schematisch ein Fortbewegungsmittel dar, in dem eine erfindungsgemäße Lösung realisiert ist;
• 5 zeigt schematisch ein Verfahren zum Trainieren eines Algorithmus des maschinellen Lernens zum Schätzen eines Reibwertes für ein Fortbewegungsmittel;
• 6 zeigt eine erste Ausführungsform einer Vorrichtung zum Trainieren eines Algorithmus des maschinellen Lernens zum Schätzen eines Reibwertes für ein Fortbewegungsmittel;
• 7 zeigt eine zweite Ausführungsform einer Vorrichtung zum Trainieren eines Algorithmus des maschinellen Lernens zum Schätzen eines Reibwertes für ein Fortbewegungsmittel;
• 8 veranschaulicht den Verlauf des Reifenrückstellmomentes über den Schräglaufwinkel;
• 9 veranschaulicht ein gleitendes Zeitfenster über Messdaten;
• 10 veranschaulicht die Erzeugung von Eingangszeitverläufen für eine Simulation zur Erzeugung von Trainingsdaten;
• 11 veranschaulicht einen Trainingsprozess; und
• 12 veranschaulicht das Verhalten eines erfindungsgemäßen Reibwertschätzers im Vergleich zu einem Reibwertschätzer gemäß dem Stand der Technik.

Further features of the present invention will become apparent from the following description and the appended claims taken in conjunction with the figures.

• 1 shows schematically a method for estimating a friction coefficient for a means of transport;
• 2 shows a first embodiment of a device for estimating a friction coefficient for a means of transport;
• 3 shows a second embodiment of a device for estimating a friction coefficient for a means of transport;
• 4 schematically represents a means of transport in which a solution according to the invention is implemented;
• 5 schematically shows a method for training a machine learning algorithm for estimating a friction coefficient for a means of transport;
• 6 shows a first embodiment of an apparatus for training a machine learning algorithm for estimating a friction coefficient for a means of transport;
• 7 shows a second embodiment of an apparatus for training a machine learning algorithm for estimating a friction coefficient for a means of transport;
• 8 illustrates the course of the tire return torque over the slip angle;
• 9 illustrates a sliding time window over measurement data;
• 10 illustrates the generation of input time courses for a simulation to generate training data;
• 11 illustrates a training process; and
• 12 illustrates the behavior of a friction coefficient estimator according to the invention in comparison to a friction coefficient estimator according to the prior art.

To better understand the principles of the present invention, embodiments of the invention are explained in more detail below with reference to the figures. It is understood that the invention is not limited to these embodiments and that the described features may also be combined or modified without departing from the scope of the invention as defined in the appended claims.

1 shows a schematic of a method for estimating a coefficient of friction for a means of transport. In a first step, measurement data is received 10, which originates from sensors of the means of transport. The measurement data indicates at least a lateral acceleration of the means of transport and forces occurring in the steering system of the means of transport. By applying a machine learning algorithm to the measurement data, a coefficient of friction is estimated 11. For example, the machine learning algorithm can use a neural network. The estimated coefficient of friction is output 12 for further use in the means of transport, e.g., as a continuous value or as a decision class. Preferably, an estimated coefficient of friction is only output 12 if the lateral acceleration or the magnitude of the lateral acceleration is sufficiently large. If the lateral acceleration or its magnitude is not sufficiently large, a minimum value of the coefficient of friction can optionally be output 12. In addition, a reserve for the coefficient of friction or a minimum reserve for the minimum value of the coefficient of friction can be output.

2 shows a simplified schematic representation of a first embodiment of a device 20 for estimating a coefficient of friction for a means of transport. The device 20 has an input 21, via which a receiving module 22 receives measurement data D from sensors 41 of the means of transport. The measurement data D indicate at least a lateral acceleration A _y of the means of transport. by means of and in the steering system of the means of transport. A friction coefficient estimator 23 is set up to estimate a friction coefficient µ by applying a machine learning algorithm A to the measurement data D. For example, the machine learning algorithm A can use a neural network. An output module 24 is set up to output the estimated friction coefficient µ via an output 27 of the device 20 for further use in the means of transport, e.g. as a continuous value or as a decision class. Preferably, an estimated friction coefficient µ is only output by the output module 24 if the lateral acceleration A _y or if the absolute value of the lateral acceleration A _y is sufficiently large. If the lateral acceleration A _y or its absolute value is not sufficiently large, a minimum value µ _min of the friction coefficient can optionally be output. In addition, a reserve for the friction coefficient µ or a minimum reserve for the minimum value µ _min of the friction coefficient can be output.

The receiving module 22, the friction coefficient estimator 23, and the output module 24 can be controlled by a control module 25. Settings of the receiving module 22, the friction coefficient estimator 23, the output module 24, or the control module 25 can be changed via a user interface 28. The data generated in the device 20 can be stored in a memory 26 of the device 20 if necessary, for example, for later evaluation or for use by the components of the device 20. The receiving module 22, the friction coefficient estimator 23, the output module 24, and the control module 25 can be implemented as dedicated hardware, for example, as integrated circuits. Of course, they can also be partially or completely combined or implemented as software running on a suitable processor, for example, a CPU or a GPU. The input 21 and the output 27 can be implemented as separate interfaces or as a combined bidirectional interface.

3 shows a simplified schematic representation of a second embodiment of a device 30 for estimating a coefficient of friction for a means of transport. The device 30 has a processor 32 and a memory 31. For example, the device 30 is a computer, a control unit, or an embedded system. Instructions are stored in the memory 31 which, when executed by the processor 32, cause the device 30 to carry out the steps according to one of the described methods. The instructions stored in the memory 31 thus embody a program executable by the processor 32 which implements the method according to the invention. The device 30 has an input 33 for receiving measurement data. Data generated by the processor 32 are provided via an output 34. In addition, data can be stored in the memory 31. The input 33 and the output 34 can be combined to form a bidirectional interface.

The processor 32 may include one or more processor units, such as microprocessors, digital signal processors, or combinations thereof.

The memories 26, 31 of the described embodiments can have both volatile and non-volatile memory areas and can comprise a wide variety of storage devices and storage media, for example hard disks, optical storage media or semiconductor memories.

4 schematically illustrates a means of transport 40 in which a solution according to the invention is implemented. In this example, the means of transport 40 is a motor vehicle. The motor vehicle has a number of sensors 41, e.g., for measuring a lateral acceleration A _y or for measuring forces F occurring in the steering system. The measurement data D from the sensors 41 are used by a device 20 according to the invention to estimate a friction coefficient µ. The device 20 can, for example, be implemented on a computer 43 of the motor vehicle. The estimated friction coefficient µ can, for example, be used by an assistance system 42 as part of a (partially) automated driving function. If necessary, the assistance system 42 can output warnings regarding the friction coefficient µ to an operator of the motor vehicle via a display device 44. A connection to a backend can be established by means of a data transmission unit 45, e.g., for transmitting settings or retrieving updated software for the components of the motor vehicle. A memory 46 is provided for storing data. Data exchange between the various components of the motor vehicle takes place via a network 47.

5 shows a schematic of a method for training a machine learning algorithm for estimating a friction coefficient for a means of transport. For example, the machine learning algorithm can use a neural network. In a first step, friction coefficients are specified 50. In addition, input time profiles for a vehicle model can be generated using random generators 51. Simulated measurement data for the specified friction coefficients are generated using the vehicle model 52. The simulated measurement data indicate at least a lateral acceleration of the means of transport and, in the steering system of the vehicle, The machine learning algorithm is trained using the specified friction values and the simulated measurement data. 53 In addition to the simulated measurement data, real measurement data can be added to account for complex, non-modelable effects. The trained algorithm is then made available for further use. 54

6 shows a simplified schematic representation of a first embodiment of a device 60 for training a machine learning algorithm A for estimating a friction coefficient for a means of transport. For example, the machine learning algorithm A can use a neural network. The device 60 has an input 61 for receiving data, for example data from a vehicle model. A specification module 62 is configured to specify friction coefficients µ. A simulation module 63 is configured to generate simulated measurement data D _s for the specified friction coefficients µ using a vehicle model. For this purpose, input time profiles for the vehicle model can be generated using random generators. The simulated measurement data D _s indicate at least a lateral acceleration A _y of the means of transport and forces F occurring in the steering system of the means of transport. A training module 64 is configured to train the machine learning algorithm A with the specified friction coefficients µ and the simulated measurement data D _s . In addition to the simulated measurement data, the training module 64 can add real measurement data to account for complex, non-modelable effects. The trained algorithm A can then be provided for further use via an output 67 of the device 60.

The specification module 62, the simulation module 63, and the training module 64 can be controlled by a control module 65. Settings of the specification module 62, the simulation module 63, the training module 64, or the control module 65 can be changed via a user interface 68. The data generated in the device 60 can be stored in a memory 66 of the device 60 if necessary, for example, for later evaluation or for use by the components of the device 60. The specification module 62, the simulation module 63, the training module 64, and the control module 65 can be implemented as dedicated hardware, for example, as integrated circuits. Of course, they can also be partially or completely combined or implemented as software running on a suitable processor, for example, a CPU or a GPU. The input 61 and the output 67 can be implemented as separate interfaces or as a combined bidirectional interface.

7 shows a simplified schematic representation of a second embodiment of a device 70 for training a machine learning algorithm for estimating a coefficient of friction for a means of transport. The device 70 has a processor 72 and a memory 71. For example, the device 70 is a computer, a workstation, or a distributed system. Instructions are stored in the memory 71 which, when executed by the processor 72, cause the device 70 to carry out the steps according to one of the described methods. The instructions stored in the memory 71 thus embody a program executable by the processor 72 which implements the method according to the invention. The device 70 has an input 73 for receiving data. Data generated by the processor 72 are provided via an output 74. In addition, data can be stored in the memory 71. The input 73 and the output 74 can be combined to form a bidirectional interface.

The processor 72 may include one or more processor units, such as microprocessors, digital signal processors, or combinations thereof.

The memories 66, 71 of the described embodiments can have both volatile and non-volatile memory areas and can comprise a wide variety of storage devices and storage media, for example hard disks, optical storage media or semiconductor memories.

In the following, further details of the invention will be explained with reference to 8 until 12 be explained.

8 illustrates the progression of the tire aligning torque M _z over the slip angle α. Also shown is the progression of the lateral force F _y over the slip angle α. The lateral force F _y behaves essentially linearly over the slip angle α in the area indicated by the dashed box. The tire aligning torque M _z also behaves linearly over the slip angle α for small values of the slip angle α. The linear range is shown in 8 indicated by the solid box. The progression of the tire aligning torque M _z to zero at larger slip angles α depends on the coefficient of friction and can therefore be used to determine the coefficient of friction. If α is still within the linear range, at least a minimum value for the coefficient of friction can be specified.

Known approaches to estimating the coefficient of friction, which are based on determining the maximum lateral acceleration during driving, are The curve of the lateral force F _y over α and, in particular, the deviation from the linear branch are plotted. The solution according to the invention takes advantage of the fact that the tire restoring torque M _z collapses earlier than the lateral force F _y with respect to the slip angle α. Therefore, the coefficient of friction can be determined even at lower lateral accelerations than is possible when evaluating the lateral force F _y .

In production vehicles, neither the tire aligning torque M _z nor the slip angle α are usually available as measured variables. Therefore, the inventive solution uses other measured variables. Instead of the slip angle α, the lateral acceleration is used here. Instead of the tire aligning torque M _z , forces occurring in the steering system of the vehicle are used. For example, the sum of the tie rod forces on the steered front axle can be used here. Alternatively, the sum of the steering pinion torque and the servo pinion torque can be used. Other advantageous variables are the steering wheel angle, the rack position, the driving speed, the yaw rate, the sideslip angle and the wheel speeds.

The recorded measurement data is fed into a trained machine learning algorithm, which estimates the friction coefficient based on the measured data. The algorithm can be implemented as a classifier from the field of machine learning. Classic approaches such as decision trees, nearest neighbor classification, support vector machines (SVMs), random forests, etc. can be used. However, a neural network, such as a convolutional neural network, is preferred.

The approaches mentioned require a sliding time window Z, which feeds the last a time steps in a time interval dt into the estimator. 9 illustrates such a sliding time window Z over the measurement data D. The time interval dt, the number a of time steps within the time window Z and the distance b between consecutive time windows Z are hyperparameters of the algorithm.

Other approaches, e.g. other versions of neural networks such as a recurrent network or a long short-term memory, do not require a sliding time window Z, but only the measurement data at the current time.

The solution according to the invention uses a machine learning algorithm to estimate a coefficient of friction. To train such an algorithm, measurement data from the system is usually used as training data. If, for example, the algorithm is to output friction coefficient classes, this would mean that the measurement data would be recorded during test runs with the vehicle. The test runs for each individual friction coefficient class would have to be carried out on a road surface with exactly the specified friction coefficient. Furthermore, all driving situations that occur during driving must be experienced. This is not possible in practice. According to the invention, the training data is therefore essentially obtained by simulating a corresponding vehicle model. Different values are specified for the variable "coefficient of friction", and training data is generated for each of these values. The values for the coefficient of friction correspond to the friction coefficient classes or, in the case of continuous output, are distributed across the value range. Corresponding input time profiles are provided for the simulation, e.g., time profiles for the steering wheel angle as well as braking and acceleration inputs.

10 illustrates the generation of such input time profiles for a simulation to generate training data. Preferably, the input time profiles do not simply represent simulations of typical driving situations, but rather time profiles generated with random generators are used. This approach is based on the assumption that the friction coefficient estimator trained in this way can find the correct friction coefficient or generalize sufficiently well even in a driving situation not included in the training data.

For example, an exponential random distribution can be used to generate randomly distributed time periods that define points in the time course. At each of these points in time, an amplitude is generated from a random distribution (e.g., a normal distribution).

This gives you points of the time course that can be connected with straight lines, for example, to create time courses. The solid curve in 10 represents such a time course. This can be further filtered, resulting in the time course shown with a dashed line.

11 illustrates a training process. The process includes the simulation 80 of measurement data D _s , the preprocessing 81 of the simulated measurement data D _s , the actual training 82 of the classifier, the testing 83 of the classifier in driving operation, and the post-processing 84. The simulation 80 uses a detailed vehicle model and uses the vehicle parameters FP as input variables. The simulation 80 is controlled by hyperparameters HP. The results from the simulation 80 The resulting simulated measurement data D _s are divided into time windows during preprocessing 81, ie the time courses are divided into data sets or "frames", which can also overlap due to the freely selectable window time step size. This preprocessing 81 can be omitted for approaches without a sliding time window. The division into time windows is carried out by the already described in connection with 9 The hyperparameters dt, a and b mentioned above are controlled. During the subsequent actual training 82, the classifier is trained. The concrete design of the training depends on the selected algorithm and is at the discretion of the expert. The trained classifier, i.e. the trained algorithm A, is tested in a real vehicle 83. During operation of the classifier, only the time step size dt and the time window length a × dt are relevant. The measurement data D obtained during test operation can subsequently also be subjected to preprocessing 81 and used for further training 82 of the classifier. Optionally, benchmarking can be carried out as part of follow-up 82, for example.

12 illustrates the behavior of a friction coefficient estimator according to the invention compared to a friction coefficient estimator according to the prior art. The magnitude of the measured lateral acceleration A _y is plotted on the x-axis, and the desired maximum lateral acceleration A _y,max is plotted on the y-axis. This is obtained from the desired friction coefficient µ by multiplying it by a vehicle-dependent factor (e.g., 10, ignoring the units). The solid line shows the output of the friction coefficient estimator according to the invention, and the dashed line shows the function of a friction coefficient estimator that operates without tire aligning torque and only with the measured lateral acceleration A _y . The latter can output the minimum value of the maximum lateral acceleration A _y,max indicated by the dashed line. If there is also information that the vehicle has reached the maximum lateral acceleration A _y,max , it can determine and output this from the measured lateral acceleration A _y . In this example, the friction coefficient estimator according to the invention cannot directly estimate the friction coefficient in a driving range FB _0.5 up to a friction coefficient of 0.5. However, it can derive a minimum value from twice the measured lateral acceleration A _y . In the driving range FB _1.0 extending beyond this, up to a friction coefficient of 1.0, the friction coefficient estimator according to the invention can directly determine the maximum lateral acceleration A _y,max , or the friction coefficient.

It is clearly visible that the output values for the maximum lateral acceleration A _y,max (or the coefficient of friction) of the friction coefficient estimator according to the invention are significantly closer to the value of the maximum lateral acceleration A _y,max than of the friction coefficient estimator according to the prior art. This applies across the entire value range of the measured lateral acceleration A _y . In addition, a minimum reserve R _min can be output for the lateral acceleration when outputting the minimum value of the maximum lateral acceleration A _y,max or the coefficient of friction, and a reserve R can be output when outputting the estimated value of the maximum lateral acceleration A _y,max or the coefficient of friction.

In 12 It can be seen that the explanations outlined for the friction coefficients 0.5 and 1.0 apply to all friction coefficients. The value of the measured lateral acceleration A _y below which the minimum value for the friction coefficient (or for the maximum lateral acceleration A _y,max ) is determined, and above which the estimated value of the friction coefficient (or the maximum lateral acceleration A _y,max ) is determined, is therefore not a value that is applied or fixed, but results from the actual friction coefficient and the behavior of the trained friction coefficient estimator. The numbers and factors mentioned are example values and are for illustrative purposes only.

List of reference symbols

10

Receiving measurement data

11

Estimating a friction coefficient

12

Output of the estimated friction coefficient

20

device

21

Entrance

22

Receiver module

23

Friction coefficient estimator

24

Output module

25

Control module

26

memory

27

Exit

28

User interface

30

device

31

memory

32

processor

33

Entrance

34

Exit

40

Means of transport

41

sensor

42

Assistance system

43

computer

44

Display device

45

Data transmission unit

46

memory

47

network

50

Specifying friction values

51

Generating input time profiles

52

Generating simulated measurement data

53

Training the algorithm

54

Providing the trained algorithm

60

device

61

Entrance

62

Default module

63

Simulation module

64

Training module

65

Control module

66

memory

67

Exit

68

User interface

70

device

71

memory

72

processor

73

Entrance

74

Exit

80

Simulation of training data

81

Preprocessing of training data

82

Training the classifier

83

Testing the classifier

84

Follow-up

A

algorithm

Ay

Lateral acceleration

Ay,max

Maximum lateral acceleration

α

Slip angle

D

Measurement data

Ds

Simulated measurement data

F

Power

FB0.5

Driving range up to friction coefficient 0.5

FB1.0

Driving range up to friction coefficient 1.0

FP

Vehicle parameters

Fy

Lateral force

HP

Hyperparameter

µ

Friction coefficient

µmin

Minimum value of the friction coefficient

Mz

Tire return torque

R

reserve

Rmin

Minimum reserve

Claims (11)

A method for estimating a coefficient of friction (µ) for a means of transport (40), comprising the steps of: - receiving (10) measurement data (D) from sensors (41) of the means of transport (40), wherein the measurement data (D) indicate at least one lateral acceleration (A _y ) of the means of transport (40) and forces (F) occurring in the steering system of the means of transport (40); - estimating (11) a coefficient of friction (µ) by applying a machine learning algorithm (A) to the measurement data (D); and - outputting (12) the estimated coefficient of friction (µ). Procedure according to Claim 1 , whereby an estimated coefficient of friction (µ) is only output (12) if the lateral acceleration (A _y ) or an amount of the lateral acceleration (A _y ) is sufficiently large, or whereby a minimum value (µ _min ) of the coefficient of friction is output (12) if the lateral acceleration (A _y ) or an amount of the lateral acceleration (A _y ) is not sufficiently large. Procedure according to Claim 2 , whereby a reserve (R) for the coefficient of friction (µ) or a minimum reserve (R _min ) for the minimum value (µ _min ) of the coefficient of friction is output. Method according to one of the preceding claims, wherein the machine learning algorithm (A) uses a neural network. Device (20) for estimating a coefficient of friction (µ) for a means of transport (40), comprising: - a receiving module (22) configured to receive (10) measurement data (D) from sensors (41) of the means of transport (40), wherein the measurement data (D) indicate at least a lateral acceleration (A _y ) of the means of transport (40) and forces (F) occurring in the steering system of the means of transport (40); - a coefficient of friction estimator (23) configured to estimate (11) a coefficient of friction (µ) by applying a machine learning algorithm (A) to the measurement data (D); and - an output module (24) configured to output (12) the estimated coefficient of friction (µ). Means of transport (40) with sensors (41), wherein the means of transport (40) comprises a device tion (20) according to Claim 5 has or is arranged to implement a method according to one of the Claims 1 until 4 to estimate a coefficient of friction (µ) on the basis of measurement data (D) from the sensors (41). Method for training a machine learning algorithm (A) for estimating a friction coefficient (µ) for a means of transport (40), comprising the steps of: - specifying (50) friction coefficients (µ); - generating (52) simulated measurement data (D _s ) using a vehicle model for the specified friction coefficients (µ), wherein the simulated measurement data (D _s ) indicate at least one lateral acceleration (A _y ) of the means of transport (40) and forces (F) occurring in the steering system of the means of transport (40); and - training (53) the machine learning algorithm (A) with the specified friction coefficients (µ) and the simulated measurement data (D _s ). Procedure according to Claim 7 , where input time courses for the vehicle model are generated by random generators (51). Device (60) for training a machine learning algorithm (A) for estimating a coefficient of friction (µ) for a means of transport (40), comprising: - a specification module (62) configured to specify (50) coefficients of friction (µ); - a simulation module (63) configured to generate (52) simulated measurement data (D _s ) using a vehicle model for the specified coefficients of friction (µ), wherein the simulated measurement data (D _s ) indicate at least one lateral acceleration (A _y ) of the means of transport (40) and forces (F) occurring in the steering system of the means of transport (40); and - a training module (64) configured to train (53) the machine learning algorithm (A) with the specified coefficients of friction (µ) and the simulated measurement data (D _s ). Algorithm (A) of machine learning for estimating a coefficient of friction (µ) for a means of transport (40), wherein the algorithm (A) is carried out by means of a method according to Claim 7 or 8 was trained. A computer program comprising instructions which, when executed by a computer, cause the computer to carry out the steps of a method according to any one of the Claims 1 until 4 , 7 or 8 initiate.

Images