SE541357C2

SE541357C2 - Method and control arrangement for modelling spatial movement of a trailer being articulatedly attached to a vehicle

Info

Publication number: SE541357C2
Application number: SE1750664A
Authority: SE
Inventors: Jenny Eriksson; Johannes Slettengren; Jonny Andersson; Joseph Ah-King
Original assignee: Scania Cv Ab
Priority date: 2017-05-29
Filing date: 2017-05-29
Publication date: 2019-08-13
Also published as: DE102018004110A1; SE1750664A1

Abstract

The present disclosure relates to a method for modelling spatial movement of a trailer being articulatedly attached to a vehicle. According to one aspect the disclosure proposes a method for modelling spatial movement of a trailer being articulatedly attached to a vehicle at a coupling point. The method comprises determining (S1) a mathematical model describing the movement of the trailer, wherein the mathematical model comprises at least one unknown model parameter, obtaining (S3) sensor data recorded by at least one sensor attached to the vehicle, wherein the sensor data comprises at least one observation of the trailer, and updating (S4) a value of the at least one unknown model parameter based on the obtained sensor data. The present disclosure also relates to a control arrangement arranged to model spatial movement of a trailer being articulatedly attached to a vehicle. The present disclosure also relates to a computer program and a computer program product implementing the method.

Description

Method and control arrangement for modelling spatial movement of a trailer being articulatedly attached to a vehicle Technical Field The present disclosure relates to a method for modelling spatial movement of a trailer being articulatedly attached to a vehicle. The present disclosure also relates to a control arrangement arranged to model spatial movement of a trailer being articulatedly attached to a vehicle, and to a vehicle comprising the control arrangement. The present disclosure also relates to a computer program and a computer program product implementing the method.

Background Vehicles with articulation points pose difficult challenges for operators. As an example, in a trailer-truck configuration with an articulation point between the tractor and the trailer, the operator must carefully monitor the angle between the tractor and the trailer to keep within a lane. Similar challenges may face operators of articulated buses, lightduty trucks with trailers (e.g., boat/vehicle trailers, cargo trailers, etc.), or the like.

With recent advances in technology, Advanced Driver Assistance Systems, ADAS, (e.g. lane keeping systems and collision avoidance systems) are becoming more viable. In addition, the progressive development of vehicle electronics allows the use of automatic driving functions in which both the longitudinal control and the lateral control of the vehicle is carried out automatically (without any manual intervention). This implies that autonomous driving may be performed without any driver being present in the vehicle.

When implementing automatic driving functions in articulated vehicles, it is essential to know the position of the trailer. Different solutions for determining and predicting the position of a trailer has been proposed in prior art.

For example, WO2004109326 discloses that the spatial orientation of a trailer may be determined from sensor readings. As another example, US2012200706 presents that a vehicle towing a trailer is fitted with three video cameras fitted to the rear of the vehicle and on each door mirror. A predicted trailer path, calculated, is presented to the driver at a display as guide lines overlaid on the camera view.

However, present solutions are typically not suitable for use in ADAS functions.

Summary It is an object of the disclosure to be able to operate a vehicle automatically, or even autonomously, in a safe manner. Hence, it is a further object to provide a way of predicting the behavior of the trailer, that enables safe operation of ADAS functions in articulated vehicles. It is a still further object to provide a way of predicting the behavior of the trailer, without knowing the trailer properties.

These objects and others are at least partly achieved through a method according to a first aspect, for modelling spatial movement of a trailer being articulatedly attached to a vehicle at a coupling point. The method comprises determining a mathematical model describing the movement of the trailer, wherein the mathematical model comprises at least one unknown model parameter, wherein the mathematical model is based on the approximation that the coupling point has a uniform circular motion with regards to a rotation center of the trailer and, wherein the at least one unknown model parameter is the distance D between the rotation center of the trailer and the coupling point.. The method further comprises obtaining sensor data recorded by at least one sensor attached to the vehicle, wherein the sensor data comprises at least one observation of the trailer, and updating a value of the at least one unknown model parameter based on the obtained sensor data.

By using a generic mathematical model for modeling the behavior of a trailer being articulatedly attached to a vehicle and updating a generic mathematical model by data from sensor observations, the behavior of the trailer can be predicted even when knowing very little about the trailer. This can be used for “path planning” by any automatic steering function, or for systems reacting to objects along the side of the vehicle, not to react on detections of the trailer.

According to some embodiments, the method comprises detecting that the vehicle is driving in at least one steady state curve and then the obtaining comprises obtaining the sensor data while the vehicle is driving in the at least one steady state curve. By utilizing a model that is theoretically only valid when trailer is in a steady state, the computations may be simplified.

According to some embodiments, the updating comprises updating the at least one unknown model parameter of the mathematical model such that the estimated angle ? between a longitudinal center line of the trailer and the longitudinal center line of the vehicle is the same when derived from the mathematical model as when calculated based on the sensor data. Thus, the mathematical model is verified through comparison with sensor data.

According to some embodiments, the mathematical model neglects any side slip on a rear axle of the trailer. This condition is valid for low lateral accelerations and makes the computations and the model simpler.

According to some embodiments, the method comprises predicting the position of the trailer in a future turn based on the mathematical model. Thus, an accurate position of the trailer may be considered when automatically controlling the vehicle, or to assist the driver.

According to some embodiments, the predicting comprises analyzing the curvature of a future path of the vehicle, determining the position of the vehicle in a maximum curvature of the future path, and calculating, using the mathematical model, an angle ? between a longitudinal center line of the trailer and the longitudinal center line of the vehicle, at the determined position. Hence, the position of the trailer may be predicted.

According to some embodiments, the predicting comprises assuming that the calculated angle ? is the maximum angle ? between a longitudinal center line of the trailer and the longitudinal center line of the vehicle during the path. Hence, it is possible to at least assure that the trailer stays on road or within a lane.

According to some embodiments, the method comprises controlling the vehicle in an automatic driving mode based on the mathematical model. Thus, trailer movement may also be controlled.

According to some embodiments, the controlling comprises taking trailer dynamics into account when automatically steering the vehicle and/or disregarding sensor data caused by observations of the trailer.

According to some embodiments, the obtaining comprises obtaining sensor data from a plurality of measurements and wherein the updating comprises updating the value of the at least one unknown model parameter based on the plurality of measurements. By using data from a plurality of measurements, higher accuracy is achieved.

According to a second aspect, the disclosure relates to a control arrangement for use in a vehicle having a trailer being articulatedly attached to the vehicle at a coupling point. The control arrangement is configured to determine a mathematical model describing the movement of the trailer, wherein the mathematical model is based on the approximation that the coupling point has a uniform circular motion with regards to a rotation center of the trailer and, wherein the at least one unknown model parameter is the distance D between the rotation center of the trailer and the coupling point and wherein the mathematical model comprises at least one unknown model parameter, to obtain sensor data recorded by at least one sensor attached to the vehicle, wherein the sensor data comprises at least one observation of the trailer, and to update a value of the at least one unknown model parameter based on the obtained sensor data.

The control arrangement is further configured to perform the method according to any of the embodiments described above and below.

According to a third aspect, the disclosure relates to a vehicle comprising at least one sensor attached to the vehicle, a coupling point configured to articulatedly attach a trailer to the vehicle and a control arrangement configured to perform the method according to any of the embodiments described above and below.

According to a fourth aspect, the disclosure relates to a computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the method described above and below.

According to a fifth aspect, the disclosure relates to computer-readable medium comprising instructions, which when executed by a computer, cause the computer to carry out [the steps of] the method described above and below.

Brief description of the drawings Embodiments of the disclosure are described in more detail with reference to attached drawings illustrating examples of embodiments of the disclosure in which: Fig.1a illustrates a vehicle where the proposed method can be used.

Fig.1b illustrates a control arrangement of the vehicle of Fig.1a in further detail.

Fig. 2 illustrates the vehicle of Fig.1a with a trailer attached.

Fig. 3 illustrates the velocity of the coupling point with reference to the rotation center of the trailer.

Fig. 4 illustrates sensor detections in a steady state curve.

Fig. 5a illustrates a flow chart of a method according to a first aspect.

Fig. 5b illustrates the step of predicting of a future path in further detail.

Detailed description The disclosure proposes a method for modelling spatial movement of a trailer being articulatedly attached to a vehicle at a coupling point. For better understanding of the proposed technique problems related to using automatic driving functions in articulated vehicles will first be identified and discussed.

Articulation points pose special challenges for automatic driving functions. In systems that use automatic lateral control to assist the driver or to control the vehicle, it is essential to know the position and behavior of the trailer. If the position of the trailer is unknown, radar detections of the trailer may be misinterpreted to be objects, and may cause false warnings when used in safety functions that react to objects along the sides of the vehicle.

Another problem for ADAS functions is related to the control of the lateral position of the vehicle and the trailer. If the trailer dynamics is not considered by the ADAS function, the steering functions may drive the trailer outside the intended area (typically a lane) or even crash the trailer into objects that could be prevented by modelling and predicting the trailer behavior.

Hence, to operate a vehicle automatically, or even autonomously, in a safe manner, an accurate assessment of the trailer position of the vehicle is required. As mentioned above, the presently available solutions do not fulfil this requirement. For example, with the solution proposed in the above-mentioned document WO2004109326, only the present trailer position is determined. This information is typically not sufficient for determining a future path of the vehicle. Furthermore, the prediction presented in US2012200706 the trailer is predicted to follow the circumference of a circle of a turning radius R. However, this approximation might if used by an ADAS function cause the trailer to drive outside the lane or even worse out of the road. Hence, the inventors have realized that there is a need for a model that can predict the behavior of a trailer being attached to a vehicle in a future turn. The inventors have further realized that the maximum tow angle, is of interest. Such a model should preferably be independent on the trailer properties, as one single tow vehicle is generally used with different trailers.

To solve these deficiencies this disclosure introduces a method that uses a trailer model. In the model one or more unknown model parameters are updated based on observations from a sensor e.g. a radar, in one example embodiment, the model sees the trailer as a pendulum that starts in the trailer's center of rotation and ends in the coupling point between the trailer and a tractor. Since the velocity of the connection point is known, it is possible to calculate the rotational or angular speed of the trailer and thus its angle relative to the tractor. Side slip for the trailer axle is neglected, which is a key to modelling the trailer using a pendulum model.

In the following a control arrangement and a method for modelling spatial movement of a trailer being articulatedly attached to a vehicle will be described.

Fig.1a illustrates a vehicle 1 in which the proposed method can be used. The vehicle 1 is e.g. a work vehicle such as a truck or tractor unit. The vehicle 1 of Fig.1a comprises a coupling point 11, a control arrangement 12 and sensors 13. However, it must be appreciated that Fig.1a is only a schematic illustration and that it only shows parts of the vehicle 1 that are associated with the disclosure.

The coupling point 11, which may also be referred to as the articulation point, is the physical coupling between the vehicle 1 and the trailer 2. For example, the coupling point 11 comprises a coupling of a fifth-wheel type.

The control arrangement 12, herein an Electronic Control Units, ECU, is basically digital computer that controls one or more electrical systems (or electrical sub systems) of the vehicle 1 based on e.g. information read from sensors 13 placed at various parts and in different components of the vehicle 1. ECU is a generic term that is used in automotive electronics, for any embedded system that controls one or more of the electrical system or sub systems in a transport vehicle. For simplicity, only one ECU 12 configured to perform the proposed method is shown in the example of Fig.1a. This may e.g. be a ECU particularly designated to implement an ADAS function or it may be any other ECU or even multiple ECUs. However, it must be appreciated that the vehicle 1 typically comprises many more ECUs. According to some embodiments, the control arrangement 12 comprises more than one ECU.

The sensors 13 illustrated in Fig.1a are radar sensors. For example, the sensors comprise one side looking radar sensor and one rear looking radar sensor. However, it must be understood that the vehicle 1 typically comprises many sensors of different types that may be used for different purposes. The at least one sensor 13 referred to in this application is any sensor usable to observe a position of the trailer 2.

The dynamics of the vehicle 1 and the trailer 2 will now be described with reference to Fig. 2. In Fig. 2 the trailer is attached to the vehicle 1 at the coupling point 11.

The vehicle 1 in Fig 2 includes three pairs of wheels 14. Each pair of wheels 14 is attached to a wheel axle 15a, 15b, respectively. The front wheels of the vehicle 1 are attached to a front wheel axle 15a. The rear wheels of the vehicle 1 are attached to respective rear wheel axles 15b. When the vehicle 1 is driving, the vehicle’s 1 lateral movement is controlled e.g. by a steering system.

When driving on a curvy road, the vehicle 1 will rotate around its rotation center 16. The rotation center 16, also called instantaneous velocity center, is the point fixed to a vehicle undergoing planar movement that has zero velocity at a particular instant of time. The rotation center 16 is typically located between the rear wheel axles 15b. The rotational speed ?tractor ,may be measured by a yaw-rate sensor, which is a gyroscopic device that measures a vehicle's angular velocity around its vertical axis.

The width of the trailer W is expected to be roughly known as most trailers are similar in terms of width. However, the distance D from the rotation center 21 of the trailer 2 to the coupling point 11 (i.e. the rotation length of the trailer) is typically unknown. This value is not expected to be known as it is different for different trailers. However, the rotation length may be estimated using measurement data, as will be further explained below.

When the vehicle 1 is driving, the movement of the vehicle 1 will generate a force on the trailer 2 at the coupling point. The force will drag the trailer 2 forward. If the vehicle 1 is turning, the force will also cause the trailer to turn. In other words, the force will cause the trailer 2 to rotate around its rotation center 21. Consequently, the trailer 2 will be angled relative the vehicle 1 during a turn. The tow angle ? is the angle created between the tow vehicle 1 and trailer 2 when the trailer moves away from the centerline of the tow combination, i.e. the angle between a longitudinal center line of the trailer 2 and the longitudinal center line of the vehicle 1. During a turn, the tow angle ?, will typically increase, until a maximum angle occurs and then it will decrease. In between the increase and the decrease a steady state may be reached, where the tow angle ? is constant.

This disclosure proposes using a mathematical model for modelling the dynamics of the trailer 2 and the vehicle 1. The mathematical model defines a state of the vehicle 1, based on a number of parameters i.e. state parameters. The state parameters are changing over time. The mathematical model is defined by a number of model parameters. The model parameters are static for the individual vehicle.

In some example embodiments, the mathematical model is based on the approximation that the coupling point 11 has a uniform circular motion with regards to a rotation center 21 of the trailer 2. One could say that this mathematical model models the trailer as a pendulum, where the coupling point 11 represents a bob that swings around the rotation center 21 of the trailer, see Fig. 3. The velocity (in longitudinal and lateral direction) of the coupling point 11 point in the vehicle’s coordinate system is typically known to the vehicle 1 . Hence, the rotational speed ?trailerof the trailer 2 may be calculated using the pendulum approximation, as will be further explained below. Furthermore, side slip ? for trailer rear axle is zero, which is a key to approximating the trailer as a pendulum. The side slip angle is the angle between the trailer’s back axle and trailers actual movement direction.

The equations used in the model are in theory only valid when the circular motion of the trailer 2 around the trailer’s rotation center 21 is constant. This condition is fulfilled in a steady state curve. A steady state curve refers to a condition during a curve when the entire vehicle equipage is in a steady state. This condition will typically occur when the yaw-rate of the vehicle ( ?tractor) has been constant for some time, e.g. a few seconds. Then the yaw-rate (?trailer) of the trailer will typically also stabilize. Hence, in the steady state curve the tow angle ? is constant. Hence, in a steady state curve the trailer 2 has reached one of the outer positions, if the trailer movement is modelled as a pendulum movement.

It is not certain that such a steady state is reached in every curve. However, the model assumes that an estimate of what the angle ? would have been if a steady state was reached at the sharpest point of the curve, corresponds to or exceeds what the actual angle will be in that point. Hence, the model will give a maximum value for the angle ?, which is a value that is usable for controlling the vehicle 1. This will be further explained below.

The example mathematical model is expressed as follows. The change Image available on "Original document" in the angle between a longitudinal center line of the trailer 2 and the longitudinal center line of the vehicle 1 may be calculated as the yaw-rate of the vehicle 1 and the trailer 2 is known.

Image available on "Original document" From the equation of a particles motion in a constant curve, i.e. when ? is constant, the lateral velocity v'ymay be calculated. The apostrophe indicates that the velocity is in the coordinate system of the trailer.

Image available on "Original document" The lateral velocity v'yin the coordinate system of the trailer may then be transposed to the coordinate system of the vehicle 1 using standard formulas (equation 3) where vyis the lateral velocity of the vehicle 1 in the trailer coupling point 11 and similarly, vxis the longitudinal velocity of the vehicle in the coupling point 11 (Fig.3).

Vy= — vxsin(?) vycos(?) (equation 3) Then, the angular speed of the trailer 2 is given by equation 4. As mentioned above, the example mathematical model neglects any side slip (i.e. ? = 0) on the rear axle of the trailer, which works at low lateral accelerations.

Vy= vx? D ?tractor(equation 4) The trailer dynamics may be modelled by combining equation 1-4.

Image available on "Original document" A method according to a first aspect of this disclosure will now be explained referring to Figs. 5a and 5b, where Fig. 5a shows a flow chart diagram for modelling spatial movement of a trailer 2 being articulatedly attached to a vehicle 1 at a coupling point 11. The method is e.g. performed by the above-mentioned control arrangement 12. The method is typically performed continuously when an automated driving function in the vehicle 1 is activated. It is also possible that some of the steps of the method are performed by external processing means being located outside the vehicle 1.

As described above, the proposed method uses a mathematical model, or trailer model, for modelling spatial movement of a trailer 2 being articulatedly attached to a vehicle 1. Thus, the method comprises determining S1 a mathematical model describing the movement of the trailer 2, wherein the mathematical model comprises at least one unknown model parameter. Initially, the at least one unknown model parameter, e.g. the distance D, is given an initial value. The initial value is typically an approximation.

The mathematical model is e.g. the example mathematical model described above. Thus, according to some embodiments, the at least one unknown model parameter is the distance D between the rotation center 21 of the trailer 2 and the coupling point 11. The proposed method will now be described using the mathematical model described above as an example. However, as readily understood by a skilled person, the method may also be used using other similar mathematical models. For example, the unknown model parameter may be the position of the coupling point.

The method further comprises, obtaining S3 sensor data recorded by at least one sensor 13 attached to the vehicle 1, wherein the sensor data comprises at least one observation of the trailer 2. In other words, the sensor 13 is for example a rear and/or a side looking sensor. The sensor 13 may be a radar sensor or an image sensor.

The mathematical model described above, is valid when the yaw-rate ?trailerof the trailer 2 is constant, which is the case in a so called steady state curve. Hence, to acquire correct model parameters the sensor data should be captured when the vehicle 1 is driving in, or is likely to be driving in, a steady state curve. In other words, according to some embodiments, the method comprises detecting S2 that the vehicle 1 is driving in at least one steady state curve and obtaining the sensor data while the vehicle 1 is driving in the at least one steady state curve. A steady state curve may be detected by detecting that the velocity and change in the vehicle’s yaw-rate and velocity is below a predetermined threshold value for a period of time.

In a steady state curve and for small angles, it can be approximated that: 0 ~ (vx* (-?) vy)/D - ?tractor(equation 6) The unknown model parameter D, is then calculated as follows: Image available on "Original document" Hence, when driving in a steady state curve, the detections that are “probable” detections on the trailer 2 are used for updating the parameter D. “Probable" detections are for example several detections that are in line with each other, i.e. multiple hits on the trailer. Probable detections may also be hits are close to a current estimation of the trailer position.

Fig. 4 illustrates sensor detections in a steady state curve. If the sensor detection is a radar detection, it may e.g. indicate the coordinates of the detection point. For a detection that is assumed to be on a trailer 2, the expected trailer angle ? is easily calculated based on the sensor data (see geometry in Fig. 4). Provided that the yawrate, the lateral velocity vyand the longitudinal velocity vxof the coupling point is known, the rotational length D for each measurement may then be calculated using equation 7.

The method then comprises updating S4 a value of the at least one unknown model parameter based on the obtained sensor data. In other words, the initial value of D, which is typically an approximation, is updated based on real measurement data. For example, the updating S4 comprises updating the at least one unknown model parameter of the mathematical model such that the estimated angle ? between a longitudinal center line of the trailer 2 and the longitudinal center line of the vehicle 1 is the same when derived from the mathematical model as when calculated based on the sensor data. In other words, the sensor measurements provide data that may be used to verify the accuracy of the model, or rather of the at least one model parameter. The model at least one model parameter may then be adjusted accordingly.

Typically, multiple measurements are performed to get a more accurate result. Hence, the final value of D is calculated from the mean values from several measurements or similar. In other words, according to some embodiments, the obtaining S3 comprises obtaining S3a sensor data from a plurality of measurements and the updating S4 comprises updating S4a the value of the at least one unknown model parameter based on the plurality of measurements. Data from several measurements may be combined e.g. by studying a median, mean or average.

According to some embodiments, the method further comprises predicting S5 the state of the vehicle 1 of the trailer 2 in a future turn based on the model. For example, the model, which has now been updated with accurate model parameters is applied at the maximum curvature of a future curve. Hence, the method approximates that the steady state occurs at the maximum curvature of the curve. However, this is only an approximation.

An example implementation of the predicting S5 is illustrated in further detail in Fig. 5b. In this example, the predicting S5 comprises analyzing S5a the curvature of a future turn of the vehicle 1 and determining S5b the state of the vehicle 1 e.g. position and speed, of the vehicle 1 in a maximum curvature of the future path. The “path” refers to a limited distance of a pre-determined length of the upcoming road. The predetermined length may have different values depending on the application and the vehicle 1. The state of the vehicle 1 is defined by state parameters that are used by the mathematical model.

Then, the method comprises calculating S5c, using the mathematical model, an angle ? between a longitudinal center line of the trailer 2 and the longitudinal center line of the vehicle 1, for the determined state of the vehicle 1. It is not certain that a steady state will ever be reached in a certain curve. However, an estimate of what the angle would have been in a steady state at the sharpest point of the curve corresponds to or exceeds what the actual angle will be in that point. Hence, in the case when the steady state occurs after the maximum curvature the model will anyhow give a larger angle than the actual angle.

Finally, the method comprises assuming S5d that the calculated angle ? is the maximum angle ? between a longitudinal center line of the trailer 2 and the longitudinal center line of the vehicle 1 during the path. Hence, the result calculated in the previous step S5c would give a “safe” or conservative angle, that is usable for controlling the vehicle, while making sure that the trailer stays on the road.

According to some embodiments, the method further comprises controlling S6 the vehicle 1 in an automatic driving mode based on the mathematical model. The controlling may for example imply taking trailer 2 dynamics into account when automatically steering the vehicle 1 and/or disregarding sensor data caused by observations of the trailer 2. In other words, the vehicle 1 may be controlled using the angle ? given by the mathematical model. Then, the trailer may always stay on the road.

In a second aspect, the disclosure relates to a control arrangement 12 for use in a vehicle 1 having a trailer 2 being articulatedly attached to the vehicle 1 at a coupling point 11.

Fig.1b illustrates an exemplary control arrangement 12, here an ECU, in more detail. The control arrangement is configured to model spatial movement of a trailer 2 being articulatedly attached to a vehicle 1 at a coupling point 11. The ECU comprises hardware and software. The hardware basically comprises various electronic components on a Printed Circuit Board, PCB. The most important of those components is typically a processing unit/circuitry 121 e.g. a microprocessor, along with a memory 122 e.g. EPROM or a Flash memory chip. The software (also called firmware) is typically lower-level software code that runs in the microcontroller.

The control arrangement 12 is configured to determine a mathematical model describing the movement of the trailer 2, wherein the mathematical model comprises at least one unknown model parameter and to obtain sensor data recorded by at least one sensor 13 attached to the vehicle 1, wherein the sensor data comprises at least one observation of the trailer 2. The control arrangement is further configured to update a value of the at least one unknown model parameter based on the obtained sensor data. Furthermore, the control arrangement 12 is configured to perform all the embodiments of the method described above singly or in combination.

According to some embodiments, the control arrangement 12 is configured to detecting that the vehicle 1 is driving in at least one steady state curve and to the obtain the sensor data while the vehicle 1 is driving in the at least one steady state curve.

According to some embodiments, the control arrangement 12 is configured to updating the at least one unknown model parameter such that the estimated angle ? between a longitudinal center line of the trailer 2 and the longitudinal center line of the vehicle 1 is the same when derived from the mathematical model as when calculated based on the sensor data.

According to some embodiments, the control arrangement 12 is configured to predict the position of the trailer 2 in a future turn based on the mathematical model.

According to some embodiments, the control arrangement 12 is configured to analyze the curvature of a future path of the vehicle 1, determine the position of the vehicle 1 in a maximum curvature of the future path, and calculate, using the mathematical model, an angle ? between a longitudinal center line of the trailer 2 and the longitudinal center line of the vehicle 1, at the determined position.

According to some embodiments, the control arrangement 12 is configured to assume that the calculated angle ? is the maximum angle ? between a longitudinal center line of the trailer 2 and the longitudinal center line of the vehicle 1 during the path.

According to some embodiments, the control arrangement 12 is configured to control the vehicle 1 in an automatic driving mode based on the mathematical model.

According to some embodiments, the control arrangement 12 is configured to obtain sensor data from a plurality of measurements and update the value of the at least one unknown model parameter based on the plurality of measurements.

The method modelling spatial movement of a trailer 2 being articulatedly attached to a vehicle 1 at a coupling point 11, is typically implemented in a computer program which, when it is executed in a computer, such as the processing unit 22, instructs the computer to execute the method. The computer program is for example stored in the memory 122 of the control arrangement 12.

The computer program is usually constituted by a computer program product P stored on a non-transitory/non-volatile digital storage medium, in which the computer program is incorporated in the computer-readable medium of the computer program product. The computer-readable medium comprises a suitable memory, such as, for example: ROM (Read-Only Memory), PROM (Programmable Read-Only Memory), EPROM (Erasable PROM), Flash memory, EEPROM (Electrically Erasable PROM).

Claims

1. A method for modelling spatial movement of a trailer (2) being articulatedly attached to a vehicle (1) at a coupling point (11), the method comprising: determining (S1) a mathematical model describing the movement of the trailer (2), - wherein the mathematical model comprises at least one unknown model parameter, wherein the mathematical model is based on the approximation that the coupling point (11) has a uniform circular motion with regards to a rotation center (21) of the trailer (2) and, wherein the at least one unknown model parameter is the distance D between the rotation center (21) of the trailer (2) and the coupling point (11). - obtaining (S3) sensor data recorded by at least one sensor (13) attached to the vehicle (1), wherein the sensor data comprises at least one observation of the trailer (2), and - updating (S4) a value of the at least one unknown model parameter based on the obtained sensor data.

2. The method according to claim 1, wherein the method comprises: - detecting (S2) that the vehicle is driving in at least one steady state curve and wherein the obtaining comprises obtaining (S3a) the sensor data while the vehicle (1) is driving in the at least one steady state curve.

3. The method according to any of the preceding claims, wherein the updating (S4) comprises updating the at least one unknown model parameter of the mathematical model such that the estimated angle ? between a longitudinal center line of the trailer (2) and the longitudinal center line of the vehicle (1) is the same when derived from the mathematical model as when calculated based on the sensor data.

4. The method according to any of the preceding claims, wherein the mathematical model neglects any side slip on a rear axle of the trailer (2).

5. The method according to any of the preceding claims, wherein the method comprises: - predicting (S5) the state of the vehicle (1) of the trailer (1) in a future turn based on the mathematical model.

6. The method according to claim 5, wherein the predicting (S5) comprises: analyzing (S5a) the curvature of a future path of the vehicle (1), determining (S5b) the state of the vehicle (1) in a maximum curvature of the future path, and calculating (S5c), using the mathematical model, an angle ? between a longitudinal center line of the trailer (2) and the longitudinal center line of the vehicle (1), for the determined state of the vehicle (1).

7. The method according to claim 6: assuming (S5d) that the calculated angle ? is the maximum angle ? between a longitudinal center line of the trailer (2) and the longitudinal center line of the vehicle (1) during the path.

8. The method according to any of the preceding claims, wherein the method further comprises: - controlling (S6) the vehicle (1) in an automatic driving mode based on the mathematical model.

9. The method of claim 8, wherein the controlling comprises taking trailer (2) dynamics into account when automatically steering the vehicle (1) and/or disregarding sensor data caused by observations of the trailer (2).

10. The method according to any of the preceding claims, wherein the obtaining (S3) comprises obtaining (S3a) sensor data from a plurality of measurements and wherein the updating (S4) comprises updating (S4a) the value of the at least one unknown model parameter based on the plurality of measurements.

11. A computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the method according to any one of the preceding claims.

12. Computer-readable medium comprising instructions, which when executed by a computer, cause the computer to carry out the method according to any one of the preceding claims 1-10.

13. A control arrangement (12) for use in a vehicle (1) having a trailer (2) being articulatedly attached to the vehicle (1) at a coupling point (11), the control arrangement being configured to: - determine a mathematical model describing the movement of the trailer (2), wherein the mathematical model comprises at least one unknown model parameter, wherein the mathematical model is based on the approximation that the coupling point (11) has a uniform circular motion with regards to a rotation center (21) of the trailer (2) and, wherein the at least one unknown model parameter is the distance D between the rotation center (21) of the trailer (2) and the coupling point (11). - obtain sensor data recorded by at least one sensor (13) attached to the vehicle (1), wherein the sensor data comprises at least one observation of the trailer (2), and - update a value of the at least one unknown model parameter based on the obtained sensor data.

14. The control arrangement (12) according to claim 13, wherein the control arrangement is configured to perform the method according to any of claims 2-10.

15. A vehicle (1) comprising: - at least one sensor (13) attached to the vehicle (1), - a coupling point configured to articulatedly attach a trailer (2) to the vehicle (1), - a control arrangement (12) configured to perform the method according to any of claims 1-10.