Method for Estimating an Articulation Angle between a Towing Vehicle and a Trailer, Respective Device, Driving Assistance System, Commercial Vehicle and Computer Program Product

Abstract

A method estimates an articulation angle between a towing vehicle and a trailer with respect to a pivot. The method determines a distance between an instantaneous center of velocity of the towing vehicle and a center of at least one axle of the towing vehicle representative for a rotation of the towing vehicle about the instantaneous center of velocity of the towing vehicle and/or a distance between an instantaneous center of velocity of the trailer and a center of at least one axle of the trailer representative for a rotation of the trailer about the instantaneous center of velocity of the trailer. The method determines at least one instantaneous speed representative for a wheel speed of at least one wheel of the towing vehicle and/or the trailer, wherein the at least one instantaneous speed refers to the at least one determined distance, and estimates the articulation angle based on the at least one determined instantaneous speed and the at least one determined distance.

Claims

1. A method for estimating an articulation angle (φ) between a towing vehicle and a trailer with respect to a pivot (K), comprising: determining a distance (r) between an instantaneous center of velocity (P) of the towing vehicle and a center of at least one axle (R) of the towing vehicle representative for a rotation of the towing vehicle about the instantaneous center of velocity (P) of the towing vehicle and/or a distance (r.sub.T) between an instantaneous center of velocity (D) of the trailer and a center of at least one axle (T) of the trailer representative for a rotation of the trailer about the instantaneous center of velocity (D) of the trailer; determining at least one instantaneous speed (ν.sub.R, ν.sub.T, ν.sub.TL, ν.sub.TR) representative for a wheel speed of at least one wheel of the towing vehicle and/or the trailer, wherein the at least one instantaneous speed (ν.sub.R, ν.sub.T, ν.sub.TL, ν.sub.TR) refers to the at least one determined distance (r, r.sub.T); and estimating the articulation angle (φ) based on the at least one determined instantaneous speed and the at least one determined distance (r, r.sub.T).

2. The method according to claim 1, wherein the at least one instantaneous speed (ν.sub.R, ν.sub.T, ν.sub.TL, ν.sub.TR) is determined for: at least one non-steered axle of the towing vehicle, as speed (ν.sub.R) of the center of at least one rear axle (R) of the towing vehicle, and/or at least one non-steered axle of the trailer, as speed (ν.sub.T) of the center of at least one rear axle (T) or as speed (ν.sub.TL, ν.sub.TR) of at least one wheel of at least one rear axle of the trailer.

3. The method according to claim 2, wherein the distance (r) between the instantaneous center of velocity (P) of the towing vehicle and the center of at least one axle (R) of the towing vehicle is calculated, based on a distance (b) between a steering axle of the towing vehicle and a non-steering axle of the towing vehicle, and a steering angle (ϑ) of the steering axle.

4. The method according to claim 3, wherein the distance (r) between the instantaneous center of velocity (P) of the towing vehicle and the center of at least one axle (R) the towing vehicle is calculated by:
r=b/tan(ϑ).

5. The method according to claim 1, wherein the distance (r.sub.T) between the instantaneous center of velocity (D) of the trailer and the center of at least one axle (T) of the trailer is calculated based on a distance (r.sub.0) between a center of at least one wheel on the at least one axle of the trailer facing towards the instantaneous center of velocity of the trailer and a distance (w) between the center of the at least one wheel on the at least one axle facing towards the instantaneous center of velocity (D) of the trailer and at least one wheel on the other side of the at least one axle.

6. The method according to claim 5, wherein the distance (r.sub.T) between the instantaneous center of velocity (D) of the trailer and the center of at least one axle (T) of the trailer is calculated by:
r.sub.T=r.sub.0+w/2, wherein r.sub.0 is defined by $r_0=w.Math.\frac{\min \left({\upsilon }_{\mathrm{TL}},{\upsilon }_{\mathrm{TR}}\right)}{\mathrm{abs}\left({\upsilon }_{\mathrm{TL}}-{\upsilon }_{\mathrm{TR}}\right)}.$ wherein ν.sub.TL is the speed of wheel(s) of the at least one axle facing towards the instantaneous center of velocity (D) of the trailer and ν.sub.TR is the speed of wheel(s) of at least one axle facing away from the instantaneous center of velocity (D) of the trailer.

7. The method according to claim 1, wherein the method further comprises: determining an angle (ε) of a velocity vector (ν.sub.K) of the pivot (K) and the velocity vector (ν.sub.R) of the at least one axle (12) of the towing vehicle (10), calculated by: $\epsilon ={\tan }^{-1}\left(\frac{c}{r}\right).$ wherein c is defined as distance between the center of at least one axle (R) of the towing vehicle and the pivot (K).

8. The method according to claim 7, wherein the articulation angle (φ) is estimated by: $\phi ={\cos }^{-1}\left(\frac{{\upsilon }_T}{{\upsilon }_K}\right)-\epsilon ,$ wherein ν.sub.T is defined as speed of the center of at least one axle (T) of the trailer, ν.sub.K is defined as speed of the center of the pivot (K), calculated by:
υ.sub.K=υ.sub.R/cos(ε), and the ratio between the speeds (ν.sub.T, ν.sub.K) of the center of the at least one rear axle (T) of the trailer and the center of the pivot (K) is expressed by: $\frac{{\upsilon }_T}{{\upsilon }_K}=\cos \left(\epsilon +\phi \right).$

9. The method according to claim 7, wherein the articulation angle (φ) is estimated by: $\phi ={\tan }^{-1}\left(\frac{L}{r_T}\right)-\epsilon ,$ wherein L is defined as distance between the at least one axle of the trailer and the pivot (K).

10. The method according to claim 1, wherein the articulation angle (φ) is estimated by: $\phi ={\tan }^{-1}\left(\frac{L}{r_T}\right),$ wherein L is defined as distance between the at least one axle of the trailer and the pivot (K).

11. A device for estimating an articulation angle (φ) between a towing vehicle and a trailer with respect to a pivot, comprising: (a) a data unit configured to receive and/or store data of: (i) a distance (b) between a steering axle of the towing vehicle and a non-steering axle of the towing vehicle, (ii) a distance (c) between the non-steering axle of the towing vehicle and the pivot, (iii) the distance (L) between the at least one axle of the trailer and the pivot (K), and/or (iv) the distance (w) between the center of the at least one wheel on the at least one axle facing towards an instantaneous center of velocity of the trailer and at least one wheel on the other side of the at least one axle; (b) a determination unit configured to determine: (i) the steering angle (ϑ) of the steering axle, (ii) the speed (ν.sub.R) of the center of at least one axle (R) of the towing vehicle, (iii) the speed (ν.sub.T) of the center of at least one axle (T) of the trailer, and/or (iv) the speed (ν.sub.TL, ν.sub.TR) of at least one wheel of at least one rear axle of the trailer, with respect to the center of the at least one axle (T); (c) an estimation unit configured to determine: (i) the distance (r) between the instantaneous center of velocity (P) of the towing vehicle and the center of at least one axle (R) the towing vehicle representative for a rotation of the towing vehicle about the instantaneous center of velocity (P) of the towing vehicle, (ii) the distance (r.sub.T) between the instantaneous center of velocity (D) of the trailer and the center of at least one axle (T) of the trailer representative for a rotation of the trailer about the instantaneous center of velocity (D) of the trailer, (iii) the speed (ν.sub.K) of the center of the pivot (K), (iv) the angle (ε) of the velocity vector (ν.sub.K) of the pivot (K) and the velocity vector (ν.sub.R) of the at least one axle of the towing vehicle, and/or (v) the ratio between the speeds (ν.sub.T, ν.sub.K) of the center of the at least one rear axle (T) of the trailer and the center of the pivot, in order to estimate the articulation angle (φ); and (d) an output unit configured to output the articulation angle (φ).

12. The device according to claim 11, wherein the speed of at least one wheel of at least one rear axle are the speeds (ν.sub.TL, ν.sub.TR) of opposing wheels of the at least one axle.

13. The device according to claim 11, wherein the estimation unit comprises a calculation unit to calculate at least one of: (i) the distance (r) between the instantaneous center of velocity (P) of the towing vehicle and the center of at least one axle (R) the towing vehicle representative for a rotation of the towing vehicle about the instantaneous center of velocity (P) of the towing vehicle, (ii) the distance (r.sub.T) between the instantaneous center of velocity (D) of the trailer and the center of at least one axle (T) of the trailer representative for a rotation of the trailer about the instantaneous center of velocity (D) of the trailer, (iii) the speed (ν.sub.K) of the center of the pivot (K), (iv) the angle (ε) of the velocity vector (ν.sub.K) of the pivot (K) and the velocity vector (ν.sub.R) of the at least one axle of the towing vehicle, or (v) the ratio between the speeds (ν.sub.T, ν.sub.K) of the center of the at least one rear axle (T) of the trailer and the center of the pivot.

14. A driving assistance system for a towing vehicle, comprising: the device for estimating an articulation angle between the towing vehicle and a trailer with respect to a pivot according to claim 11.

15. A commercial vehicle comprising the driving assistance system according to claim 14.

16. A computer product comprising a non-transitory computer readable medium having stored thereon program code which, when executed by one or more processors, carries out the acts of: determining a distance (r) between an instantaneous center of velocity (P) of the towing vehicle and a center of at least one axle (R) of the towing vehicle representative for a rotation of the towing vehicle about the instantaneous center of velocity (P) of the towing vehicle and/or a distance (r.sub.T) between an instantaneous center of velocity (D) of the trailer and a center of at least one axle (T) of the trailer representative for a rotation of the trailer about the instantaneous center of velocity (D) of the trailer; determining at least one instantaneous speed (ν.sub.R, ν.sub.T, ν.sub.TL, ν.sub.TR) representative for a wheel speed of at least one wheel of the towing vehicle and/or the trailer, wherein the at least one instantaneous speed (ν.sub.R, ν.sub.T, ν.sub.TL, ν.sub.TR) refers to the at least one determined distance (r, r.sub.T); and estimating the articulation angle (φ) based on the at least one determined instantaneous speed and the at least one determined distance (r, r.sub.T).

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0056] FIG. 1 is a top view on a towing vehicle and a trailer attached thereto showing different data applicable for an estimation of the articulation angle between the towing vehicle and the trailer with respect to a pivot;

[0057] FIG. 2 is a diagram showing the geometric relationships between speed vectors and angles, respectively;

[0058] FIG. 3 is an enlarged view of a rear axle portion of the trailer and respective geometric ratios; and

[0059] FIG. 4 is a schematic representation of a device for estimating an articulation angle between the towing vehicle and the trailer with respect to the pivot.

DETAILED DESCRIPTION OF THE DRAWINGS

[0060] FIG. 1 shows top view on a towing vehicle 10 and a trailer 20 attached thereto showing different data applicable for an estimation of the articulation angle φ between the towing vehicle 10 and the trailer 20 with respect to a center of a king pin K as pivot.

[0061] The towing vehicle 10 comprises a front axle 11, which is the steering axle in the given exemplary embodiment, and a rear axle 12, which is the non-steering axle in the given exemplary embodiment. The center of the front axle 11 is denoted by F and the center of the rear axle 12 is denoted by R. Accordingly, a wheelbase as the distance b between the front axle 11 and the rear axle 12 is the distance between point F and point R. In accordance with a steering angle the direction of a vector of the speed ν.sub.F of the center of the front axle 11 with respect to the point F corresponds to the steering angle of the wheels of the front axle 11 with respect to the longitudinal axis of the towing vehicle, which extends between point F and point R. Since the rear axle 12 is a non-steering axle, a vector of the speed ν.sub.R of the center of the rear axle 12 with respect to the point R remains directed in the longitudinal direction of the towing vehicle 10.

[0062] The towing vehicle 10 comprises the king pin K about which the trailer 20 pivots in response to the instantaneous steering angle ϑ resulting in the articulation angle φ between the longitudinal axis of the towing vehicle 10 and the longitudinal axis of the trailer 20, which extends between the king pin K and a center T of rear axles 21, 22, 23 of the trailer 20 to be described later. A vector of the speed ν.sub.K of the center of the king pin K corresponds an angle ε. A distance c is the distance between the center of the kingpin K and point R in the longitudinal direction of the towing vehicle.

[0063] Upon application of the steering angle the towing vehicle 10 represents a rotating rigid body rotating about point P as instantaneous center of velocity (ICV) of the towing vehicle 10. A distance r as the distance between point P and point R can be expressed by:

r=b/tan(ϑ)  (equation (1)).

[0064] Accordingly, the instantaneous distance r can be determined based on the distance b between point F and point R as given input data and the instantaneous steering angle ϑ.

[0065] The trailer 20 comprises a first rear axle 21, a second rear axle 22 and a third rear axle 23. The rear axles 21, 22 and 23 are represented by a point T as center of the rear axles 21, 22, 23 of the trailer 20. Since the rear axles 21, 22 and 23 are non-steering axles, a vector of the speed ν.sub.T of the center of the rear axles 21, 22, 23 with respect to the point T remains directed in the longitudinal direction of the trailer 20. A distance L is the distance between the point T and the center of the king pin K in the longitudinal direction of the trailer 20.

[0066] Upon application of the steering angle on the front axle 11 of the towing vehicle 10, the trailer 20 represents a rotating rigid body rotating about point D as instantaneous center of velocity (ICV) of the trailer 20. A distance r.sub.T is the distance between point D and point T.

[0067] FIG. 2 is a diagram showing the geometric relationships between speed vectors ν.sub.R, ν.sub.K and ν.sub.T and angles ε and φ.

[0068] As apparent from FIG. 2, the angle ε is the angle between the vector of the speed ν.sub.K with respect to point K and the vector of the speed ν.sub.R with respect to point R and can be expressed by:

[00009]$\begin{array}{cc}\epsilon ={\tan }^{-1}\left(\frac{c}{r}\right).& \left(\mathrm{equation}\left(4\right)\right)\end{array}$

[0069] Further, the speed ν.sub.K with respect to the center of the king pin K can be calculated by:

υ.sub.K=υ.sub.R/cos(ε)  (equation (6)).

[0070] Accordingly, the speed ν.sub.T with respect to point T and the angle between ν.sub.K and ν.sub.T being ε+φ can be expressed by:

[00010]$\begin{array}{cc}{v}_T=v_K\cos \left(\epsilon +\phi \right)=v_R\frac{\cos \left(\epsilon +\phi \right)}{\cos \left(\epsilon \right)}=v_R\cos \left(\epsilon +\phi \right)/\cos \left(\epsilon \right).& \left(\mathrm{equation}\left(10\right)\right)\end{array}$

[0071] FIG. 3 shows an enlarged view of a rear axle portion of the trailer and respective geometric ratios. In concrete, the rear part of the trailer 20 comprising the rear axles 21, 22, 23 is shown.

[0072] Each of the rear axles 21, 22, 23 of the trailer 20 comprises a left wheel as wheel facing towards the instantaneous center of velocity D, and a right wheel as wheel facing away from the instantaneous center of velocity D. Even though the exemplary embodiment shows only one left and one right wheel per axle, each of the axles may provide more than one left and/or right wheel, which may be represented by one left or right wheel in FIG. 3.

[0073] A distance between point D as instantaneous center of velocity of the trailer 20 and each wheel of the rear axles 21, 22, 23 is proportional to the wheel speed of such wheels. For example, if the trailer 20 turns to the left, the following equation may be used:

[00011]$\begin{array}{cc}\frac{v_{TL}}{r_0}=\frac{v_{\mathrm{TR}}}{r_0+w},& \left(\mathrm{equation}\left(11\right)\right)\end{array}$

[0074] wherein ν.sub.TL is the speed of the left wheel, ν.sub.TR the speed of the right wheel, r.sub.0 the distance between the point D as instantaneous center of velocity of the trailer 20 and the left wheel and w is the distance between the left and the right wheel.

[0075] Accordingly, the distance r.sub.0 can by expressed by:

[00012]$\begin{array}{cc}{r}_0=w.Math.\frac{\min \left(v_{\mathrm{TL}},v_{\mathrm{TR}}\right)}{abs\left(v_{\mathrm{TL}}-v_{\mathrm{TR}}\right)},& \left(\mathrm{equation}\left(3\right)\right)\end{array}$

[0076] Further, the distance r.sub.T between point D as instantaneous center of velocity of the trailer 20 and point T can be expressed by:

r.sub.T=r.sub.0+w/2  (equation (2)),

[0077] In accordance with the geometric relationships and speeds ν.sub.F, ν.sub.R, ν.sub.K and ν.sub.T or ν.sub.TL and ν.sub.TR, respectively, representative of respective wheel speeds, the articulation angle φ between the respective longitudinal axes of the towing vehicle 10 and the trailer 20 with respect to the center of the king pin K as pivot can be estimated based on the geometric data and instantaneous wheel speeds. In the following, exemplary embodiments of respective methods are presented.

[0078] According to a first exemplary embodiment of the method for estimating the articulation angle φ, the method uses the geometric data of the towing vehicle 10, here the distance b between the front axle 11 and the rear axle 12, and the distance c between the rear axle 12 and the center of the king pin K, the instantaneous steering angle ϑ, the speed ν.sub.R of the center of the rear axle 12 of the towing vehicle with respect to point R, and the speed ν.sub.T of the center of the rear axles 21, 22, 23 of the trailer 20 with respect to point T as input data. In principle, the geometric data may be provided by a database to be selected according to the specific towing vehicle 10 and trailer 20 as preset and/or as constant preset. The steering angle may be provided in accordance with a control signal causing the steering and/or by respective sensor data. The speeds ν.sub.R and ν.sub.T may also be estimated in accordance with respective control signals with respect to a driving speed, acceleration or deceleration, and/or by a sensor signals, for example by direct measurements or indirect measurements representative of the speeds ν.sub.R and/or ν.sub.T.

[0079] Based on the distance b between the front axle 11 and the rear axle 12 of the towing vehicle 10 and the instantaneous steering angle ϑ, the distance r between point P as instantaneous center of velocity of the towing vehicle 10 and the rear axle 12 of the towing vehicle 10 is calculated by equation (1), that is:

r=b/tan(ϑ)  (equation (1)).

[0080] Further, the angle ε between the vectors of the speed ν.sub.R of the center of the rear axle 12 of the towing vehicle 10 and the speed ν.sub.K of the center of the kingpin K is calculated by equation (4), that is:

[00013]$\begin{array}{cc}\epsilon ={\tan }^{-1}\left(\frac{c}{r}\right).& \left(\mathrm{equation}\left(4\right)\right)\end{array}$

[0081] According to the available data, the speed ν.sub.K of the center of the king pin K is calculated by equation (6), that is:

υ.sub.K/υ.sub.R/cos(ε)  (equation (6)).

[0082] However, the speed ν.sub.K of the center of the king pin K may also be determined as input data in term of being available in accordance with a control signal or by sensor data as direct or indirect measurement. Nevertheless, the calculation may reduce the required amount of data to be provided as input data.

[0083] As the ratio between the speed ν.sub.T of the center of the rear axles 21, 22, 23 of the trailer 20 and the speed ν.sub.K of the center of the kingpin K can be expressed by:

[00014]$\begin{array}{cc}\frac{v_T}{v_K}=\cos \left(\epsilon +\phi \right),& \left(\mathrm{equation}\left(5^{\prime }\right)\right)\end{array}$

[0084] the articulation angle φ is estimated by equation (5), that is:

[00015]$\begin{array}{cc}\phi ={\cos }^{-1}\left(\frac{{\upsilon }_T}{{\upsilon }_K}\right)-\epsilon ,& \left(\mathrm{equation}\left(5\right)\right)\end{array}$

[0085] In summary, the articulation angle φ according to the first embodiment of the method for estimating the articulation angle φ is estimated based on the input data, i.e. the distance b between the front axle 11 and the rear axle 12, and the distance c between the rear axle 12 and the center of the king pin K, the instantaneous steering angle ϑ, the speed ν.sub.R of the center of the rear axle 12 of the towing vehicle with respect to point R, and the speed ν.sub.T of the center of the rear axles 21, 22, 23 of the trailer 20 with respect to point T, and the respectively calculated variables, i.e. the distance r between point P as instantaneous center of velocity of the towing vehicle 10 and the rear axle 12 of the towing vehicle 10, the angle ε between the vectors of the speed ν.sub.R of the center of the rear axle 12 of the towing vehicle 10 and the speed ν.sub.K of the center of the kingpin K, and the speed ν.sub.K of the center of the king pin K.

[0086] Consequently, as a basic principle, the articulation angle φ is estimated by using the wheel speed(s) of the towing vehicle 10 and the trailer 20 and steering angle as time varying signals. Specifically, the articulation angle φ is estimated by using the wheel speed(s) of the non-steering axle of the towing vehicle 10 and/or the non-steering axle of the trailer 20 and steering angle as time varying signals. More specifically, the articulation angle φ is estimated by using the geometric parameters of towing vehicle axle- and king pin bases.

[0087] According to a second exemplary embodiment of the method for estimating the articulation angle φ, the method uses the geometric data of the trailer 20, here the distance L between the point T and the center of the king pin K in the longitudinal direction of the trailer 20 and the distance w between the left and the right wheels of the rear axles 21, 22, 23 of the trailer 20, and the speed ν.sub.TL of the left wheels of the rear axles 21, 22, 23 of the trailer 20 as well as the speed ν.sub.TR of the right wheels of the rear axles 21, 22, 23 of the trailer 20 as input data.

[0088] Based on the distance w between the left and the right wheels of the rear axles 21, 22, 23 of the trailer 20 and the speed ν.sub.TL of the left wheels of the rear axles 21, 22, 23 of the trailer 20 as well as the speed ν.sub.TR of the right wheels of the rear axles 21, 22, 23 of the trailer 20, the distance r.sub.0 between the point D as instantaneous center of velocity of the trailer 20 and the left wheel is calculated by equation (3), that is:

[00016]$\begin{array}{cc}{r}_0=w.Math.\frac{\min \left({\upsilon }_{\mathrm{TL}},{\upsilon }_{\mathrm{TR}}\right)}{\mathrm{abs}\left({\upsilon }_{\mathrm{TL}}-{\upsilon }_{\mathrm{TR}}\right)}.& \left(\mathrm{equation}\left(3\right)\right)\end{array}$

[0089] Further, the distance r.sub.T between point D as instantaneous center of velocity of the trailer 20 and point T is calculated by equation (2), that is:

r.sub.T=r.sub.0+w/2  (equation (2)).

[0090] Since the sum of the angle ε and articulation angle φ can be expressed by:

[00017]$\begin{array}{cc}\epsilon +\phi ={\tan }^{-1}\left(\frac{L}{r_T}\right),& \left(\mathrm{equation}\left(8^{\prime }\right)\right)\end{array}$

[0091] the articulation angle φ can be expressed by equation (8), that is:

[00018]$\begin{array}{cc}\phi ={\tan }^{-1}\left(\frac{L}{r_T}\right)-\epsilon .& \left(\mathrm{equation}\left(8\right)\right)\end{array}$

[0092] According to the second exemplary embodiment of the method for estimating the articulation angle φ, the angle ε is set to 0 as being neglected. Consequently, the articulation angle φ is estimated by equation (9), that is:

[00019]$\begin{array}{cc}\phi ={\tan }^{-1}\left(\frac{L}{r_T}\right).& \left(\mathrm{equation}\left(9\right)\right)\end{array}$

[0093] As per the above, the second exemplary embodiment of the method for estimating the articulation angle φ does not require any data with respect to the towing vehicle 10.

[0094] In summary, the articulation angle φ according to the second embodiment of the method for estimating the articulation angle φ is estimated based on the input data of the trailer 20, i.e. the distance L between the point T and the center of the king pin K in the longitudinal direction of the trailer 20, and the distance w between the left and the right wheels of the rear axles 21, 22, 23 of the trailer 20, and the speed ν.sub.TL of the left wheels of the rear axles 21, 22, 23 of the trailer 20 as well as the speed ν.sub.TR of the right wheels of the rear axles 21, 22, 23 of the trailer 20, and the respectively calculated variables, i.e. the distance r.sub.0 between the point D as instantaneous center of velocity of the trailer 20 and the left wheel, and the distance r.sub.T between point D as instantaneous center of velocity of the trailer 20 and point T.

[0095] Consequently, as a basic principle, the articulation angle φ is estimated by using the wheel speed(s) of the trailer 20 as the only time varying signals. Specifically, the articulation angle φ is estimated by using the wheel speed(s) of the non-steering axle of the trailer 20 as time varying signals. More specifically, the articulation angle φ is estimated by using the wheel speed(s) of the trailer 20 on both sides on the same axle, preferably on the non-steering axles, as time varying signals. Preferably, the geometric input data may be restricted to the geometric data of the axle- and wheelbases of the trailer 20.

[0096] According to a third exemplary embodiment of the method for estimating the articulation angle φ, the method combines the first and second embodiment of the method for estimating the articulation angle φ. Accordingly, the input data comprises the geometric data of the towing vehicle 10, here the distance b between the front axle 11 and the rear axle 12, and the distance c between the rear axle 12 and the center of the king pin K, and the geometric data of the trailer 20, here the distance L between the point T and the center of the king pin K in the longitudinal direction of the trailer 20, and the distance w between the left and the right wheels of the rear axles 21, 22, 23 of the trailer 20. Further, the input data comprises the instantaneous steering angle ϑ, the speed ν.sub.R of the center of the rear axle 12 of the towing vehicle 10 with respect to point R, and the speed vim of the left wheels of the rear axles 21, 22, 23 of the trailer 20 as well as the speed ν.sub.TR of the right wheels of the rear axles 21, 22, 23 of the trailer 20.

[0097] Based on the distance b between the front axle 11 and the rear axle 12 of the towing vehicle 10 and the instantaneous steering angle ϑ, the distance r between point P as instantaneous center of velocity of the towing vehicle 10 and the rear axle 12 of the towing vehicle 10 is calculated by equation (1), that is:

r=b/tan(ϑ)  (equation (1)).

[0098] Further, the angle ε between the vectors of the speed ν.sub.R of the center of the rear axle 12 of the towing vehicle 10 and the speed ν.sub.K of the center of the kingpin K is calculated by equation (4), that is:

[00020]$\begin{array}{cc}\epsilon ={\tan }^{-1}\left(\frac{c}{r}\right).& \left(\mathrm{equation}\left(4\right)\right)\end{array}$

[0099] Based on the distance w between the left and the right wheels of the rear axles 21, 22, 23 of the trailer 20, and the speed vim of the left wheels of the rear axles 21, 22, 23 of the trailer 20, as well as the speed ν.sub.TR of the right wheels of the rear axles 21, 22, 23 of the trailer 20, the distance r.sub.0 between the point D as instantaneous center of velocity of the trailer 20 and the left wheel is calculated by equation (3), that is:

[00021]$\begin{array}{cc}{r}_0=w.Math.\frac{\min \left({\upsilon }_{\mathrm{TL}},{\upsilon }_{\mathrm{TR}}\right)}{\mathrm{abs}\left({\upsilon }_{\mathrm{TL}}-{\upsilon }_{\mathrm{TR}}\right)}.& \left(\mathrm{equation}\left(3\right)\right)\end{array}$

[0100] Further, the distance r.sub.T between point D as instantaneous center of velocity of the trailer 20 and point T is calculated by equation (2), that is:

r.sub.T=r.sub.0+w/2  (equation (2)).

[0101] Since the sum of the angle ε and articulation angle φ can be expressed by:

[00022]$\begin{array}{cc}\epsilon +\phi ={\tan }^{-1}\left(\frac{L}{r_T}\right),& \left(\mathrm{equation}\left(8^{\prime }\right)\right)\end{array}$

[0102] the articulation angle φ is calculated by equation (8), that is:

[00023]$\begin{array}{cc}\phi ={\tan }^{-1}\left(\frac{L}{r_T}\right)-\epsilon .& \left(\mathrm{equation}\left(8\right)\right)\end{array}$

[0103] Consequently, as a basic principle, the articulation angle φ is estimated by using the wheel speed(s) of the towing vehicle 10 and the trailer 20 and steering angle as time varying signals. Specifically, the articulation angle φ is estimated by using the wheel speed(s) of the non-steering axle of the towing vehicle 10 and/or the non-steering axle of the trailer 20 and steering angle as time varying signals. More specifically, the articulation angle φ is estimated by using the geometric parameters of towing vehicle axle- and king pin bases. More specifically, the articulation angle φ is estimated by using the wheel speed(s) of the trailer 20 on both sides on the same axle, preferably on the non-steering axles, as time varying signals. Preferably, the geometric input data refers to the trailer geometric parameters of the towing vehicle axle- and kingpin bases plus the trailer axle- and wheelbases.

[0104] FIG. 4 shows a schematic representation of a device for estimating an articulation angle φ between the towing vehicle 10 and the trailer 20 with respect to the center of the king pin K as pivot.

[0105] The device comprises: [0106] a data unit 30 configured to receive and/or store data of: [0107] the distance b between a steering axle, preferably the front axle 11, of the towing vehicle 10 and a non-steering axle, preferably the rear axle 12, of the towing vehicle 10, [0108] the distance c between the non-steering axle of the towing vehicle 10 and the center of the king pin K as pivot, [0109] the distance L between the at least one axle 21, 22, 23 of the trailer 20 and the center of the king pin K as pivot, and/or [0110] the distance w between the center of the at least one wheel on the at least one axle 21, 22, 23 of the trailer 20 facing towards the instantaneous center of velocity D of the trailer 20 and at least one wheel on the other side of the at least one axle 21, 22, 23 of the trailer 20, [0111] a determination unit 40 configured to determine: [0112] the steering angle of the steering axle, [0113] the speed VR of the center of at least one axle represented by point R of the towing vehicle 10, [0114] the speed ν.sub.T of the center of at least one axle represented by point T of the trailer 20, and/or [0115] the speed ν.sub.TL and/or ν.sub.TR of at least one wheel of at least one rear axle 21, 22, 23 of the trailer 20, preferably the speeds ν.sub.TL and ν.sub.TR of opposing wheels of the at least one axle 21, 22, 23 with respect to the center of the at least one axle represented by point T, [0116] an estimation unit 50 configured to determine: [0117] the distance r between the instantaneous center of velocity P of the towing vehicle 10 and the center of at least one axle R the towing vehicle 10 representative for a rotation of the towing vehicle 10 about the instantaneous center of velocity P of the towing vehicle 10, [0118] the distance r.sub.T between the instantaneous center of velocity D of the trailer 20 and the center of at least one axle represented by point T of the trailer 20 representative for a rotation of the trailer 20 about the instantaneous center of velocity D of the trailer 20, [0119] the speed ν.sub.K of the center of the king pin K as pivot, [0120] the angle ε of the velocity vector ν.sub.K of the king pin K as pivot and the velocity vector w of the at least one axle 12 of the towing vehicle 10, and/or [0121] the ratio between the speeds ν.sub.T and ν.sub.K of the center of the at least one rear axle represented by point T of the trailer 20 and the center of the king pin K as pivot, [0122] to estimate the articulation angle φ; and [0123] an output unit 60 configured to output the articulation angle φ.

[0124] The device may be configured to execute any of the previously described methods for estimating an articulation angle φ between the towing vehicle 10 and the trailer 20 with respect to the pivot according to the first to second embodiment. However, the device may be alternatively configured to provide only one or two of such methods or any other applicable method in accordance with the invention. Accordingly, the respective device is configured to determine and calculate data at least required for such execution.

[0125] The invention has been described with respect to exemplary embodiments. However, the invention is not limited to the exemplary embodiments.

[0126] The foregoing disclosure has been set forth merely to illustrate the invention and is not intended to be limiting. Since modifications of the disclosed embodiments incorporating the spirit and substance of the invention may occur to persons skilled in the art, the invention should be construed to include everything within the scope of the appended claims and equivalents thereof.

LIST OF REFERENCE SIGN

[0127] 10 towing vehicle [0128] 11 front axle (towing vehicle) [0129] 12 rear axle (towing vehicle) [0130] 20 trailer [0131] 21 first rear axle (trailer) [0132] 22 second rear axle (trailer) [0133] 23 third rear axle (trailer) [0134] 30 data unit [0135] 40 determination unit [0136] 50 calculation unit (estimation unit) [0137] 60 output unit [0138] b distance between front and rear axle (towing vehicle) [0139] c distance between rear axle and king pin (towing vehicle) [0140] D instantaneous center of velocity (ICV) point (trailer) [0141] F center of front axle (towing vehicle) [0142] K center of king pin (pivot) [0143] L distance between K (king pin (pivot)) and T (center of rear axle(s) of trailer) [0144] P instantaneous center of velocity (ICV) point (towing vehicle) [0145] r distance between P (ICV point of towing vehicle) and R (center of rear axle of towing vehicle) [0146] r.sub.T distance between D (ICV point of trailer) and T (center of rear axle(s) of trailer) [0147] r.sub.0 distance between D (ICV point of trailer) and facing wheel(s) of rear axle(s) (trailer) [0148] R center of rear axle (towing vehicle) [0149] T center of rear axle(s) (trailer) [0150] w distance between wheels on opposite sides of the rear axle(s) (trailer) [0151] ε angle between velocity vectors ν.sub.K and ν.sub.R [0152] ϑ steering angle [0153] ν.sub.F speed of center of front axle (towing vehicle) [0154] ν.sub.K speed of center of king pin (pivot) [0155] ν.sub.R speed of center of rear axle (towing vehicle) [0156] ν.sub.T speed of center of rear axle(s) (trailer) [0157] ν.sub.TL speed of left wheel(s) of rear axle(s) (trailer; facing towards D) [0158] ν.sub.TR speed of right wheel(s) of rear axle(s) (trailer; facing away from D) [0159] φ articulation angle