EP4702537A1

EP4702537A1 - Calibration of sensors on articulated vehicle

Info

Publication number: EP4702537A1
Application number: EP24721254.1A
Authority: EP
Inventors: Rui OLIVEIRA; Sandipan Das
Original assignee: Scania CV AB
Current assignee: Scania CV AB
Priority date: 2023-04-25
Filing date: 2024-04-18
Publication date: 2026-03-04
Also published as: SE2350492A1; WO2024225951A1; SE547120C2

Abstract

A method and control arrangement for extrinsic calibration of a vehicle sensor (D2). A reference frame (RF) is located on a first body (3a) of an articulated vehicle (1) and the vehicle sensor (D2) is arranged on a second body (3b) of the articulated vehicle (1), wherein the first body (3a) and the second body (3b) are connected with a coupling (2). The method comprises calibrating (S31) the vehicle sensor (D2) by finding a transformation between the reference frame (RF) and the vehicle sensor (D2) based on first sensor data indicative of a pose of the reference frame (RF) obtained at a plurality of points in time, second sensor data indicative of a pose of the vehicle sensor (D2) obtained at the plurality of points in time, and a model defining an articulation angle (β) between the first body (3a) and the second body (3b).

Description

Calibration of sensors on articulated vehicle Technical Field The present disclosure relates to calibration of sensors, and in particular to calibration of sensors on articulated vehicles. Background Autonomous vehicles and Advance Driver-Assistance System, ADAS, technologies rely on accurate perception systems. These perception systems use information from a multitude of sensors of different modalities, such as cameras, radars, lidars, and others, to provide a rich view of the surroundings. Before information from these sensors can be combined into a single reference frame, a transformation between the sensors must be found. The exact locations of the sensors are then estimated, also referred to as extrinsic calibration. Extrinsic calibration of sensors on vehicles may be performed offline when the vehicle is standing still, or online while the vehicle is driving. Offline calibration techniques are often time consuming and require additional hardware such as fiducial markers. Online calibration techniques may be performed by comparing estimated states of the sensor to those in a relevant sensor frame. However, vehicle sensors on articulated vehicles have not yet been considered for online calibration. Hence, there is a need for improved calibration techniques for sensors arranged on articulated vehicles that can be performed online. Summary It is an objective to provide techniques that facilitate calibration of sensors arranged on articulated vehicles. These objectives and others are at least partly achieved by the method, control arrangement and vehicle according to the independent claims, and by the embodiments according to the dependent claims. According to a first aspect, the disclosure relates to a method for extrinsic calibration of a vehicle sensor. A reference frame is located on a first body of an articulated vehicle and the vehicle sensor is arranged on a second body of the articulated vehicle, wherein the first body and the second body are connected with a coupling. The method comprises calibrating the vehicle sensor by finding a transformation between the reference frame and the vehicle sensor frame based on first sensor data indicative of a pose of the reference frame obtained at the plurality of points in time, second sensor data indicative of a pose of the vehicle sensor obtained at a plurality of points in time, and a model defining an articulation angle between the first body and the second body. The method enables calibration of vehicle sensors on articulated vehicles where the transformation between vehicle sensors on a first body and second body changes over time. This has until now been an unsolved problem. By modelling the articulation angle, the change in articulation angle can be considered during calibration, thereby enabling accurate calibration to be performed online while the vehicle is driving, i.e., in real-time. According to some embodiments, the method is performed online while the vehicle is driving. Hence, the method may be performed with onboard computing in real-time, or at least via data processing in real-time, e.g., in the cloud. Online calibration enables, for example, continuous refinement of previous calibration during driving. According to some embodiments, the calibrating comprises modelling a transform between the reference frame and the vehicle sensor between multiple time points of the plurality of points in time using a hand-eye equation including an additional component modelling articulation between the first body and the second body, based on the model of the articulation angle. According to some embodiments, the additional component comprises a transformation matrix describing the articulation angle between the first body and the second body of the articulated vehicle between the multiple time points of the plurality of points in time, based on the model of the articulation angle. According to some embodiments, the model of the articulation angle is based on one or more of kinematics of the articulated vehicle, a measure indicative of a turning angle of a foremost of the first body and the second body of the articulated vehicle, such as a steering angle or a wheel angle, and a velocity of a foremost of the first body and the second body of the articulated vehicle. ^{According to some embodiments, the articulation angle is defined as ^^^^ = 2 ∙} ^^^^₁ is the rate of change of the foremost of the first body and the second body of the articulated vehicle, ^^^^₂ is the length of the second body from its rear axle to the coupling point, Δt is a time between two measurements, and const is a constant. According to some embodiments, the method comprises providing calibrated sensor data from the vehicle sensor to a control arrangement of the vehicle for use in autonomous driving. The autonomous driving functionality will then have better data to rely on. According to some embodiments, the method comprises obtaining, from a sensor having a known pose in the reference frame, the first sensor data indicative of a pose of the reference frame obtained at the plurality of points in time, wherein the calibrating comprises determining estimated poses of the reference frame based on the first sensor data indicative of a pose of the reference frame obtained at the plurality of points in time, and using the estimated poses of the reference frame for finding a transformation between the reference frame and the vehicle sensor. According to some embodiments, the method comprises obtaining, from the vehicle sensor, the second sensor data indicative of the pose of the vehicle sensor obtained at the plurality of points in time, wherein the calibrating comprises determining estimated poses of the vehicle sensor based on the second sensor data indicative of the pose of the vehicle sensor obtained at the plurality of points in time and using the estimated poses of the vehicle sensor for finding a transformation between the reference frame and the vehicle sensor. According to some embodiments, the calibration comprises performing an optimization for minimizing an error between the estimated poses of the reference frame and the vehicle sensor with the model of the articulation angle as a constraint. According to some embodiments, the calibrating comprises determining extrinsic parameters of the vehicle sensor. According to some embodiments, the vehicle sensor is any of an image sensor, a lidar, a radar or any other vehicle sensor. According to some embodiments, the calibrating comprises determining extrinsic parameters of the vehicle sensor including estimating a rotation component and a translation component. According to some embodiments, the reference frame is one of a base frame or a sensor frame of an image sensor, a lidar, a radar or any other vehicle sensor. According to a second aspect, the disclosure relates to a computer program comprising instructions which, when the computer program is executed by a computer, cause the computer to carry out the method according to the first aspect. According to a third aspect, the disclosure relates to a computer-readable medium comprising instructions which, when executed by a computer, cause the computer to carry out the method according to the first aspect. According to a fourth aspect, the disclosure relates to a control arrangement for extrinsic calibration of a vehicle sensor arranged on an articulated vehicle, comprising control circuitry to perform the method according to any step of the first aspect. The same effects as of with the first aspect can be achieved. According to a fifth aspect, the disclosure relates to an articulated vehicle comprising the control arrangement according to the fourth aspect Brief description of the drawings The embodiments disclosed herein are illustrated by way of example, and by not by way of limitation, in the figures of the accompanying drawings. Like reference numerals refer to corresponding parts throughout the drawings, in which Fig.1 illustrates an angled side view of an example rigid vehicle. Fig.2 illustrates transformations between measurements at two time instances with two vehicle sensors on the vehicle in Fig.1. Fig.3 illustrates an angled side view of an example non-rigid vehicle. Fig.4 illustrates transformations between measurements at two time instances with two vehicle sensors on the vehicle in Fig.3. Fig.5 is an illustration of a tractor-trailer vehicle and notations. Fig. 6 is a control arrangement according to an example embodiment of the disclosure. Figs. 7-8 are flowcharts of example methods for extrinsic calibration of vehicle sensors on an articulated vehicle. Detailed description Calibration of sensors is needed to perform advanced vehicle operations such as driver assistance and autonomous driving. During calibration, the exact location of the sensors in the vehicle is determined, which is a basis to obtain good perception estimates in a common reference frame when using data from a multitude of sensors. To obtain the best results, this calibration needs to be performed regularly in an online fashion, i.e., as the vehicle is driving along the road. Online calibration may be defined as calibration that is performed with onboard computing in real- time, or at least via data processing in real-time, e.g., in the cloud. The calibration is performed without any human intervention, e.g., automatically. For example, online calibration is performed on the fly directly in the vehicle itself without manual intervention, typically when some driving maneuvers are performed in the vehicle to create rich sensor data. No external means are needed, like fiducial markers or similar. Calibration of a sensor is generally made in relation to a known reference frame. In online calibration, this reference frame may be a frame of another sensor, or a base frame of the vehicle. For a vehicle with only one rigid body, there exists techniques for online calibration where the states, for example the poses, of the sensor and the reference frame are estimated from sensor data at different time instances while the vehicle is moving, and a relation between the estimated poses is established using the well-known hand-eye equation taking the vehicle movement into account. As the vehicle body is rigid, there is no change in the relation stemming from the body during movement. However, for an articulated vehicle, the rear body will move differently from the front body, and there will then be a change in the relation from the articulation between the front body and the rear body. The inventors have realized how to track how the articulation angle changes during movement, and to take this into consideration when performing calibration in articulated scenarios. The present disclosure relates to extrinsic calibration. Extrinsic calibration aims to obtain the extrinsic parameters that define the geometric relationship, that is, the rotation matrix and translation vector, between two coordinate frames. Extrinsic parameters include the rotation matrix R and translation vector t between two coordinate frames. The extrinsic parameters typically include six degrees of freedom (DoF). A frame in this disclosure may be defined as a coordinate frame with an origin and three orthogonal axes, typically referred to as the x, y and z-axes. A frame may also be referred to as a coordinate system. A reference frame is a coordinate frame that is known in relation to a known coordinate frame, such as the world coordinate frame, i.e., a world coordinate system. The reference frame may be a vehicle reference frame, i.e., a base frame, or the reference frame may be a sensor reference frame, i.e., a sensor frame of the sensor. The base frame of a vehicle is typically located in the center of a vehicle rear axis. The pose of an object comprises the position and orientation of an object. If coordinate frames are located on the object and another object, a geometric relationship between these two coordinate frames may be represented by a transformation matrix including a rotation matrix R and a translation vector t. The rotation matrix R describes the orientation of one coordinate frame relative to the other coordinate frame. The translation vector describes the position of the origin of one coordinate frame with respect to the other coordinate frame. Hence, a pose comprises a rotation component and a translation component. The pose includes, for example, six DoF. A vehicle sensor is a sensor used in a vehicle for perception purposes, for example a lidar, a radar or an image sensor. The vehicle sensor is a kind of exteroceptive sensor, or external state sensor, that perceives and gathers information from the vehicle’s environment. A vehicle sensor may also be referred to as an autonomous sensor as it is used by an autonomous vehicle in autonomous driving. Lidar stands for Light detection and ranging. Lidar is a distant sensing technique that produces infrared or laser light pulses that reflect off target objects. The lidar detects these reflections and the time between emissions and reception of the light pulse allows for distance estimate. A lidar is an active sensor. The output of a lidar is typically a point cloud. Radar stands for Radio detection and ranging. A radar emits electromagnetic (EM) waves within a region of interest and receives reflections from targets for signal processing and range information. It can be used to determine relative speed and position of identified obstacles using the Doppler property of the EM waves. A radar is an active sensor. An image sensor is for example a camera. The camera or image sensor produces images of the surroundings by detecting lights emitted from the surroundings on a photosensitive surface (image plane) using a camera lens. A camera is a passive sensor. For better understanding of the invention, an example with a rigid vehicle will first be described in relation to Figs.1 and 2. Fig.1 illustrates an angled side view of an example vehicle 1a. Vehicle 1a is for example a car, bus, truck, or other kind of vehicle, in particular a land/road vehicle. Any such vehicle 1a comprises a body and chassis, engine/motor parts, drive transmission and steering parts, suspension and brake parts, and electrical parts. The body may be integrated with the chassis, or the body and the chassis may be different parts that are fixed to each other, e.g., with bolts. The chassis is the main mounting for all parts of the vehicle and comprises a steel frame. The chassis further comprises a front axis and a rear axis. The electrical parts comprise an electronic system including electronic control units (ECUs). Vehicle 1a is a rigid vehicle, meaning that it only comprises one body. Hence, vehicle sensors will typically be mounted on the same rigid body. For illustrative purposes, two vehicle sensors D1, D2 are illustrated on vehicle 1a, whereof vehicle sensor D1 is located in the front-right and vehicle sensor D2 is located in rear-left corners of the vehicle 1a. A base frame ‘B’ is also denoted, located at a rear axis of vehicle 1a. To perform calibration between the vehicle sensors D1, D2, one needs to figure out the transformation ^^^^ _{^^^^1 ^^^^2} which relates the front-right vehicle sensor D1 with the rear-left vehicle sensor D2, as illustrated in Fig. 2. Fig. 2 illustrates transformations between measurements at two time instances t(i-1) and t(i) with the two vehicle sensors D1, D2 on the vehicle in Fig.1a. Sensor frames of the sensors D1, D2 are illustrated as SF _^^^^1 and SF _^^^^2, respectively. To figure out the transformation ^^^^ _{^^^^1 ^^^^2} online, the vehicle 1a gathers or collects multiple measurements from the vehicle sensors D1, D2 as it is driving, and afterwards processes this information by taking into account the vehicle movement between measurements, which is given by transformation The transformation ^^^^ _{^^^^1( ^^^^−1) ^^^^(1)} corresponds to the transformation of the vehicle poses between time ^^^^( ^^^^ − 1) and time ^^^^( ^^^^). To determining the transformation ^^^^ _{^^^^1 ^^^^2}, a hand-eye equation can be established as: The hand-eye equation can be further decomposed into a rotation part and a translation part. The rotation part of the hand-eye equation can be solved as known to the skilled person using various solution strategies, for example a least-square method. Examples how to formulate and solve hand-eye equations can be found from R. Y. Tsai and R. K. Lenz, "A new technique for fully autonomous and efficient 3D robotics hand/eye calibration," in IEEE Transactions on Robotics and Automation, vol. 5, no. 3, pp. 345-358, June 1989, doi: 10.1109/70.34770. Thereafter the translation part of the hand-eye equation can be solved when the rotation matrix ^^^^ _{^^^^ ^^^^ ^^^^ ^^^^} is known. Alternatively, the rotation part and the translation part can be solved simultaneously, for example using dual quaternions or a least- square based method. An example method for calibrating sensors with rigid body constraints is outlined in S. Das, L. a. Klinteberg, M. Fallon and S. Chatterjee, "Observability-Aware Online Multi-Lidar Extrinsic Calibration," in IEEE Robotics and Automation Letters, vol. 8, no. 5, pp. 2860-2867, May 2023, doi: 10.1109/LRA.2023.3262176, hereafter referred to as Sandipan et al, (2023). The article presents methods for real-time extrinsic calibration of multiple lidars in a vehicle base frame. Here, absolute Global Navigation Satellite System (GNSS) and estimated lidar poses are matched in real-time. The error between poses estimated by a lidar(s) and the GNSS are minimized in an optimization process to find the extrinsic calibration parameters. Rotation components are compared to improve the robustness of the solution. Also, only a set of poses comprising maximum mutual information is selected based on observability criteria, instead of using all corresponding poses. This allows to identify a subset of the poses helpful for real- time calibration. Stopping criteria is used for ensuring calibration completion. The inventors of the present invention have realized how the calibration technique in Sandipan et al, (2023) and other techniques for calibration of sensors on rigid bodies can be modified to also cover calibration of vehicle sensors on articulated vehicles. Such techniques will be exemplified in the following with relation to Figs.3 to 9. Fig.3 illustrates an angled side view of an example articulated vehicle 1b. Vehicle 1b comprises a truck with a tractor 2 and two trailers 3a, 3b connected via a respective coupling 4a, 4b, but vehicle 1b may be any kind of articulated vehicle such as a truck, a bus or even a train. Vehicle 1b may include one, two or three, or more, trailers, connected in series with a respective coupling to a trailer. Each of the tractor 2 and trailers 4a, 4b comprises three axes, but could alternatively have more or less axes. An articulated vehicle is a non-rigid vehicle. Such a vehicle comprises two or more bodies connected in series by a respective coupling. Each body also comprises an individual chassis, and optionally one or more of: engine/motor parts, drive transmission and steering parts, suspension and brake parts, and electrical parts. Each body may be integrated with the respective chassis in a unibody design, or each body and the respective chassis may be different parts that are fixed to each other, e.g., with bolts. The respective chassis is the main mounting for all parts and comprises a steel frame. The chassis further comprises at least a front axis and a rear axis. The body is typically rigid. The electrical parts comprise an electronic system including electronic control units (ECUs). The coupling 4a, 4b is for example a pivot joint, or any other suitable joint. The coupling 4a, 4b enables a preceding body to turn relative to a succeeding body, or opposite. Vehicle 1b is illustrated with a first vehicle sensor D1 and a second vehicle sensor D2. It should be understood that the vehicle 1b may comprise more vehicle sensors of the same or different modalities. However, for brevity, only two vehicle sensors D1, D2 are illustrated. The vehicle sensors D1, D2 may be any kind of vehicle sensor as explained herein. The first vehicle sensor D1 is arranged on a front-right corner of the first trailer 3a, and the second vehicle sensor D2 is arranged on a rear-left corner of the second trailer 3b. The first vehicle sensor D1 is already calibrated, hence, it has a known pose in a reference frame of vehicle 1b. The reference frame is for example a sensor frame of the first vehicle sensor D1, that is known in a base frame, e.g., base frame B2 of the first trailer 3a, of the vehicle 1b. Alternatively, the reference frame is the base frame B2 of the first trailer 3a. In other words, a reference frame RF is located on a first body 3a of the articulated vehicle 1b, and a vehicle sensor D2 is arranged on a second body 3b of an articulated vehicle 1b, wherein the first body 3a and the second body 3b are connected with a coupling 4b. In the following a method for extrinsic calibration of a vehicle sensor arranged on an articulated vehicle, for example the vehicle 1b in Fig. 3, will be described. The method may be performed online while the vehicle is driving. Thereby the vehicle sensors may be calibrated repeatedly (or continually in an ongoing manner) without any interruption of the operation of the vehicle 1b. The method may be performed by a control arrangement 30 (Fig.6) arranged in vehicle 1b. The control arrangement 30 is for example one or more ECUs. The vehicle sensor is any kind of sensor as explained herein. For simplicity, in the following the vehicle sensor will be referred to as vehicle sensor D2 arranged on the second trailer 3b, but it should be understood that the vehicle sensor may be arranged on any of the vehicle bodies of an articulated vehicle. The vehicle sensor is calibrated in relation to a reference frame. As explained, the reference frame is a frame located on another body than the vehicle sensor is arranged on. In the following the reference frame will be referred to as located on the first trailer 3a and is a sensor frame of another vehicle sensor D1. The disclosure also relates to an articulated vehicle comprising the control arrangement 30 as described herein, for example the vehicle in Fig.1b. It should be understood that vehicle 1b in Fig.2 is an example only, and that a vehicle in this disclosure may have, e.g., more or less axes and other means not illustrated herein. The method will now be described with reference to the flowchart in Fig.7 and Figs.4-5. The method aims to calibrate a vehicle sensor, for example vehicle sensor D2, with respect to a reference frame. The method is with advantage performed online while the vehicle 1 is driving. Hence, online calibration of vehicle sensors D2 on articulated vehicles 1b is enabled. The method is based on finding a transformation between the vehicle sensor D2 and the reference frame RF, where the vehicle sensor D2 and the reference frame RF are located on different bodies of the same articulated vehicle. For finding the transformation, the method needs measurement data while the vehicle is driving. In the method, sensor data from a first sensor D1 and the second sensor D2 are used to find the transformation. To find here means to determine, estimate or calculate. The sensors are capturing sensor data at a plurality of points in time as the vehicle is moving. The type of sensor data depends on what type of sensors being used. For example, if the sensors are lidar sensors, the measurements are typically given as point clouds. The pose of the frame of the respective sensors D1, D2 may be determined by state estimation, as will be more explained in the following. Hence, the sensor data is indicative of the pose of the sensor, respectively. The first sensor data is sensor data from a sensor D1, for example a vehicle sensor, that has a known pose in the reference frame. Hence, by determining the pose of the vehicle sensor D1 will inherently also determine the pose of the reference frame, as the relation between the vehicle sensor D1 and the reference frame RF is known. The reference frame is for example a base frame of the vehicle. In other words, in some embodiments, the method comprises obtaining S21, from a sensor D1 having a known pose in the reference frame RF, first sensor data indicative of a pose of the reference frame RF obtained at the plurality of points in time. The vehicle sensor D1 is here exemplified as a lidar, but it should be understood that the vehicle sensor D1 may be any kind of vehicle sensor, such as an image sensor, a lidar, a radar or any other vehicle sensor. In a special case the sensor D1 is a GNSS-module. The reference frame may thus be any one of a base frame or a sensor frame of an image sensor, a lidar, a radar or any other vehicle sensor. The second sensor data comprises measurements by the second sensor at a plurality of points in time. For example, if the vehicle sensor D2 is a lidar, the second sensor data comprises measurements by the lidar at a plurality of points in time. In other words, the method comprises obtaining S11, from the vehicle sensor D2, second sensor data indicative of the pose of the vehicle sensor D2 obtained at the plurality of points in time. The vehicle sensor D2 is here exemplified as a lidar, but it should be understood that the vehicle sensor D2 may be any kind of vehicle sensor, such as an image sensor, a lidar, a radar or any other vehicle sensor. In some embodiments, the calibration requires finding the poses of the frames of the first sensor D1 and the second sensor D2, respectively. For this purpose, state estimation can be used. State estimation methods take the sensor data as input and output a state of the same sensor, for example a pose of the frame. For a lidar, state estimation is referred to as estimating lidar odometry. Instead of lidar odometry, other kinds of state estimation may be used, for example in case the vehicle sensor is another type of sensor than lidar. Estimated poses may be determined using common estimation techniques as known to the skilled person, for example as outlined in D. Wisth, M. Camurri, S. Das and M. Fallon, “Unified Multi-Modal Landmark Tracking for Tightly Coupled Lidar-Visual-Inertial Odometry,” in IEEE Robotics and Automation Letters, vol.6, no.2, pp.1004-1011, April 2021, or W. Xu, Y. Cai, D. He, J. Lin and F. Zhang, "FAST-LIO2: Fast Direct LiDAR-Inertial Odometry," in IEEE Transactions on Robotics, vol. 38, no. 4, pp. 2053-2073, Aug. 2022, doi: 10.1109/TRO.2022.3141876. Hence, in some embodiments, the method comprises determining estimated poses of the reference frame RF based on the second sensor data indicative of a pose of the reference frame RF obtained at the plurality of points in time, and using the estimated poses of the reference frame RF for finding a transformation between the reference frame RF and the vehicle sensor D2. The estimated poses of the reference frame are typically in a base frame of the vehicle. In some embodiments, the method comprises determining estimated poses of the vehicle sensor D2 based on the first sensor data indicative of the pose of the vehicle sensor D2 obtained at the plurality of points in time, and using the estimated poses of the vehicle sensor D2 for finding a transformation between the reference frame RF and the vehicle sensor D2. The estimated poses of the vehicle sensor D2 are in the vehicle sensor frame. Hence, the calibration S31 is based on first sensor data indicative of a pose of the reference frame RF obtained at the plurality of points in time, and second sensor data indicative of a pose of the vehicle sensor D2 obtained at a plurality of points in time. The method comprises calibrating S31 the vehicle sensor D2 by finding a transformation between the reference frame RF and the vehicle sensor D2, based on the above-mentioned sensor data. The calibration is a kind of extrinsic calibration, and typically includes determining extrinsic parameters of the vehicle sensor D2. Hence, the calibrating S31 may comprise determining extrinsic parameters of the vehicle sensor D2 including estimating a rotation component and a translation component. Calibration S31 may use any available technique that details finding a transformation between the vehicle sensor D2 and the reference frame RF, based on the above-mentioned sensor data, for example the techniques outlined in Sandipan et al, (2023). The method described herein complements such techniques by modelling an articulation angle β between the first body 3a and the second body 3b. Modelling here includes making a representation of the articulation angle. Hence, the calibration S31 is further based on a model defining an articulation angle β between the first body 3a and the second body 3b. In the following it will be described how such techniques can be complemented, and how the articulation angle β can be modelled. Fig. 4 illustrates transformations between measurements at two time instances t(i-1) and t(i) with two vehicle sensors D1, D2 on the articulated vehicle in Fig.3. The tractor 2 is here obviated for ease of illustration. If it was a rigid body motion as illustrated with a dashed second trailer (and as in Fig. 2), the frame ^^^^ ^^^^ _{^^^^2( ^^^^−1)} of vehicle sensor D2 would end up at ^^^^ ^^^^_D2(i)′ at timestamp t(i), as illustrated in Equation (1). However, since the rear part of the vehicle 1b is not rigid, the actual frame position of the vehicle sensor D2 at t(i) would be ^^^^ ^^^^ _{^^^^2( ^^^^)}. Based on this, a new transformation matrix can be established as depicted in the modified hand-eye equation below: Compared to Equation (1), the Equation (2) has an additional term, a transformation between D2’ to D2, in other words ^^^^ _{^^^^2( ^^^^)}′ _{^^^^2( ^^^^)}. The additional term models the articulation, thus, the articulation angle ^^^^, based on vehicle kinematics. Hence, in some embodiments, the calibrating S31 comprises modelling a transformation between the reference frame RF and the vehicle sensor D2 between multiple time points of the plurality of points in time using a hand-eye equation including an additional component modelling articulation between the first body 3a and the second body 3b, based on the model of the articulation angle β. An example how this transformation ^^^^ _{^^^^2( ^^^^)}′ _{^^^^2( ^^^^)} can be modelled will now be explained with reference to Fig.5. Fig.5 is a schematic illustration of a tractor-trailer vehicle with notations, but it should be understood that the tractor-trailer vehicle represents any kind of articulated vehicle including two bodies connected with a coupling. The model of the tractor is given by: where, and ^^^^₁ are the positional coordinates of the middle of the rear axle of the tractor, and ^^^^₁ is the orientation of the tractor. is the rate of orientation change of the tractor, or foremost body, of the vehicle. Here it is basically the angular velocity around the z-axis. The orientation of the tractor is for example obtained from a steering angle sensor as a steering angle, or a wheel angle sensor as a wheel angle. Such measurement may be retrieved from the CAN network, ^^^^₁ is the tractor wheelbase length and ^^^^ is the angle of the steering wheels. ^^^^₂ is the length of the trailer from its rear axle to the coupling point, also referred to as a hitching point. ^^^^ =� ^^^^ _^^^^, ^^^^ _^^^^�, is the linear velocity of the tractor, where ^^^^ _^^^^ and ^^^^ _^^^^ are the longitudinal _{and lateral velocity components.} ^‖ _. ^‖ _{denotes norm of ^^^^ given by,} ^‖ _^^^^ ^‖ At any given point in time [ ^^^^, ^^^^₁, ^^^^₁, ^^^^₁, ^^^^₁, ^^^^₂] are known. Thus, the trailer axle center can be calculated as, ^^^^₂ = ^^^^₁ − ^^^^₂ cos ^^^^₂ (6) ^^^^₂ = ^^^^₁ − ^^^^₂ sin ^^^^₂ (7) The change of orientation of the trailer, ^^^^₂, can be obtained using, where, ^^^^ = ^^^^₁ − ^^^^₂. Considering that ^^^^₁ = 0 gives: ‖ ^^^^‖. (9) Since ^^^^ = ^^^^₁ − ^^^^₂, then follows that, This is a system of ordinary differential equations (ODE) of the form, where ^^^^ = ^^^^ 1, and ^^^^ = _^^^^2. This ODE can be solved as known in the art, for example using a MATLAD ODE solver. The result is the articulation angle ^^^^ as follows: where, ∆ ^^^^ denotes the time period during which ^^^^ is supposed to be determined. “const” is a constant from the integration when solving the ODE. Hence, equation (12) describes the model of the articulation angle. Thus, in some embodiments, the model of the articulation angle β is based on one or more of kinematics of the articulated vehicle 1b, a measure indicative of a turning angle α of a foremost of the first body 3a and the second body 3b of the articulated vehicle 1, such as a steering angle or a wheel angle, and a velocity v of a foremost of the first body 3a and the second body 3b of the articulated vehicle 1b. The kinematics of the vehicle is typically known beforehand and for example saved in a memory means 32 (Fig.6) in the vehicle. The steering angle or wheel angel may be retrieved from the CAN network, for example as measured by a steering angle sensor or wheel angle sensor, respectively. The velocity v may also be retrieved from the CAN network, for example as measured by a velocity sensor. After computing ^^^^, the articulation angle can be transformed into the transformation matrix for the additional term in equation (2). Since the rotation of the trailer is planar, only the rotation around the z-axis is used in the transformation matrix. Also, only the change in trailer angle is considered, and the translation component is discarded, as the vehicle sensors are rigidly attached on the vehicle. Thus, the transformation becomes: Hence, in some embodiments, the additional component comprises a transformation matrix ^^^^ _{^^^^2( ^^^^)}′ _{^^^^2( ^^^^)} describing the articulation angle β between the first body 3a and the second body 3b of the articulated vehicle 1b between the multiple time points of the plurality of points in time, based on the model of the articulation angle β. In other words, the transformation matrix is the articulation angle ^^^^ represented in rotation matrix form. The calibration S31 typically also comprises performing an optimization for solving the Equation (2). Hence, according to some embodiments, the calibration S31 comprises performing an optimization for minimizing an error between estimated poses of the reference frame RF and the vehicle sensor D2, with the model of the articulation angle as a constraint. The optimization will result in determining the rotation component of the extrinsic parameters and/or the translation component of the extrinsic parameters. In the optimization, the hand- eye equation can be further decomposed into a translation part using the determined rotation component in the previous step. The optimization may be based on any available technique, such as a least-square based method. Alternatively, the rotation part and the translation part can be solved simultaneously, for example using dual quaternions or a least-square based method. The flowchart in Fig. 8 illustrates an example calibration method which includes additional steps that can be included in the calibration method illustrated in Fig.7. The example calibration method follows the steps of the “Algorithm 1” as outlined on page 5 in Sandipan et al, (2023). The method as outlined in Sandipan et al, (2023) assumes rigid body constraints, but can be used with non-rigid body constraints if using hand-eye equation complemented with the additional term as previously described for modelling articulation based on vehicle kinematics. It should be noted that in Sandipan et al, (2023), data from sensors along with collocated IMUs are used for pose estimation of the sensor. However, alternatively, the poses of the sensors may be estimated only using the sensor data without the need for any collocated IMU. The method in Fig.8 presumes that the steps S11 and S12 of Fig.7 have already been made, and takes the information obtained from these steps as input. Step S31 of Fig.7 may then include some or all of the steps S12-S132. These steps will now be explained in more detail. Step S12 includes determining sensor poses in corresponding sensor frames. The sensor poses are determined based on the first sensor data indicative of the pose of the vehicle sensor obtained in step S11, and the second sensor data indicative of a pose of a reference frame obtained in step S21. In “Algorithm 1”, the first sensor data is GNSS, reference measurements using a GNSS unit located in one body in the vehicle. Hence, the GNSS data is indicative of the pose, over time, of the GNSS unit. All the GNSS poses are in base frame, B are normalized with respect to the initial pose. The GNSS unit also provides Inertial Measurement Unit (IMU) measurements in the G frame using its internally embedded IMU. These measurements are then transformed to base frame, B. The second sensor data is lidar measurements with a vehicle sensor being a lidar located in another body of the vehicle. In some embodiments, step S12 includes to estimate senor poses in corresponding sensor frames using common estimation techniques as known to the skilled person and as previously illustrated, again for example as outlined in D. Wisth, M. Camurri, S. Das and M. Fallon, “Unified Multi-Modal Landmark Tracking for Tightly Coupled Lidar-Visual-Inertial Odometry,” in IEEE Robotics and Automation Letters, vol.6, no.2, pp.1004-1011, April 2021, or W. Xu, Y. Cai, D. He, J. Lin and F. Zhang, "FAST-LIO2: Fast Direct LiDAR-Inertial Odometry," in IEEE Transactions on Robotics, vol.38, no.4, pp.2053-2073, Aug.2022, doi: 10.1109/TRO.2022.3141876. In some embodiments, where an integrated Inertial Measurement Unit (IMU) with a lidar is used as vehicle sensor, step S12 may include to estimate the frame ^^^^ _{^^^^1 ^^^^ ^^^^} of the lidar from lidar measurement with lidar odometry and the frame ^^^^ _{^^^^1 ^^^^ ^^^^} of the IMU, from time t(1) to time t(N), using inertial state propagation equations as outlined in Eq.1 in Das, Sandipan et al, (2023). The following steps S22 to S42 refer to the general online calibration algorithm description between any sensor and reference GNSS poses. In an initial calibration step S22, the sensor poses are aligned. This may include to compute an initial transformation from the base frame B to lidar frame L in terms of rotation and translation, hence ^^^^ _{^^^^ ^^^^} and ^^^^ _{^^^^ ^^^^}, by aligning the set of translation components ^^^^ _{^^^^ ^^^^} with respect to ^^^^ _{^^^^ ^^^^}, for example as outlined in S. Umeyama, “Least-squares estimation of transformation parameters between two point patterns,” IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 13, no. 04, pp. 376–380, 1991, or B. K. Horn, “Closed-form solution of absolute orientation using unit quaternions,” Journal of the Optical Society of America, vol. 4, no.4, pp.629–642, 1987. Hence, the initial extrinsics can be recovered using a 3D-point cloud alignment method by aligning the initial set of translation components, by breaking the problem into rotation and translation parts. The method thereafter checks in step S32 if an initial calibration is found. If not, and ^^^^ _{^^^^ ^^^^} is unknown, then ^^^^ _{^^^^ ^^^^} is estimated using Eq.3 and Eq.5 in Sandipan et al, (2023). In step S42, trajectory and rotation alignment errors are defined as cost functions, for example as outlined in Eq.33 in Sandipan et al, (2023). These errors, or cost functions, are used as stopping criteria for a following optimization process. The following steps S52 to S122 are included in an optimization process where the errors from step S42 are used as stopping criteria. Hence, the optimization process is conducted until the errors are below certain predefined thresholds. In step estimated using lidar odometry as commonly known. Instead of lidar odometry, other kinds of state estimation may be used, for example in case the vehicle sensor is another type of sensor than lidar. Step S62 includes finding a close correspondence of poses based on timestamp. Hence, finding closest ^^^^ _^^^^ with respect to ^^^^ _{^^^^( ^^^^)} based on timestamp correspondence of the poses. The method then checks in step S72 if the number of corresponding poses is equal to a predefined size, e.g., N number of poses. If not, the method returns to step S52. If yes, the method comprises in a step S82 to estimate rotation component by aligning rotation part in poses with known initial calibration. In Sandipan et al, (2023), this corresponds to computing ^^�^^^ _{^^^^ ^^^^} between ^^^^ _^^^^ and ^^^^ _^^^^ by solving for ^^^^ using Eq.26 in Sandipan et al, (2023), where ^^^^ is the Davenport matrix. After step S82, the rotation alignment error is computed in step S92 as defined in step S42. In step 102, it is checked if the alignment error improved. This may be done by checking if the error of the estimated rotation component is smaller or equal to the error of the previously estimated rotation component in step S82. If not, the method returns to step S52. If yes, then the rotation component, ^^^^ _{^^^^ ^^^^} is updated with the estimated rotation component. If yes in step S102, in a step S112 the translation component is estimated. Here, this corresponds to solving Eq. (2). In Sandipan et al, (2023), this corresponds to solving for^� ^^^^ using Eq.28 and Eq.29 in Sandipan et al, (2023), complemented with the additional term for the articulation as outlined in Equation (2) above. Step S112 also includes computing the trajectory alignment error using the definition determined in step S42, after the translation component has been estimated. In a step S122, the method checks if the trajectory alignment error has improved and is less than a threshold. This may be done by checking if the error of the estimated translation component is smaller or equal to the error of the previously estimated translation component in step S52. If not, the method returns to step S52. If yes, the estimated translation component becomes the actual translation component ^^^^ _{^^^^ ^^^^}. Thereafter the extrinsic calibration parameters of the vehicle sensor are updated with the new rotation component ^^^^ _{^^^^ ^^^^} and the translation component ^^^^ _{^^^^ ^^^^}. Typically, these parameters are saved in a memory, e.g., memory 32. Sensor measurements, that is sensor data, from the vehicle sensor can then be calibrated using the updated extrinsic calibration parameters of the vehicle sensor. The calibrated sensor data may be used for various purposes. In some embodiments, the method includes providing S41 calibrated sensor data from the vehicle sensor 10 to a control arrangement 30 of the vehicle 1 for use in autonomous driving. The sensor data in the reference frame can then be fused with other sensor data in the same reference frame into a common picture of the surroundings of vehicle 1 and provide a more accurate base for decisions. Fig. 6 illustrates a control arrangement 30. The control arrangement 30, comprises control circuitry to perform the method according to any one of the steps, examples or embodiments as described herein. The method may be implemented as a computer program. The computer program then comprises instructions which, when the computer program is executed by a computer, cause the computer to carry out the method according to any one of the aspects, embodiments or examples as described herein. The computer is for example included in the control arrangement 30. More in detail, the control arrangement 30 comprises processor means 34 and memory means 32. The processor means 34 comprises one or more processors. Memory means 32 comprises one or more memories. The control arrangement 30 may include one or more Electronic Control Units (ECUs). The output from the vehicle sensors may provide input to an autonomous control system of the control arrangement 30, for use in autonomous driving. Each sensor converts sensed events or changes of a property into a signal or data that is sent to or collected by the control arrangement 30. Such signals or data are, for example, sent over a CAN (controller area network), or similar, of vehicle 1b. The disclosure also relates to a 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 aspects, embodiments or examples as described herein. The computer-readable memory is for example one or more of the memories in the control arrangement 30. An autonomous vehicle may be defined as a vehicle that can travel without human input. Autonomous vehicles typically use vehicle sensors to sense their surroundings. Autonomous driving may be defined as assisted driving at different levels from driver assistance such as cruise control where the vehicle only controls accelerating/decelerating, up to full driving automation where the vehicle performs all driving tasks without driver interaction. ADAS is an abbreviation for Advance Driver-Assistance System, where the vehicle only can control steering and accelerating/decelerating without driver interaction. The terminology used in the description of the embodiments as illustrated in the accompanying drawings is not intended to be limiting of the described method, control arrangement or computer program. Various changes, substitutions and/or alterations may be made, without departing from disclosure embodiments as defined by the appended claims. The term “or” as used herein, is to be interpreted as a mathematical OR, i.e., as an inclusive disjunction; not as a mathematical exclusive OR (XOR), unless expressly stated otherwise. In addition, the singular forms "a", "an" and "the" are to be interpreted as “at least one”, thus also possibly comprising a plurality of entities of the same kind, unless expressly stated otherwise. It will be further understood that the terms "includes", "comprises", "including" and/ or "comprising", specifies the presence of stated features, actions, integers, steps, operations, elements, and/ or components, but do not preclude the presence or addition of one or more other features, actions, integers, steps, operations, elements, components, and/ or groups thereof. A single unit such as e.g., a processor may fulfil the functions of several items recited in the claims. The present disclosure is not limited to the above-described preferred embodiments. Various alternatives, modifications and equivalents may be used. Therefore, the above embodiments should not be taken as limiting the scope of the disclosure, which is defined by the appending claims.

Claims

Claims 1. A method for extrinsic calibration of a vehicle sensor (D2), wherein the method is performed by a control arrangement (30), and wherein a reference frame (RF) is located on a first body (3a) of an articulated vehicle (1b), and the vehicle sensor (D2) is arranged on a second body (3b) of the articulated vehicle (1b), wherein the first body (3a) and the second body (3b) are connected with a coupling (4b), the method comprising: - calibrating (S31) the vehicle sensor (D2) by finding a transformation between the reference frame (RF) and the vehicle sensor (D2) based on: o first sensor data indicative of a pose of the reference frame (RF) obtained at a plurality of points in time, o second sensor data indicative of a pose of the vehicle sensor (D2) obtained at the plurality of points in time, and o a model defining an articulation angle (β) between the first body (3a) and the second body (3b).

2. The method according to claim 1, wherein the method is performed online while the vehicle (1b) is driving.

3. The method according to claim 1 or 2, wherein the calibrating (S31) comprises modelling a transform between the reference frame (RF) and the vehicle sensor (D2) between multiple time points of the plurality of points in time using a hand- eye equation including an additional component modelling articulation between the first body (3a) and the second body (3b), based on the model of the articulation angle (β).

4. The method according to claim 3, wherein the additional component comprises a transformation matrix describing the articulation angle (β) between the first body (3a) and the second body (3b) of the articulated vehicle (1b) between the multiple time points of the plurality of points in time, based on the model of the articulation angle (β).

5. The method according to any one of the preceding claims, wherein the model of the articulation angle (β) is based on one or more of kinematics of the articulated vehicle (1b), a measure indicative of a turning angle (α) of a foremost of the first body (3a) and the second body (3b) of the articulated vehicle (1b), such as a steering angle or a wheel angle, and a velocity (v) of a foremost of the first body (3a) and the second body (3b) of the articulated vehicle (1b).

6. The method according to claim 5, wherein the articulation angle (β) is defined the rate of orientation change of the foremost of the first body (3a) and the second body (3b) of the articulated vehicle (1b) , ^^^^₂ is the length of the second body (3b) from its rear axle to the coupling point, Δt is a time between two measurements, and const is a constant.

7. The method according to any one of the preceding claims, comprising providing (S41) calibrated sensor data from the vehicle sensor (D2) to a control arrangement (30) of the vehicle (1b) for use in autonomous driving.

8. The method according to any one of the preceding claims, comprising: - obtaining (S11), from a sensor (D1) having a known pose in the reference frame (RF), the first sensor data indicative of a pose of the reference frame (RF) obtained at the plurality of points in time, wherein the calibrating (S31) comprises o determining estimated poses of the reference frame (RF) based on the first sensor data indicative of a pose of the reference frame (RF) obtained at the plurality of points in time, and o using the estimated poses of the reference frame (RF) for finding a transformation between the reference frame (RF) and the vehicle sensor (D2).

9. The method according to any one of the preceding claims, comprising: - obtaining (S21), from the vehicle sensor (D2), the second sensor data indicative of the pose of the vehicle sensor (D2) obtained at the plurality of points in time, wherein the calibrating (S31) comprises o determining estimated poses of the vehicle sensor (D2) based on the second sensor data indicative of the pose of the vehicle sensor (D2) obtained at the plurality of points in time and o using the estimated poses of the vehicle sensor (D2) for finding a transformation between the reference frame (RF) and the vehicle sensor (D2).

10. The method according to claims 8 and 9, wherein the calibration (S31) comprises performing an optimization for minimizing an error between estimated poses of the reference frame (RF) and the vehicle sensor (D2) with the model of the articulation angle as a constraint.

11. The method according to any one of the preceding claims, wherein the calibrating (S31) comprises determining extrinsic parameters of the vehicle sensor (D2).

12. The method according to any one of the preceding claims, wherein the vehicle sensor (D2) is any of an image sensor, a lidar, a radar or any other vehicle sensor.

13. The method according to any one of the preceding claims, wherein the calibrating (S31) comprises determining extrinsic parameters of the vehicle sensor (D2) including estimating a rotation component and a translation component.

14. The method according to any one of the preceding claims, wherein the reference frame is one of a base frame or a sensor frame of an image sensor, a lidar, a radar or any other vehicle sensor.

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

16. A 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 claims 1 to 14.

17. A control arrangement for extrinsic calibration of a vehicle sensor (D2) arranged on an articulated vehicle (1b), comprising control circuitry to perform the method according to any one of the claims 1 to 14.

18. An articulated vehicle (1b) comprising the control arrangement (30) according to claim 17.