TECHNICAL FIELD

The present invention relates to a three-dimensional target for a vehicle wheel alignment system, and to a related method. BACKGROUND ART

Vehicle wheel alignment systems are known, in particular for a motor vehicle, which enable automatic measurement of one or more characteristic angles of the set-up of the vehicle, for example the angles of convergence and camber, in order to check the correct reciprocal alignment of the wheels.

In general, vehicle wheel alignment systems are configured to detect the orientation of the plane of each wheel with respect to a reference system (it should be noted that the term "wheel plane" is intended herein as the plane on which the external side surface of the wheel lies), so as to enable suitable corrective actions to be taken, to restore the reciprocal alignment of the wheels.

These systems generally contemplate the use of image acquisition (or capture) devices, which may be positioned on the vehicle lift (which raises, in a known manner, the vehicle under examination) , or on fixed structures, or provided with autonomous movement, located at a distance and freestanding with respect to both the vehicle and the vehicle lift.

Usually, these systems also use suitable targets coupled the wheels of the vehicle to allow highlighting rotation spatial position.

The image acquisition devices are configured to acquire images of the targets, which are then suitably processed by a processing unit to determine the characteristic set-up angles. This operation enables dynamically determining the orientation of the target in space, and then defining the elementary roto- translations regarding the linear and angular movement of each wheel within a single reference system (for example, the reference system of the vehicle) . Afterwards, when these elementary roto-translations are suitably linked with one another, they are used to define further, more complex, rotations and translations, which more specifically concern the set-up and alignment characteristics of the vehicle.

In particular, known systems have traditionally used two- dimensional targets, i.e. comprising a flat surface on which suitably-shaped two-dimensional images are shown and which may be recognised by the image acquisition devices.

However, it has been shown that the use of such two- dimensional targets has the drawback of requiring a stereo system for capturing the images, which entails the presence of a plurality of image acquisition devices and captured images for each observed target. Alternatively, in the case where a single image acquisition device is used, it is necessary to perform a suitable identification procedure for the orientation of the target with respect to the single image acquisition device, by observing the target during a suitable manoeuvre (for example, forwards and backwards, the so-called 'run-out' operation) of the vehicle, or during a suitable manoeuvre of the target. In addition, the acquisition of the geometric characteristics of the two-dimensional target becomes difficult as the inclination of the target changes, and this results in non-uniformity in the accuracy of the measurements taken.

Thus, to overcome the above-mentioned drawbacks, the use of three-dimensional targets (also known as "3D targets") has recently been proposed. For example, International Patent Application

WO 2008/143614 describes a target, defined as three- dimensional, for use in a vehicle wheel alignment system, which comprises two or more flat faces, set at a predetermined angle to each other, on each of which a certain number of two- dimensional target elements are arranged, in particular circular elements having predetermined geometric characteristics .

In this case, the alignment measurement algorithm provides for determining the centres, or barycentres, of the circular shapes of the target elements, and executing a so-called ^> best-fit' algorithm between the detected positions of the above-mentioned centres on the respective planes they belong to and the known positions of the target elements on the real target. For the purposes of executing the processing operations, the target elements are thus assimilated to point elements belonging to a respective plane.

In Patent Applications WO 2011/138662 and WO 2012/090187, in the name of the Applicant, a different target, effectively or actually three-dimensional (i.e. not constituted by the assembly of a number of flat target portions) has been proposed, again for use in a vehicle wheel alignment system.

This target comprises a support structure, to the inner surface of which a plurality of separate target elements, also having three-dimensional shape, in particular a spherical shape, is coupled.

In this case, the alignment measurement algorithm provides for determining the centres, or barycentres, of the spherical shapes of the target elements, and then exploiting, for processing purposes, the fact that the centres are interlinked by a mathematical relation, given by the coupling to a geometric shape, the characteristics of which are known by design. In particular, this algorithm provides for defining a set of three orthogonal axes integral with the target (through the identification of target reference elements) and determining the angles of rotation of this set of three axes with respect to a reference system.

The solution described in the above-mentioned Patent Applications WO 2011/138662 and WO 2012/090187 has several advantages, in particular regarding the precision and reliability of the measurements, related to the three- dimensional configuration of the target and the use of target elements that are also three-dimensional. In fact, three- dimensional information are intrinsically associated with the target, through which it is possible to determine the target's spatial orientation even from just a single two-dimensional image (transforming the two-dimensional information provided by the image capture device into three-dimensional information thanks to the special geometric structure of the target) .

However, three-dimensional target elements, in particular spherical ones, require precision machining to improve the overall measurement result and have to be made of a reflective material to improve acquisition by the image acquisition devices .

It follows that among the components of the alignment measuring system, the cost of producing the targets is normally not negligible.

Furthermore, processing of the acquired images for identifying the individual spherical target elements may not be easy; in fact, due to the three-dimensional surface to which they belong, the target elements tend to overlap, reciprocally hiding each other as the orientation of the target in the reference system of the image acquisition device changes. This drawback may cause measurement errors and also lengthen the measurement times, thereby reducing the number or measurements that may be taken per unit time.

The fact must also be considered that, although having associated the model of the target to a canonical geometric shape (for example a spherical shape) to mathematically link together the positions of the individual target elements (for example spherical ones) and make the correspondence between the real object and the mathematical more stable, the elements used for the construction of the model are still points and, numerically, not fully adequate to compensate for possible imperfections of the real object.

In this field, the need is felt for further perfecting systems of known type for determining the orientation of the wheels of a vehicle, and in particular the targets used, for example with regard to measurement precision, costs, and simplicity of production and implementation.

DISCLOSURE OF INVENTION

The object of the present invention is that of fully, or at least partially, satisfying the above-mentioned need.

According to the present invention, a system and method for determining the orientation of the wheels of a vehicle is provided, substantially as set forth in the appended claims. BRIEF DECRIPTION OF THE DRAWINGS

For a better understanding of the present invention, some preferred embodiments will now be described, purely by way of a non-limitative example and with reference to the accompanying drawings, where:

- Figure 1 is a schematic representation of a vehicle wheel alignment system;

- Figures 2a and 2b are perspective views of a three- dimensional target used in the system of Figure 1, according to different embodiments of the present invention;

- Figures 3a and 3b schematically show the generation of rotation surfaces that may be defined on the target;

- Figures 3c and 3d schematically show the generation of respective rotation surfaces, respectively related to a horizontal or vertical axis of rotation of the target;

- Figures 4a and 4b show schematic perspective views of the target in Figure 2a coupled to the wheel of a vehicle, when the wheel has different angles of orientation;

- Figures 4c and 4d show schematic perspective views of the target in Figure 2b coupled to the wheel of the vehicle, when the wheel has different angles of orientation;

- Figure 5 shows the image of the target in Figure 4b, acquired by an image capture device of the system in Figure 1, in the image plane of that image capture device;

- Figure 6 shows a flowchart of orientation determination operations performed by a processing device of the system in Figure 1 and used for determining the set-up of a vehicle;

- Figures 7a-7c show images of respective embodiments of the target in Figure 2a acquired by an image capture device of the system in Figure 1, in the image plane of that image capture device; and

- Figures 7d-7e show images of the target in Figure 2b, acquired by the image capture device, in the image plane of that image capture device.

BEST MODE FOR CARRYING OUT THE INVENTION

Figure 1 shows, by way of example, a system, indicated as a whole by reference numeral 1, for determining the orientation of the wheels 2 of a vehicle 3 (shown schematically) .

In the example shown, the vehicle 3 is a motor vehicle with four wheels 2, arranged, with respect to a longitudinal axis A of the vehicle, in pairs on the left-hand and right-hand sides, respectively; the vehicle 3 is shown on a vehicle lift 4, of a known type and therefore only shown schematically.

The system 1 comprises a plurality of targets 5, the structure and function of which will be described in detail hereinafter, their number being the same as the number of wheels 2; each target 5 is mechanically coupled to a respective wheel 2 by a coupling element, or coupler 6.

This coupling element (not described in detail herein) may, for example, be made as described in Italian Utility Models IT-0000254272 and IT-0000254273, in the name of the Applicant.

In particular, it is possible to associate with each target 5, a set of three orthogonal axes X _t r _g , Ytrg , Z _{t rg} defining a target reference system SdR _trg A the orientation in space of which corresponds to the orientation of the wheel 2 to which that target 5 is integrally coupled.

The system 1 further comprises a first and a second sensing device 7a and 7b, arranged laterally with respect to the vehicle 3 and with respect to the area where the vehicle 3 is positioned on the vehicle lift 4, respectively on the left- hand side and right-hand side of the vehicle 3 with respect to the longitudinal axis A. The sensing devices 7a and 7b are laterally positioned in a fixed manner with respect to the vehicle 3 (at respective sensing positions) and aligned in a direction transversal to the longitudinal axis A; for example, the sensing devices 7a and 7b are rigidly coupled to the vehicle lift 4, each one to a respective platform of the vehicle lift 4, by a respective releasable coupling mechanism. Furthermore, the sensing devices 7a and 7b are positioned so as to be interposed, along the longitudinal axis A, between the two wheels 2 of the vehicle 3 located on the same side with respect to the longitudinal axis A.

Each sensing device 7a and 7b is equipped with two image capturing devices 8, for example, including a video camera, a camera or similar image capturing instrument, each configured to frame the target 5 associated with a respective wheel 2 of the pair of wheels 2 located on the same side of the longitudinal axis A.

Each image capturing devices 8 has a given optical aperture (or field of view) , for example with a conical shape, indicated by ^λ ν' ; this optical aperture has a sufficient angular opening to allow correct framing of the front and rear targets 5.

In addition, each image capturing device 8 has a respective image reference system SdR defined by a set of three orthogonal axes X _te i, Ytei , Z _te i, where the transverse axes X _te i and Ytei define the image plane associated with the captured two-dimensional images (i.e. the plane on which the dimensions of the objects are evaluated in numbers of pixels), and the orthogonal axis Z _te i coincides with the optical axis of the image capturing device 8.

The system 1 further comprises a processing device 9, for example, in the form of a personal computer or any other processing device provided with a processor or similar processing instrument, operatively coupled to the first and second sensing devices 7a and 7b by means of a suitable communications interface configured to implement wired or preferably wireless data transfer (using any known technique, for example, Bluetooth or WiFi) .

The processing device 9 is configured to process the two- dimensional images of the targets 5 supplied by the sensing devices 7a and 7b, referred to the respective image reference systems SdR on the basis of a suitable alignment algorithm, in order to determine the orientation characteristics of the wheels 2 of the vehicle 3 and the alignment characteristics of the vehicle 3, in a single common reference system (for example that associated with the vehicle 3) .

Each sensing device 7a and 7b may internally include a hardware-based pre-processing unit (not shown here) , for example, including an FPGA (Field Programmable Gate Array) capable of performing, for each image capturing device 8, preliminary processing of the acquired images of the targets 5, identifying certain significant elements on these images. This information is sent to the processing device 9 for implementation of the alignment algorithm. Alternatively, this pre-processing unit, if present, may be separate from the sensing devices 7a and 7b.

Furthermore, to ensure that the sensing devices 7a and 7b provide correct framing of the targets 5 even in the case where the dimensions of the vehicle 3 differ substantially from the average ones, or to remedy inaccurate positioning of the vehicle on the vehicle lift 4, the image capturing devices 8 inside each sensing device 7a and 7b are moveable; in particular, they may be automatically operated to perform a controlled rotation in the horizontal plane.

To this end, a manoeuvring unit (not shown here) is provided, integrated into the respective sensing device 7a and 7b, and designed to jointly rotate the respective optical apertures of the image capturing devices 8 by the same angle of orientation until optimal framing is achieved (in other words, to automatically make use of the positions of the respective targets 5) . In this way, it is possible to adjust the spatial area framed, in order to optimally frame the respective target 5 (i.e. to position, for example, the target 5 substantially at the centre of the optical aperture), as the position of the associated wheel 2 changes, due to, for example: approximative alignment of the vehicle 3 with respect to the vehicle lift 4 ; variation in wheelbase and track from vehicle to vehicle; or even the variation in placement of the wheel 2 internally or externally with respect to the track defined by the platform of the vehicle lift 4 (along a direction orthogonal to the longitudinal axis A) . The system 1 may also comprise a coupling structure, not shown, configured to ensure that a desired relation of reciprocal positioning and orientation is maintained between the image reference systems SdR _te i associated with the sensing devices 7a and 7b, so as to establish a link between the relative angular measurements, and so determine the alignment characteristics of the wheels 2 in a single common reference system (for example, the reference system of the vehicle 3) .

According to one aspect of the present invention, and also referring to Figure 2a, which shows a possible embodiment by way of example, each target 5 has an effective or "real" three-dimensional geometry.

In particular, each target 5 comprises a body 10 having a concave cap shape, defining an inner surface 10a. In one possible embodiment, this inner surface 10a is constituted by, or includes, a rotation surface (i.e. generated by the rotation of a curve about an axis) .

For example, and as schematically shown in Figures 3a and 3b, this rotation surface may be generated by the rotation about an axis A of:

a circular arc, indicated by C, which generates a portion of a hemisphere (Figure 3a); or

an elliptical arc, indicated by C, which generates a portion of an ellipsoid (Figure 3b) .

In greater detail, and as shown in Figures 3c and 3d, considering the plane (XY) of the target reference system SdRtrg , the rotation surface may be alternatively generated by the rotation of a curve (conic) C about axis X _trg (Figure 3c), or about axis Y _trg (Figure 3d) .

In the embodiment shown in Figure 2a and 2b, the inner surface 10a is, or includes, a spherical surface, and the body 10 is constituted by a concave hemisphere, or by a portion of a hemisphere .

The target 5 further comprises a plurality of target regions 12, defined and distributed on the inner surface 10a, and shaped to match the inner surface 10a.

In particular, the target regions 12 have the shape of bands, or strips, arranged along respective characteristic curves of the inner surface 10a, i.e. that identify and characterize the geometry of that single inner surface 10a.

In particular, these characteristic curves interpolate the above-mentioned strips and may be described by conies, which may be interrelated with each other by a known mathematical relation (for example, via a characterization operation) .

In one embodiment, the above-mentioned curves define and identify the rotation surface of the inner surface 10a, representing the intersections between the rotation surface and a set of planes passing through a single line.

Referring again to the schematically shown examples, for example in Figure 2a, the target regions 12 may, for example, be ("horizontally" or "vertically") arranged along:

respective meridians that divide the portion of a hemisphere into horizontal or vertical segments, which all depart from the axis of rotation; or

respective meridians that again divide the portion of an ellipsoid into horizontal or vertical segments.

In a further embodiment, the curves that identify the inner surface 10a may be represented by closed conies, as shown in Figure 2b; also in this case, the curves, linked to each other by mathematical constraints, identify the inner surface 10a of the target 5.

In any case, the above-mentioned curves identify the orientation and position of the target 5 and, in particular, are represented by conies, for example, circular or elliptical arcs or closed conic curves resting on the inner surface 10a of the target 5 and belonging to mutually non-parallel planes (the curves being inclined with respect to each other by a given angle) ; all of the curves may be identified inside the images acquired by the image capturing devices 8.

In the embodiment shown in Figure 2a, the target regions 12 are located along meridians arranged vertically on the spherical inner surface 10a of the body 10, extending in a continuous manner from a top end to a bottom end of the body 10, with respect to a longitudinal axis of symmetry of the body 10.

Alternatively, these target regions 12 could be distributed along meridians arranged horizontally on the inner surface 10a.

In yet another alternative, according to the embodiment shown in Figure 2b, the target regions could be interpolated by respective closed conic curves.

The target regions 12 include reflective material, formed, for example, by adhesive or depositing application techniques or the application of reflective material (for example, by spraying, pad printing or other known techniques), on the inner surface 10a of the body 10 of the target 5.

If necessary, the definition of the bands of the target regions 12 could be aided by the use of a grid (or similar element) , suitably shaped to leave the target regions 12 uncovered and having the desired shape. Advantageously, the target regions 12 are in contrast against the background defined by the inner surface 10a, which includes light radiation absorbent material.

In one possible embodiment, the target regions 12 include an adhesive elastic film, in which high-refractivity glass microspheres are partially incorporated.

In the embodiment shown in Figure 2a, the target regions 12, numbering N (where N is a whole number greater than two) , are angularly equidistant and therefore subdivide the inner surface 10a into regular "segments". For example, the target regions 12 are angularly separated from each other by an angle of 15° and are thirteen in number.

Furthermore, the number N is a function of the angular aperture of the inner surface 10a of the target 5; in the case where this surface includes a rotation surface, the number N is a function of the radius R of the rotation surface: given that, for the same angle, the linear distance on the inner surface 10a increases with the radius R, the larger this radius R, the more the angle that separates two mutually adjacent target regions 12 may decrease.

The above-mentioned angle may be defined by the following expression :

ang ¾ atan (d/R)

where R is the radius of the rotation surface and d, for example equal to 10 mm, is the above-mentioned linear distance on the inner surface 10a.

Therefore, the number N may be given by the following relation :

N ¾ 180/ang + 1. In the embodiment described in Figure 2b, the target regions 12 are closed curves of different sizes (in particular, in terms of a related main axis or diameter) so as to appear to be one inside the other. These curves belong to a single inner surface, and could therefore be partially covered due to the effect of rotation of the target 5, but could never cross each other. Furthermore, the curves belong to surfaces that are not parallel to each other, so that the observation of the behaviour of these curves will completely define the set of three angles it is wished to identify. The numbering of these curves could be set starting from the innermost one, always visible, and, in general, it will not be needed to use reference elements to identify the rotation; the two reference notches in Figure 2b, indicated by the wording 'ref' , could be used to position one of the transverse axes in an absolute manner .

In general, the target regions 12 are arranged in a known manner (or defined during the characterization of the target 5) on the inner surface 10a.

In any case, in the described solution for the target 5, the target regions 12 constitute the elements that are framed and processed by the respective image capturing device 8 (the so- called "target marks" of the target 5) .

Advantageously, distributed regions of the target 5 (arranged along the above-mentioned characteristic curves of the associated inner surface 10a) are then used for processing purposes .

In particular, the above-mentioned processing provides for establishing a link between a set of conies defined in three- dimensional space (for example, circles or, more generically, ellipses) of the reference system (SdR _trg ) of the target 5 and a corresponding set of conies (for example ellipses) identified in the reference system (SdR _te i ) of the image capturing device 8. The determination of the rotation between these two sets of conies corresponds to the calculation of the rotation between the target reference system SdR _trg associated with the target 5 and the image reference system SdR _te i associated with the image capturing device 8, i.e. to the solution of the problem of determining the set-up angles of the wheel 2 coupled to the target 5.

The description of the target 5 or the associated body 10 by using conies is more compact with respect to using points, and contains the position and orientation information of the body 10 in a more accurate manner. The result of the roto- translation calculation is therefore more stable, as it less subject to errors made during acquisition of the image (in this case, identified by continuous lines, instead of a limited number of individual points) .

The circumferences or, more generically, the ellipses (defined on the target 5 by arranging the bands of reflective material inside its concave, spherical inner surface 10a, for example, along its meridians or along closed curves), may be identified with greater precision in the acquired image. For example, in the representation in Figure 2a, where the meridians appear as vertically arranged segments of ellipses, the processing is relatively simple from the image scanning standpoint.

In particular, it is also known that the mathematical representation of a conic results in a symmetrical matrix, which is easy to process mathematically.

For processing purposes, it is also convenient to define, in the case of the embodiment in Figure 2a, one of the target regions 12 as the reference area, indicated by Ref in Figure 2a; this reference area is recognisable, for example by geometric characteristics, for example by a different thickness of the relevant band of reflective material (a greater thickness in the example in Figure 2a) .

The detection of this reference area Ref in the acquired images may enable reconstructing the order of the target regions 12 on the inner surface 10a of the target 5 and the orientation of the target reference system SdR _trg (as pointed out, this operation may be omitted in the case where the target 5 implements the embodiment in Figure 2b) .

In particular, the origin could be located at the centre of the "zero order" ellipse (i.e. the one located on plane (XY) , the orthogonal direction of which identifies axis Z _trg ) ; the origin and the above-mentioned plane identify the reference system, except for a degree of freedom (the rotation of the axes X _trg and Y _trg about axis Z _trg ) · This rotation may be blocked by defining the direction of axis Y _trg by means of the intersection between plane (XY) and the plane on which the reference area Ref lies, in the case of the representation in Figure 2a (while in the case of Figure 2b, the two ¾ef references could define the direction of one of the transverse axes during the characterization of the target) .

In Figure 4a, the target 5 is schematically shown in a possible embodiment (in particular, that of Figure 2a), coupled to wheel 2 of the vehicle 3 in such a way that the plane defined by axes Y _trg and Z _trg approximates to that parallel to the wheel plane, and axis X _trg approximates to the perpendicular .

Figure 4b shows the effect of a different angle of the wheel 2 of the vehicle 3, which is rotated by a given angle with respect to the arrangement shown in Figure 4a; it should be noted how the orientation of the target 5 associated with the wheel 2 and of the set of three orthogonal axes, here indicated as X _rg , Y' t _rg and Z' _trg , of the associated target reference system SdR _tr g ' have consequently changed. In this case, the plane of the target 5 takes a given position and inclination (approximately 30° in the example) with respect to the plane of the image capturing device 8.

Figures 4c and 4d show similar arrangements of the target 5 of the embodiment in Figure 2b, for different angles of the wheel 2 of the vehicle 3.

Figure 5 shows the two-dimensional image acquired in the image plane of the image capturing device 8 and regarding the arrangement of the target 5 shown in Figure 4b (in Figure 5, the reference curve Ref is emphasized for greater clarity of illustration) .

In this embodiment, the meridians on the target 5 are identified by circular arcs in the target reference system SdR _trg associated with the real target (the position, size and orientation of which are known by design or because they are measured with suitable measuring devices, for example, of the laser type) , while in the processed images from the image capturing device 8, characteristic curves, indicated by C _± and, in this case, constituted by elliptical arcs, are identified, these being detected on the image plane and therefore described in the image reference system SdR _te i of the image capturing device 8. The curve corresponding to the reference target region is also indicated by ⁽ Ref in Figure 5.

The mathematical model used for implementing the processing of the acquired images will now be described in greater detail, in a possible embodiment of the present invention.

In a preliminary step of characterization, or calibration, of the target 5, the real position and orientation of each target region 12 are identified in the target reference system SdR _trg by measuring a certain number of points p _± (x,y,z) distributed on the inner surface 10a of the body 10.

These measurements may be taken with a contact sensor, a so- called ^x feeler pin', controlled by a measuring machine, designed to detect the edge of the bands of the target regions 12, or by using a contactless sensor, for example of the imaging type, using laser triangulation to determine the depth of the points localized on the transition (for example light/dark or thickness) of the bands in the captured image.

As the mathematical model is applied to elliptical curves, it is indifferent whether a target 5 based on meridians rather than on closed conic curves is used, because both cases lead to processing elliptical equations. In the following, the algorithm will thus be described with reference, by way of example, to the model with meridians.

The points in three-dimensional space identified on the target regions 12, which (by corresponding to meridians in the example) should theoretically describe circular arcs, as they are superimposed on a concave hemisphere, are processed in a more generic manner to identify ellipses (in order to take into account possible deformations or manufacturing imperfections of the real target 5) .

The points belonging to each meridian are then described in a respective meridian reference system SdR _M i , the plane (XY) _M± of which is represented by the plane on which the curve lies. The 3D-space that is used is thus a special 3D-space, as each curve is defined on the plane (XY) _M± on which it lies; to arrive to a 2D-space in which the curves displayed on the image plane are described, one may thus speak of homography, namely the relation between two spaces of the same dimension.

Each meridian is therefore described by the equation of an ellipse that lies on plane (XY) _M± and by a matrix MRot _± which expresses the rotation of that plane (XY)± with respect to a reference plane (XY) i.e. the plane (XY) of the target reference system SdR _trg .

Each ellipse is therefore described by the equation:

Ax ² +Bxy+Cy ² +Dx+Ey+F=0

where parameters A, B, C, D, E and F are given by:

B=-8 (x _F i-x _F2 ) (y _F i-y _F 2)

D=4 (x _F i-x _F2 ) (x _F i ² -x _F2 ² +y _F i ² -y _F2 ² ) -16dMA _X ² (x _Fi +x _F2 )

E=4 (y _F i-y _F2 ) (x _F i ² -x _F2 ² +y _F i ² -y _F2 ² ) -16dMA _X ² (y _F i+y _F2 )

F=4 (x _F1 ² +y _F1 ² ) (x _F2 ² +y _F2 ² ) - (x _F1 ² +x _F2 ² +y _F1 ² +y _F2 ² -4dMAx ² ) ²

where d^x is the major semi-axis of the ellipse (coinciding with the radius in the case where the curve is a circle) , and (X _FI ,Y _FI ) and (x _F2 ,y _F2 ) are the coordinates of the foci in the respective plane (XY) _± (coincident, in the case where the curve is a circle) .

The meridian thus defined lends itself to being described in matrix form, much more compact and, among other features, useful for mathematically expressing the spatial rotation of the curve, and therefore for more easily solving the problem of identifying this curve with respect to the image reference system Sdr of the image capturing device 8.

By introducing the two-dimensional vector V= | x y 1|, the curve that identifies the meridian on plane (XY)± is thus described by means of the equation:

V _± ^T * | Mdefi *V _± =0

where Mdefi is given by:

A B/2 D/2

B/2 C E/2

D/2 E/2 F In the image reference system Sdr _te i _/ the elliptical images of the meridians will be expressed with a matrix A _± using the same logic, and will be expressed by means of the equation:

Indicating the matrix that describes the video camera calibration parameters as W, the following auxiliary matrix is also introduced:

B= (W ^T *A*W)

Defining the rotation matrix as R and the translation vector between the target reference system SdR _trg and the image reference system SdR _te i as T , it is possible to define the roto-translation matrix M=R | T (having four columns I ri r ₂ r ₃ T | ) that defines the relation sought between the real target and the image reference system SdR _te i of the image capturing device 8 .

In particular, indicating the rotation of SdR _trg with respect to SdRtei about axis Y _trg as a , the rotation of SdR _trg with respect to SdR _te i about axis Z _trg as β , and the rotation of SdR _trg with respect to SdR _te i about axis X _trg as γ , the expression of matrix R is the following:

A link may thus be established between the descriptions of the meridians belonging to the three-dimensional space and the elliptical images identified in the image reference system SdR _te i ^ by means of the following expression (valid for each meridian) :

IMdefil = A*Mi ^T *B*Mi where M _± is the roto-translation matrix ( 1¾± | Τι ) , which in its more general form is indicated as I r _Mi i r _Mi2 r _Mi3 T _± | , but, given that the generic point has coordinates of the |X Y 0| type, it may be reduced to the form | ri r ₂ T | .

In particular, l¾i provides the rotation between the plane on which the i-th curve lies and SdR _te i, i.e. , while T _± expresses the position of the origin of SdR _M± in SdR _te i _/ i.e. T _i= ( T+v _M1 *R) , with v _M1 expressing the position of the origin of SdR _M1 in SdRtrg-

In all the equations of the above-specified system, the unknowns are represented by values of rotation and translation of the entire SdR _trg with respect to SdR _te i the remaining quantities are instead known quantities, determined in a step of characterization of the target 5.

The above-specified matrix λ*Μ _± ^τ *Β*Μ _± may then be written in the form (for each meridian M _± ) :

where only six elements of the matrix are independent, as the matrix is symmetrical (six equations are always obtained from this relation) .

A further equation may be obtained by imposing orthogonality between the first two columns, and another two relations by imposing that the vectors formed from the first two columns are unit vectors.

In this way, nine cubic equations with ten unknowns are obtained for each meridian. Putting together these equations for each of the N available meridians, a surplus system of (9*N) cubic equations with ten unknowns is obtained, which may be solved with a numerical method (of any known type and not described in detail herein) .

In particular, solving the above-indicated system of equations IMdefj.1 = λ*Μ _± ^τ *Β*Μ _± allows obtaining values of the unknowns {a, β , γ , T } , i.e. the angles of rotation and translation that completely identify the roto-translation of the target 5 with respect to the image capturing device 8 and, in particular, between the target reference system SdR _trg and the image reference system SdR _te i-

Starting from the values detected for each target 5 (and referring to the orientation of the associated wheel 2), it is possible to trace (in a manner which is known) the values of the characteristic angles that define the set-up of the vehicle 3.

In particular, once the orientation (in terms of the rotation angles α, β and γ ) of each target 5 is determined, inside the image reference system SdR _te i of the relevant image capturing device 8, it is possible to determine the alignment of the wheels 2 of the vehicle 3 in a single reference system (for example, the reference system identified for the vehicle 3) . To this end, the reciprocal orientation between the image capturing devices 8 may be determined with respect to a single reference system, and the determined angular and linear values consequently converted into corresponding values valid in this single reference system.

On the basis of what discussed in the foregoing, the operations performed by the processing device 9 of the system 1 for determining the alignment of the wheels 2 of the vehicle 3 will now be briefly described, with reference to the flowchart in Figure 6.

In a first step, indicated by reference numeral 20, the first and the second image capturing device 8 take the respective targets 5 and send the two-dimensional images acquired in the respective image reference systems SdR _te i (containing, in a known manner, a set of pixels representative of the captured images) to the pre-processing hardware unit, which extracts the significant elements. Only these significant elements are sent from this unit to the processing device 9.

Then, in a successive step 21, the processing device 9 performs digital processing on the two-dimensional images of each target 5 in order to group the received information in characteristic curves, in particular conies (for example meridians or closed curves) associated with the target regions 12.

The processing device 9, in step 22, then describes the identified characteristic curves in matrix form, and links these curves, from a mathematical viewpoint, with corresponding curves obtained during the calibration step of the target 5, as previously discussed in detail.

In particular, in step 23, the processing device 9 determines the orientation of the targets 5 through the calculation of the roto-translational parameters of the target seen as a set of conies, referring to a single reference system.

In this way, in step 24, the processing device 9 determines the characteristic set-up angles of the wheels 2 of the vehicle 3, for example the angles of convergence and camber, expressed in a single reference system, for example the reference system associated with the vehicle 3; the processing device 9 also controls the display of these results on a suitable display device, for example, to show them to an operator and display any corrections to be made to achieve the correct alignment condition.

The advantages of the present solution clearly emerge from the foregoing description.

In particular, the production costs of the target 5 are significantly lower with respect to three-dimensional solutions of known type. Providing the bands of the target regions 12 on the single inner surface 10a is, in fact, particularly easy, exploiting the three-dimensional shape of the structure of the target 5 (for example, of the semi- spherical cap type) , to give three-dimensionality characteristics to shapes that still have an easiness of identification in the image comparable to that of two- dimensional shapes.

Furthermore, the configuration of the target makes processing simpler and less onerous from the computational viewpoint, and enables increasing the accuracy of measurements.

The layout of the target regions 12 along the meridians of the inner surface 10a of the body 10 of the target 5 also enables displaying substantially entire target regions 12 for a wide range of rotation angles of the target 5 with respect to the corresponding image capturing device 8 (i.e. avoiding overlapping, which does not happen, because the individual targets are constituted by flat figures resting on a single inner surface) .

Furthermore, the described solution enables significantly reducing the bulk of the targets 5, which, for example, may have diameters in the order of just 100-150 mm. In this regard, it should be noted that traditional solutions, for example using spherical target elements coupled to a support structure, do not allow a similar reduction in size, due to constructional and image-processing related constraints.

The described solution thus allows obtaining the maximum benefit from the advantages associated with the use of three- dimensional targets in the alignment system.

Finally, it is clear that modifications and variants may be made regarding that described and illustrated herein without departing from the scope of the present invention, as defined in the appended claims.

For example, the target 5 could have a different three- dimensional shape.

As previously indicated, the arrangement of the target regions 12 may be horizontal or vertical with respect to the inner surface 10a, or, in general, may vary still further with respect to what previously indicated.

In this regard, Figures 7a and 7b schematically show the two- dimensional image that may be acquired in the image plane of the image capturing device 8, regarding a "horizontal" and a "vertical" arrangement, respectively, of a possible embodiment of the target 5 (again, the reference curve Ref is emphasized for greater clarity of illustration) , while Figures 7d and 7e show the two-dimensional image acquired in the image plane by the image capturing device 8, regarding a different configuration with closed curves.

It is also evident that a further embodiment of the target 5 is possible, that includes a first plurality of target regions 12 with a "horizontal" arrangement and a second plurality of target regions 12 with a "vertical" arrangement, as indicated in Figure 7c, which again schematically shows a two- dimensional image that may be acquired in the image plane.

The target regions 12 could also include active material, i.e. capable of emitting electromagnetic radiation, in the visible frequency range or in the infrared range, instead of reflecting incident radiation. The advantage of a solution of the active type with respect to using passive-type target regions 12 consists in that an illuminator device is not required, which, apart from possibly being a disturbance for the operator, by having to light the target from a certain distance, and even if infrared radiation is emitted, entails higher energy consumption.

The described system could also comprise a larger number of image capturing devices. Furthermore, if required, it is possible to use a single image capture device, capable of framing all the targets associated with the wheels 2 of the vehicle 3 for which it is desired to determine the orientation .

The sensing devices 7a and 7b could also be arranged frontally with respect to the vehicle 3, for example carried on a suitable support structure, instead of laterally with respect to the vehicle.

Finally, as clearly evident, the described system and method could also enable determining the spatial orientation of a single wheel 2 of the vehicle 3, the image of which is captured by a single image capturing device 8.