Alignment system for approaching a vehicle to a spatially separated target object

Abstract

Alignment system for approaching a vehicle (10) to a spatially spaced target object (40), comprising an object recognition means (20) attached to the vehicle (10) and a connecting element (30) with which the target object (40) is releasably held in an end position, wherein the object recognition means (20) is aligned in the direction of the target object (40) and an image is generated using the data of the object recognition means (20) in which the target object (40) is shown together with a guide marker (50) during the approach of the vehicle (10), characterized in that the guide marker (50) is applied to at least one component (11) of the vehicle (10) arranged in an entry area (31) of the connecting element (30).

Description

[0001] The invention relates to an alignment system for approaching a vehicle to a target object spatially spaced apart from it, according to the features set out in the preamble of claim 1.

[0002] The object recognition device can be, in particular, a camera that provides the driver with an image of the area behind the vehicle, including the target object, as the vehicle approaches it. Using this image, the towing vehicle can be maneuvered more precisely towards the target object.

[0003] EP 2 987 663 A1 describes a driver assistance system for a commercial vehicle combination as a semi-trailer truck, consisting of a tractor unit and a semi-trailer, or as an articulated vehicle, consisting of a tractor unit and a trailer. A video camera is mounted on the tractor unit, and its video image is displayed on a screen within the driver's field of vision. The video camera is positioned in the direction of travel, either in front of or within the coupling device on the tractor unit, such that both an area of ​​the coupling device and the area behind it, including the coupling element of the semi-trailer truck or articulated vehicle, are visible in the video image. A guide marker is also superimposed on the video image to aid in coupling, enabling a safe, quick, and convenient coupling process.However, it has proven to be difficult to program the displayed guide marking specifically, depending on the geometric characteristics of the towing vehicle and coupling receiver part as well as the coupling element.

[0004] Another example of the prior art is DE 10 2019 201 572 A1, which describes a guidance system for attaching an implement to a tractor. A camera is mounted on the tractor, and a reference guide with an edge is positioned directly in front of its lens. The camera lens is configured so that both the edge and the implement connections are visible in the image, allowing for a better estimation of the distance behind the implement.

[0005] German patent application DE 10 2004 008 928 A1 discloses a method for coupling a trailer using vehicle level control. A reversing camera is mounted above a trailer coupling located at the rear of the vehicle. This camera captures the trailer coupling, the area behind the vehicle, and any trailer that may be parked there. Using the reversing camera, the vehicle can be maneuvered backwards to the immediate vicinity of the trailer and then lowered by means of the vehicle level control, so that the trailer-side coupling does not need to be raised for mechanical coupling.

[0006] German patent DE 20 2009 018 636 U1 proposes a targeting device as a coupling aid for a vehicle and a trailer. The targeting device comprises a rod that can be mounted on the ball head of a trailer coupling, with a rearward-facing laser light source attached to its end. A magnetic base is used to attach another rod to the trailer's drawbar, this rod also having a target with a marking attached to its end. When the vehicle is approaching from behind, the laser's point of impact on the marking on the target is visible and can be used for improved maneuvering towards the trailer. The targeting device must be removed immediately before the coupling halves are mechanically connected.

[0007] WO 2009 / 006 529 A1 deals with an electronic trailer coupling system, comprising a stereo camera preferably mounted on the trailer drawbar, which has at least two image sensors, and a processor that processes the image data from the image sensors. The evaluated image data is intended to allow the towing vehicle to autonomously approach the trailer.

[0008] All maneuvering aids known from the state of the art share the disadvantage that they are complex to install and place an additional burden on the driver during use.

[0009] For this reason, the invention was based on the objective of developing a technically simpler solution for representing a guide marking.

[0010] The problem is solved using the features of claim 1.

[0011] An object detection device is, for example, a camera that can operate in the non-visible spectrum, such as the infrared range, and / or in the visible spectrum. In addition to 2D image sensors, imaging sensors capable of capturing 3D information are also suitable. These include, in particular, laser scanners, radar sensors, and ultrasonic sensors. For better protection against external influences, the object detection device can be enclosed in a housing and preferably form a single unit with it.

[0012] The object recognition device is fixed in position relative to the guide marker and aligned with it.

[0013] The image provided by the object recognition device can be displayed on a screen in the driver's cab, serving as a visual maneuvering aid for coupling the trailer. However, it is also possible for the data provided by the object recognition device to be fed into the towing vehicle's electronic data system without displaying the image, allowing the towing vehicle to couple the trailer autonomously or semi-autonomously based on this data. Semi-autonomous coupling is an assistance system for the driver to support them during maneuvering.

[0014] Advantageously, the guide marking is permanently present in a physical manner. It has proven particularly beneficial if the guide marking is painted, glued, embossed, milled, and / or raised from the component in relief.

[0015] According to a particularly advantageous embodiment, the guide marking comprises at least one sighting element rigidly or movably mounted on the component. A rigid sighting element may have one or more projecting bases, recesses, or protrusions. If two of these sighting elements are arranged in the direction of the target object's final position and / or aligned with the object detection device, a sighting line is formed along which the vehicle can approach the target object.

[0016] Another preferred embodiment involves projecting the guide marking onto the component using a light source. In this embodiment, the guide marking is only temporary. Switching the light source on or off causes the guide marking to appear or disappear. This is advantageous because the guide marking only needs to be activated immediately before the connecting element and the target object are joined. No painting or bonding work on vehicle components is necessary. The light source can be a lamp with a lens shaped like the guide marking, a projector, or a laser pointer. Complex guide markings can be generated using holographic optics.

[0017] Ideally, the guide marking consists of at least one boundary line converging on the target object's final position and / or the object detection device. This boundary line limits the intended travel path of the target object, particularly in the transverse direction. To ensure accurate connection of the connecting element to the target object, the target object must always be kept between the boundary line(s) as the vehicle approaches.

[0018] The boundary line(s) can be conically widened or tapered in the distal direction. A boundary line that widens conically in the distal direction has the advantage that the target object can initially be easily placed within the boundary line, and more precise positioning is achieved as the object approaches. A boundary line that tapers in the distal direction, on the other hand, is advantageous because the target object, due to its constant focal length, is perceived as smaller at greater distances from the object detection device and, as the distance decreases, grows in size along with the boundary line in the image plane.

[0019] Advantageously, the guide marking is shaped according to the contour of the target object or is derived taking perspective distortion into account. The contour of the target object depicted as the guide marking is preferably congruent with the target object as it passes over it, or at least defines a dimensional frame within which the target object must be located for accurate contact with the connecting element.

[0020] Ideally, the guide marking extends in an xy-plane (horizontal), yz-plane (vertical in the direction of movement) and / or xz-plane (perpendicular to the direction of movement) or at least has sections that extend over at least two of these planes.

[0021] An electronic control unit may be present, which determines the distance to the target object from the ratio of a known size of the guide marker to a known size of the target object. In this embodiment, the distance along the longitudinal axis can be derived from the size ratios of the guide marker and the target object.

[0022] In a favorable embodiment, the connecting element is a fifth wheel coupling and the target object is a kingpin attached to a second vehicle. In this embodiment, the vehicle is a tractor unit and the second vehicle is a semi-trailer.

[0023] The component is formed primarily by opposing flanks of coupling horns arranged laterally to the entry area. These flanks form a tapered entry area that guides the kingpin even with a slight lateral misalignment. A guide marking applied to the flanks of the coupling horns allows the vehicle to be positioned more precisely against the kingpin.

[0024] It is also possible that the component consists of a transverse bridge positioned below the entry area. The transverse bridge can extend completely beneath the entry area of ​​the fifth wheel coupling and be connected to the underside of the coupling plate on both sides, thereby significantly increasing the fifth wheel coupling's strength. In principle, it would also be possible to connect the transverse bridge to the coupling plate only on one side and use it as a holder for the guide marker.

[0025] Another alternative embodiment could consist of a connector console for an automated quick-connect coupling system for supply lines, arranged below the entry area. The connector console is positioned below the fifth wheel coupling's entry area, allowing a kingpin to pass over it. The connector console has a housing, the upper surface of which, as a vehicle component, is suitable for applying a guide marking.

[0026] The connecting element can also be a container lock, and the target object a corner fitting formed on a container or swap body. Using the guide marker arranged on a component of the vehicle, the vehicle can be maneuvered with exceptional precision to the container or swap body, ensuring that the corner fitting engages with the corresponding container lock.

[0027] It is also possible that the connecting element is a guide roller and the target object is a guide frame formed on a swap body. As the vehicle approaches from behind, the guide roller engages with a guide frame formed on the underside of the container or swap body. This guide frame must be brought into contact with the guide marking during the vehicle's approach. Typically, the component with the guide marking is formed from a vehicle frame part or a body panel of the vehicle.

[0028] According to a further embodiment, the connecting element can be a tool holder located at the distal end of a front loader, and the target object can be a receptacle for an implement to be attached to the front loader. An implement could be, for example, a bucket or forks. The implement can typically be removed from the front loader and replaced with another via a quick-change system. Since the area around the distal end of the front loader is difficult to see from the driver's seat, the vehicle can be driven towards the implement using the object detection system until its receptacle has moved into the guide marking. In this embodiment, the component can be formed from the tool holder itself.

[0029] For better understanding, the invention is explained in more detail below with reference to 15 figures. These show the Fig. 1: a top view of a connecting element in the form of a fifth wheel coupling with a guide marking arranged on the flanks of the coupling horns; Fig. 2: a top view of a connecting element in the form of a fifth wheel coupling with a guide marking arranged on a crossbar; Fig. 3: a top view of a connecting element in the form of a fifth wheel coupling with a guide marking arranged in the transition area of ​​the crossbar and flanks of the coupling horns; Fig. 4: a top view of a connecting element in the form of a fifth wheel coupling with a guide marking arranged on a connector console; Fig. 5: an enlarged top view of a locking section of a fifth wheel coupling with a guide marking in the form of a broken line arranged on a crossbar; Fig. 6: An enlarged top view of a locking section of a fifth wheel coupling with a trapezoidal guide mark arranged on a crossbar; Fig. 7: an enlarged top view of a locking section of a fifth wheel coupling with a guide marker arranged on a crossbar with the contour of the target object; Fig. 8: an enlarged top view of a locking section of a fifth wheel coupling with a guide mark projected onto the crossbar by a light source; Fig. 9: an enlarged top view of a locking section of a fifth wheel coupling with a guide marking arranged on a crossbar in the form of two boundary lines diverging conically in the direction of the object detection means; Fig. 10: an enlarged top view of a locking section of a fifth wheel coupling with a guide marking arranged on a crossbar in the form of two boundary lines converging conically in the direction of the object detection means; Fig. 11: a top view of a connecting element in the form of a fifth wheel coupling with a guide marker in the form of a sighting element arranged on a cross bridge according to a first embodiment; Fig. 12: a top view of a connecting element in the form of a fifth wheel coupling with a guide marker in the form of a sighting element arranged on a cross bridge according to a second embodiment; Fig. 13: A top view of a vehicle with a guide marking on the vehicle frame and body components before the insertion of a swap body; Fig. 14: A side view of a front loader with implement and Fig. 15: A perspective front view of the front loader with object recognition device without working equipment.

[0030] The Fig. Figure 1 shows a top view of a connecting element 30 in the form of a fifth wheel coupling 32, which is attached to vehicle frame parts 13 of a vehicle 10 by means of a mounting plate 16. The vehicle 10 is in particular a semi-trailer tractor.

[0031] Vehicle 10 has moved backwards along a longitudinal axis y towards a second vehicle 60, in particular a semi-trailer. When vehicle 10 is traveling straight ahead, the longitudinal axis y corresponds to its direction of travel. The second vehicle 60 is shown schematically as a dotted line and already extends beyond vehicle 10, including its fifth wheel coupling 32. On its underside, the second vehicle 60 has a target object 40 in the form of a downwardly projecting kingpin 41.

[0032] The fifth wheel coupling 32 is formed on its side facing the kingpin 41 with two coupling horns 33, the opposing flanks 34 of which form a V-shaped entry area 31 within the contour of the fifth wheel coupling 32. The entry area 31 continues in the rearward direction as an extension of the flanks 34. The entry area 31 terminates in the longitudinal axis y in a locking section 32a of the fifth wheel coupling 32, in which the kingpin 41 is detachably connected to the fifth wheel coupling 32 after reaching its end position.

[0033] To couple the second vehicle 60, vehicle 10 must approach it in such a way that the kingpin 41, in the longitudinal axis x, enters an entry area 31 of the fifth wheel coupling 32 with the smallest possible offset in the transverse axis x. This approach is facilitated by an object detection device 20, for example, positioned in the longitudinal axis y of the locking section 32a, in whose field of view the second vehicle 60 with its kingpin 41 is already visible when vehicle 10 is roughly aligned.

[0034] Additionally, a guide marking 50 is applied to a component 11 arranged in the entry area 31 such that it is also detected by the object detection means 20. In the exemplary embodiment of the Fig. 1. The guide marking 50 is a high-contrast paint finish permanently applied to the two facing flanks 34 of the coupling horns 33, in contrast to the fifth wheel coupling 32. The guide marking 50 can, in particular, cover the entire surface of the respective flank 34. For accurate coupling of the kingpin 41, the driver only needs to keep the kingpin 41 within the guide marking 50 while reversing, i.e., between the high-contrast surfaces of the flanks 34.

[0035] The Fig. Figure 2 shows an alternative embodiment in which the guide marking 50 supporting component 11 is formed from a transverse bridge 35 arranged on the fifth wheel coupling 32. The transverse bridge 35 is located in the transition from the entry area 31 to the locking section 32a in the vertical axis z (compare Figure 2). Fig. 14, Fig. 15) below the level of the entry area 31, so that a kingpin 41 moving into the fifth wheel coupling 32 can cross the crossbar 35 without collision. The crossbar 35 can engage the fifth wheel coupling 32 on both sides of the entry area 31 to stiffen it.

[0036] The guide marking 50 is applied to the crossbeam 35 as a continuous line running along the longitudinal axis y. Both the crossbeam 35 and the guide marking 50 applied to it are within the field of view of the object detection device 20. During the approach of the vehicle 10 (see FIG. 1), the aim is to keep the kingpin 41, detected by the object detection device 20, as centrally as possible with respect to the guide marking 50 by means of appropriate steering maneuvers.

[0037] In the Fig. Figure 3 shows a further embodiment in which the guide marking 50 is also applied to the crossbeam 35 as component 11. However, the guide marking 50 comprises two boundary lines 53 that diverge conically in the rearward direction along the longitudinal axis y and are laterally bounded outwards by the flanks 34 of the coupling horns 33. Both boundary lines 53 lie within the field of view of the object detection device 20. For accurate coupling of the kingpin 41, it must be positioned between the two boundary lines 53 as the vehicle 10 approaches.

[0038] The Fig. Figure 4 shows an alternative embodiment with a connector console 36 of an automatic plug-in coupling system for supply lines arranged below the entry area 31. During coupling, the approaching kingpin 41 first passes over the connector console 36 without contact and then connects it to a connector console on the trailer side, which is not shown here. The component 11, which carries the guide marking 50, is the connector console 36. The guide marking 50 is applied to the upper surface of the connector console 36, which is oriented upwards along the vertical axis z, and is therefore within the field of view of the object detection device 20.

[0039] The guide marking 50 is formed as a continuous line aligned along the longitudinal axis y, which extends completely across the connector console 36. An approaching kingpin 41 should be kept as centrally as possible above the line of the guide marking 50 by steering movements of the vehicle 10.

[0040] In the Fig. Figure 5 shows an enlarged section of the locking section 32a of a fifth wheel coupling 32 together with the crossbar 35. The guide marking 50 is comparable to the embodiment in Figure 5. Fig. 2 on the transverse bridge 35. However, instead of a continuous line lying on the longitudinal axis y, a broken or dotted line was chosen as the guide marking 50.

[0041] The Fig. 6 shows the same view as Fig. 5 A further embodiment of the guide marking 50 applied to the transverse bridge 35 in a trapezoidal shape. The two diverging sides of the guide marking 50 are each essentially equidistant from the flanks 34 of the coupling horns 33 and form a boundary line 53 in the direction of the transverse axis x for the kingpin 41. During an approach of the vehicle 10 to the kingpin 41, the latter should be kept as far as possible between the opposing boundary lines 53.

[0042] The Fig. 7 shows the same view as the Fig. 5 and Fig. 6. The guide marking 50 is also applied to the transverse bridge 35 and is therefore visible to the object recognition device 20. However, the guide marking 50 has a simplified contour of the target object 40, in this embodiment that of the kingpin 41. As the vehicle 10 approaches the kingpin 41, the latter should be aligned as closely as possible with the similarly shaped guide marking 50 when passing the transverse bridge 35.

[0043] In the embodiment of the Fig. Figure 8 shows a temporarily visible guide marker 50, which is projected onto the transverse bridge 35 (component 11) by means of visible light from a light source 52 located higher on the vertical axis z. After successful coupling of the kingpin 41, the light source 52 can be switched off, so that no guide marker is visible.

[0044] The Fig. Figure 9 shows a guide marking 50 applied to the transverse bridge 35 as component 11, which is formed from two boundary lines 53 tapering conically towards the locking section 32a, between which the kingpin 41 is to be positioned during coupling. Fig. 10 The guide markings 50 formed from two boundary lines 53 run conically towards the locking section 32a.

[0045] The Fig. Reference 11 relates to a further, alternative embodiment with a guide marking 50 in the form of a sighting element 51 formed on the transverse bridge 35. The sighting element 51 comprises two wall sections extending along the transverse axis x and standing upright with respect to the transverse bridge 35, and a recess formed therein along the longitudinal axis y. Both the wall sections and the recess are visible to the object detection device 20 when approaching the kingpin 41. During the approach of the vehicle 10, it should be maneuvered such that the kingpin 41 is visible behind the recess in the image generated by the object detection device 20.

[0046] In the Fig. Figure 11 shows a second embodiment of a guide marker 50 using two sighting elements 51. The guide marker 50 is formed from two sighting elements 51, which are formed in the transverse bridge 35 and aligned with each other along the longitudinal axis y. These sighting elements may be, for example, recess(s) and / or protrusion(s). During approach, the target object 40, in the form of the kingpin 41, is sighted according to the sight-sight principle by extending the lines of sight from the two sighting elements 51.

[0047] The Fig. Figure 13 shows a vehicle 10 for transporting a container or swap body 42 placed behind it.

[0048] The vehicle 10 has several container locks 37 as connecting elements 30, which, when a container or swap body 42 is correctly picked up, engage in corner fittings 43 provided therein and hold it releasably during transport. The target object 40 of such a vehicle 10 can be the corner fittings 43 of the container or swap body 42. In order to approach these as precisely as possible, an object detection device 20 is mounted in close proximity to at least one of the container locks 37, which detects an entry area 31 behind the vehicle 10 and in the direction of the nearest corner fitting 43. A guide marking 50 is applied to a component 11 in the form of a body part 14, which can also be a mudguard or other cladding component, between the object detection device 20 and the target object 40.During a reversing maneuver of the vehicle 10 towards the stationary container or swap body 42, the maneuvering should be such that the target object 40 in the form of one of the corner fittings 43 is positioned flush within the contour of the guide marking 50.

[0049] The target object 40 can be, instead of one or more of the corner fittings 43, a guide frame 44 running parallel to the longitudinal axis y on the underside of the container or swap body 42. This guide frame 44 engages with a connecting element 30 of the vehicle 10 in the form of guide rollers 38 during the picking-up of the container or swap body 42. The guide rollers 38 are rotatably mounted about the vertical axis z and are located within the guide frame 44 when the container or swap body 42 is loaded. For precise positioning of the guide frame 44, an object detection device 20 is attached to a vehicle frame section 13 in close proximity to at least one of the guide rollers 38. The field of view of this device is directed towards the container or swap body 42. A guide marker 50, also mounted on the vehicle frame section 13, is located within the field of view of the object detection device 20.

[0050] Within the driver's line of sight, a display device 15 is arranged in the vehicle 10, which displays a visible image of the target object 40, in particular the corner fitting 43 and / or the guide frame 44, relative to the guide marking 50.

[0051] The Fig. 14 and Fig. Figure 15 shows the alignment system on a front loader 39, whose connecting element 30 is a tool holder 39a for the detachable attachment of a work implement 46, such as a bucket. The work implement 46 has a receptacle 45 as its target object 40, designed to be complementary to the tool holder 39a, into which the tool holder 39a can be maneuvered with precision.

[0052] Maneuvering is simplified by means of the guide marker 50 attached to the tool holder 39a, which lies within the field of vision of the object recognition device 20 arranged on the front loader 39. When approaching the implement 46, only its holder 45 needs to be brought into the contour of the guide marker 50. REFERENCE MARK LIST 10 vehicles 11 components 12 Control unit 13 Vehicle frame part 14 Body component 15 Display device 16 Mounting plate 20 object recognition tools 30 connecting element 31 Entrance area 32 fifth wheel coupling 32a Locking section 33 clutch horns 34 Flank Clutch horn 35 Cross bridge 36 connector console 37 Container locking 38 Instruction roll 39 front loaders 39a Tool holder 40 Target object 41 kingpins 42 containers / swap bodies 43 Corner fitting for container / swap body 44 guide frames 45 Recording work equipment 46 Work equipment 50 guide marker 51 bearing element 52 Light source 53 Boundary line 54 Guide marker with contour target object 60 second vehicle x transverse axis y Longitudinal axis z vertical axis

Claims

[1] Alignment system for approaching a vehicle (10) to a spatially spaced target object (40), comprising an object recognition means (20) attached to the vehicle (10) and a connecting element (30) with which the target object (40) is releasably held in an end position, wherein the object recognition means (20) is aligned in the direction of the target object (40) and an image is generated using the data of the object recognition means (20) in which the target object (40) together with a guide marker (50) is shown during the approach of the vehicle (10), characterized by , that the guide marking (50) is applied to at least one component (11) of the vehicle (10) arranged in an entry area (31) of the connecting element (30). [2] Alignment system according to claim 1, characterized by , that the guide marker (50) is physically permanent. [3] Alignment system according to claim 1 or 2, characterized by, that the guide marking (50) is painted, glued, embossed, milled and / or formed in relief from the component (11) on the component (11). [4] Alignment system according to claim 1 or 2, characterized by , that the guide marking (50) comprises at least one locating element (51) rigidly or movably mounted on the component (11). [5] Alignment system according to claim 1, characterized by , that the guide marking (50) is projected onto the component (11) by means of a light source (52). [6] Alignment system according to any one of claims 1 to 5, characterized by , that the guide marking (50) is formed from at least one boundary line (53) converging towards the final position of the target object (40) and / or towards the object recognition means (20). [7] Alignment system according to claim 6, characterized by , that the boundary line(s) (53) is / are conically widened or tapered in the distal direction. [8] Alignment system according to any one of claims 1 to 5, characterized by , that the guide marking (50) is shaped according to a contour (54) of the target object (40) or results taking into account a perspective distortion. [9] Alignment system according to any one of claims 1 to 8, characterized by , that the guide marker (50) extends in an xy-plane (horizontal), yz-plane (vertical in direction of movement) and / or xz-plane (perpendicular to the direction of movement) or at least has subsections that extend over at least two of these planes. [10] Alignment system according to any one of claims 1 to 9, characterized by , that an electronic control unit (12) is present, with which a distance to the target object (40) is determined from the ratio of a known size of the guide marker (50) and a known size of the target object (40). [11] Alignment system according to any one of claims 1 to 10, characterized bythat the connecting element (30) is a fifth wheel coupling (32) and the target object (40) is a kingpin (41) attached to a second vehicle (60). [12] Alignment system according to claim 11, characterized by , that the component (11) is formed from opposite flanks (34) of coupling horns (33) arranged laterally to the entry area (31). [13] Alignment system according to claim 11, characterized by , that the component (11) is formed from a transverse bridge (35) arranged below the entry area (31). [14] Alignment system according to claim 11, characterized by , that the component (11) is formed from a plug console (36) of an automated plug coupling system for supply lines arranged below the entry area (31). [15] Alignment system according to any one of claims 1 to 10, characterized by, that the connecting element (30) is a container lock (37) and the target object (40) is a corner fitting (43) formed on a container (42) or a swap body. [16] Alignment system according to any one of claims 1 to 10, characterized by , that the connecting element (30) is a guide roller (38) and the target object (40) is a guide frame (44) formed on a swap body (42). [17] Alignment system according to claim 15 or 16, characterized by , that the component (11) is formed from a vehicle frame part (13) or a body component (14) of the vehicle (10). [18] Alignment system according to any one of claims 1 to 10, characterized by , that the connecting element (30) is a tool receptacle (39a) arranged at the distal end of a front loader (39) and the target object (40) is a receptacle (45) of a work implement (46) to be attached to the front loader (39). [19] Alignment system according to claim 18, characterized by, that the component (11) is formed from a section of the distal end of the front loader (39) that is aligned with the tool holder (39a).

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