Device and method for assessing a virtual position

The invention relates to an agricultural vehicle or implement with a Satel-litenempfangseinheit for position determination and to a method for determining the position according to the preamble of claims 1 and 13.

The use of satellite navigation systems, such as the Global Positioning System (GPS), is already known in agricultural vehicles or implements for the creation of crop registers and soil elevation profiles, as well as for the control of fertilizer application. In the meantime, satellite navigation systems (DGPS) with correspondingly powerful evaluation units are available that provide accuracy of the position determination, ie Determining the position of a GPS antenna, in the centimeter range.

For example, from DE 196 47 523 an agricultural vehicle with a satellite navigation system is known. The vehicle described there has a processing device, wherein it is proposed there to determine the position of a reference point on the processing device instead of, for example, the position of the vehicle center. However, there is a problem in this case if, for some reason, the satellite receiving unit (GPS antenna) can not be attached to the reference point of the processing apparatus. Reasons for the fact that the GPS antenna can not be attached directly to the location whose position is actually to be determined, for example, are lack of mechanical attachment options, shading of the signals by the vehicle itself, the risk of damage or heavy wear. In these cases, the reference point whose position is to be determined is spatially distant from the GPS antenna whose position is actually determined by the satellite navigation system at a distance (D). This requires a coordinate conversion; ie from each determined by means of satellite navigation coordinates of the GPS antenna, which is located for example on the vehicle roof, must be concluded by conversion to the coordinates of, for example, lower reference point on the processing unit. In the event that the processing unit is rigidly connected to the vehicle, obtained from DE 196 47 523 the reference for the determination of the height coordinate (Z) of the reference point in each case the height difference between the mounting location of the GPS antenna and the reference point of the means Satellite navigation to subtract Z-coordinate of the installation location of the GPS antenna for the conversion. In the event that the processing unit is not rigidly connected to the vehicle, but arranged, for example, height-adjustable, this is obtained from DE 196 47 523 the reference to provide a sensor that measures the change in height of the processing equipment relative to the vehicle, and this Measured height change in the coordinate determination described above to incorporate as a correction.

In addition, however, there is a general problem of position determination when the location (reference point) whose position is to be determined does not coincide with the location of the GPS antenna, but there is a distance (D) between them. And there is an indeterminacy, which stems from the fact that in principle all points on the surface of a sphere with radius (D), in the center of which the location of the GPS antenna is, come as a possible position of the reference point into consideration. Since the distance (D) between the reference point and the GPS antenna can be quite several meters in an agricultural vehicle, there is a correspondingly large uncertainty in the position of the reference point, which is very unsatisfactory in view of increasingly accurate navigation systems in itself.

Although the direction of travel and the orientation of the vehicle can be determined iteratively while traveling from the temporally successive position coordinates of the GPS antenna, this method is inaccurate and fails when the vehicle is stationary and when starting off. Furthermore, the direction of travel in some applications is correct (For example, when driving in a crab or on a slope) with the vehicle longitudinal direction do not match.

Only if restrictions on freedom of movement were made - for example, driving only in NS and / or OW direction or only in the horizontal plane - could this vagueness be avoided. However, this is not possible with agricultural vehicles and implements attached to them.

It is therefore the object of the invention to enable the accurate determination of a reference point, which is spatially removed from the mounting location of the navigation antenna, reliable.

This object is achieved by the characterizing features of claims 1 and 13.

According to the invention, the agricultural vehicle has at least one sensor (S, S1, S2, S3) for determining the position of the vehicle. Position means the orientation of the vehicle and the orientation in the horizontal plane of the terrestrial reference system (x, y, z), where orientation means the angle (φ) that the vehicle longitudinal direction corresponds to, for example with the NS direction (y coordinate of the terrestrial reference system) forms and orientation means the direction to which, for example, the vehicle front shows. The location of the vehicle but also means the longitudinal or Bank (α, β) of the vehicle relative to the vertical direction (Z-coordinate) of the reference system. The coordinates of the GPS antenna are marked with (X_A, Y_A, Z_A) designated; the coordinates of the reference point with (X_P, Y_P, Z_P).

As a sensor for determining the orientation (φ) of the vehicle in the horizontal plane, a mechanical gyro compass or a laser gyro known in the art is preferably used. As sensors for the longitudinal or transverse inclination (α, β) preferably Lotpendel be used with electrical signal transmitters, which are also known in the art. The person skilled in the art can also use a single sensor which is able to detect the various deviations (φ, α, β).

Furthermore, according to the invention, vehicle-specific basic conversion variables (X_P0-X_A0; Y_P0-Y_A0; Z_P0-Z_A0; φ₀; α₀; β₀d₁d₂d₃), which reflect the geometric relationships of the reference point and GPS antenna arrangement on the vehicle for a particular, aligned attitude of the vehicle. As the aligned position of the vehicle is preferably selected that, where the longitudinal direction of the vehicle in the NS direction is aligned with front to the north and where there is no longitudinal or Bank of the vehicle there, ie for the excellent position, it is assumed that the vehicle is standing on a flat, unidirectional inclined field. These base conversion quantities are virtually part of a vehicle specification.

Here is in detail:<ul id="ul0001" list-style="dash" compact="compact"><li>(X_P0-X_A0) the difference of the x coordinates of the reference point and location of the GPS antenna,</li><li>(Y_P0-Y_A0) the corresponding difference of the y-coordinates,</li><li>(Z_P0-Z_A0) the corresponding difference of the z coordinates,</li><li>d₁ the projection of the distance (D, distance from the location of the GPS antenna to the reference point) to the horizontal plane (x, y) of the reference frame,</li><li>d₂ the projection of the distance (D, distance from the location of the GPS antenna to the reference point) to the y, z plane of the reference frame,</li><li>d₃ the projection of the distance (D, distance from the location of the GPS antenna to the reference point) to the horizontal plane x, z-plane of the reference frame,</li><li>φ₀ the angle between d₁ and the NS direction (x direction),</li><li>α₀ the angle between d₂ and the vertical of the reference system (z-direction),</li><li>β₀ the angle between d₃ and the vertical of the frame of reference (z-direction).</li></ul>

By way of illustration, for example, a fictitious Cartesian coordinate system fixed relative to the vehicle can be defined for the agricultural vehicle. The axes of this coordinate system are denoted by (bx, by, bz). The origin (zero point) of this coordinate system is placed at the location of the GPS antenna. It is crucial that this coordinate system is firmly connected to the vehicle, ie that apply to this coordinate system all horizontal and vertical changes in position and all rotations and inclinations of the vehicle.

In the aligned position is:<ul id="ul0002" list-style="dash" compact="compact"><li>the coordinate axis (bx) of this coordinate system parallel to the WO direction (x-coordinate axis of the terrestrial frame of reference),</li><li>the coordinate axis (by) of this coordinate system parallel to the NS direction (y coordinate axis of the terrestrial frame of reference),</li><li>the coordinate axis (bz) of this coordinate system parallel to the vertical (z coordinate axis of the terrestrial frame of reference).</li></ul>

The vehicle-specific base conversion quantities (X_P0-X_A0; Y_P0-Y_A0; Z_P0-Z_A0; φ₀; α₀; β₀, d₁, d₂, d₃) can be stored in a memory of the evaluation unit or in another memory of the vehicle, to which the evaluation unit has access.

According to the invention, the sensor (s) now respectively detect a deviation (φ, α, β) of the vehicle attitude from the aligned attitude, which is described in detail above. The evaluation unit (AWE) now determines on the basis of these deviations (φ, α, β) and taking into account the vehicle-specific base conversion quantities (φ₀, α₀, β₀, d₁, d₂, d₃) each time the current conversion size for the determination of the coordinates (X_P, Y_P, Z_P) of the spatially spaced from the satellite receiving unit reference point from the known position coordinates (X_A, Y_A, Z_A) of the satellite receiving unit (GPS antenna).

The determination of the absolute position for the location of the GPS antenna is carried out by a known computing algorithm that processes the transmission data from GPS satellites. This is known to the person skilled in the art and can be carried out with sufficient accuracy. The satellite receiver unit (GPS antenna) may already comprise an evaluation unit, which already determines position data for the location of the GPS antenna from the GPS transmission data, from which then in this evaluation unit or in a separate evaluation unit according to the invention the position of the reference point is determined. However, it is also within the scope of the invention, if only one evaluation unit is provided, which does not belong directly to the satellite receiving unit, wherein the GPS transmission data for determining the position of the location of the GPS antenna are directed to this evaluation.

In a preferred embodiment of the invention, a transformation matrix is ​​calculated from the respective conversion variables determined in accordance with the invention, and with this transformation matrix from the known position vector (X._A, Y_A, Z_A) of the GPS antenna, the position vector to be determined (X_P, Y_P, Z_P) of the reference point.

The relevance of the present invention will be illustrated by the concrete example of a combine driving up a (15%, α = 8.5 °) inclined slope in the SN direction. The vehicle-specific basic conversions relative to the aligned position (as explained above) of the combine harvester are: GPS antenna on the roof of the combine harvester at 4 m above ground level, reference point at the cutting unit 1 m above the ground, ie ΔZ0 = - 3m, furthermore ΔX0 = -3.5m and ΔY0 = -5m.

Without the consideration of the slope inclination according to the invention, for example, according to DE 196 47 523, only the changing position of the GPS antenna would be measured and subtracted for determining the position of the reference point from the changing z-coordinate of the GPS antenna always ΔZ0 = 3m and to the changing one y-coordinate of the GPS antenna always ΔY0 = 5m added. However, this does not correspond to reality; in fact, the differences are dependent on the slope. In this case, for a precise determination of the reference point from the z-coordinate of the GPS antenna, a difference of ΔZ = 2.23 m and from the y-coordinate of the GPS antenna, a difference of ΔY = 5.39 m would have to be subtracted. Thus, the prior art position determination deviates by 77 cm for the z-coordinate and 39 cm for the y-coordinate from the actual value. These deviations are greater than the inaccuracy of satellite navigation per se.

A detailed derivation of these quantities is given below with reference to the drawings.

The invention enables the exact position determination of a spatially spaced from the GPS antenna reference point and indeed for a variety of layers of an agricultural vehicle or implement in the terrestrial frame of reference. This makes it much easier to create crop cadastre and soil height profiles.

A special improvement also provides the invention for automatic steering systems, so that, for example, a combine harvester can be automatically steered along a virtual grain edge. The virtual grain edge is derived from previously recorded reference position data and compared to the determined, current reference position of the cutting edge. From the deviations of the vehicle direction and the reference point distance, a control signal for the automatic steering system is determined.

The invention provides a further advantage for the control of distributing devices which are suitable for applying agents, for example spraying or fertilizers, to fields. With the aid of the virtual position, it is very easy to set up an automatic working width control. The position data of the impact boundaries or impact areas which are not to be supplied with resources are prepared today before the application of the funds according to the working process and transferred to the implement control. If, according to the invention, the reference point is placed in the place of the outermost application position, the working width can be correspondingly reduced when the reference point is exceeded via the stored impact limits and automatically adapted dynamically to the beat boundary profile. By recording the reference points, a virtual processing edge can also be recorded here, at which a vehicle, based on the current working width, can be automatically controlled along during the next travel. If one places further reference points, for example in the working direction, at the beginning or at the end of the application range, switching on or off of the working device can be realized in a simple manner.

The invention may also be used to advantage on agricultural implement combinations, such as towing vehicles having a directional or deceleration device coupled to the satellite receiving antenna, such as an attached towed fertilizer control or syringe. On the implements then additional own inclination or direction sensors are attached, which determine the orientation of the implement advantageously on the crosspoint with the towing vehicle. The base distance (D) of the virtual reference point from the receiving antenna is then composed of individual sub-distances, which are specific to the respective implement and the tractor together and can be calculated in an advantageous manner via a defined cross-over between tractor and implement.

Reference to the accompanying drawings, the invention will be explained in more detail below, wherein an embodiment of Figures 1-7 does not fall under the independent claims 1-13. It shows:<dl id="dl0001" compact="compact"><dt>Fig. 1</dt><dd>the side view of a combine harvester with GPS antenna on the roof and attached cutting unit where the reference point is located</dd><dt>Fig.2</dt><dd>a schematic plan view of the horizontal plane with a combine, aligned zero position with the longitudinal direction to the north,</dd><dt>Figure 3</dt><dd>as in FIG. 2, however, the combine harvester is twisted relative to the aligned layer on the horizontal plane,</dd><dt>Figure 4</dt><dd>a schematic side view with the combine in the yz plane in an aligned neutral position,</dd><dt>Figure 5</dt><dd>as in FIG. 4, however, the combine is twisted with respect to the aligned layer in the yz plane,</dd><dt>Figure 6</dt><dd>a schematic side view with the combine of the xz plane in an aligned neutral position,</dd><dt>Figure 7</dt><dd>as in FIG. 6, however, the combine is twisted with respect to the excellent position in the xz-plane,</dd><dt>Figure 8</dt><dd>a schematic plan view of a combine with a lying in front of the cutting virtual workspace,</dd><dt>Figure 9</dt><dd>a side view of a combine harvester with lying in front of the cutting virtual reference point,</dd><dt>Figure 10</dt><dd>as in FIG. 9, with reference point further ahead of the cutting mechanism,</dd><dt>Figure 11</dt><dd>a schematic plan view of a tractor with attached via the three-point hitch fertilizer spreader and two virtual reference points,</dd><dt>Figure 12</dt><dd>a block diagram with the evaluation unit and the various sensors.</dd></dl>

In Fig. is shown a combine harvester with attached cutting unit. The GPS antenna is located on the roof of the combine in approx. 4 m height. The reference point is placed here on the outside of the cutting unit in a height of 1m. This side view shows the combine in the yz plane of the terrestrial coordinate system. Also marked is the fictitious coordinate system (bx, by, bz) fixed to the combine harvester. The distance between the location of the GPS antenna and the reference point is designated by the reference character (D). In this side view, however, only the projection (i.e.₂) of the distance line (D) on the yz plane representable.

In FIGS. 2, 4, 6, the combine harvester is shown in an aligned neutral position in the associated plane. The illustrations are schematic and not to scale.

2 shows the top view of a combine in an aligned neutral position. The GPS antenna is located on the roof of the combine harvester. As an illustration, four GPS satellites from which the GPS antenna can receive satellite navigation signals are also drawn. The drawn position is chosen so that the vehicle longitudinal direction is parallel to the NS direction (y-coordinate) and the cutting unit is oriented to the north. Of course, in the context of the invention, another aligned position can be selected. The choice of this location for easy determination of the vehicle-specific base conversion quantities is merely a convention. However, the aligned situation, taking into account conventions of the satellite navigation system used, should be chosen so that the determination of the basic conversion factors is as simple as possible. The base conversion quantities are referred to as "vehicle-specific" because, once the aligned position is conventionally determined, they are uniquely determinable by the location of the GPS antenna on the vehicle and the desired position of the reference point for that "vehicle-specific" constellation. The determination of the basic conversion quantities can be done by measuring and / or mathematical calculations.

In the example shown in FIG. 2, the difference (X_P0-X_A0) between the x-coordinate of the reference point and the x-coordinate of the GPS antenna equal to 3.5 m; the difference (Y_P0-Y_A0) between the y-coordinate of the reference point and the y-coordinate of the GPS antenna is equal to 5 m. d₁ is the projection of the distance line (D) between the GPS antenna and the reference point on the horizontal plane (x, y). The same applies to d₂ and d₃ regarding the respective levels.<maths id="math0001" num=""><math display="block"><mi mathvariant="normal">D</mi><mo>=</mo><msqrt><mrow><mo>(</mo><msup><mrow><mn>3</mn><mo>.</mo><mn>5</mn></mrow><mn>2</mn></msup><mo>+</mo><msup><mn>5</mn><mn>2</mn></msup><mo>+</mo><msup><mn>3</mn><mn>2</mn></msup><mo>)</mo><msup><mi mathvariant="normal">m</mi><mn>2</mn></msup></mrow></msqrt><mo>=</mo><mn>6</mn><mo>.</mo><mn>8th</mn><mo>⁢</mo><mi mathvariant="normal">m</mi></math><img file="EP0970595B2_D0001.tif" /></maths><maths id="math0002" num=""><math display="block"><msub><mi mathvariant="normal">d</mi><mn>1</mn></msub><mo>=</mo><msqrt><mfenced separators=""><msup><mrow><mn>3</mn><mo>.</mo><mn>5</mn></mrow><mn>2</mn></msup><mo>+</mo><msup><mn>5</mn><mn>2</mn></msup></mfenced><mo>⁢</mo><msup><mi mathvariant="normal">m</mi><mn>2</mn></msup></msqrt><mo>=</mo><mn>6</mn><mo>.</mo><mn>1</mn><mo>⁢</mo><mi mathvariant="normal">m</mi></math><img file="EP0970595B2_D0002.tif" /></maths> φ₀ denotes the angle between d₁ and the NS direction / vehicle longitudinal direction. φ₀ is determined by:<maths id="math0003" num=""><math display="block"><mi>tan</mi><mspace width="1em" /><mfenced><msub><mi mathvariant="normal">φ</mi><mn>0</mn></msub></mfenced><mo>=</mo><mi>tan</mi><mfenced separators=""><mn>3</mn><mo>.</mo><mn>5</mn><mo>/</mo><mn>5</mn></mfenced><mo>⇒</mo><msub><mi mathvariant="normal">φ</mi><mn>0</mn></msub><mo>=</mo><msup><mn>35</mn><mn>0</mn></msup><mn>,</mn></math><img file="EP0970595B2_D0003.tif" /></maths> φ₀ and d₁ can as well as α₀, β₀, d₂ and d₃ be used as vehicle-specific base conversion quantities.

4 shows the side view (yz plane) of the combine in the aligned position. The GPS antenna is located on the roof of the combine harvester at 4 m height, the reference point at the cutting unit at 1 m height. The difference (Y_P0-Y_A0) between the y-coordinate of the reference point and the y-coordinate of the GPS antenna is, as already apparent from Figure 2, equal to 5 m; the difference (Z_P0-Z_A0) between the z-coordinate of the reference point and the z-coordinate of the GPS antenna is equal to -3 m. <maths id="math0004" num=""><math display="block"><msub><mi mathvariant="normal">d</mi><mn>2</mn></msub><mo>=</mo><msqrt><mfenced separators=""><msup><mn>3</mn><mn>2</mn></msup><mo>+</mo><msup><mn>5</mn><mn>2</mn></msup></mfenced><mo>⁢</mo><msup><mi mathvariant="normal">m</mi><mn>2</mn></msup></msqrt><mo>=</mo><mn>5</mn><mo>.</mo><mn>83</mn><mo>⁢</mo><mi mathvariant="normal">m</mi></math><img file="EP0970595B2_D0004.tif" /></maths> α₀ denotes the angle between d₂ and the vertical / z direction α₀ is determined by:<maths id="math0005" num=""><math display="block"><mi>tan</mi><mspace width="1em" /><mfenced><msub><mi mathvariant="normal">α</mi><mn>0</mn></msub></mfenced><mo>=</mo><mi>tan</mi><mfenced separators=""><mn>5</mn><mo>/</mo><mn>3</mn></mfenced><mo>⇒</mo><msub><mi mathvariant="normal">α</mi><mn>0</mn></msub><mo>=</mo><mn>59</mn><mo>⁢</mo><mi mathvariant="normal">°</mi><mn>,</mn></math><img file="EP0970595B2_D0005.tif" /></maths>

Fig. 6 shows the side view (x, z-plane) of the combine in the aligned position. The GPS antenna is located on the roof of the combine harvester at 4 m height, the reference point at the cutting unit at 1 m height. The difference (X_P0-X_A0) between the x-coordinate of the reference point and the x-coordinate of the GPS antenna is, as already apparent from Figure 2, equal to 3.5 m; the difference (Z_P0-Z_A0) between the z-coordinate of the reference point and the z-coordinate of the GPS antenna is equal to -3 m. <maths id="math0006" num=""><math display="block"><msub><mi mathvariant="normal">d</mi><mn>3</mn></msub><mo>=</mo><msqrt><mfenced separators=""><msup><mn>3</mn><mn>2</mn></msup><mo>+</mo><msup><mrow><mn>3</mn><mo>.</mo><mn>5</mn></mrow><mn>2</mn></msup></mfenced><mo>⁢</mo><msup><mi mathvariant="normal">m</mi><mn>2</mn></msup></msqrt><mo>=</mo><mn>4</mn><mo>.</mo><mn>61</mn><mo>⁢</mo><mi mathvariant="normal">m</mi></math><img file="EP0970595B2_D0006.tif" /></maths> β₀ denotes the angle between d₃ and the vertical / z direction. β₀ is determined by:<maths id="math0007" num=""><math display="block"><mi>tan</mi><mspace width="1em" /><mfenced><msub><mi mathvariant="normal">α</mi><mn>0</mn></msub></mfenced><mo>=</mo><mi>tan</mi><mfenced separators=""><mn>3</mn><mo>.</mo><mn>5</mn><mo>/</mo><mn>3</mn></mfenced><mo>⇒</mo><msub><mi mathvariant="normal">β</mi><mn>0</mn></msub><mo>=</mo><msup><mn>59</mn><mn>0</mn></msup><mn>,</mn></math><img file="EP0970595B2_D0007.tif" /></maths>

During the use of the combine harvester, the deviations (.phi.,. Alpha., .Beta.) Are measured and, according to the invention, respective current conversion variables for the determination of the reference point are determined using the basic conversion variables described above.

Fig. 3 shows the top view of a combine deviating from the aligned zero position on a flat field. The corresponding conversion factors are:<maths id="math0008" num=""><math display="block"><mi mathvariant="normal">.DELTA.X</mi><mo>=</mo><msub><mi mathvariant="normal">d</mi><mn>1</mn></msub><mspace width="1em" /><mi>sin</mi><mfenced separators=""><msub><mi mathvariant="normal">φ</mi><mn>0</mn></msub><mo>-</mo><mi mathvariant="normal">φ</mi></mfenced></math><img file="EP0970595B2_D0008.tif" /></maths> and<maths id="math0009" num=""><math display="block"><mi mathvariant="normal">.DELTA.Y</mi><mo>=</mo><msub><mi mathvariant="normal">d</mi><mn>1</mn></msub><mspace width="1em" /><mi>cos</mi><mfenced separators=""><msub><mi mathvariant="normal">φ</mi><mn>0</mn></msub><mo>-</mo><mi mathvariant="normal">φ</mi></mfenced><mn>,</mn></math><img file="EP0970595B2_D0009.tif" /></maths>

Fig. 5 shows a side view of a combine deviating from the aligned zero position, which ascends a slope in the SN direction. The corresponding conversion factors are:<maths id="math0010" num=""><math display="block"><mi mathvariant="normal">.DELTA.Y</mi><mo>=</mo><msub><mi mathvariant="normal">d</mi><mn>2</mn></msub><mspace width="1em" /><mi>sin</mi><mfenced separators=""><msub><mi mathvariant="normal">α</mi><mn>0</mn></msub><mo>+</mo><mi mathvariant="normal">α</mi></mfenced></math><img file="EP0970595B2_D0010.tif" /></maths> and<maths id="math0011" num=""><math display="block"><mi mathvariant="normal">.DELTA.Z</mi><mo>=</mo><msub><mi mathvariant="normal">d</mi><mn>2</mn></msub><mspace width="1em" /><mi>cos</mi><mfenced separators=""><msub><mi mathvariant="normal">α</mi><mn>0</mn></msub><mo>+</mo><mi mathvariant="normal">α</mi></mfenced><mn>,</mn></math><img file="EP0970595B2_D0011.tif" /></maths>

For slopes with 15% slope (α = 8.5 °), the values ​​given in the introduction are:<maths id="math0012" num=""><math display="block"><mi mathvariant="normal">.DELTA.Y</mi><mo>=</mo><mn>5</mn><mo>.</mo><mn>39</mn><mo>⁢</mo><mi mathvariant="normal">m</mi></math><img file="EP0970595B2_D0012.tif" /></maths> and<maths id="math0013" num=""><math display="block"><mi mathvariant="normal">.DELTA.Z</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>23</mn><mo>⁢</mo><mi mathvariant="normal">m</mi><mn>,</mn></math><img file="EP0970595B2_D0013.tif" /></maths>

7 shows a front view of a combine deviating from the aligned zero position in the SN direction, which is inclined along a slope in the OW direction. The corresponding conversion factors are:<maths id="math0014" num=""><math display="block"><mi mathvariant="normal">.DELTA.X</mi><mo>=</mo><msub><mi mathvariant="normal">d</mi><mn>3</mn></msub><mspace width="1em" /><mi>sin</mi><mfenced separators=""><msub><mi mathvariant="normal">β</mi><mn>0</mn></msub><mo>+</mo><mi mathvariant="normal">β</mi></mfenced></math><img file="EP0970595B2_D0014.tif" /></maths> and<maths id="math0015" num=""><math display="block"><mi mathvariant="normal">.DELTA.Z</mi><mo>=</mo><msub><mi mathvariant="normal">d</mi><mn>3</mn></msub><mspace width="1em" /><mi>cos</mi><mfenced separators=""><msub><mi mathvariant="normal">β</mi><mn>0</mn></msub><mo>+</mo><mi mathvariant="normal">β</mi></mfenced><mn>,</mn></math><img file="EP0970595B2_D0015.tif" /></maths>

Hereinafter, the examples described above are represented in the vector and matrix notation known from mathematics.

General coordinate transformation:

Determination for the position vector (X_P, Y_P, Z_P) of the reference point from the position vector (X_A, Y_A, Z_A) of the GPS antenna and the transformation matrix with the matrix elements (a_ij) and the unit vector (1,1,1) in the Cartesian, terrestrial coordinate system:<maths id="math0016" num=""><math display="block"><mrow><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mi mathvariant="normal">X</mi><mi mathvariant="normal">P</mi></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Y</mi><mi mathvariant="normal">P</mi></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Z</mi><mi mathvariant="normal">P</mi></msub></mtd></mtr></mtable></mfenced><mo>=</mo><mo>[</mo><mtable><mtr><mtd><msub><mi mathvariant="normal">X</mi><mi mathvariant="normal">A</mi></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Y</mi><mi mathvariant="normal">A</mi></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Z</mi><mi mathvariant="normal">A</mi></msub></mtd></mtr></mtable><mo>]</mo><mo>+</mo><mo>[</mo><mtable><mtr><mtd><msub><mi mathvariant="normal">a</mi><mn>11</mn></msub></mtd><mtd><msub><mi mathvariant="normal">a</mi><mn>12</mn></msub></mtd><mtd><msub><mi mathvariant="normal">a</mi><mn>13</mn></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">a</mi><mn>21</mn></msub></mtd><mtd><msub><mi mathvariant="normal">a</mi><mn>22</mn></msub></mtd><mtd><msub><mi mathvariant="normal">a</mi><mn>23</mn></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">a</mi><mn>31</mn></msub></mtd><mtd><msub><mi mathvariant="normal">a</mi><mn>32</mn></msub></mtd><mtd><msub><mi mathvariant="normal">a</mi><mn>33</mn></msub></mtd></mtr></mtable><mo>]</mo><mo>[</mo><mtable><mtr><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr></mtable><mo>]</mo></mrow></math><img file="EP0970595B2_D0016.tif" /></maths><maths id="math0017" num=""><math display="block"><mrow><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mi mathvariant="normal">X</mi><mi mathvariant="normal">P</mi></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Y</mi><mi mathvariant="normal">P</mi></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Z</mi><mi mathvariant="normal">P</mi></msub></mtd></mtr></mtable></mfenced><mo>=</mo><mo>[</mo><mtable><mtr><mtd><msub><mi mathvariant="normal">X</mi><mi mathvariant="normal">A</mi></msub><mo>+</mo><msub><mi mathvariant="normal">a</mi><mn>11</mn></msub><mo>+</mo><msub><mi mathvariant="normal">a</mi><mn>12</mn></msub><mo>+</mo><msub><mi mathvariant="normal">a</mi><mn>13</mn></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Y</mi><mi mathvariant="normal">A</mi></msub><mo>+</mo><msub><mi mathvariant="normal">a</mi><mn>21</mn></msub><mo>+</mo><msub><mi mathvariant="normal">a</mi><mn>22</mn></msub><mo>+</mo><msub><mi mathvariant="normal">a</mi><mn>23</mn></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Z</mi><mi mathvariant="normal">A</mi></msub><mo>+</mo><msub><mi mathvariant="normal">a</mi><mn>31</mn></msub><mo>+</mo><msub><mi mathvariant="normal">a</mi><mn>32</mn></msub><mo>+</mo><msub><mi mathvariant="normal">a</mi><mn>33</mn></msub></mtd></mtr></mtable><mo>]</mo></mrow></math><img file="EP0970595B2_D0017.tif" /></maths>

Coordinate transformation for the excellent position (NS orientation, no tilt):

<maths id="math0018" num=""><math display="block"><mrow><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mi mathvariant="normal">X</mi><mi mathvariant="normal">P</mi></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Y</mi><mi mathvariant="normal">P</mi></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Z</mi><mi mathvariant="normal">P</mi></msub></mtd></mtr></mtable></mfenced><mo>=</mo><mo>[</mo><mtable><mtr><mtd><msub><mi mathvariant="normal">X</mi><mi mathvariant="normal">A</mi></msub><mo>+</mo><mn>3</mn><mo>.</mo><mn>5</mn></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Y</mi><mi mathvariant="normal">A</mi></msub><mo>+</mo><mn>5</mn></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Z</mi><mi mathvariant="normal">A</mi></msub><mo>-</mo><mn>3</mn></mtd></mtr></mtable><mo>]</mo></mrow></math><img file="EP0970595B2_D0018.tif" /></maths>

Ride in the horizontal plane (see Fig.3):

<maths id="math0019" num=""><math display="block"><mrow><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mi mathvariant="normal">X</mi><mi mathvariant="normal">P</mi></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Y</mi><mi mathvariant="normal">P</mi></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Z</mi><mi mathvariant="normal">P</mi></msub></mtd></mtr></mtable></mfenced><mo>=</mo><mo>[</mo><mtable><mtr><mtd><msub><mi mathvariant="normal">X</mi><mi mathvariant="normal">A</mi></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Y</mi><mi mathvariant="normal">A</mi></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Z</mi><mi mathvariant="normal">A</mi></msub></mtd></mtr></mtable><mo>]</mo><mo>+</mo><mo>[</mo><mtable><mtr><mtd><msub><mi mathvariant="normal">d</mi><mn>1</mn></msub><mo>⁢</mo><mi>sin</mi><mfenced separators=""><msub><mi mathvariant="normal">φ</mi><mn>0</mn></msub><mo>-</mo><mi mathvariant="normal">φ</mi></mfenced></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><msub><mi mathvariant="normal">d</mi><mn>1</mn></msub><mo>⁢</mo><mi>cos</mi><mfenced separators=""><msub><mi mathvariant="normal">φ</mi><mn>0</mn></msub><mo>-</mo><mi mathvariant="normal">φ</mi></mfenced></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr></mtable><mo>]</mo><mo>[</mo><mtable><mtr><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr></mtable><mo>]</mo></mrow></math><img file="EP0970595B2_D0019.tif" /></maths><maths id="math0020" num=""><math display="block"><mrow><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mi mathvariant="normal">X</mi><mi mathvariant="normal">P</mi></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Y</mi><mi mathvariant="normal">P</mi></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Z</mi><mi mathvariant="normal">P</mi></msub></mtd></mtr></mtable></mfenced><mo>=</mo><mo>[</mo><mtable><mtr><mtd><msub><mi mathvariant="normal">X</mi><mi mathvariant="normal">A</mi></msub><mo>+</mo><msub><mi mathvariant="normal">d</mi><mn>1</mn></msub><mo>⁢</mo><mi>sin</mi><mfenced separators=""><msub><mi mathvariant="normal">φ</mi><mn>0</mn></msub><mo>-</mo><mi mathvariant="normal">φ</mi></mfenced></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Y</mi><mi mathvariant="normal">A</mi></msub><mo>+</mo><msub><mi mathvariant="normal">d</mi><mn>1</mn></msub><mo>⁢</mo><mi>cos</mi><mfenced separators=""><msub><mi mathvariant="normal">φ</mi><mn>0</mn></msub><mo>-</mo><mi mathvariant="normal">φ</mi></mfenced></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Z</mi><mi mathvariant="normal">A</mi></msub><mo>-</mo><mn>3</mn></mtd></mtr></mtable><mo>]</mo></mrow></math><img file="EP0970595B2_D0020.tif" /></maths>

Drive in NS direction at a slope in the direction of travel (see Fig.5):

<maths id="math0021" num=""><math display="block"><mrow><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mi mathvariant="normal">X</mi><mi mathvariant="normal">P</mi></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Y</mi><mi mathvariant="normal">P</mi></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Z</mi><mi mathvariant="normal">P</mi></msub></mtd></mtr></mtable></mfenced><mo>=</mo><mo>[</mo><mtable><mtr><mtd><msub><mi mathvariant="normal">X</mi><mi mathvariant="normal">A</mi></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Y</mi><mi mathvariant="normal">A</mi></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Z</mi><mi mathvariant="normal">A</mi></msub></mtd></mtr></mtable><mo>]</mo><mo>+</mo><mo>[</mo><mtable><mtr><mtd><mn>3</mn><mo>.</mo><mn>5</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><msub><mi mathvariant="normal">d</mi><mn>2</mn></msub><mo>⁢</mo><mi>sin</mi><mfenced separators=""><msub><mi mathvariant="normal">α</mi><mn>0</mn></msub><mo>+</mo><mi mathvariant="normal">α</mi></mfenced></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mo>-</mo><msub><mi mathvariant="normal">d</mi><mn>2</mn></msub><mo>⁢</mo><mi>cos</mi><mfenced separators=""><msub><mi mathvariant="normal">α</mi><mn>0</mn></msub><mo>+</mo><mi mathvariant="normal">α</mi></mfenced></mtd></mtr></mtable><mo>]</mo><mo>[</mo><mtable><mtr><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr></mtable><mo>]</mo></mrow></math><img file="EP0970595B2_D0021.tif" /></maths><maths id="math0022" num=""><math display="block"><mrow><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mi mathvariant="normal">X</mi><mi mathvariant="normal">P</mi></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Y</mi><mi mathvariant="normal">P</mi></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Z</mi><mi mathvariant="normal">P</mi></msub></mtd></mtr></mtable></mfenced><mo>=</mo><mo>[</mo><mtable><mtr><mtd><msub><mi mathvariant="normal">X</mi><mi mathvariant="normal">A</mi></msub><mo>+</mo><mn>3</mn><mo>.</mo><mn>5</mn></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Y</mi><mi mathvariant="normal">A</mi></msub><mo>+</mo><msub><mi mathvariant="normal">d</mi><mn>2</mn></msub><mo>⁢</mo><mi>sin</mi><mfenced separators=""><msub><mi mathvariant="normal">α</mi><mn>0</mn></msub><mo>+</mo><mi mathvariant="normal">α</mi></mfenced></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Z</mi><mi mathvariant="normal">A</mi></msub><mo>-</mo><msub><mi mathvariant="normal">d</mi><mn>2</mn></msub><mo>⁢</mo><mi>cos</mi><mfenced separators=""><msub><mi mathvariant="normal">α</mi><mn>0</mn></msub><mo>+</mo><mi mathvariant="normal">α</mi></mfenced></mtd></mtr></mtable><mo>]</mo></mrow></math><img file="EP0970595B2_D0022.tif" /></maths>

Drive in NS direction with a slope perpendicular to the longitudinal direction of the vehicle (see Fig. 7):

<maths id="math0023" num=""><math display="block"><mrow><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mi mathvariant="normal">X</mi><mi mathvariant="normal">P</mi></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Y</mi><mi mathvariant="normal">P</mi></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Z</mi><mi mathvariant="normal">P</mi></msub></mtd></mtr></mtable></mfenced><mo>=</mo><mo>[</mo><mtable><mtr><mtd><msub><mi mathvariant="normal">X</mi><mi mathvariant="normal">A</mi></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Y</mi><mi mathvariant="normal">A</mi></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Z</mi><mi mathvariant="normal">A</mi></msub></mtd></mtr></mtable><mo>]</mo><mo>+</mo><mo>[</mo><mtable><mtr><mtd><msub><mi mathvariant="normal">d</mi><mn>3</mn></msub><mo>⁢</mo><mi>sin</mi><mfenced separators=""><msub><mi mathvariant="normal">β</mi><mn>0</mn></msub><mo>+</mo><mi mathvariant="normal">β</mi></mfenced></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>5</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mo>-</mo><msub><mi mathvariant="normal">d</mi><mn>3</mn></msub><mo>⁢</mo><mi>cos</mi><mfenced separators=""><msub><mi mathvariant="normal">β</mi><mn>0</mn></msub><mo>+</mo><mi mathvariant="normal">β</mi></mfenced></mtd></mtr></mtable><mo>]</mo><mo>[</mo><mtable><mtr><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr></mtable><mo>]</mo></mrow></math><img file="EP0970595B2_D0023.tif" /></maths><maths id="math0024" num=""><math display="block"><mrow><mfenced open="[" close="]"><mtable><mtr><mtd><msub><mi mathvariant="normal">X</mi><mi mathvariant="normal">P</mi></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Y</mi><mi mathvariant="normal">P</mi></msub></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Z</mi><mi mathvariant="normal">P</mi></msub></mtd></mtr></mtable></mfenced><mo>=</mo><mo>[</mo><mtable><mtr><mtd><msub><mi mathvariant="normal">X</mi><mi mathvariant="normal">A</mi></msub><mo>+</mo><msub><mi mathvariant="normal">d</mi><mn>3</mn></msub><mo>⁢</mo><mi>sin</mi><mfenced separators=""><msub><mi mathvariant="normal">β</mi><mn>0</mn></msub><mo>+</mo><mi mathvariant="normal">β</mi></mfenced></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Y</mi><mi mathvariant="normal">A</mi></msub><mo>+</mo><mn>5</mn></mtd></mtr><mtr><mtd><msub><mi mathvariant="normal">Z</mi><mi mathvariant="normal">A</mi></msub><mo>-</mo><msub><mi mathvariant="normal">d</mi><mn>3</mn></msub><mo>⁢</mo><mi>cos</mi><mfenced separators=""><msub><mi mathvariant="normal">β</mi><mn>0</mn></msub><mo>+</mo><mi mathvariant="normal">β</mi></mfenced></mtd></mtr></mtable><mo>]</mo></mrow></math><img file="EP0970595B2_D0024.tif" /></maths>

As already mentioned above, the invention is not limited to the determination of a reference point. Rather, it is quite possible for two or more reference points to be provided. Furthermore, it is provided that the reference point (s) are located as virtual reference points outside the vehicle and outside the processing device.

Furthermore, it is also provided that, according to the invention, a reference line, reference surface or reference volume consisting of two or more reference points can be determined. FIG. 8 shows such a virtual reference surface in front of the cutting unit.

Moreover, it is provided in one embodiment of the invention that the evaluation unit (AWE) in the determination of a virtual reference point at least one parameter of the vehicle such as the vehicle speed considered, so that the position of the virtual reference point relative to the satellite receiving unit (GPS antenna ) is dynamically controllable as a function of at least one parameter. This is based on the driving speed in Figs. 9 and FIG. 10. At a higher driving speed you can drive more or less anticipatory.

In addition, it is provided that in each case, when the reference point lying ahead in the direction of travel has reached the field end (which can be determined, for example, by comparison with a stored field cadastre), with an adjustable time delay, certain operations (eg lifting the cutting deck, lifting and turning the plow) be triggered automatically.

Furthermore, it is provided that at least one position parameter (relative bending angle of the trailer to the towing vehicle, relative height of the three-point hitch, relative intake channel angle, and others) of a vehicle-mounted processing unit of the evaluation unit (AWE) is taken into account, so that the position of the virtual reference point for the satellite receiving unit (GPS antenna) is dynamically controlled as a function of this position parameter. In Fig.11, for example, a tractor is shown with a fertilizer spreader. It is provided to make the position of the virtual reference point of the rotational speed of the spreading disc or the working width of the spreader dependent, so that the reference point is located in each case at the edge of the scattering range. So that the theoretical working width can be determined even better, the position parameters of the three-point hitch are also taken into account in the calculation of the reference point.

In the case of a fertilizer spreader with a plurality of spreading plates, a plurality of corresponding reference points can exist if required, wherein individual reference points can be deactivated and reactivated by the operator of the vehicle. What makes sense in the drawn case of the two scattering plates, for example, when driving at the edge of the field, the speed of the peripheral scattering plate is first reduced and then turned off, then a position determination of the corresponding reference point is superfluous and possibly even disturbing. By incorporating other parameters from the working process, such as the driving speed or fertilizer specific sizes, the working width of the control can be controlled so that even the flight time of the material to be spread (for example, to select the right power on or Ausschaltmomentes the applicator) is taken into account.

The invention has been described herein with reference to a combine harvester and an attached fertilizer spreader. However, it will also be apparent to one skilled in the art that it is also applicable to other utility vehicles, such as construction machinery, that manipulate or reshape a ground contour and also to simple attached implements having their own navigation equipment.