Patent Publication Number: US-2021161060-A1

Title: Guidance working depth compensation

Description:
TECHNICAL FIELD 
     The present disclosure is generally related to agriculture technology, and, more particularly, computer-assisted farming. 
     BACKGROUND 
     Efforts to automate or semi-automate farming operations have increased considerably over recent years. Such efforts serve not only to reduce operating costs but also improve working conditions for operators and reduce operator error, enabling gains in operational efficiency and yield. For instance, agricultural machines may employ an auto-guidance system to reduce operator fatigue and costs. Auto-guidance systems enable traversal through a field based on a navigation point on the vehicle which are matched with waypoints (geographic location points that define or correspond with a wayline, a path plan or a swath plan) by influencing the vehicles steering system. The system continually compares updated positional coordinates of reference points, e.g. the navigation point and the waypoints to enable guidance operations. As used herein the term “reference points” includes both navigation points and waypoints which are necessary to guide a vehicle on a wayline. The navigation point may be defined by  3 D coordinates with reference to a coordinate system on a vehicle while waypoints may be defined by  3 D coordinates with reference to a coordinate system used for satellite navigation. Navigation points are typically offset from an antenna location, and hence depend on where the antenna is mounted on the vehicle. Typically, a navigational point is chosen close to ground. 
     Yet another reference point for use with auto-guidance systems may be associated with an implement towed by an agricultural machine. By way of example, an implement reference point may be a navigation point defined by an offset from a navigation point associated with a towing vehicle. 
     However, the nature of the terrain may cause farming operations for such guided machines to render unintended results. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Many aspects of the disclosure can be better understood with reference to the following drawings. The components in the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the present disclosure. Moreover, in the drawings, like reference numerals designate corresponding parts throughout the several views. 
         FIG. 1  is a schematic diagram that illustrates in front elevation view an agricultural machine demonstrating geotropism and shortcomings to farming using auto-guidance on sloped terrain. 
         FIG. 2  is a schematic diagram that illustrates in front elevation view an agricultural machine demonstrating dam formation for specialized crops and shortcomings to farming using auto-guidance on sloped terrain. 
         FIG. 3  is a schematic diagram that illustrates in front elevation view an agricultural machine demonstrating the determination of the navigation point in a vehicle. 
         FIG. 4A  is a schematic diagram that illustrates in front elevation view an agricultural machine in which a first embodiment of a working depth compensator determines a navigation point on sloped terrain for an initial operation. 
         FIG. 4B  is a schematic diagram that illustrates the view in the reference plane used in satellite navigation in which references used for guiding the vehicle are depicted for the initial operation shown in  FIG. 4A . 
         FIG. 5A  is a schematic diagram that illustrates in front elevation view an agricultural machine in which a first embodiment of a working depth compensator determines a navigation point on sloped terrain for a subsequent operation. 
         FIG. 5B  is a schematic diagram that illustrates the view in the reference plane used in satellite navigation in which relative points and waylines used for guiding the vehicle are depicted for the subsequent operation shown in  FIG. 5A . 
         FIG. 6A  is a schematic diagram that illustrates in front elevation view an agricultural machine in which a first embodiment of a working depth compensator determines a navigation point on sloped terrain for a further subsequent operation. 
         FIG. 6B  is a schematic diagram that illustrates the view in the reference plane used in satellite navigation in which references used for guiding the vehicle are depicted for the further subsequent operation shown in  FIG. 6A . 
         FIG. 6C  is a schematic diagram that illustrates the view in the reference plane used in satellite navigation in which references used for guiding the vehicle are compared for varying working depth 
         FIG. 7A  is a schematic diagram that illustrates in front elevation view an agricultural machine in which a second embodiment of a working depth compensator determines a waypoint on sloped terrain for an initial operation. 
         FIG. 7B  is a schematic diagram that illustrates the view in the reference plane used in satellite navigation in which references used for guiding the vehicle are depicted for the initial operation shown in  FIG. 7A . 
         FIG. 8A  is a schematic diagram that illustrates in front elevation view an agricultural machine in which a second embodiment of a working depth compensator determines a wayline point on sloped terrain for a subsequent operation. 
         FIG. 8B  is a schematic diagram that illustrates the view in the reference plane used in satellite navigation in which references used for guiding the vehicle are depicted for the subsequent operation shown in  FIG. 8A . 
         FIG. 9A  is a schematic diagram that illustrates in front elevation view an agricultural machine in which a second embodiment of a working depth compensator determines a wayline point on sloped terrain for a further subsequent operation. 
         FIG. 9B  is a schematic diagram that illustrates the view in the reference plane used in satellite navigation in which references used for guiding the vehicle are depicted for the further subsequent operation shown in  FIG. 9A . 
         FIG. 9C  is a schematic diagram that illustrates the view in the reference plane used in satellite navigation in which references used for guiding the vehicle are depicted for an alternative initial operation. 
         FIG. 9D  is a schematic diagram that illustrates the view in the reference plane used in satellite navigation in which references used for guiding the vehicle are depicted for an alternative subsequent operation. 
         FIG. 9E  is a schematic diagram that illustrates the view in the reference plane used in satellite navigation in which references used for guiding the vehicle are depicted for an alternative subsequent operation. 
         FIG. 10A  is a schematic diagram that illustrates in front elevation view an agricultural machine in which an embodiment of a working depth compensator determines a reference point on a surface of a sloped terrain. 
         FIG. 10B  is a schematic diagram that illustrates in front elevation view an agricultural machine in which an embodiment of a working depth compensator determines a reference point above a surface of a sloped terrain. 
         FIG. 11A  is a schematic diagram that illustrates in front elevation view an agricultural machine and an implement in which a third embodiment of a working depth compensator determines an implement reference point on sloped terrain for a subsequent operation with reference to an initial operation shown in  FIG. 9A . 
         FIG. 11  B is a schematic diagram that illustrates the view in the reference plane used in satellite navigation in which references used for guiding the implement are depicted for the initial operation shown in  FIG. 11A . 
         FIGS. 12A-12D  are schematic diagrams that illustrate in front elevation view an agricultural machine and an implement in which a third embodiment of a working depth compensator determines an implement reference point on sloped terrain for an initial and subsequent operation for the application of grape production. 
         FIG. 13A  is a block diagram that illustrates an embodiment of a control system implemented in an embodiment of a working depth compensator. 
         FIG. 13B  is a block diagram of an embodiment of a computing system used in the control system of  FIG. 5A . 
         FIG. 14  is a flow diagram that illustrates an embodiment of a working depth compensating method. 
     
    
    
     DESCRIPTION OF EXAMPLE EMBODIMENTS 
     Overview 
     In the embodiments, a system comprising a receiver comprising an antenna configured to receive position information; and a computing system in communication with the receiver, the computing system configured to: record values corresponding to the position information and a working depth beneath a soil surface along a first path; determine reference points for a second path based on the recorded values, a slope of the soil surface, and a working depth or height along the second path; and guide movement of a machine along the second path. 
     DETAILED DESCRIPTION 
     Certain embodiments of a working depth compensator, including associated systems and methods, are disclosed that determine reference points for auto-guidance traversal of a field during multi-stage farming operations by considering a working depth of at least a first stage of operations and computing a path or path corrections on sloped terrain for subsequent (second, third, fourth, etcetera stages) operations. In other words, the depth of a first farming or agricultural operation is considered in planning or proceeding to a second, subsequent farming operation. 
     Embodiments of the working depth compensator, including associated systems and methods, use reference points to guide a vehicle or an implement relative to a wayline. Generally these reference points are described with three-dimensional coordinates with reference to a coordinate system used and defined for satellite navigation when a wayline or its associated waypoints are described. If the reference point is associated with a vehicle, such as, for example, a vehicle navigation point, the three-dimensional coordinates may be determined with reference to a vehicle coordinate system. The coordinate systems used to define reference points may be, for example, Cartesian coordinate systems (using X,Y,Z coordinates). As depicted in  FIG. 1 , a coordinate system for the vehicle (CS-V) and a coordinate system for the satellite positioning system (CS-GPS) may both be Cartesian coordinate systems, but the two systems may not be aligned. An offset to a reference point may be described herein in terms of a single coordinate or axis, with the understanding that the offset does not affect other coordinates or axes. Furthermore, the present description and drawings may describe changes to reference points in terms of two dimensions and using two-dimensional views even though the calculation of coordinates, especially of wayline points of a wayline, may require three-dimensional transformation of coordinates using known mathematical methods. This is provided for simplicity reasons. 
     Digressing briefly, it is known that plants grow in a direction of Earth center, an effect referred to as geotropism. This gravitational influence of plant growth may result in problems if the plants are grown on sloped terrain and worked with machines that use guidance systems. For instance, and referring to  FIG. 1 , in a first operation (e.g., planting) of a multi-stage farming operation (e.g., the stages involving different/distinct functions occurring in non-overlapping intervals, such as separated by days, weeks or months), seeds (e.g., seed, S) may be placed in the soil at a predetermined working depth, WDx from a soil surface as dispensed from a machine (or from a towed implement, not shown, coupled to the machine). During the planting operation, a guidance system for the machine may consider a navigation point (e.g., referred to as NP) for use in guiding the vehicle along a predetermined path delineated by the wayline points. Assume the soil surface is along a slope as illustrated in  FIG. 1 . An effect of geotropism is that the plant grows at an angle to the ground  18  and not along axis A of the machine being the symmetric axis of the vehicle  10  in front view and any predetermined position in longitudinal direction. In other words, the plant does not grow through the navigation point, NP. Consequently, any subsequent operation using automatic guidance and a wayline/path determined in a previous operation (or a shared wayline/path plan) considers an incorrect position of the plant. For instance, during a second stage (high-precision weed control) of the farming operation using, say, a mechanical harrow/rake that agitates the soil surface, the harrow is guided via satellite signals and auto-steer control along a path that matches the now unsuitable navigation point, NP, in which case the plant, P, may be destroyed instead of the weeds, W. 
     Similarly, if the second stage, or even later stages, of the farming operation involves a precision fertilizer application, the weeds, W, may be treated instead of the plants, P. In contrast, by using certain embodiments of a working depth compensator according to the present invention, precision or ecological farming (e.g., in the case of weed control, using mechanical harrows instead of blanket application of pesticides) may be implemented with a mitigated or eliminated risk to plant growth. 
     Attention is now directed to  FIG. 2 , which is a schematic diagram that illustrates how a sloped terrain can influence soil dam formation during guidance-based farming. Certain specialized crops, such as asparagus, are grown in soil dams, such as the soil dam D illustrated in  FIG. 2 . In the case of asparagus, the asparagus plant P is normally planted at point S (aligned with the axis, A, of the machine  10 ) located beneath the soil surface  18  using reference point NP for guidance. In a subsequent operation, the soil dam, D, is built-up by using a known dam former using the same path as before. However, on a slope, the effect is that the plant, P, may grow and break the soil dam, D, at the side of the dam instead of through the top plane as desired. This condition makes harvesting, especially automated harvesting, difficult. 
     Grape production is another agricultural operation that benefits from the advantages of the present invention. Grape production is often done on hilly ground and requires agricultural work at or near the ground surface, such as weed control, but also requires work done at a considerable height above the ground surface, such as when cutting leaves or removing leaves with a leaf cutter or blower so that the sunlight can reach each the grapes. Thus, the effects of geotropism can create severe problems in using guidance systems for multiple operations in grape production. 
     Having summarized certain features of a working depth compensator of the present disclosure, reference will now be made in detail to the description of a working depth compensator as illustrated in the drawings. While the working depth compensator will be described in connection with these drawings, there is no intent to limit it to the embodiment or embodiments disclosed herein. For instance, in the description that follows, one focus is on a self-propelled machine having a global navigation satellite systems (GNSS) receiver arranged centrally atop the machine and using a single antenna, however it should be appreciated by one having ordinary skill in the art in the context of the present disclosure that the GNSS receiver may be located elsewhere and/or comprise additional antennas in some embodiments and hence is contemplated to be within the scope of the disclosure. Further, though the correction for the terrain (e.g., sloped surface) is deemed suitable for guiding subsequent operations for the machine and an integrated or towed (e.g., through a tow bar, three-point hitch, etc.) implement, in some embodiments, appropriate correction (e.g., using GNSS modules on both the implement and the towing machine, and/or communicating differences between computing systems used in towed and towing machines, etc.) may be performed for offsets in travel direction/angle between the towing machine and towed implement while traversing a slope or turns in some embodiments. Regarding the determination of working depth, an operator may enter at a user interface the value for the working depth, or this value may be provided automatically by the implement (e.g., implement controller or sensor) forwarding settings via ISOBUS to the computing system  16 . Alternatively, the working depth may be determined by measuring the position of a three-point hitch and calculate the working depth based on the geometry of the three-point hitch and/or the implement. Further, although the description identifies or describes specifics of one or more embodiments, such specifics are not necessarily part of every embodiment, nor are all various stated advantages necessarily associated with a single embodiment or all embodiments. On the contrary, the intent is to cover all alternatives, modifications and equivalents included within the spirit and scope of the disclosure as defined by the appended claims. Further, it should be appreciated in the context of the present disclosure that the claims are not necessarily limited to the particular embodiments set out in the description. 
     Note that reference points comprise spatial coordinate values that are used by the machine to compare with continually updated, satellite-based positional coordinates to autonomously or semi-autonomously guide a machine over a ground surface through one or more fields. 
       FIG. 3  illustrates an exemplary method of determining a vehicle navigation point NP which is known in the art. An exemplary tractor  10  including an automated guidance system  16  is illustrated. The tractor  10  includes a GNSS receiver assembly  12  operable to receive navigational signals from a plurality of GNSS satellites and to calculate its geographic location as a function of the signals. The GNSS receiver assembly  12  typically corresponds to the location of a satellite signal receiver associated with the component  12 . While for practical purposes the location of the GNSS receiver assembly  12  and the location of the satellite receiver antenna (or other receiver antenna) are often identical, the location of the satellite receiver antenna will be referred to herein as the antenna point AP. The antenna point AP corresponds to the geographic location of the tractor used by the guidance system unless an offset or adjustment is applied, as explained herein. The GNSS receiver assembly  12  may be placed at or near a top of the vehicle, such as on the top of the cabin of the tractor  10 , to maximize satellite signal reception. Placing the GNSS receiver assembly  12  on top of the vehicle results in an antenna point AP corresponding to a geographic location of the top of the vehicle that may be several meters removed from the ground surface  18 . Modern precision agriculture relies on positioning with an accuracy of less than one meter and sometimes an accuracy within the range of one or two centimeters, such that using an antenna point AP located several meters from the ground surface  18  may result in errors in automated guidance. For these reasons, most agricultural applications based on satellite navigation require that the vehicle be guided using a point other than the antenna point AP. The navigation point (NP) is a virtual point used by the guidance system  16  to guide the vehicle along a defined wayline/path. For example, algorithms run by vehicle guidance system  16  may control vehicle steering so that the navigation point of the vehicle moves along a defined or desired path (or matches with waypoints associated with the path). 
     Alternatively, rather than applying an offset or adjustment Y to the antenna point AP to generate the navigation point NP, another virtual point referred to as intermediate point IP may be introduced. One advantage of using the intermediate point IP is that the distance Y 1  between antenna point AP and intermediate reference point IP is mostly fixed and depends on the design of the tractor  10  while the distance Y 2  between intermediate point IP and navigation point NP is variable when the tire size or the tire inflation pressure is changed. Thus, this intermediate point IP is commonly defined as the intersection point between vertical axis A and the horizontal rotational axis of the rear axle. A system to determine the distance Y 2  is described in published United States Patent Application Publication No. 2016/0355187. 
     United States Patent Application Publication No. 2018/0024252 describes another system for determining a navigation point on a vehicle. In that system a position of a first portion of the mobile machine (e.g., the vehicle cabin with GNSS receiver assembly on its top being attached to the chassis via a cab suspension system) relative to a second portion of the mobile machine (e.g., the chassis) is determined to calculate the offset of a navigation point according to the position of the first portion of the mobile machine relative to the second portion of the mobile machine. 
     While the systems disclosed in US 2016/0355187 and US 2018/0024252 work well in some conditions, neither system considers working depth and ground surface slope to adjust a reference point for auto-guidance. 
     It should be appreciated that, though the machine  10  is illustrated as a tractor in the embodiments described below, other machines (or combination of machines) may be used, including self-propelled machines with an integrated implement (e.g., an ACCO Terragator) or a machine (e.g., tractor, combine, etc.) with a towed implement, such as a planter, sprayer, mechanical harrow, etc. The machine  10  is illustrated with a GNSS receiver assembly  12 , which includes a GNSS receiver and an antenna. In some embodiments, the GNSS receiver assembly  12  may include any one or a combination of multiple GNSS receivers or multiple antennas. The GNSS receiver assembly  12  is configured to receive position information for the machine  10  from plural satellites of one or more GNSS satellite networks (e.g., Global Positioning System (GPS), Galileo, Compass, GLONASS, etc.), as is known. The position information may be augmented with public and/or proprietary differential correction signals (e.g., DGPS, SBAS, etc.) and/or real-time kinematic (RTK) satellite services, as is known. For purposes of discussion, a single GNSS receiver using a single antenna is described for the GNSS receiver assembly  12 , though it should be appreciated by one having ordinary skill in the art that additional antennas may be used in some embodiments, and/or that additional GNSS receivers may be used (e.g., plural receivers on the machine  10  and/or added to a towed implement). The antenna of the GNSS receiver assembly  12  is centrally located atop the machine  10 , as indicated by a central axis, A. In some embodiments, the antenna and/or GNSS receiver assembly  12  may be located elsewhere on the machine  10 . The machine  10  further comprises a computing system  16 , which includes one or more computing devices or electronic control units (ECUs) comprising guidance software, among other software. In some embodiments, the functionality of the computing system  16  may reside entirely within the machine  10  or be distributed amongst the machine  10  and a coupled implement. In some embodiments, all or a portion of the functionality of the computing system  16  may reside remotely, such as at a farm computing network, server farm, cloud computing platform, etc. located remote from the farm. For brevity and clarity in describing certain features of a working depth compensator, the computing system  16  is described in the context of the invention as residing in the machine  10 , with further description of the computing system  16  set forth further below. 
     In a first preferred embodiment of the invention a working depth compensator adjusts a navigation point on the vehicle depending on the working depth and ground surface slope. With this embodiment of the invention a single set of waylines, such as a set of parallel A-B waylines covering the complete field, is used for a first initial operation as well as any subsequent stage of operations without adjustment or modification. 
     As used herein, the term “working depth” generally refers to a distance between an operating point and the ground surface. Thus, working depth includes a distance below the ground surface as well as a distance above the ground surface, depending on the particular agricultural operation and the operating point associated with the operation. 
     Turning now to  FIG. 4A , an agricultural machine  10  with a guidance system including a working depth compensator according to embodiments of the invention is illustrated operating on a field with a ground surface slope of angle α. The working depth compensator of the guidance system  16  offsets the navigation point NP 1  along axis A during the initial operation by considering the current operating position OP 1 , working depth WD 1 , and slope α. By using the offset navigation point NP 1  (offset to match with operating point OP 1 ) for guidance on wayline WL (indicated with a vertical line), the position of the vehicle  10  is shifted laterally from position  11 A (corresponding to position A of the vertical axis) distance m 1  along the ground surface  18  to position  11 B (corresponding to position A 1  of the vertical axis) when driving along the slope. The values for the offset distance n 1  (in the satellite reference plane and perpendicular to gravity) and m 1  (along ground surface  18 ) can be calculated using slope α and working depth WD 1  according to known trigonometric equations. However, as the working depth compensator according the first embodiment of the invention may determine the offset using WD 1  without determining n 1  or m 1  or otherwise considering the slope α for calculation, this is not discussed further. 
       FIG. 4B  is a view in the reference plane used in satellite navigation indicated by arrow GPS in  FIG. 4A . The reference plane depicted in  FIG. 4B  is perpendicular to the direction of gravity and tangential to a flat surface of the earth and/or a reference ellipsoid (e.g., WGS-84). The geographic position of the machine  10  as it moves along the ground surface  18  (shown in  FIG. 4A ) is depicted with a horizontal line designated as NP 1 /OP 1 . By offsetting the navigation point NP 1  and using this reference point (that is, the offset navigation point) for guiding the machine  10  along the predetermined wayline WL, the ground based navigation point NP (being the intersection between vehicle axle A and soil surface  18 ) is only aligned with wayline WL on a ground surface that is level (perpendicular to the direction of gravity). With increasing slope α (dramatically depicted by the curved broken lines in  FIG. 4B ), ground surface based navigation point NP diverges from wayline WL (indicated by distance n 1  for NP 1 ) and approaches wayline WL as slope α decreases. The same applies to the position of the vehicle  10 , which moves away from the position  11 A in a downhill direction toward position  11  B with increasing slope α and moves toward position  11 A in an uphill direction as the angle α decreases toward zero. The wayline WL always corresponds to the position of the seed S. Generally the offset of the navigation point along a wayline is a continuous, smooth process (as slope α is also continuously changing) without abrupt changes, as abrupt changes may result in abrupt lateral offsets of the vehicle which are not feasible for most agricultural operations, e.g. if an implement is operated in the soil. 
     Additional waylines (e.g., parallel A-B or contoured waylines) are travelled by the machine  10  accordingly. For clarity reasons the subsequent operations are explained by just depicting one single A-B wayline being part of a set of waylines which are not shown but which may be necessary to work a complete field. 
     In a second subsequent operation depicted with  FIG. 5A  at the same geographic position as shown in  FIG. 4A , but with a new working depth WD 2  corresponding to operating point OP 2 . The new working depth WD 2  is still below, but closer to, the ground surface  18  and may be used, for example, for operating a harrow or similar implement to work the soil. The plant P is illustrated in  FIG. 5A  with a growth level approximately matching working depth WD 2  at operating point OP 2 . The application of the new working depth WD 2  results in an offset of navigation point NP along axis A, wherein navigation point NP 2  is used to guide the vehicle along the same wayline WL used in the previous operation shown in  FIG. 4A . When using the offset navigation point NP 2  to guide the vehicle  10  along wayline WL (indicated with a vertical line), the vehicle  10  is shifted laterally along the ground surface  18  to position  11 C (corresponding to position A 2  of the vertical axis) compared to the position  11 A (corresponding to position A of the vertical axis) when ground based navigation point NP is considered. As shown in  FIG. 5B  with a view indicated by arrow GPS in  FIG. 5A , by offsetting the navigation point NP 2  and using this reference point to guide the tractor  10  along the predetermined wayline WL corresponding to the position of seed S and plant P, the ground based navigation point NP is only aligned with wayline WL on even surface. With increasing slope α, ground based navigation point NP diverges from wayline WL (indicated with distance n 2  for NP 2 ) and moves towards WL when slope α is reduced. The same applies to the position  10 . 2  of the vehicle which moves away from the position  10 . 0  in a downhill direction with increasing slope angle α. The geographic position shown in  FIG. 5A  is depicted with a horizontal line at NP 2 /OP 2  in  FIG. 5B . 
     In a third subsequent operation depicted in  FIG. 6A  at the same geographic position as shown in  FIG. 4A and 5A , a further working depth WD 3  (corresponding to new operating point OP 3 ) is used by the working depth compensation system. The working depth WD 3  approximately corresponds to the top of a soil dam D and is located above ground surface  18 . The new working depth WD 3  results in a new navigation point NP 3  that, when used by the machine  10  to guide the machine  10  along wayline WL, shifts the vehicle  10  laterally in an uphill direction to position  11  D (corresponding to position A 3  of the vertical axis). It should be noted that the navigation point NP 3  still corresponds to wayline WL used in in the previous operations depicted in  FIGS. 4A and 5A . 
     As shown in  FIG. 6B  with a view indicated by arrow GPS in  FIG. 6A , the curve on which ground navigation point NP travels with reference to wayline WL (and seed position S) is on the left side of WL indicating a working point OP 3  above ground. The geographical position shown in  FIG. 6A  is depicted with a horizontal line at NP 3 /OP 3  in  FIG. 6B . 
     The working depth compensation shown in  FIGS. 6A and 6B  may be used to ensure that a soil dam D for planting asparagus is created with plant P breaking through at the top surface (parallel to soil surface  18 ) of the soil dam D rather than through a side of the dam D as shown in  FIG. 2 . This eases harvesting and further processing. 
     In the embodiment illustrated in  FIGS. 4A-6B , the initial stage was provided with an offset of the navigation point NP 1  based on working depth WD 1  as shown in  FIG. 4A . Alternatively, the initial operation may be provided without offsetting the navigation point (so that NP is used as the first navigation point) while in subsequent stages of operation, the navigation point is offset depending on working depth. Furthermore, the working depth compensator may provide the correction of the navigation point for subsequent operations by considering actual working depth, determining actual slope α during driving along the wayline and dynamically calculate and adjust the navigation point on the fly. Alternatively the working depth compensator may determine an adjusted navigation point in advance by recording slope α during an initial operation and calculating the adjusted navigation point depending on working depth for at least the next wayline (and each waypoint associated with the wayline) for subsequent operations as an off-line path planning procedure. Alternatively, the working depth compensator may receive data regarding slope α for import by map data. Furthermore, in the above described embodiment, the working depth compensator considered subsequent operations with constant working depth, so that the correction of the navigation point simply depends on the change of slope α during said operation. However, the working depth compensator may consider simultaneous changes to both parameters slope α and working depth WD. Again, due to the nature of some agricultural operations, this requires a smooth change in working depth to avoid abruptly offsetting the navigation point and, as a consequence, abrupt lateral offsets to the vehicle travel path which would not be feasible for most agricultural operations, including operations involving an implement working the soil. This is depicted in  FIG. 6C  with a view indicated with arrow GPS in  FIG. 6B  wherein a first curve (indicated with NP-WD 3 ) represents the offset of ground based navigation point NP with constant working depth WD 3  shown in  FIG. 6B  and a second curve (indicated with NP-WD 4 ) represents the offset of ground based navigation point NP with constant further working depth WD 4 . With reference to  FIG. 6A  but not shown therein, the working depth WD 4  is smaller compared to WD 3  but still above ground surface  18 . In this subsequent operation, the working depth is changed from working depth WD 3  when the vehicle passes geographical position G 1  to WD 4  at geographical position G 2  while simultaneously the slope α changes from first slope α 1  (at G 1 ) to a 2  (at G 2 ) along wayline WL. As a consequence, the curve representing the position of the ground based navigation NP shows a transition area T in which the distance to WL is influenced by the simultaneous changes in working depth WD and slope a. 
     One advantage of the embodiment of the invention described above is that a machine performing a multiple operations on a crop growing on sloped terrain can use a single wayline (or set of waylines) for each operation, even though the actual position of the machine performing the operation may shift laterally relative to the wayline to accommodate changes in the operating point of the various operations. This is possible because the system adjusts the location of the machine&#39;s navigation point (rather than the wayline) according to the working depth and the ground surface slop angle. Thus, the machine&#39;s guidance system does not need to store different waylines for different applications that require varying working depths, or for different machines with different working depth settings. The guidance system always works with one set of waylines in terms of the absolute geographical position. This requires less storage and computational capacity and enables the transfer of waylines to different applications/machines even when working depth varies. 
     In a second embodiment of the invention the working depth compensator adjusts a wayline and waypoints associated with the wayline that are used for guiding the vehicle, wherein adjustments to the wayline are based on a working depth and the ground surface slope angle α. This embodiment differs from the first embodiment, described above, in that when using this second embodiment the waylines (associated with the crop or field) are adjusted rather than the navigation point (associated with the machine). While this embodiment of the invention may result in multiple different waylines being used over time on the same crop or field, it may be desirable or advantageous in some circumstances. Some machine guidance systems, for example, may not import or export waylines and/or may simply generate waylines on-the-fly based on an initial path manually driven by an operator. These systems would not benefit from sharing common waylines for subsequent operations. 
     Further waylines (e.g. parallel A-B or contoured waylines) are travelled accordingly. For clarity reasons the subsequent operations are explained by just depicting one single wayline being part of a set of waylines which are not shown but which may be necessary to work a complete field 
       FIG. 7A  illustrates an agricultural machine  10  on a field with a ground surface  18  which is at least partly sloped according to an angle α. During an initial first operation, the working depth compensator records the slope α and the working depth WD 1  corresponding to a current operating position OP 1  and the machine records or follows wayline WL 1  using the ground based navigation point NP at the geographic position depicted in  FIG. 7A . The waypoint WP 1  corresponds to the intersection of wayline WL 1  and ground surface  18  such that it matches the ground based navigation point NP which is also determined on ground surface  18 . It will be appreciated, however, that wayline point WP 1  (or any subsequent waypoint) could be moved to any vertical position along wayline WL 1  without influencing the positioning of vehicle  10  as the positioning is provided in the two-dimensional view indicated with arrow GPS, so that the vertical position of wayline point WP 1  is not relevant. Therefore, the offset of any subsequent wayline is only determined by a horizontal offset while in the figures, the waypoint must be seen as a virtual point and is drawn on the ground  18  to match with navigation point NP. 
     The wayline WL 1  may be either stored or imported for use during this initial first operation. Slope a and the working depth WD 1  may then be recorded during initial driving or included in the imported or stored map data. 
     With reference to  FIG. 7B  showing the view in the reference plane used in satellite navigation and indicated by arrow GPS in  FIG. 7A , the initial operation uses wayline WL 1 . The geographic position of the machine  10  shown in  FIG. 7A  is depicted in  FIG. 7B  by a horizontal line at WP 1 /OP 1 . With increasing slope α (dramatically depicted by curve a rotated onto drawing plane), seed point S and operating point OP 1  diverge from wayline WL 1 . Similarly, seed point S and operating point OP 1  move toward WL 1  as slope α decreases. Thus, on sloped terrain the location of the row of sees does not correspond to the wayline WL 1 . 
     In a second subsequent operation depicted in  FIG. 8A  at the same geographic position as shown in  FIG. 7A , a new working depth WD 2  (or operating point OP 2 ) is considered which is below ground surface  18 , e.g. as used for operating a harrow or similar implement at or near the ground surface  18 . According to this embodiment of the invention, and in contrast to the first embodiment described above corresponding to FIGS. 5 A and  5 B for the same parameters, the working depth compensator of the guidance system  16  is uses the same ground based navigation point NP for different operations but determines a new wayline WL 2  for each operation according to working depth WD and slope a. The machine&#39;s guidance system  16  uses the wayline WL 2  for guidance by steering the machine  16  so that the ground based navigation point NP follows the wayline WL 2 . The new wayline WL 2  may be determined using one or more virtual waypoints, such as virtual waypoint WP 2  ( FIG. 8A ), and an initial waypoint WP 1 . As mentioned above, the vertical positions of waypoint WP 1  and waypoint WP 2  are not relevant for navigation but are shown on ground surface  18  to illustrate how they correspond to navigation point NP. 
     The wayline offset w 2  to the initially recorded or used wayline WL 1  or virtual waypoint (depicted with WP 1 ) is determined in the horizontal direction by the equation: 
         w 2= d 2×sin(α)
     Wherein d 2  is the distance between the initially considered operating point OP 1  (or seed position) and operating point OP 2  of the subsequent operation, perpendicular to ground  18 . In  FIG. 8A , the distance D 2  can be calculated by subtracting the working depth WD 2  from the working depth WD 1 :   

         d 2=WD1−WD2
     The horizontal position of wayline WL 2  (depicted by virtual wayline point WP 2 ) is determined by applying a horizontal offset w 2  to the wayline WL 1  (depicted by virtual point WP 1 ) as the vertical offset of WP 2  compared to WP 1  is not relevant. The application of the offset w 2  results in the vehicle  10  shifting laterally along the ground surface  18  to position  11 C (corresponding to axis A 2 ) from position  11 A (indicated by broken lines) when wayline point WP 1  is considered. As shown in  FIG. 8B  the curve followed by waypoint WP 2  is only aligned with wayline WL 1  on level ground surfaces. The geographic position of the machine  10  shown in  FIG. 8A  is depicted with a horizontal line at WP 2 /OP 2  in  FIG. 8B . With increasing slope α (dramatically depicted with a curve a rotated onto drawing plane), wayline point WP 2  and wayline WL 2  diverge from wayline WL 1 , and move towards WL 1  as slope α decreases. The same applies to the curve on which the operating point OP 2  (seed location S) moves relative to wayline WL 1 . Again also the position  11 C of the vehicle moves away from the position  11 A with increasing slope α. Generally the adjustment of the wayline or waypoints is a continuous, smooth process (as slope α is also continuously changing) without abrupt adjustments or offsets as that would cause undesired abrupt lateral shifts of the vehicle which are not feasible for most agricultural operations, such as operations involving an implement working the soil.   

     A third subsequent operation is depicted in  FIG. 9A  at the same geographic position as shown in  FIGS. 7A and 8A , wherein another working depth WD 3  (corresponding to operating point OP 3 ) is used. The working depth WD 3  is located above the ground surface  18  and corresponds to the top and center of a soil dam D. The working depth compensator of the guidance system  16  uses the ground based navigation point NP and determines a new wayline WL 3  calculated from the working depth WD and slope α. The guidance system  16  guides the machine  10  such that the navigation point NP follows the wayline WL 3 . The new wayline WL 3  may be determined using one or more virtual waypoints, such as virtual waypoint WP 3  ( FIG. 9A ), and an initial waypoint WP 1 . 
     The wayline offset w 3  from the initially recorded or used wayline WL 1  or virtual waypoint (depicted as WP 1 ) is determined in horizontal direction by the equation: 
         w 3= d 3×sin(α)
     Where d 3  is the distance between the initially considered operating point OP 1  (or seed position S) and operating point OP 3  in a direction perpendicular to ground surface  18 . In  FIG. 9A , the distance d 3  can be calculated as the sum of the working depth WD 3  and the working depth WD 1 :   

         d 3=WD1+WD3     The horizontal position of wayline WL 3  (depicted by virtual waypoint WP 3  in  FIG. 9B ) is determined by applying a horizontal offset w 3  to the wayline WL 1  (depicted by virtual point WP 1 ) as the vertical offset of WP 3  compared to WP 1  is not relevant for guidance purposes. The application of the offset w 3  to the wayline used by the machine  10  results in the position of the vehicle  10  shifting laterally in an uphill direction along the ground surface  18  to position  11 D (corresponding to the vertical axis of the vehicle  10  located at A 3 ) in contrast to position  11 A indicated with broken lines (corresponding to the vertical axis of the vehicle  10  located at A 1 ) when waypoint WP 1  is used. As shown in  FIG. 9B  with the view in the reference plane used in satellite navigation and indicated with arrow GPS in  FIG. 9A , the curve on which wayline point WP 3  travels is only aligned with wayline WL 1  on level ground surfaces. The geographical position of the machine  10  shown in  FIG. 9A  is indicated in  FIG. 9B  with a horizontal line at WP 3 /OP 3 . With increasing slope α (dramatically depicted with a curve a rotated onto drawing plane), waypoint WP 3  and wayline WL 3  diverge from wayline WL 1 . Similarly, WP 3  and WL 3  and move towards WL 1  as slope α decreases. The same applies to the curve on which the operating point OP 3  (seed S) moves relative to wayline WL 1 . Again also the position  11 D of the vehicle moves away from the position  11 A as slope α increases.   
     The working depth compensation shown in  FIGS. 9A and 9B  may be used to form soil dam D. In the illustrated embodiment, the subsequent waylines WL 2  and WL 3  were both determined based on WL 1 , which was stored during an initial operation. Alternatively, any subsequent wayline (or waypoint), such as WL 3  shown in  FIGS. 9A and 9B , may be determined by applying an offset or adjustment to the previously-used wayline (e.g., WL 2  shown in  FIGS. 8A and 8B ) using equations set forth above or similar techniques. Alternatively the working depth compensator may provide the offset or adjustment to the wayline in advance by recording slope α during an initial operation (or using map data) and calculating the offset or adjustment to subsequent waylines according to the working depth for at least the next wayline (and each waypoint on the wayline) for subsequent operations as an off-line path planning procedure, which may be completed prior to the machine  10  entering or working the field. 
     With reference to  FIGS. 9C-9E , the second embodiment of the invention may be adapted to provide a similar result as the first embodiment in that the seed location S or operating point may always be on a straight line (in the plan or GPS view) independent of any ground surface slope. As best seen in  FIGS. 7B, 8B, 9B  as the waylines WL 1 , WL 2 , and WL 3  are straight A-B type waylines, the initial stage would result in seeds being placed along a curve S and not in a straight line (in terms of the GPS coordinate system). To mitigate this problem, the working depth compensator may be adapted according to embodiments of the invention and as shown in  FIG. 9C . In this case, the ground surface slope must be known to adapt the wayline WL  4  so that seeds (indicated by S) are placed in a straight line (in the plan or GPS view).  FIG. 9C  shows the seed path S of  FIG. 7B  indicated by C 4 . If a seed path S 4  must be a straight line, the wayline WL 4  is offset as needed so that the path S 4  remains straight. Thus, at the geographical position indicated in  FIG. 7B , an offset n 5  would be provided (relative to WL 1  of  FIG. 7B ). Stated differently, the seed line S of  FIG. 7B  is mirrored (about an axis corresponding to the wayline WL 1  on an unsloped surface) to receive new wayline WL 4 . Applying the offset n 4  (which corresponds to N 1  of  FIG. 7B ) based on the slope α to compensate for deviations resulting from working depth WD 1  (applied also in  FIG. 9C ), the seed path S 4  forms a straight line. As shown with  FIG. 9D to 9E , any subsequent operation starts from wayline WL 4  and the working depth compensator applies new offset values depending on the working depth WD 5 , WD 6  and slope α so that similar to  FIG. 8B and 9B , an offset w 5  (which is the same value as w 2  in  FIG. 8B ) and w 6  (which is the same value as w 3  in  FIG. 8B ) is calculated similar to w 2  and w 3 . In contrast to  FIGS. 8B and 9B , however, these offsets are applied from the curved initial wayline WL 4  so that waylines WL 5  and WL 6  present different shapes while the seed path remains on the same straight line S. Again, the offsets n 4 , n 5 , n 6  of the ground based navigation point NP compared to operating points OP 4 , OP 5 , OP 6  present the same values as n 1 , n 2  and n 3  of  FIGS. 7A,7B, 8A, 8B, 9A, 9B  but are offset from an initially curved line. As previously discussed, the working depth compensator can work with any shape of wayline, whether straight or curved. 
     In the above-described embodiments, the working depth compensator assumes that the working depth remains constant or nearly constant as the machine  10  performs an operation, such that the adjustment of reference points (e.g., waypoints or navigation points) depends only on the ground surface slope a during said operation. The invention is not so limited, however. In other embodiments of the invention the working depth compensator is configured to determine an offset or adjustment to reference points (e.g., waypoints or navigation points) by simultaneously considering changes to two parameters—the ground surface slope α and the working depth WD. This may be done using the following equation: 
         w ( n )= d ( n )×sin(α)
 
     wherein both parameters d (being the distance of operating point with changing working depth) and slope angle α may be continuously changing. 
     Comparing  FIGS. 4A / 4 B (illustrating the first embodiment of the invention wherein the navigation point NP is adjusted) with  FIGS. 7A / 7 B (illustrating the second embodiment of the invention wherein the wayline WL is adjusted), wherein the same agricultural operation is performed based on the same working depth WD 1  and the same slope angle α, it can be seen that the offset of the ground based navigation point NP relative to the operating point OP 1  is the same (distance n 1 ) in both embodiments of the invention. That is also true when comparing distance n 2  for operating point OP 2  (described in  FIGS. 5A / 5 B and  8 A/ 8 B) and distance n 3  for operating point OP 3  (described in  FIGS. 6A / 6 B and  9 A/ 9 B), even if the derivation (shown with the curves e.g. in  FIGS. 4B, 5B, 6B  and  7 B,  8 B,  9 B) are different. Thus, independent of the method applied, the distances n 1 , n 2 , n 3  are equal, which means that when the same working depth WD and slope α are considered, the lateral position of the vehicle (defined by the navigation point NP being the intersection between vehicle axle A and ground surface  18 ) is the same relative to the . If in both embodiments, shown in  FIGS. 4A and 7A  the initial operation is started with the ground based navigation point NP to guide the machine  10  and offsets are only provided for the subsequent operations (and not at the initial operation such as shown in  FIG. 4A ), the lateral position of the machine  10  on the ground surface  18  relative to the operating point OP is the same independent of whether the working depth compensator adjusts the navigation point NP or the wayline WL. In other words, the machine  10  would use the same traffic lane for the operation regardless of whether the first embodiment of the invention (which adjusts the vehicle&#39;s navigation point) or the second embodiment of the invention (which adjusts the wayline) is used. 
     Furthermore, various different approaches may be used to determine the offset of the wayline WL. The offset w described in  FIGS. 7A-9B  represents the horizontal offset of the wayline (and associated waypoints). Alternatively, wayline can be adjusted using on offset value along ground surface  18 . As illustrated in  FIGS. 10A and 10B , the machine  10  is driven along a terrain comprising a ground surface  18  that is sloped according to an angle α. Also shown labeled in  FIGS. 10A and 10B  are a plant (P), weeds (W), and a seed (S). Certain embodiments of a working depth compensator compute reference points, such as waypoints, based on a recorded working depth and the slope angle α. More particularly, and referring to  FIGS. 10A-10B , the computing system  16  records the working depth, wd 1  (e.g., the seeding depth from the soil surface  18  to S) of a seeding operation while driving (e.g., via auto-guidance) along a given path during the seeding operation, that path indicated by the dashed line depicted to the right of and parallel with the axis A. The slope angle α, may be accessed from local memory of the computing system  16  or via communication functionality to a remote data structure that stores map data of one or more farms. The system  16  uses the slope angle to compute an offset O, necessary to provide a reference point, RP (in fact, a plurality of waypoints to guide the machine  10 ). In one embodiment, the offset O for the new waypoint (for a subsequent stage of operations) is computed according to the following formula: 
         O=d /cot (α)  (Eqn. 1a)
 
     or 
         O=d ×tan (α)  (Eqn. 1b)
 
     where for  FIG. 10A , the offset is O 1  for RP 1  (=WP 1 ) and d=d 1 , and for  FIG. 10B , the offset is O 2  for RP 2  (=WP 2 ) and d=wd 1 +wd 2  (where wd 2  is a working height). The reference point(s) may match a plant P position ( FIG. 10A ) or be above ( FIG. 10B ) the soil surface  18  and the plant P for the subsequent operation. That is, the system  16  determines a path plan based on the offset, O (e.g., O 1  or O 2 ), and depending on the working depth (d 1  to the soil surface) or height (wd 1 +wd 2  above the soil surface) of the subsequent operation, the reference point matches WP 1 =RP 1  ( FIG. 10A ) or WP 2 =RP 2  ( FIG. 10B ). In one embodiment, the reference point RP 2  ( FIG. 10B ) depends on acquired knowledge of the height wd 2 . For instance, an operator may enter at a user interface the value for wd 2 , or this value (and the depth, wd 1 ) may be provided automatically by the implement (e.g., implement controller or sensor) forwarding settings via ISOBUS to the computing system  16 . 
     The embodiments of the invention described above apply corrections to the navigation point NP on the vehicle or to the wayline WL (or waypoints) such that the machine  10  is operated at a lateral offset along ground  18  during subsequent operations. In other words, the machine  10  is uses varying traffic lanes for subsequent operations. This may not be acceptable for some agricultural operations. For example, Controlled Traffic Farming (CTF) employs the principle that a small number of traffic lanes (preferably one for each swatch) on the field is permanently used for multiple operations even with different machines so that excessive soil compaction (impairing soil health and crop growth) is reduced to a limited area of the field. Similarly, crop cultivation in narrow rows may prevent a machine path being offset in a subsequent operation, such as in grape production where only small tractors can pass on one traffic lane between the rows of grapevine and attempting to laterally offset the machine path from one operation to another would cause damage to the grapevines. 
     In a third embodiment of the invention, the working depth compensator uses the wayline (and the waypoints defining the wayline) determined or used in an initial operation (or otherwise determined, e.g., by importing map data) and the navigation point on the vehicle used in the initial operation for geographic positioning of the vehicle in all subsequent operations. Thus, the machine  10  operates without a lateral offset along ground  18  during subsequent operations and uses the same traffic lane. To address the problem of geotropism as described above, the working depth compensator according the invention provides a correction of the reference point on the implement towed by or mounted on an agricultural machine. 
     As the initial first operation can be similar to the operations illustrated in  FIG. 4A or 7A , reference is made to  FIG. 7A . An agricultural machine  10  is operated on a field with a ground surface  18  which is at least partly sloped, with  FIG. 7A  depicting the machine on a slope according to an angle α. During this initial first operation, the working depth compensator records the slope α and the working depth WD 1  referring to current operating position OP 1  while the machine is guided along wayline WL 1  using the ground based navigation point NP at the geographic position depicted in  FIG. 7A . 
     In a second subsequent operation depicted in  FIG. 11A , working depth WD 3  (or operating point OP 3 ) is considered which is above ground surface  18 . This subsequent operation may be, for example, forming a dam D with a dam former  20  attached to machine  10  and is identical to the operation described in  FIG. 9A , so the same numerals are used. In contrast to the embodiment described in  FIG. 9A , however, the working depth compensator of the guidance system  16  uses ground based navigation point NP and wayline WL 1  (or waypoint WP 1 ) of the initial operation without applying any offset. 
     According the third embodiment of the invention, instead the reference point on the implement, referred to as implement reference point (IRP 3 ), is offset from a first implement reference point IRP 1 . The first implement reference point IRP 1  is aligned with the center axis Al of the machine  10 , and the reference point IRP 3  is laterally offset from the center axis Al. This implement offset a 3  is provided on the machine  10 , e.g., by lateral movements of a linkage system (not shown in  FIG. 11A ) or parts thereof so that the implement is completely or partially laterally shifted. Alternatively, the offset may be provided on the implement by a hydraulic cylinder for lateral adjustment of the dam forming tool relative to the implement frame which attaches to the machine  10 . 
     The implement offset a 3  from the center axis Al or implement reference point IRP 1  (used without lateral offset) is determined along ground  18  by the equation: 
         a 3= d 3×tan(α)
     Where d 3  is the distance between the initially considered operating point OP 1 / (or seed position) and operating point OP 3  perpendicular to ground  18 . In  FIGS. 9A and 11A , the distance d 3  can be calculated by summing the working depth WD 3  and the working depth WD 1 :   

         d 3=WD1+WD3     The application of the offset a 3  results in the implement  20  (including the dam forming tool) moving laterally along the ground surface  18  as indicated with to IA 3 . As shown in  FIG. 11B  with the view in the reference plane used in satellite navigation and indicated with arrow GPS in  FIG. 11A , the navigation point NP is always aligned with wayline WL 1  independently of slope a. The geographic position of the machine  10  shown in  FIG. 11A  is depicted with a horizontal line at IRP 3 /OP 3  in  FIG. 11B . As slope α increases (dramatically depicted by a curve a rotated onto drawing plane), operating point OP 3  and IRP 3  (seed position S) shifts relative to wayline WL 1 . The position of the implement  20  moves away from the machine axis Al as slope α increases. Another application for the third embodiment of the invention is illustrated in  FIGS. 12A-12D  for grape production operations. In an initial operation shown in  FIG. 12A  a first implement  20 , such as a harrow, is used to work the ground. The ground based navigation point NP (corresponding to the intersection between ground surface  18  and center axis A 0  of the machine  10 ) is used to record wayline WL 0  (indicated by waypoint WP 0 ). The implement reference point IRP 0  defines the position of implement  20  relative to the towing machine  10  during initial operation.   
     In a subsequent operation shown in  FIG. 12B , the machine  10  uses the same wayline WL 0  and the same ground based navigation point NP as in the first operation illustrated in  FIG. 12A , but uses a different implement  21 . The implement  21  operates at a higher level over the ground surface  18  and thus has a greater working depth WD 1  and a new implement reference point IRP 1 . The implement  21  (and other implements used during subsequent operations) may be a leaf cutter or a leaf blower to remove leafs so that the sun can reach each of the grapes. Generally such an implement may be provided with lateral positioning means  21   a,  such as a hydraulic cylinder, to laterally offset implement tools such as cutting knives attached to a support  21   b.  The lateral offset may be manually entered by the driver prior to the operation to adjust the tools relative to the position of the grapevines depending on different growth stages and patterns of the grapevines. Challenges arise when the ground surface  18  is sloped. As shown in  FIG. 12C , the machine  10  and implement  21  are operated on sloped ground which is common for vineyards. Even if parts of the implement  21 , such as the support  21   b,  can be pivoted for angular adaption to slope α, the relative position to the grapevine is incorrect due to the effect of geotropism and slope. So the driver is forced to manually adapt the position of tool support  21   b  by adjusting lateral position means  21   a.  When slope changes, the driver has to re-adjust again which can be fatiguing over time. According to embodiments of the invention, the working depth compensator adjusts the implement reference point on the vehicle or implement depending on the working depth and slope. 
     With reference to  FIG. 12D , the offset a 3  of the implement reference point IRP 3  with regard to implement reference point IRP 1  (used without lateral offset) is determined (parallel to ground surface  18 ) by the equation: 
         a 3= d 3×tan(α)
     Where d 3  is the distance between the implement reference point IRP 1  and the implement reference point IRP 0  used for initial operation perpendicular to ground surface  18 :   

       d3=WD1     The application of the offset a 3  results in the implement  21  including tool support  21   b  shifting laterally parallel to the ground surface  18 .   
     As a result, the position of the tool relative to the grapevine is automatically and continuously adjusted depending on the slope of the ground surface  18 . The working depth compensator may be configured to assume a constant working depth, or may be configured to adjust the implement reference point IRP according to changes in both parameters slope α and working depth WD using the equation 
         a ( n )= d ( n )×tan(α)
     Where both depth d and slope angle α may be continuously change.   

     Attention is now directed to  FIG. 13A , which illustrates an embodiment of a control system  22  used in an embodiment of a working depth compensator. It should be appreciated within the context of the present disclosure that some embodiments may include additional components or fewer or different components, and that the example depicted in  FIG. 13A  is merely illustrative of one embodiment among others. The control system  22  comprises a computing system  16  comprising one or more computing devices or electronic control units (ECUs). In one embodiment, the working depth compensator may include all of the components depicted in  FIG. 13A , or a subset thereof (e.g., the computing system  16  only). Note that the computing system  16  is depicted as a component of the control system  22  residing in the machine  10 , all or a portion of the functionality of the computing system  16  may be implemented remotely from the field to be farmed or at least external to the machine  10  or distributed among the machine and any one or combination of a towed implement and a remote computing device or devices. The computing system  16  is described hereinafter (with exceptions where noted) as a component of (e.g., hosted by) the machine  10 , with the understanding that all or a portion of the computing system functionality may be distributed among plural devices and/or located remotely or otherwise external to the machine  10  in some embodiments. The computing system  16  is coupled to one or more networks, such as a network  26 , which in one embodiment may comprise a controller area network (CAN) bus(es), such as implemented according to the ISO 11783 standard (also referred to as “ISOBUS”) and using a J1939 messaging protocol. In some embodiments, the network  26  may be configured according to one or more other industry and/or proprietary communication specification or standards, and is not limited to a single network. Also coupled to the network  26  is a position determining system  28  (e.g., which may be embodied as the above-described GNSS receiver assembly  12 ,  FIG. 4A ), a drive/navigation (Drive/Nav) system  30 , an implement control system  32  (e.g., an electronic control unit (ECU) dedicated to controls/settings for a coupled implement), a user interface  34 , and a network interface  36 . In some embodiments, functionality of one or more of the components may be combined into a single unit, (e.g., functionality of the implement control system  32  may be embodied in the computing system  16 ). 
     In one embodiment, the position determining system  28  comprises a GNSS receiver and an antenna to enable autonomous or semi-autonomous operation of the machine  10  in cooperation with the drive/navigation system  30  and the computing system  16  (e.g., via auto-guidance software residing in the computing system  16 ). In some embodiments, the position determining system  28  may comprise plural GNSS receivers and/or plural antennas. The position determining system  28 , alone or in cooperation with the network interface  36 , may also comprise functionality for receiving signals from one or more public and/or proprietary differential correction sources, including DGPS radio beacons, Space-Based Augmentation Systems (SBAS), L-Band, RTK, etc. 
     The drive/navigation system  30  collectively comprises controls for the various power drive, gearing (e.g., transmission), and/or steering functionality, including actuators (e.g., hydraulic actuators, including proportional electro-hydraulic valves, electromagnetic actuators, etc.), sensors (e.g., steering angle sensors), and/or control subsystems (e.g., based on electrical or electronic, pneumatic, hydraulic mechanisms) residing on the machine  10 , including those used to control machine navigation (e.g., speed, direction (such as a steering system), etc.), among others. 
     The implement control system  32  comprises the controls (e.g., actuators, switches) for the various valves, pumps, flowmeters, and/or control subsystems residing on the machine  10  to cause dispensing of product (e.g., chemicals, water, etc.) from the machine  10 , as well as to cause control operations (e.g., turn on/off, proportional control, sectional control, etc.), including positioning, of the coupled implement, such to change height position and/or orientation (e.g., folding), and/or directional (e.g., independent steering) control. The implement control system  32  may, alone or in cooperation with the computing system  16 , control the various operational functions of the implement. The implement control system  32  also control lateral position means  21   a  shown in  FIGS. 12B to 12D   
     The user interface  34  may comprise any one or a combination of a keyboard, mouse, microphone, touch-type or keyboard/mouse/voice controlled display screen, headset, joystick, multifunctional handle (e.g., to enable nudge commands), steering wheel, or other devices (e.g., switches) that enable input by an operator and also enable monitoring and/or feedback to an operator of machine operations. Note that in some embodiments, the user interface  34  may be implemented remotely from the machine  10  or integrated with the computing system  16  in some embodiments. 
     The network interface  36  comprises hardware and software that enables remote control and/or monitoring of the machine  10  and its associated operations. For instance, the network interface  36  may comprise a radio and/or cellular modem to enable connectivity with other devices of one or more networks, including a cellular network local area network, the Internet, and/or a local network. Internet connectivity may be further enabled using interface software (e.g., browser software) in the computing system  16 . For instance, the computing system  16  may cause the network interface  36  to access map data from a remote server device to determine a slope of a field to be worked. As indicated above, at least some of the functionality of the network interface  36  (or other components of the control system  22 ) may be integrated into the computing system  16  or other components of the control system  22  in some embodiments. 
     The computing system  16  is configured to receive and process information from, and in some cases output data to, the components of the control system  22 . For instance, the computing system  16  may receive operator (or other user) input from the user interface  34 , such as a working height (e.g., above ground) for determining reference points for a subsequent operation. As another example, the computing system  16  may receive working depth information from the implement control system  32  to determine reference points for a subsequent operation. The computing system  16  may receive input from the position determining system  28  that includes updated position information from the machine  10  (based on satellite data and optionally differential correction signal information). The user interface  34  may cooperate with the computing system  16  to enable operator intervention of machine operations, enable auto-guidance, facilitate generation of waylines (via starting and ending recording of AB paths, contour paths, etc.), retrieval of past waylines, and/or access of machine and/or field/map data. In some embodiments, the computing system  16  may receive input from the position determining system  28  and the implement control system  32  (e.g., to enable feedback as to the position or status of certain devices, such as an implement height and/or orientation and/or articulation angle, direction of the machine  10 , direction or angle of a towed implement relative to the machine  10 , etc.). The computing system  16  may also access a local or remote data structure to use data to enable path planning or corresponding operations, including map data for terrain slope angle values. The data structure may reside at a remote location (e.g., accessed via the network interface  36 ) or locally, such as from a storage device (e.g., memory stick, memory, etc.). 
       FIG. 13B  further illustrates an embodiment of the example computing system  16 . One having ordinary skill in the art should appreciate in the context of the present disclosure that the example computing system  16  is merely illustrative, and that some embodiments of computing systems may comprise fewer or additional components, and/or some of the functionality associated with the various components depicted in  FIG. 13B  may be combined, or further distributed among additional modules, in some embodiments. As indicated above, the computing system  16  may comprise plural (e.g., networked) devices (e.g., plural ECUs) in some embodiments, but for purposes of brevity, the computing system  16  is described in association with  FIG. 13B  as a single device. It should be appreciated that, though described in the context of residing in the machine  10 , in some embodiments, the computing system  16  or its corresponding functionality may be implemented in a computing device or devices located external to the machine  10  and/or remote from the field. For instance, path planning, including depth correction, may be implemented off-site (remote from the machine  10 ) on a device with functionality of the computing system  16 . Such remote, off-line prepared path plans may be communicated to the computing system  16  of the machine  10 , such as via wireless communication and connection to the network interface  36 , or via loading from a storage device, such as a portable memory that couples to an input interface (e.g., Universal Serial Bus connection, Near Field Communications Interface, Bluetooth interface, etc.) of the computing system  16  or control system  22 . In some embodiments, path planning may be implemented all or in part in real-time as the machine  10  enters and/or navigates a field. 
     The computing system  16  is depicted in this example as a computer system (e.g., a personal computer or workstation, an electronic control unit or ECU, etc.), but may be embodied as a programmable logic controller (PLC), FPGA, among other devices. It should be appreciated that certain well-known components of computer systems are omitted here to avoid obfuscating relevant features of the computing system  16 . In one embodiment, the computing system  16  comprises one or more processors, such as processor  38 , input/output (I/O) interface(s)  40 , and memory  42 , all coupled to one or more data busses, such as data bus  44 . The memory  42  may include any one or a combination of volatile memory elements (e.g., random-access memory RAM, such as DRAM, SRAM, and SDRAM, etc.) and nonvolatile memory elements (e.g., ROM, Flash, solid state, EPROM, EEPROM, hard drive, CDROM, etc.). The memory  42  may store a native operating system, one or more native applications, emulation systems, or emulated applications for any of a variety of operating systems and/or emulated hardware platforms, emulated operating systems, etc. In the embodiment depicted in  FIG. 13B , the memory  42  comprises an operating system  46  and auto-guidance software  48 . The auto-guidance software  48  comprises path planning software  50 , auto-steer software  54 , and data module  56  (e.g., a data structure, such as a database). The path planning software  50  comprises working depth compensator software  52 , and the data modules  56  comprise map information and machine information. It should be appreciated that in some embodiments, additional (e.g., browser, APIs and/or web-hosting software, such as if located remotely) or fewer software modules (e.g., combined functionality) may be employed in the memory  42  or additional memory. In some embodiments, a separate storage device may be coupled to the data bus  44  (or to network  26 ,  FIG. 13A ), such as a persistent memory (e.g., optical, magnetic, and/or semiconductor memory and associated drives). In some embodiments, the software modules  50 - 56  may be further distributed among additional application, or their respective functionality combined into fewer modules. 
     The path planning software  50  enables reference determinations for path pre-planning or while in the field. For instance, as is known, the operator may position the machine  10  ( FIG. 4A ) at or near a starting point in the field, engage auto-guidance functionality, and record start and end points of a path (e.g., A-B waylines, contour waylines, etc.). The path planning software  50  may access the machine information from the data module  56  and based on, for instance, implement width, and generate wayline points for parallel paths that cover the field to be worked. These points, as well as other field information (e.g., sloped terrain, field hazards or relevant features, including easements, water ponds, etc.) may be recorded for subsequent operation. In some embodiments, the field information may be obtained via access to prior map information, such as stored in data module  56  or elsewhere. The working depth compensator software  52  records (or receives via path planning software  50 ) the working depth (e.g., as communicated by the implement control system  32  or entered by an operator at the user interface  34  and communicated over the network  26  to the working depth compensator software  52 ), which is also used for subsequent operations. As is known, the auto-steer software  54  compares the wayline points to position information that it receives via satellite (and optionally corrected using correction systems as explained above) and communicates steering commands to the drive/navigation system  30  to guide the machine  10  along the wayline points. Operations performed from the machine  10  may include a first or early stage of multi-stage farming operations, including seeding. 
     In subsequent farming operations (e.g., agitating the soil, fertilizing, applying pesticides, etc.), the path planning software  50  accesses the recorded wayline points from a prior traversal of the field to be worked and invokes the working depth compensator software  52  to handle traversals along sloped terrain. As set forth above, the working depth compensator software  52  uses the recorded working depth, the slope of the soil surface (e.g., as recorded in the prior traversal or as accessed from map data), and a working height or depth (according to operator input or as communicated by the implement control system  32 ) and applies these values to Eqn.  1  to generate an offset from the prior reference points along the sloped terrain. The path planning software  50  then uses the new reference points for the sloped sections of the field and communicates these and other reference values to the auto-steer software  54  to enable, in cooperation with the drive/navigation system  30 , guided traversal of the field for a second (and subsequent) farming operation. In one embodiment, the reference points for the sloped terrain may be computed in just-in-time fashion (e.g., as the machine  10  approaches within a predetermined distance from the sloped terrain), whereas in some embodiments, the computations may be achieved as a pre-planning tool (at a time of just entering the field, or prior to then). 
     Note that the data module  56  may include information useful to the generation of reference points, including field maps, which may comprise image data, boundaries, topography, including terrain slope, among other field feature identification and/or location. Some field information may also be inputted manually (e.g., the operator entering information at the user interface  34 , which is communicated over the network  26  to the path planning software  50 ). Field information may also include bodies of water, power lines, easements, conduit locations, etc. Field information may also be extracted from images acquired via manned or unmanned scouting vehicles, satellite, or aerial vehicles (e.g., drones, planes, gliders, helicopters, etc.). 
     The data module  56  may also include machine information, which may include dimensions and/or performance features of the machine  10  and coupled (including integrated and towed) implements. In other words, the data module  56  may include towing machine information (e.g., width, length, height, track width, ground clearance, function and/or type of machine, performance capabilities, etc.) and implement information (e.g., width, length, height, ground clearance, dispensing performance, such as nozzle types and dispensing trajectory range or other performance, type and/or function of the implement, working height, working depth, angle of articulation, etc.), the implement information being either for integrated implements and/or implements coupled to the front or rear of the towing machine via hitch assemblies or other mechanisms. In some embodiments, the data stored in data module  56  may reside external to the computing system  16 , such as in separate storage coupled to the network  26  or in a remote device in communication with the computing system  16  (e.g., accessed via the network interface  36 ). 
     The reference points may also be sent to the implement control system  32 , which may be used along with map or other information to control implement operations (e.g., which sections or subsections above the field to seed, fertilize, apply pesticides, when to apply, when to raise the tool bar (e.g., at headlands), etc.). The reference points may also be used to enable any offset computations for differences in path travel between the machine  10  and the towed implement. 
     Execution of the auto-guidance software  48  (and associated software modules  50 - 56 ) is implemented by the processor  38  under the management and/or control of the operating system  46 . The processor  38  may be embodied as a custom-made or commercially available processor, a central processing unit (CPU) or an auxiliary processor among several processors, a semiconductor based microprocessor (in the form of a microchip), a macroprocessor, one or more application specific integrated circuits (ASICs), a plurality of suitably configured digital logic gates, and/or other well-known electrical configurations comprising discrete elements both individually and in various combinations to coordinate the overall operation of the computing system  16 . 
     The I/O interfaces  40  provide one or more interfaces to the network  26  and other networks. In other words, the I/O interfaces  40  may comprise any number of interfaces for the input and output of signals (e.g., analog or digital data) for conveyance of information (e.g., data) over the network  26 . The input may comprise input by an operator or user (operator or user used interchangeably hereinafter, such as to control and/or monitor operations of the machine  10  locally or remotely) through the user interface  34 , and input from other devices or systems coupled to the network  26 , such as the position determining system  28 , the drive/navigation system  30 , the implement control system  32 , and/or the network interface  36 , among other systems or devices. 
     When certain embodiments of the computing system  16  are implemented at least in part as software (including firmware), as depicted in  FIG. 13B , it should be noted that the software can be stored on a variety of non-transitory computer-readable medium for use by, or in connection with, a variety of computer-related systems or methods. In the context of this document, a computer-readable medium may comprise an electronic, magnetic, optical, or other physical device or apparatus that may contain or store a computer program (e.g., executable code or instructions) for use by or in connection with a computer-related system or method. The software may be embedded in a variety of computer-readable mediums for use by, or in connection with, an instruction execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. 
     When certain embodiment of the computing system  16  are implemented at least in part as hardware, such functionality may be implemented with any or a combination of the following technologies, which are all well-known in the art: discreet logic circuit(s) having logic gates for implementing logic functions upon data signals, an application specific integrated circuit (ASIC) having appropriate combinational logic gates, a programmable gate array(s) (PGA), a field programmable gate array (FPGA), etc. 
     In view of the above description, it should be appreciated that one embodiment of a working depth compensating method  58 , depicted in  FIG. 14 , comprises recording values corresponding to position information and a working depth beneath a soil surface along a first path ( 60 ); determining reference points for a second path based on the recorded values, a slope of the soil surface, and a working depth or height along the second path ( 62 ); and guiding movement of a machine along the second path via issuance of auto-steer commands ( 64 ). 
     Any process descriptions or blocks in flow diagrams should be understood as representing modules, segments, or portions of code which include one or more executable instructions for implementing specific logical functions or steps in the process, and alternate implementations are included within the scope of the embodiments in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the present disclosure. 
     It should be emphasized that the above-described embodiments of the disclosure, particularly, any “preferred” embodiments, are merely possible examples of implementations, merely set forth for a clear understanding of the principles of a working depth compensator. Many variations and modifications may be made to the above-described embodiment(s) of the working depth compensator without departing from the scope of the disclosure. All such modifications and variations are intended to be included herein within the scope of this disclosure and protected by the following claims.