Three-dimensional steering of wheeled machinery moving on non-flat surfaces

Abstract

In precision agriculture, high-precision navigation, attitude determination, and obstacle detection methods are used to conserve resources and achieve better results. The collected machine position and attitude data, as well as obstacle location data, can be effectively utilized to synthesize control algorithms for autonomous agricultural machinery. These algorithms are applied to coverage path planning, route planning, motion stabilization along a specified path, obstacle avoidance, and ensuring guaranteed behavior.

Description

[Technical Field]

[0001] This disclosure relates in general to methods and apparatus for operating autonomous machines, and more particularly to methods for steering wheeled agricultural machinery on non-flat surfaces. [Background technology]

[0002] The use of agricultural machinery for cultivating crops has enabled increased efficiency and yield. Operators typically control the movement of the machinery and its equipment. However, efficient control of machinery requires experienced operators. This experience is generally gained through trial and error over time. Inexperienced operators often control machinery inefficiently, resulting in wasted time and potential crop damage. What is needed is a method for efficiently controlling and operating machinery, regardless of the operator's experience level. [Overview of the project] [Means for solving the problem]

[0003] A method for steering agricultural machinery includes the steps of receiving position data from a GNSS receiver and receiving inertial data from a plurality of inertial sensors. Based on the position data, inertial data, the angle between the direction of movement of the agricultural machinery and the tangent to the target path at the point closest to the agricultural machinery, path parameters, a function of the target path to the path parameters, and a signed distance from the center of the rear axle of the agricultural machinery to the target path, the instantaneous curvature of the steering of the agricultural machinery is determined. The signed distance has a positive sign when the agricultural machinery is on one side of the target path and a negative sign when the agricultural machinery is on the other side of the target path. The agricultural machinery is steered based on the determined instantaneous curvature of the steering of the agricultural machinery.

[0004] In one embodiment, the instantaneous curvature of the steering of agricultural machinery is given by the formula

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[0005] In one embodiment, the GNSS receiver receives GNSS satellite signals from at least one antenna, and agricultural machinery attitude estimation is performed using a relational expression.

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[0006] In one embodiment, the GNSS receiver receives GNSS satellite signals from at least three antennas, and agricultural machinery attitude estimation is performed using a relational expression. b calib,i =Rb mes,i i=1,2 Based on this, the vector measurements from one of the three antennas to the remaining antennas are corrected.

[0007] In the formula, b calib,i i=1,2 are two baselines represented by the body coordinate frame of the agricultural machine, determined based on the calibration procedure, and b mes,i i=1,2 are two baselines measured instantaneously.

[0008] In one embodiment, the initial agricultural machine posture is determined using a calibration operation, and the agricultural machine posture estimation is further based on the initial agricultural machine posture.

[0009] In one embodiment, the calibration operation includes moving the agricultural machine in a known direction of movement.

[0010] In one embodiment, the instantaneous curvature of the steering of the agricultural machine is given by the formula

Equation

[0011] where δ is the norm of the lateral deviation, β is a positive scale factor, and Π(X) is the potential generated by the entire point cloud.

[0012] The apparatus includes a plurality of antennas, a GNSS receiver that receives signals from the plurality of antennas, and a plurality of inertial sensors. The apparatus also includes a controller configured to receive position data from the GNSS receiver, receive inertial data from the plurality of inertial sensors, and perform a method for steering the agricultural machine described herein.

Brief Description of the Drawings

[0013] [Figure 1] Shows an agricultural machine configured according to one embodiment.

[0014] [Figure 2] Shows the body frame of a machine following a trajectory according to one embodiment.

[0015] [Figure 3A] Shows a point cloud generated by a 2D LIDAR according to one embodiment.

[0016] [Figure 3B] Shows an artificial potential according to one embodiment generated based on the point cloud shown in FIG. 3A.

[0017] [Figure 4] Shows a flowchart of a method according to one embodiment.

[0018] [Figure 5] A high-level block diagram of a computer according to one embodiment is shown. [Modes for carrying out the invention]

[0019] The use of agricultural machinery has made it possible for humanity to obtain crops (such as food) while reducing production costs. Precision agriculture uses high-precision navigation systems to improve crop cultivation techniques, producing better results while saving resources such as cultivated area and working time. Agricultural machinery equipped with Global Navigation Satellite (GNSS) receivers that provide positional data and other sensors that provide additional data can be used for crop mapping, crop yield monitoring, differentiated fertilization and pesticide application, and crop harvesting.

[0020] This disclosure describes the application of a mathematical formulation of the motion control problem of an autonomous wheeled machine, such as the agricultural machine 100 shown in Figure 1, to precision agriculture. The machine 100 is shown to have three antennas 102A, 102B, and 102C for receiving GNSS satellite signals. Although the machine 100 is shown to have three antennas, it should be noted that in various embodiments the machine 100 may have one or more antennas. Antennas 102A, 102B, and 102C communicate with a GNSS receiver 104 that determines position data based on the signals received by the antennas. The GNSS receiver 104 communicates with a controller 106 that controls the operation of one or more systems or components of the machine 100. In one embodiment, the controller 106 also receives inertial data from a plurality of inertial sensors 108. The inertial data can be used to augment the GNSS position data and / or to enable position determination using various techniques such as dead reckoning. In one embodiment, the controller 106 is used to perform the methods, calculations, and operations described herein.

[0021] In one embodiment, the field is first divided into substantially parallel paths. Then, the routes on which the agricultural machinery will travel are planned. As each agricultural machine travels along its route, methods are performed to ensure path stabilization, obstacle detection, and desired behavior. In one embodiment, existing non-moving (i.e., static) obstacles are considered during the route planning step, and the agricultural machinery control system takes into account new non-moving obstacles while the machinery is in motion. In one embodiment, a real-time kinematic (RTK) positioning method using a reference station can be used to provide centimeter-level accuracy for the movement of agricultural machinery and the movement of tools attached to or associated with agricultural machinery.

[0022] The general principles described herein can be applied to various types of vehicle motion systems, but in relation to the motion control problem of autonomous wheeled vehicles, this specification describes two types of wheeled agricultural machinery: wheeled agricultural machinery with an Ackerman steering mechanism and wheeled agricultural machinery with differential rear-wheel drive. In the case of wheeled agricultural machinery with an Ackerman steering mechanism, the machine rotates by the front wheels during motion, and the rotational limit of the wheels also limits the normal curvature u of the motion path (the projection of the curvature vector onto the normal of the tangent plane).

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[0023] For agricultural machinery with a single-antenna receiver, the machine's attitude can be accurately determined assuming no cross-track slip. This is called a non-holonomic constraint. Generally, when the machine operates in a field with significant undulations and cross-track slip is unavoidable, a two-antenna or even three-antenna navigation receiver should be used. The longer the antenna baseline, the higher the accuracy of attitude estimation. In one embodiment, attitude data is further smoothed by an extended Kalman filter (EKF) or other filtering method that fuses data from a GNSS receiver built into the machine equipment (e.g., GNSS receiver 104 in Figure 1) and a strapdown inertial navigation system (SINS).

[0024] In one embodiment, the autonomous operation of the agricultural machinery is performed using light-detection ranging (LIDAR) and an optical stereo camera to generate point clouds received from obstacles encountered along the machine's path. However, LIDAR and optical stereo camera data may not be considered in the path planning step. Data from additional sensors installed on various parts of the machine are fused into a common local obstacle map that takes the machine's attitude into account. Based on this data, a generalized artificial potential is calculated, which synthesizes artificial repulsive forces to modify pre-synthesized steering and speed controls to avoid collisions with obstacles. While the agricultural machinery is moving, the control algorithm analyzes whether the machine state should operate in an attractive region where path stabilization is possible.

[0025] This section describes the stabilization of mechanical motion along the planned path. Next, it describes the estimation of the gravitational region and obstacle avoidance. Finally, it describes a navigation system used according to one embodiment.

[0026] Assuming the path is planned, the curved path is followed with high precision, often in the centimeter range. To synthesize the control laws according to one embodiment, the machine kinematic scheme must be described in a system of differential equations, and the control objectives must be formulated as algebraic relations. The control objectives can be such that lateral and angular deviations from the desired path are zero. In one embodiment, several known methods for synthesizing nonlinear system controls, such as feedback linearization, can be applied. The controllers can be formally synthesized using algebraic methods. The application of this method to a wheeled machine with an Ackermann front-wheel steering mechanism is described below.

[0027] Figure 2 shows the main frame of a machine that follows a track according to one embodiment, having Ackerman front-wheel steering. X∈R 3 Let be the position of the target point in WGS-84, and let C be the rotation matrix from BF to WGS-84. The origin of BF is at the operating point. Its first axis is directed forward along the platform centerline, and its second axis lies in the platform plane and is perpendicular to the first axis. The third axis points downward perpendicular to the first two axes, as shown in schematic diagram 200 of Figure 2, and complements them with respect to the right-hand frame. Vectors are considered columns, and the symbol T below represents the transpose. Assume the operating point is located at the center of the machine's rear axle. The velocity vectors of the operating point in BF and WGS-84 are given as follows:

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[0028] In one embodiment, the machine travels on a surface that is unknown in advance. For simplicity, it is assumed that the machine moves without slip, that is, all four wheels touch the surface simultaneously and roll without slipping. In this case, the equation of motion in the form of Equation (6) can be used. This idealization can be realistic when the length dimension of the machine is small enough to be negligible compared to the inverse maximum surface curvature. Let the path (the trajectory determined in the machine route planning step) be given by p(s), where s is the path parameter. The function p(s) is considered to be twice continuously differentiable, which holds for a cubic B-spline. The path parameter may have no dimension or may have the dimension of path length. The distance from point X to the path p(s) is given as follows. ||Δ||, Δ = X - p(s * ) (6) In the formula, p(s * ) is the path point closest to X, and ||·|| is the vector Euclidean norm. Assume that s * is clearly defined, that is, the minimum ||X - p(s)|| at s is achieved at a unique point.

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[0029] Note that all differentiation, equation solutions, and simplifications can be performed using algebraic methods. Point s * In this case, the relation in equation (8) is calculated. The notation indicating the dependence on s is omitted.

[0030]

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[0031] Furthermore, considering equations (3), (4), and (9), we obtain the following equation.

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[0032] Note C T Δ is the lateral deviation Δ at BF. Since the Δ vector lies in the plane tangent to the surface, the third component of this vector is 0.

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[0033] Using the last equation and equation (4), we rewrite equation (10) as follows:

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[0034] Considering equation (11), equation (9) takes the following form:

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[0035] Following the feedback linearization method, the desired differential equation that provides an exponential decrease in δ is as follows:

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[0036] Substituting equations (12) and (13) into the equation, we obtain the following algebraic equation:

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[0037] According to equation (1), control u is

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[0038] A method for formally deriving a control law according to one embodiment is shown, based on a mechanical motion model (13) and a formulated control objective. The path curvature required by the control law according to one embodiment is provided by the mechanical steering mechanism. Under the low motion speeds typical of agricultural machinery, transient processes resulting from gear dynamics have little effect on the mechanical motion. The control (16) provides an exponentially decreasing δ, but additional constraints (18) can effectively counteract this characteristic.

[0039] Ensuring safe machine behavior requires considering the construction of guaranteed gravitational regions. During machine motion, the machine state falls within these regions, satisfying pre-defined geometric constraints. Agricultural machinery may come into contact with the living environment or unexpected obstacles, and may cause harm due to hardware or software problems. Therefore, while these machines enhance the efficiency of production processes, they also pose potential hazards in the event of improper operation.

[0040] One approach to improve the safety and predictability of machine behavior is to estimate the invariant region of phase space to which the machine's phase trajectory belongs. If motion begins within this region, it will continue within it because it is invariant. The invariant region is also the attractive region of the equilibrium state corresponding to the operating mode. In the case of the equations of motion described in the previous section, the operating mode is the equilibrium state of the differential equation system (14).

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[0041] A standard approach to estimating the attractive domain of a nonlinear dynamic system uses a Lyapunov function V(Z) of a specific parametric class, where z is a phase space vector obtained by substituting a variable. Using the Lyapunov function, the attractive domain is derived from the system dynamics.

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[0042] The constant α controls the size of the attractive region. The larger the constant, the larger the region. Thus, using a set of constants α1 < α2 < α3 < ..., a set of regions Ω(α1) ⊂ Ω(α2) ⊂ Ω(α3) ⊂ ... is generated. Each region is invariant and guarantees an attractive force to the equilibrium state z=0, describing motion along a path with zero lateral and angular deviations. The widest region corresponds to the largest possible constant α. Each constant value can be assigned an identifier (e.g., shade or color) and displayed on a display that can be installed, for example, in a monitoring center to monitor the operation of the machine. The widest region is defined so as not to violate geometric constraints. One constraint can be the maximum possible deviation from the path, and another constraint can be the distance between the machine's central axis and point p(s *The tangent of the angle between the tangent to the path and the path in the region Ω(α) can be taken. If the tangent of the angle is finite at the start of the motion, it remains finite throughout the entire motion due to the boundedness of the region Ω(α), and the machine neither positions itself perpendicular to the path nor follows it in the opposite direction. The boundedness of the gravitational region is ensured by adopting an exact positive definite function (e.g., a quadratic form with a positive definite matrix or a Lurie-Postnikov function) as the Lyapunov function. The proposed estimates are generated in phase space (δ;δ).

[0043] Agricultural machinery uses additional sensors, such as LiDAR or stereo cameras, to detect obstacles and generates data about the obstacles within the sensor's field of view in the form of a point cloud.

[0044] The i-th point in the point cloud corresponds to the coordinate Y in BF. i It can be assumed that it has. After conversion to WGS-84,

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[0045] In one embodiment, the vector potential is given by the equation:

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[0046] In one embodiment, the control law is not δ as described above.

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[0047]

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[0048] In the formula, β is a positive scale coefficient, and e x is the unit direction vector of the agricultural machine, and <·,·> represents the dot product. By calculating δ near the obstacle in this way, the agricultural machine can follow a special curved trajectory relative to its original trajectory. Obstacle avoidance capability is obtained by composing the control law using the function of equation (20).

[0049] For precision navigation and attitude determination, one to three GNSS antennas (e.g., antennas 102A, 102B, and 102C in Figure 1) are placed on the roof of the machine (e.g., machine 100 in Figure 1) and connected to a GNSS receiver (e.g., GNSS receiver 104 in Figure 1). When three antennas are used, one of the receiver inputs is multi-frequency. Generally, for reliable RTK operation, the first (master) input should receive GPS (L1, L2, L5), GLONASS (L1, L2), Galileo (E1, E5a), and Beidou (B1, B3) signals; i.e., it should be multi-frequency. The remaining two (slave) inputs are single-frequency and can receive, for example, GPS L1, GLONASS L1, and Beidou B1 signals.

[0050] The navigation system also includes a strapdown inertial navigation system (SINS), which measures the angular velocity of the machine body and the linear acceleration at the SINS position.

[0051] The GNSS receiver determines the position of the phase center of the master antenna, as well as the slave 1 master vector and slave 2 master vector (b1 and b2, respectively) using WGS-84. These vectors at BF are known,

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[0052] The use of SINS is optional, but it improves the estimation of motion parameters. GNSS-SINS integration to obtain smoothed target point position and attitude C is performed using an extended Kalman filter, which is not described herein. For the 3-antenna case, the following relation is used in the measurement model for attitude determination:

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[0053] In one embodiment, the steering algorithm controls the dynamic system using a feedback linearization approach, which is applied to a mathematical model of a wheeled machine that can move on non-flat surfaces, such as agricultural machinery. The change in the center position of the rear axle of the machine r is determined by the control action on the drive of the wheels and the attitude of the machine body, and is represented by the following rotation matrix.

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[0054] The angular velocity is determined by changing the orientation of the machine, and this depends on the inclination of the surface and the instantaneous curvature of the steering. u:w z =vu

[0055] To synthesize the control laws, the following variables are introduced: ξ is the path parameter, and z is the signed distance from the center of the machine's rear axis to the target path. z has a positive sign if the machine is on one side of the path, and a negative sign if the machine is on the other side of the path.

[0056] To ensure that the machine trajectory converges exponentially to the target path, the control action on the wheel drive should vary the parameter z according to the following law. z''+3λz'+3λ 2 z+λ 3 ∫zdξ=0

[0057] The following can be obtained from the mechanical motion model. z'=sinψ, and

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[0058] The resulting control law requires feedback regarding the machine's position and attitude. To provide this feedback, one embodiment uses sensors and a state estimation algorithm based on an extended Kalman filter. These algorithms can operate in two modes, in which case inertial sensors and gyroscopes are additionally installed, while three or a single GNSS antenna is used for navigation. When three antennas are used, attitude estimation correction uses measurements of the vector (baseline) from one antenna, called the master antenna, to the remaining antennas based on the following relation: b calib,i =Rb mes,i i=1,2 In the formula, b calib,i i=1,2 are two baselines represented by the machine's body coordinate frame, determined based on the calibration procedure, and b mes,i i=1,2 are two baselines measured instantaneously.

[0059] When using a single antenna, attitude estimation is corrected based on measurements of the machine's instantaneous velocity, according to a relation that indicates the absence of lateral slip.

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[0060] To initialize the machine's initial orientation in single-antenna mode, the initial calibration operation should be performed in a known direction of movement (forward or backward).

[0061] In one embodiment, machine operation is controlled by a state machine using a set of states, and transition rules between those states are used. The list of states (which can be expanded as needed) includes INITIALIZATION, INITIALIZED, AUTOCTRLON, TOROUTEMANEUVER, ONROUTE, OBSTACLEAVOIDANCE, OBSTACLEFORCEDSTOP, ENDOFROUTE, SENSORTIMEOUTERROR, and ONOUTEERROR.

[0062] In the INITIALIZATION state, subsystems and sensors are checked. If the test is successful, a transition to the INITIALIZED state occurs; otherwise, a transition to one of the error states occurs. In the INITIALIZED state, the operator command is expected to switch to the AUTOCTRLON state. In this state, the operating parameters to the starting point of the target path are calculated, and after confirming that the machine is within acceptable limits, a transition to the TOROUTEMANEUVER state occurs, and the machine begins moving towards the starting point of the path. Upon reaching the starting point of the path, the machine enters the ONROUTE state and performs its primary task by tracking the target trajectory. After completing the target path, the machine enters the ENDOFROUTE state. If an unexpected obstacle is encountered during movement, the machine will switch to the OBSTACLEAVOIDANCE state if it detects the obstacle using its sensors, and to the OBSTACLEFORCEDSTOP state in the case of a dangerous approach. The current state of the machine can be determined using indicators on the machine body, such as color indicators.

[0063] Figure 4 shows a method 400 for steering an agricultural machine according to one embodiment. In one embodiment, the controller 106 shown in Figure 1 performs the steps of method 400. In step 402, position data is received from a GNSS receiver (e.g., GNSS receiver 104 in Figure 1). In step 404, inertial data is received from a plurality of inertial sensors (e.g., a plurality of inertial sensors 108 in Figure 1). In step 406, the instantaneous curvature of the steering of the agricultural machine is determined. In step 408, the agricultural machine is steered based on the instantaneous curvature of the steering of the agricultural machine.

[0064] Figure 5 shows a schematic diagram of the components of machine 100 shown in Figure 1. The controller 106 communicates with a GNSS receiver 104 that receives GNSS satellite signals from antennas 102A, 102B, and 102C. The controller 106 also communicates with a plurality of inertial sensors 108. The controller 106, and the methods, calculations, and operations described herein, can be implemented using components that form a computer. Figure 5 illustrates a high-level block diagram of such computer components used to implement the controller 106. The controller 106 incorporates a processor 504 that controls the overall operation of the controller 106 by executing computer program instructions that define such operations. The computer program instructions may be stored in a storage device 512 or other computer-readable medium (e.g., a magnetic disk, CD-ROM, etc.) and loaded into memory 510 when execution of the computer program instructions is desired. Thus, the methods, techniques, and calculations described herein can be defined by computer program instructions stored in memory 510 and / or storage device 512 and controlled by a processor 504 that executes the computer program instructions. For example, computer program instructions can be implemented as computer executable code programmed by a person skilled in the art to perform algorithms defined by the methods, techniques, and calculations described herein. Thus, the processor 504 performs algorithms defined by the methods, techniques, and calculations described herein by executing computer program instructions. The controller 106 also includes one or more network interfaces 506 for communicating with other devices over a network. The controller 106 also includes input / output devices 508 (e.g., a display, keyboard, mouse, speaker, buttons, etc.) that enable user interaction with the computer 502. A person skilled in the art will recognize that implementations of the controller may include other components and that Figure 5 is a high-level representation of some of the components of such a controller for illustrative purposes.The GNSS receiver 104 can also be implemented using computer components in the same manner as described above in relation to the controller 106.

[0065] The above detailed description should be understood to be illustrative and representative in all respects, but not limiting, and the scope of the inventive concept disclosed herein should be interpreted in accordance with the full scope permitted by patent law. The embodiments shown and described herein are merely illustrative of the principles of the inventive concept, and those skilled in the art should understand that various modifications can be implemented without departing from the scope and spirit of the inventive concept. Those skilled in the art can also implement various other combinations of features without departing from the scope and spirit of the inventive concept.

Claims

1. A method for steering agricultural machinery, wherein the method is Receiving position data from a GNSS receiver, Receiving inertial data from multiple inertial sensors, Determining the instantaneous curvature of the steering of the agricultural machine based on the position data, the inertia data, the angle between the direction of movement of the agricultural machine and the tangent to the target path at the point closest to the agricultural machine, path parameters, a function of the target path to the path parameters, and a signed distance from the center of the rear axle of the agricultural machine to the target path, wherein the signed distance has a positive sign when the agricultural machine is on one side of the target path and a negative sign when the agricultural machine is on the other side of the target path. Steering the agricultural machinery based on the instantaneous curvature of the steering of the agricultural machinery that has been determined, Methods that include...

2. The instantaneous curvature of the steering of the agricultural machine is given by the formula [Math 1] Determined using, In the formula, ψ is the angle between the direction of movement of the agricultural machine and the tangent to the target path at the point closest to the agricultural machine, ξ is the path parameter, z is the signed distance from the center of the rear axis of the agricultural machine to the target path, having a positive sign when the agricultural machine is on one side of the target path and a negative sign when the agricultural machine is on the other side of the target path, P is the function of the target path to the path parameter, z' = sinψ, and the position data and the inertia data are used to determine ψ, ξ, z, and P. The method according to claim 1.

3. The GNSS receiver receives GNSS satellite signals from at least one antenna, and agricultural machinery attitude estimation is performed using the relational expression. [Math 2] The instantaneous speed of the agricultural machine is corrected according to the formula, where r is determined by the control action on the drive of the wheels of the agricultural machine and the posture of the body of the agricultural machine. The method according to claim 2.

4. The GNSS receiver receives GNSS satellite signals from at least three antennas, and agricultural machinery attitude estimation is performed using the following relational equation. b ｃａｌｉｂ，ｉ =Rb ｍｅｓ，ｉ ,i=1,2 Based on this, the measurement of the vector from one of the three antennas to the remaining antennas is corrected, In the formula, b ｃａｌｉｂ，ｉ i = 1, 2 are two baselines represented by the coordinate frame of the agricultural machine body, determined based on the calibration procedure, and b ｍｅｓ，ｉ i = 1, 2 are two baselines measured instantaneously. The method according to claim 2.

5. The method according to claim 4, wherein the initial agricultural machine posture is determined using a calibration operation, and the agricultural machine posture estimation is further based on the initial agricultural machine posture.

6. The method according to claim 5, wherein the calibration operation includes moving the agricultural machine in a known direction of movement.

7. The instantaneous curvature of the steering of the agricultural machine is given by the formula [Math 3] Determined using, In the equation, δ is the norm of the lateral deviation, β is the positive scale coefficient, and Π(X) is the potential generated by the entire point cloud. The method according to claim 1.

8. Multiple antennas, A GNSS receiver that receives signals from the aforementioned multiple antennas, Multiple inertial sensors, A controller configured to receive position data from the GNSS receiver, receive inertial data from the plurality of inertial sensors, and perform the method according to claim 1 for steering agricultural machinery, A device equipped with the following features.

9. The instantaneous curvature of the steering of the agricultural machine is given by the formula [Math 4] Determined using, In the formula, ψ is the angle between the direction of movement of the agricultural machine and the tangent to the target path at the point closest to the agricultural machine, ξ is the path parameter, z is the signed distance from the center of the rear axis of the agricultural machine to the target path, having a positive sign when the agricultural machine is on one side of the target path and a negative sign when the agricultural machine is on the other side of the target path, P is the function of the target path to the path parameter, z' = sinψ, and the position data and the inertia data are used to determine ψ, ξ, z, and P. The apparatus according to claim 8.

10. The GNSS receiver receives GNSS satellite signals from at least one antenna, and agricultural machinery attitude estimation is performed using the relational expression. [Math 5] The instantaneous speed of the agricultural machinery is corrected accordingly based on the measured value. In the formula, r is determined by the control action on the drive of the wheels of the agricultural machine and the posture of the main body of the agricultural machine. The apparatus according to claim 9.

11. The GNSS receiver receives GNSS satellite signals from at least three antennas, and agricultural machinery attitude estimation is performed using the following relational equation. b ｃａｌｉｂ，ｉ =Rb ｍｅｓ，ｉ ,i=1,2 Based on this, the measurement of the vector from one of the three antennas to the remaining antennas is corrected, In the formula, b ｃａｌｉｂ，ｉ i = 1, 2 are two baselines represented by the coordinate frame of the agricultural machine body, determined based on the calibration procedure, and b ｍｅｓ，ｉ i = 1, 2 are two baselines measured instantaneously. The apparatus according to claim 9.

12. The apparatus according to claim 11, wherein the initial agricultural machine posture is determined using a calibration operation, and the agricultural machine posture estimation is further based on the initial agricultural machine posture.

13. The apparatus according to claim 12, wherein the calibration operation includes moving the agricultural machine in a known direction of movement.

14. The instantaneous curvature of the steering of the agricultural machine is given by the formula [Math 6] Determined using, In the equation, δ is the norm of the lateral deviation, β is the positive scale coefficient, and Π(X) is the potential generated by the entire point cloud. The apparatus according to claim 8.

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