A multi-unmanned agricultural machine generalized super-spiral formation control method with field of view and performance constraints

Abstract

This invention discloses a generalized superspiral formation control method for multiple unmanned agricultural machines with field of view and performance constraints. A kinematic model of the multiple unmanned agricultural machines is established, and relative distance and relative azimuth angle are defined and constrained respectively. Relative distance tracking error and relative azimuth angle tracking error are defined, and the corresponding constraints are substituted to obtain the boundary conditions satisfied by the tracking error. An exponentially decaying time-varying performance function is introduced to impose asymmetric time-varying constraints on the tracking error, which are then transformed into boundary constraints on the normalized error. Based on the kinematic model of the multiple unmanned agricultural machines and the tracking error, the dynamic equation of the tracking error is derived, and a sliding mode variable based on the generalized superspiral is designed based on the normalized error. A robust finite-time formation control protocol based on the generalized superspiral algorithm is designed, enabling the leader-follower pair to achieve finite-time formation tracking while maintaining fast response speed and high steady-state accuracy under complex disturbances.

Description

Technical Field

[0001] This invention relates to the field of collaborative control technology for multiple unmanned agricultural machines, and in particular to a generalized superspiral formation control method for multiple unmanned agricultural machines with field of view and performance constraints. Background Technology

[0002] In modern precision agriculture, the collaborative operation of multiple unmanned agricultural machines (such as tractors and harvesters) can significantly improve production efficiency and work quality. Through formation control, multiple agricultural machines can maintain a specific geometric formation (such as harvesting side by side or following transport) to jointly complete complex tasks.

[0003] However, the actual farmland environment is complex and ever-changing, posing numerous challenges to the platooning control of multiple unmanned agricultural machines. First, the visual sensors on the machines typically have limited fields of view; if the lead machine is lost among the following machines, the platooning will fail. Second, a safe distance must be maintained between the machines to avoid collisions. Furthermore, farmland environments present problems such as GPS signal loss and unstable communication, and the speed of the lead machine is often unpredictable and variable, all of which greatly complicate high-precision platooning control.

[0004] Existing control methods, such as linear feedback control, lack robustness, and model predictive control suffers from high computational burden. While traditional sliding mode control offers strong robustness, it is prone to chattering. Although some research has attempted to combine pre-set performance control with obstacle functions to handle constraints, or to use terminal sliding mode to achieve finite-time convergence, problems such as insufficient control smoothness and strong dependence on the navigator's speed information still exist. Therefore, how to achieve finite-time, high-precision, and robust formation control of multiple unmanned agricultural machinery systems under conditions of relying solely on local visual measurements, having field-of-view and safety constraints, and having unknown speeds of the navigator agricultural machinery is a technical challenge that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of the prior art by providing a generalized superspiral formation control method for multiple unmanned agricultural machines with field of view and performance constraints. Based on the generalized superspiral algorithm, it can handle field of view and performance constraints and achieve high-precision formation tracking within a finite time.

[0006] The present invention achieves the above-mentioned technical objectives through the following technical means.

[0007] A generalized superspiral formation control method for multiple unmanned agricultural machines with field of view and performance constraints:

[0008] Establish a kinematic model of multiple unmanned agricultural machinery that includes a lead-follow relationship. Define the relative distance and relative azimuth angle based on the positional relationship between the lead-follow pair, and apply relative distance constraints and relative azimuth angle constraints.

[0009] Define relative distance tracking error and relative azimuth tracking error Substituting the relative distance constraint and the relative azimuth constraint respectively, we obtain the boundary conditions satisfied by the tracking error; in addition, we introduce an exponentially decaying time-varying performance function to apply an asymmetric time-varying constraint to the tracking error and transform it into a boundary constraint on the normalized error.

[0010] Based on the kinematic model and tracking error of the multi-unmanned agricultural machinery, the dynamic equation of the tracking error is derived, and based on the normalized error, a sliding mode variable based on the generalized superhelix is ​​designed.

[0011] We design a robust finite-time formation control protocol based on the generalized superspiral algorithm, which enables finite-time formation tracking of all error states of the lead-follow pair while satisfying the field of view and safety constraints.

[0012] Furthermore, relative distance and relative azimuth satisfy:

[0013]

[0014]

[0015] in, , These are the camera's maximum detection distance and maximum detection angle, respectively. This is the minimum safe distance.

[0016] Furthermore, distance tracking error and azimuth tracking error for:

[0017]

[0018] in, For the desired relative distance, Let be the desired relative azimuth angle, and satisfy... , ;

[0019] The boundary conditions that the tracking error must satisfy are:

[0020] .

[0021] Furthermore, time-varying performance functions ,in, These are the initial boundary values. For steady-state boundary values, Adjusting parameters for convergence speed , Represents quantities related to distance. This represents quantities related to azimuth.

[0022] Applying an asymmetric time-varying constraint to the tracking error is as follows:

[0023]

[0024] in, , And satisfy , .

[0025] Furthermore, normalization error ,and .

[0026] Furthermore, the relative distance tracking error and relative azimuth tracking error Differentiating the equation with respect to time t and substituting the kinematic model into the differentiated equation, we obtain the dynamic equation for the tracking error:

[0027]

[0028] in, This indicates the relative heading angle between the following agricultural machinery and the lead agricultural machinery. For the first The platform follows the heading angle of the agricultural machinery. For the i-th L The heading angle of the Taiwan-led agricultural machinery.

[0029] Furthermore, define sliding mode variables. A robust finite-time formation control protocol based on the generalized superspiral algorithm for following agricultural machinery. For example, its linear velocity and angular velocity are:

[0030]

[0031] in, For the barrier function gain, The upper limit of the speed of the leading agricultural machinery The estimated value, For virtual control input, It is a general asymmetric barrier function.

[0032] Furthermore, the virtual control input satisfies:

[0033]

[0034] Where, constant ,constant , and For the gain of the generalized superspiral controller to be designed, , , ; This is an intermediate quantity.

[0035] Furthermore, a universal asymmetric barrier function ,in, , They represent The upper and lower bounds.

[0036] Furthermore, the upper limit of speed The estimated value satisfies: , where constant , , .

[0037] The beneficial effects of this invention are:

[0038] 1. This invention addresses the formation control problem of multi-unmanned agricultural machinery systems under field-of-view and safety constraints. It innovatively combines a generalized superspiral algorithm with preset performance control and a universal obstacle function. Through an asymmetric time-varying performance function, complex practical physical constraints are cleverly transformed into boundary requirements for tracking errors, simplifying the constraint processing and ensuring continuous visibility and collision avoidance safety among the agricultural machinery.

[0039] 2. The control protocol proposed in this invention relies solely on local visual measurement information, eliminating the need for continuous communication between the GPS system and the agricultural machinery. By designing an adaptive law to estimate the unknown speed of the lead agricultural machinery online, it effectively overcomes the challenges of insufficient information in environments lacking GPS and with limited communication, greatly improving the applicability and robustness of multi-unmanned agricultural machinery systems in complex farmland environments.

[0040] 3. This invention employs a generalized superspiral algorithm to design the controller, which not only retains the strong robustness of sliding mode control but also effectively suppresses chattering in traditional sliding mode control, achieving smooth and high-precision control. The multi-unmanned agricultural machinery system is practically stable over a finite time, meaning that the system state (such as formation tracking error) can converge to an arbitrarily small neighborhood near the origin within a finite time. This ensures that the system maintains a fast response speed and high steady-state accuracy under complex disturbances, meeting the demands of precision agriculture for efficient and high-precision collaborative operations. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of a pair of lead-follow unmanned agricultural machinery vehicles according to the present invention;

[0042] Figure 2 This is a schematic diagram of the motion trajectory and formation changes of each unmanned agricultural machine in the phase plane in a specific embodiment of the present invention;

[0043] Figure 3 This refers to the relative distance tracking error of each following agricultural machine in a specific embodiment of the present invention. Schematic diagram showing changes over time;

[0044] Figure 4(a) shows the relative azimuth tracking error of agricultural machinery numbered 1 and 3 in a specific embodiment of the present invention. Schematic diagram showing changes over time;

[0045] Figure 4(b) shows the relative azimuth tracking error of each following agricultural machine numbered 2 and 4 in a specific embodiment of the present invention. Schematic diagram showing changes over time;

[0046] Figure 5(a) is a schematic diagram of the linear velocity of each agricultural machine in a specific embodiment of the present invention;

[0047] Figure 5(b) is a schematic diagram of the angular velocities of various agricultural machines in a specific embodiment of the present invention;

[0048] Figure 6 This is the estimated upper bound of the speed of the leading agricultural machine by each following agricultural machine in a specific embodiment of the present invention. Schematic diagram;

[0049] Figure 7 This is a flowchart of the generalized superspiral formation control of multi-unmanned agricultural machinery with field of view and performance constraints according to the present invention. Detailed Implementation

[0050] To more clearly illustrate the technical solutions and advantages of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are merely some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0051] This invention discloses a generalized superspiral formation control method for multiple unmanned agricultural machines with field-of-view and performance constraints. It is applicable to a swarm of unmanned agricultural machines that relies solely on a vision system, is guided by a reference machine, and maintains a fixed formation along a preset trajectory. The method employs a multi-level leader-follower control structure, where each unmanned agricultural machine in the swarm has its own unique leader, forming multiple leader-follower pairs. This control structure has high distribution, allowing unmanned agricultural machines in the swarm to simultaneously act as intermediate leaders and followers. All unmanned agricultural machines are equipped with cameras to capture leader information within their field of view. The advantage of this approach is that all control decisions are obtained through local perception, eliminating the need to rely on global information and communication, thus saving computational and communication burdens.

[0052] like Figure 7 As shown, a generalized superspiral formation control method for multiple unmanned agricultural machines with field of view and performance constraints includes the following steps:

[0053] Step 1: Establish a kinematic model of multiple unmanned agricultural machinery that includes a lead-follow relationship, and define the relative distance and relative azimuth angle according to the positional relationship between the lead-follow pair.

[0054] Step 1.1: Establish a kinematic model of multiple unmanned agricultural machinery systems that includes a leader-follower relationship. Consider the following... A cluster of unmanned agricultural machines, consisting of one reference machine (number 0) and the rest being lead-follower pairs (numbered 0, ... ). Define the first A following agricultural machine and its corresponding lead agricultural machine , No. The kinematic model of a follower agricultural machine is:

[0055]

[0056] No. Each following agricultural machine corresponds to a leading agricultural machine. The kinematic model is as follows:

[0057]

[0058] in, For the first Taiwan follows agricultural machinery in the geodetic coordinate system Position coordinates in For the first Taiwan Leading Agricultural Machinery in Geodetic Coordinate System Position coordinates in For the first The platform follows the heading angle of the agricultural machinery. For the i-th L The heading angle of the Taiwan-leading agricultural machinery and These are the linear velocity and angular velocity of the following agricultural machinery, respectively. and These are the linear velocity and angular velocity of the pilot agricultural machinery, respectively.

[0059] Step 1.2, based on the pilot-follow pair ( Figure 1 , where V i Indicates following agricultural machinery, V iL Indicates leading agricultural machinery, O i Indicates the center coordinates of the agricultural machinery. The relative distance is defined as the positional relationship between the center coordinates of the pilot agricultural machinery. and relative azimuth :

[0060]

[0061]

[0062] in, It is a two-parameter arctangent function, and its return value is... Within the range; This is an intermediate quantity.

[0063] Step 2: Since the cameras installed on the unmanned agricultural machinery have certain limitations in their field of view (detection distance and width), in order to ensure that the agricultural machinery does not collide during formation and that the information of the lead agricultural machinery can always be detected by the following agricultural machinery, field of view constraints (including relative distance constraints and relative azimuth constraints) are applied.

[0064] To ensure that the following agricultural machinery can always detect the lead agricultural machinery through the camera and avoid collisions, the relative distance and relative azimuth angle must meet the following requirements:

[0065]

[0066]

[0067] in, , These are the camera's maximum detection distance and maximum detection angle, respectively. For the minimum safe distance, and satisfying , .

[0068] As long as the above constraints are not violated during formation, the connection and safety between the lead and follower agricultural machines are maintained at all times.

[0069] Step 3: Based on the kinematic model and field-of-view constraints of the multi-unmanned agricultural machinery established in Step 1 and Step 2, introduce the tracking errors of relative distance and relative azimuth angle. By substituting the tracking errors into the field-of-view constraint formula, the boundary conditions that the tracking errors need to satisfy are obtained.

[0070] Step 3.1: Define the relative distance tracking error and relative azimuth tracking error Set the desired relative distance as The desired relative azimuth angle is And satisfy , ;but:

[0071] .

[0072] Step 3.2: Substitute the field-of-view constraint from Step 2 into the relative distance tracking error from Step 3.1. and relative azimuth tracking error The boundary conditions that the tracking error must satisfy are obtained as follows:

[0073] .

[0074] Step 4: In order to ensure that the tracking error meets the preset transient and steady-state performance, an exponentially decaying time-varying performance function is introduced to apply an asymmetric time-varying constraint to the tracking error.

[0075] Step 4.1: Define the performance function ( )for:

[0076]

[0077] in, , These are the initial boundary values. For steady-state boundary values, satisfying ; Adjust the parameters for convergence speed.

[0078] Step 4.2: Based on this, apply the following asymmetric time-varying constraint to the tracking error:

[0079]

[0080] in, , And satisfy , .

[0081] Step 5: Define the normalized error, and transform the asymmetric time-varying constraint described in Step 4 into a boundary constraint on the normalized error.

[0082] To further simplify controller design, a normalized error is defined:

[0083]

[0084] in, This indicates the tracking error.

[0085] The tracking error constraint is transformed into a boundary constraint on the normalized error. At this point, the original constraint (the boundary conditions satisfied by the tracking error) is transformed into... .

[0086] As long as this error boundary is not violated during the formation process, the preset transient and steady-state performance can be satisfied.

[0087] Step 6: Based on the kinematic model and tracking error model of the multi-unmanned agricultural machinery established in Step 1 and Step 3, derive the dynamic equations of relative distance error and relative azimuth angle error, and design sliding mode variables based on generalized superhelices based on the normalized error in Step 5.

[0088] Relative distance tracking error in steps 6.1 and 3.1 and relative azimuth tracking error Differentiating the equation with respect to time t, and substituting the kinematic model from step 1.1 into the differentiated equation, we obtain the error dynamic equation:

[0089]

[0090] in, This indicates the relative heading angle between the following agricultural machinery and the lead agricultural machinery.

[0091] Step 6.2: The normalized error defined in step 5.1... Taking the derivative, the dynamic equation for the normalized error is obtained as follows:

[0092]

[0093] Substituting the formula from step 6.1 into the above equation, we can obtain the result. The specific expression.

[0094] Step 6.3: To facilitate the design of a finite-time controller, define sliding mode variables. as follows:

[0095] ,

[0096] That is, the normalized error is directly selected as the sliding surface. Thus, the control objective is transformed into: design... , This makes the sliding mode variable and It converges to a small neighborhood near zero within a finite time, and the constraints are satisfied throughout the process. .

[0097] Step 6.4: Dynamically rewrite the sliding mode variables as a second-order system in the following general form:

[0098] ,

[0099] in, For the virtual control input to be designed, it is related to , The relationship will be explicitly given through subsequent controller design; This is a lumped term that includes the known nonlinearity and unknown perturbations of the pilot-follower pair, and it is assumed that its derivative is bounded, i.e., there exists a constant. Make .

[0100] Step 7: Design a complete robust finite-time formation control protocol based on the generalized superspiral algorithm. By introducing a universal asymmetric barrier function to dynamically generate repulsive forces, the normalized error is ensured to always satisfy boundary constraints. Simultaneously, an adaptive law is designed to estimate the upper bound of the unknown speed of the lead vehicle online. Through the designed control protocol, finite-time formation tracking is achieved under the premise of satisfying the field of view and safety constraints for all error states of the lead-follow pair.

[0101] Step 7.1, for sliding mode variable dynamics The generalized superhelical controller is designed as follows:

[0102]

[0103] in, For virtual control input, constant , , and For the gain of the generalized superspiral controller to be designed, ( ), ; This is an intermediate quantity.

[0104] Step 7.2: Introduce a universal asymmetric barrier function Ensure normalization error The barrier function is defined as follows, ensuring that the boundary constraints are never violated:

[0105] ,

[0106] in, , They represent The upper and lower bounds.

[0107] This function is in Approaching the lower bound When the upper bound is 1, its value tends to infinity, thus generating a strong repulsive force in the control law to ensure that the constraints are not violated.

[0108] Step 7.3: Design an adaptive law to update the estimated upper bound of the velocity online. :

[0109]

[0110] in, , , This adaptive law can effectively handle situations where the speed of the navigating agricultural machinery is unknown, and ensures that the estimated value is bounded.

[0111] Step 7.4: Design a complete generalized superspiral formation control protocol to follow agricultural machinery. For example, its linear velocity and angular velocity are:

[0112]

[0113] in, For the barrier function gain, To set the upper speed limit for pilot agricultural machinery The estimated value (assuming) ,but unknown).

[0114] This control protocol enables finite-time formation tracking of all error states of the pilot-follower pair while satisfying field of view and safety constraints.

[0115] Steps 1-7 are all implemented in the controller. The controller takes the desired formation position as input and outputs linear velocity and angular velocity commands to the navigator-follower pair to drive the unmanned agricultural machinery to move forward in the desired formation.

[0116] In this embodiment, one reference agricultural machine is considered. (Number 0) and 4 pilot-follower agricultural machines ( The kinematic model of the multi-unmanned agricultural machinery system, consisting of [various components], is shown in the formula in step 1.1. The initial pose of each agricultural machine is set as follows:

[0117]

[0118]

[0119]

[0120]

[0121]

[0122] The reference trajectory for agricultural machinery is a segmented path as follows:

[0123]

[0124] Among them, intermediate quantity , , .

[0125] For all pilot-follower agricultural machinery Set the appropriate constraints: , , The desired formation setting is: desired distance. Desired azimuth angle , Select the performance function according to the formula in step 4.1:

[0126]

[0127] Based on step 5, the normalization error constraint is as follows: , , Parameter selection for the generalized superspiral controller: , , , , , , Barrier function gain The adaptive parameters are: , , All estimated initial values .

[0128] Figure 1 This is a schematic diagram of a pair of lead and follow vehicles. Figure 2 The diagram shows the movement trajectory and formation changes of each unmanned agricultural machine in the phase plane. It can be seen that each following agricultural machine can quickly form a predetermined formation and maintain its formation to follow the lead agricultural machine in the subsequent path without leaving the field of view. Figure 3 Figures 4(a) and 4(b) show the relative distance tracking error, respectively. and relative azimuth tracking error The convergence process shows that all errors converge rapidly to near zero within the performance function boundary, strictly satisfying the constraint conditions. Figures 5(a) and 5(b) show the curves of linear velocity and angular velocity, respectively. The curves are smooth and free of chattering, indicating that the generalized superspiral algorithm effectively suppresses the chattering problem of sliding mode control. Figure 6 The diagram shows the estimated upper bound of the speed of the lead agricultural machine for each following agricultural machine. The estimated value eventually converged to a constant value, verifying the effectiveness of the adaptive law.

[0129] In summary, the control method proposed in this invention can achieve high-precision, finite-time formation control of multiple unmanned agricultural machinery systems under conditions of field-of-view constraints, safety constraints, and unknown navigator speed, demonstrating strong robustness and promising application prospects.

[0130] The embodiments described above are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments. Any obvious improvements, substitutions or modifications that can be made by those skilled in the art without departing from the essence of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for controlling the generalized superspiral formation of multiple unmanned agricultural machines with field-of-view and performance constraints, characterized in that: Establish a kinematic model of multiple unmanned agricultural machinery that includes a lead-follow relationship. Define the relative distance and relative azimuth angle based on the positional relationship between the lead-follow pair, and apply relative distance constraints and relative azimuth angle constraints. Definition of relative distance tracking error and relative azimuth angle tracking error and substitute into the relative distance constraint and the relative azimuth angle constraint respectively to obtain boundary conditions that the tracking errors satisfy; in addition, an exponentially decaying time-varying performance function is introduced to impose asymmetric time-varying constraints on the tracking errors and is converted into boundary constraints on the normalized errors; Based on the kinematic model and tracking error of the multi-unmanned agricultural machinery, the dynamic equation of the tracking error is derived, and based on the normalized error, a sliding mode variable based on the generalized superhelix is ​​designed. We design a robust finite-time formation control protocol based on the generalized superspiral algorithm, which enables finite-time formation tracking of all error states of the lead-follow pair while satisfying the field of view and safety constraints.

2. The multi-unmanned agricultural machinery generalized superspiral formation control method according to claim 1, characterized in that, relative distance and relative azimuth angle satisfies: in, , These are the camera's maximum detection distance and maximum detection angle, respectively. This is the minimum safe distance.

3. The multi-unmanned agricultural machinery generalized superspiral formation control method according to claim 2, characterized in that, Distance tracking error and azimuth tracking error for: in, For the desired relative distance, Let be the desired relative azimuth angle, and satisfy... , ; The boundary conditions that the tracking error must satisfy are: 。 4. The multi-unmanned agricultural machinery generalized superspiral formation control method according to claim 3, characterized in that, Time-varying performance function ,in, These are the initial boundary values. For steady-state boundary values, Adjusting parameters for convergence speed , Represents quantities related to distance. This represents quantities related to azimuth. Applying an asymmetric time-varying constraint to the tracking error is as follows: in, , And satisfy , .

5. The multi-unmanned agricultural machinery generalized superspiral formation control method according to claim 4, characterized in that, Normalized error ,and .

6. The method for controlling the generalized superspiral formation of multiple unmanned agricultural machines according to claim 5, characterized in that, The relative distance tracking error and relative azimuth tracking error Differentiating the equation with respect to time t and substituting the kinematic model into the differentiated equation, we obtain the dynamic equation for the tracking error: in, This indicates the relative heading angle between the following agricultural machinery and the lead agricultural machinery. For the first The platform follows the heading angle of the agricultural machinery. For the i-th L The heading angle of the Taiwan-led agricultural machinery.

7. The multi-unmanned agricultural machinery generalized superspiral formation control method according to claim 6, characterized in that, Define sliding mode variables A robust finite-time formation control protocol based on the generalized superspiral algorithm for following agricultural machinery. For example, its linear velocity and angular velocity are: in, For the barrier function gain, The upper limit of the speed of the leading agricultural machinery The estimated value, For virtual control input, It is a general asymmetric barrier function.

8. The method for controlling the generalized superspiral formation of multiple unmanned agricultural machines according to claim 7, characterized in that, Virtual control input satisfies: Where, constant ,constant , and For the gain of the generalized superspiral controller to be designed, , , ; This is an intermediate quantity.

9. The method for controlling the generalized superspiral formation of multiple unmanned agricultural machines according to claim 7, characterized in that, Universal Asymmetric Barrier Function ,in, , They represent The upper and lower bounds.

10. The multi-unmanned agricultural machinery generalized superspiral formation control method according to claim 7, characterized in that, Speed ​​upper limit The estimated value satisfies: , where constant , , .

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