Augmented Lagrange Method for UAV Localization with Coverage of Robot Signals

Abstract

The present invention relates to an augmented Lagrange method for UAV positioning capable of covering robot signals. The method proposes the concept of agricultural and forestry robots and their demand markets. Aiming at the shortcomings of agricultural and forestry robots in terms of signal sources and positioning functions, the present invention uses optimization techniques to establish a multi-constrained complex semidefinite programming model. Through the structure of the multi-constrained complex semidefinite programming model, the model is decomposed into a multi-constrained simple semidefinite programming problem model and a sequential maximum element problem model. A cyclic strategy is used to solve the sequential maximum element problem, and an augmented Lagrange method for solving multi-constrained semidefinite programming is designed. The present invention is used to solve problems such as signal loss in covering robot signals faced by UAV positioning in agricultural and forestry production.

Description

Technical Field

[0001] The present invention belongs to the technical field of information processing, and relates to an augmented Lagrange method for UAV positioning that can cover robot signals based on optimization technology. Background Art

[0002] In agricultural and forestry production activities, robots that can be automatically operated without human intervention are needed, which are called agricultural and forestry robots. In terms of communication, the agricultural and forestry operation areas are large and wide, and it is not easy to establish a signal coverage network. In addition, compared with farm crops, the height of agricultural and forestry crops is significantly non-negligible, which is one of the important reasons affecting signal coverage and signal communication.

[0003] Robots within the agricultural and forestry scope are smaller in volume compared with farm robots because the terrain in the forest garden is narrower than that in the farmland. Moreover, the number of agricultural and forestry robots required is also related to the growth cycle and planting area of forest trees. Furthermore, due to the large height of agricultural and forestry crops, they have a shielding effect on signals, bringing non-negligible errors to the position monitoring of agricultural and forestry robots. Therefore, signals need to be supplemented for accurate monitoring.

[0004] The present invention will use the UAV airborne base station to supplement signals. Its goal is to accurately supplement the signals covering agricultural robots, use UAVs to position agricultural and forestry robots, and solve the signal coverage problem based on optimization technology. Summary of the Invention

[0005] In order to overcome the deficiencies of the prior art, the present invention designs an augmented Lagrange method for UAV positioning that can cover robot signals based on optimization technology. First, the concept of agricultural and forestry robots is proposed. Aiming at the shortcomings of agricultural and forestry robots in terms of signal sources and positioning functions, the UAV airborne base station is used to supplement signals, and an optimization technology is used to establish a model that can be decomposed into a semidefinite programming and a sequential maximum element problem. The classical cyclic strategy is used to solve the sequential maximum element problem, and an augmented Lagrange method for solving multi-constraint semidefinite programming is designed. This technology is used to solve the problems of signal loss and robot anti-collision faced by UAV positioning in agricultural and forestry production.

[0006] The agricultural and forestry robots involved in the present invention refer to: machines that use artificial intelligence technologies such as detection and calculation in agricultural and forestry production, are controlled by different program software, are suitable for various operations, can sense and adapt to crop types and environmental changes in agriculture and forestry, and can be automatically operated without human intervention. This type of robot has a broad market prospect in many agricultural and forestry operation fields such as fruit tree picking and pesticide spraying.

[0007] Robots in the scope of agriculture and forestry are smaller in volume compared to farm robots because the terrain in forest gardens is more narrow than that in farmlands. Since the height of agricultural and forestry crops is large and they block signals, signal supplementation is required for accurate monitoring.

[0008] The technical solution of the present invention is: an augmented Lagrange method for UAV positioning that can cover the signals of robots, and the hardware relied on by the method includes a UAV and multiple agricultural and forestry robots M. An airborne base station is provided on the UAV, and the airborne base station is used to supplement signals to the agricultural and forestry robots M. The distance measurement unit used in the method is meters, and the time unit is minutes. The following is to establish an optimization model for UAV positioning that can cover the signals of agricultural and forestry robots:

[0009] The activity range of the i-th agricultural and forestry robot Mi is defined as an elliptical area, denoted as E i , where i is a positive integer, its major axis is and the minor axis is Taking the position center of E i as the coordinate origin, the north-south direction as the vertical axis, denoted by t2, and the east-west direction as the horizontal axis, denoted by t1. The included angle between the major axis of E i and the positive half-axis of the horizontal axis is θi, and the rotation transformation matrix of E i is The equation of E i is:

[0010]

[0011] The equation data matrix of E i is

[0012] A i > 0 indicates that the matrix A i is positive definite, and is the inverse matrix of A i , i = 1,..., m, where m is a positive integer;

[0013] Translate the coordinate system origin to ηi = (ηi1, ηi2) T , where ηi is the plane position coordinate of the ellipse center point in the GPS position of E i , b i = A i ηi, c i = ηi T A i ηi - 1, construct a matrix Q 1i with the largest eigenvalue being λ 2i and the second largest eigenvalue being λ i , and the matrix is The reciprocal of Q i corresponds to λ 1i and λ 2i The eigenvectors of are u 1i and u 2i Then E i The minor axis direction of is parallel to u 1i and the major axis direction is parallel to u 2i E i is re-expressed as a matrix:

[0014]

[0015] i = 1, …, m, x represents the points in, is the two-dimensional real space, and the center of E i is The signal coverage range of the on-board base station of the UAV is a circle B, where β = (β1, β2) represents the coordinate point in the plane position coordinates of the GPS position of the UAV, γ is a real number, and the signal coverage radius of the UAV before takeoff is The set of tree height data is H = {h1, …, h n}, n represents the number of trees. When the height of the UAV from the ground is ρ, it is required that ρ satisfies ρ ≥ 1 + h i i = 1, … n. Then, according to the Pythagorean theorem, the radiation radius of the signal of the UAV in the air is

[0016] Since there exists a positive integer τ i such that the following equation holds:

[0017]

[0018] The UAV positioning optimization model is:

[0019]

[0020] Since the optimization of the variable ρ is independent of the variables β, γ, τ, the UAV positioning optimization model is decomposed into two independent simple optimization sub-problems:

[0021] Multi-constraint simple semi-definite programming problem:

[0022]

[0023] And the sequence maximum element problem:

[0024]

[0025] The method for solving the UAV positioning optimization model is as follows:

[0026] The first step is to solve the semidefinite programming (2):

[0027] Algorithm description: Since the number of robots is large and they are operating non-statically, an augmented Lagrange method is used to solve the semidefinite constraint optimization (2) to reduce the calculation time.

[0028] Step1.1: (Initialization) First, given the starting coordinates β of the UAV 0 , and the coverage parameters γ 0 , τ 0 , where γ 0 , τ 0 are real numbers, given the step size {a k} and the penalty parameter sequence {σ k}, define the initial third-order multiplier matrix Given the initial index set I0 = {1,..., m};

[0029] Step1.2: (Iteration): k = 0,..., N-1. For the index set I k Define the augmented Lagrangian function

[0030]

[0031] where is the projection operator onto the p-dimensional positive semidefinite cone

[0032] Step1.3 (Update β, γ, τ) Assign the optimal solution of to (β k+1 , γ k+1 , τ k+1 )

[0033] Step1.4 (Update the multiplier M)

[0034]

[0035] Step1.5 (Update the index set I k+1 )

[0036]

[0037] Steρ1.6: Output ((β N ) T , γ N , (τ N ) T ) T , obtain the coordinates β N , ​

[0038] Step 2: Solving the maximum element: Using a loop strategy to solve the maximum element of the sequence

[0039] Step 2.1: (Initialization) Let ρ = 0

[0040] Step 2.2: (Iteration) j = 1, …, n, if ρ ≤ h j , ρ = h j

[0041] Step 2.3: (Output) ρ, and finally obtain the UAV coordinate β N , and the radiation radius is Description of the Drawings

[0042] Drawings of the specification:

[0043] Figure 1 It shows the top view of agricultural and forestry operations and the signal transmission path of the robot.

[0044] Figure 2 It shows the height map of the UAV and the height limit of the UAV.

[0045] Figure 3 It shows the signal coverage effect diagram of the fixed-direction agricultural and forestry robot.

[0046] Figure 4 It shows the signal coverage effect diagram of the variable-direction agricultural and forestry robot.

[0047] Fixed-direction agricultural and forestry robot: E i The included angle between the major axis of E and the positive half-axis of the horizontal axis of the coordinate system is θi, which is constant.

[0048] Variable-direction agricultural and forestry robot: E i The included angle between the major axis of E and the positive half-axis of the horizontal axis of the coordinate system is θi, which is variable.

[0049] Advantages of the Present Invention

[0050] 1. Combining the characteristics of agricultural production and forestry production, the present invention proposes the concept of agricultural and forestry robots and their demand markets. Considering the characteristics that agricultural and forestry robots are smaller in volume, the agricultural and forestry crops are taller, and the signal is blocked, the present invention proposes a strategy of using the UAV on-board base station to supplement the signal, which is beneficial to accurate information monitoring and ensures that the UAV and the robot will not collide with agricultural and forestry crops.

[0051] 2. Combining the elliptical coverage in the horizontal range and the information of the UAV's longitudinal height, a multi-constraint complex semi-definite programming model is established, and the model can be decomposed into simple sub-problems by using the structure, which provides a guarantee for designing an efficient and fast algorithm, reduces the performance indicators required for the UAV, and can save the cost of manufacturing the UAV.

[0052] 3. Design a stochastic algorithm for solving semidefinite programming and a cyclic strategy for solving the sequential maximum element, solve the problem of a large number of agricultural and forestry robots with non-stationary operations, and ensure the real-time nature of positioning. Specific implementation manner

[0053] See Figures 1 to 4 As shown, an augmented Lagrange method for UAV positioning that can cover the signals of robots, the hardware relied on by the method includes a UAV and multiple agricultural and forestry robots M. An on-board base station is provided on the UAV, and the on-board base station is used to supplement signals to the agricultural and forestry robots M. The distance measurement unit used in the method is meters, and the time unit is minutes. The following establishes an optimization model for UAV positioning that can cover the signals of agricultural and forestry robots:

[0054] The activity range of the i-th agricultural and forestry robot Mi is defined as an elliptical region, denoted as E i , where i is a positive integer, its major axis is and its minor axis is Taking the position center of E i as the coordinate origin, the north-south direction as the vertical axis, denoted by t2, and the east-west direction as the horizontal axis, denoted by t1. The included angle between the major axis of E i and the positive half-axis of the horizontal axis is θi, and the rotation transformation matrix of E i is E i The equation of is:

[0055]

[0056] E i The equation data matrix of is

[0057] A i > 0 indicates that the matrix A i is positive definite, is the inverse matrix of A i , i = 1,..., m, where m is a positive integer;

[0058] Translate the coordinate system origin to ηi = (ηi1, ηi2) T , where ηi is the plane position coordinate of the ellipse center point in the GPS position of E i , b i = A i ηi, c i = ηi T A i ηi - 1, construct a matrix Q with the largest eigenvalue being λ 1i and the second largest eigenvalue being λ 2i and i, the matrix is the reciprocal of Q i corresponding to λ 1i and λ 2i The eigenvectors are u 1i and u 2i Then the minor axis direction of E i is parallel to u 1i , and the major axis direction is parallel to u 2i , E i is re - represented by a matrix as:

[0059]

[0060] i = 1, …, m, x represents the points in which is a two - dimensional real - number space, and the center of E i is The signal coverage range of the on - board base station of the UAV is a circle B, where β=(β1, β2) represents the coordinate point in the planar position coordinates of the GPS position of the UAV, γ is a real number, and the signal coverage radius before the UAV takes off is The set of tree height data is H = {h1, …, h n}, n represents the number of trees. When the height of the UAV from the ground is ρ, it is required that ρ satisfies ρ≥1 + h i , i = 1, …n. Then according to the Pythagorean theorem, the radiation radius of the signal of the UAV in the air is

[0061] Since So there exists a positive integer τ i , such that the following formula holds:

[0062]

[0063] The UAV positioning optimization model is:

[0064]

[0065] Since the optimization of the variable ρ is independent of the variables β, γ, τ, the UAV positioning optimization model is decomposed into two non - related simple optimization sub - problems:

[0066] Multi - constraint simple semi - definite programming problem:

[0067]

[0068] And the sequence maximum element problem:

[0069]

[0070] The solution method for the UAV positioning optimization model is as follows:

[0071] The first step is to solve the semidefinite programming (2):

[0072] Algorithm description: Since the number of robots is large and they are operating non-statically, an augmented Lagrange method is used to solve the semidefinite constraint optimization (2) to reduce the calculation time.

[0073] Step1.1: (Initialization) First, given the departure coordinates β of the UAV 0 , and the coverage parameters γ 0 , τ 0 , where γ 0 , τ 0 are real numbers. Given the step size {a k} and the penalty parameter sequence {σ k}, define the initial third-order multiplier matrix Given the initial index set I0 = {1,..., m};

[0074] Step1.2: (Iteration): k = 0,..., N - 1. For the index set I k Define the augmented Lagrangian function

[0075]

[0076] where is the projection operator onto the p-dimensional positive semidefinite cone .

[0077] Step1.3 (Update β, γ, τ) Assign the optimal solution of to (β k+1 , γ k+1 , τ k+1 )

[0078] Step1.4 (Update the multiplier M)

[0079]

[0080] Step1.5 (Update the index set I k+1 )

[0081]

[0082] Step1.6: Output ((β N ) T , γ N , (τ N ) T ) T , and obtain the coordinates βN ,

[0083] Step 2: Solve the maximum element: Use the loop strategy to solve the maximum element of the sequence

[0084] Step 2.1: (Initialization) Let ρ = 0,

[0085] Step 2.2: (Iteration) j = 1,..., n, if ρ ≤ h j , ρ = h j

[0086] Step 2.3: (Output) ρ, and finally obtain the UAV coordinate β N , and the radiation radius is

[0087] Numerical results

[0088] In the numerical experiments of the present invention, fixed-direction robots and steerable robots are involved. The signal coverage effect diagrams can be seen in Figure 3 and Figure 4 . In Figure 3 and Figure 4 , each ellipse represents an agricultural and forestry robot. Its major axis is the real-time walking direction of the agricultural and forestry robot, and the whole ellipse represents the possible positions that the robot is expected to appear after a period of time. The dashed line represents the area where the signal coverage range of the UAV intersects the ground, and all agricultural and forestry robots have been covered. The circle indicates that the robot is temporarily in a stationary state. In 20 seconds, if the moving speed of the agricultural and forestry robot in the working state is v meters per second, the major axis of the ellipse can be set to 20v meters, which can ensure that the moving agricultural and forestry robot is always within the signal coverage range of the UAV.

Claims

1. Augmented Lagrange method for UAV positioning that can cover robot signals based on optimization technology. The hardware relied on by the method includes a UAV and multiple agricultural and forestry robots M. An on-board base station is installed on the UAV to supplement signals to the agricultural and forestry robots M. The distance measurement unit used in the method is meters, and the time unit is minutes. Now, establish an optimization model for UAV positioning that can cover agricultural and forestry robot signals: The activity range of the i-th agricultural and forestry robot Mi is defined as an elliptical area, denoted as E i , where i is a positive integer, its major axis is and the minor axis is Taking the position center of E i as the coordinate origin, the north-south direction as the vertical axis, denoted by t2, and the east-west direction as the horizontal axis, denoted by t1. The included angle between the major axis of E i and the positive semi-axis of the horizontal axis is θi. The rotation transformation matrix of E i is E i The equation of is: E i The equation data matrix of is A i > 0 indicates that the matrix A i is positive definite, is the inverse matrix of A i , i = 1,…,m, where m is a positive integer; Translate the coordinate origin to ηi = (ηi1, ηi2) T , ηi is the coordinate point of the ellipse center in the plane position coordinates of the GPS position of E i , b i = A i ηi, c i = ηi T A i ηi - 1, construct a matrix Q with the largest eigenvalue being λ 1i and the second largest eigenvalue being λ 2i . The matrix i is the reciprocal of . The eigenvectors corresponding to λ i and λ 1i and λ 2i are u 1i and u 2i respectively. Then the minor axis direction of E i is parallel to u 1i , and the major axis direction is parallel to u 2i . E i is re-expressed as a matrix: For \(i = 1,\ldots,m\), \(x\) represents a point in which is a two - dimensional real - number space, and the center of \(E\) i is The signal coverage range of the on - board base station of the drone is a circle \(B\), where \(\beta=(\beta_1,\beta_2)\) represents the coordinate point in the planar position coordinates of the GPS position of the drone, \(\gamma\) is a real number, and the coverage radius of the signal of the drone before take - off is The set of height data of the trees is \(H = \{h_1,\ldots,h\) n \(n\) represents the number of trees. When the height of the drone from the ground is \(\rho\), it is required that \(\rho\geq1 + h\) i , \(i = 1,\ldots,n\). Then, according to the Pythagorean theorem, the radiation radius of the signal of the drone in the air is Since \(i = 1,\ldots,m\), there exists a positive integer \(\tau\) i such that the following formula holds: The drone positioning optimization model is: Since the optimization of the variable \(\rho\) is independent of the variables \(\beta,\gamma,\tau\), the drone positioning optimization model is decomposed into two non - related simple optimization sub - problems: A multi - constraint simple semi - definite programming problem: And a sequence maximum element problem: Its characteristics are: The solution method for the UAV positioning optimization model is as follows: The first step is to solve the semidefinite programming (2): Use an augmented Lagrange method as described to solve the semidefinite constraint optimization (2), Step 1.1: Initialize. First, given the starting coordinates β of the drone 0 , and the coverage parameter γ 0 , τ 0 , where γ 0 , τ 0 are real numbers. Given the step size {a k} and the penalty parameter sequence {σ k}, define the initial third-order multiplier matrix Given the initial index set I0 = {1,…,m}; Step1.2: Iteration: k = 0, …, N - 1. For the index set I k Define the augmented Lagrangian function where, is the projection operator onto the p-dimensional positive semi-definite cone ​ Step 1.3: Update the optimal solution of the parameter combination (β, γ, τ) and assign it to (β k+1 , γ k+1 , τ k+1 ) Step 1.4: Update the multiplier matrix Step 1.5: Update the index set I k+1 Step1.6: Output ((β N ) T , γ N , (τ N ) T ) T , and obtain the coordinate β N ; Step 2, maximum element solving, using a loop strategy to solve the maximum element of the sequence Step 2.1: Initialize, set ρ = 0, Step 2.2: Iterate, j = 1, …, n. If ρ ≤ h j , ρ = h j Step 2.3: Output ρ, and finally obtain the UAV coordinates β N , with a radiation radius of

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