Formation Optimization Method for Master-Slave Multi-AUV Cooperative System Based on Simulated Annealing Algorithm

Abstract

A method for optimizing the formation of a master-slave multi-AUV cooperative system based on the simulated annealing algorithm, the method comprising the following steps: (1) constructing a motion model and a measurement model of a master-slave multi-AUV (Autonomous Underwater Vehicle, AUV) cooperative positioning system; (2) designing a positioning performance evaluation function for the master-slave multi-AUV cooperative system; (3) designing an optimization of the performance evaluation function based on the simulated annealing algorithm, i.e., a formation optimization method. The present invention provides a simulated annealing algorithm for optimizing the formation of a master-slave multi-AUV cooperative system. During the cooperative positioning process, by moving the positions of some AUVs, the system reaches the optimal positioning performance formation, improving the cooperative positioning accuracy.

Description

Technical Field

[0001] The present invention belongs to the technical field of navigation, and specifically relates to a formation optimization method for a master-slave multi-AUV cooperative system based on a simulated annealing algorithm. Background Art

[0002] Marine resources play an indispensable role in the sustainable development of human society. In 1953, the first unmanned remotely operated vehicle came out. After decades of development, underwater robots can complete the assigned tasks in the face of harsh marine environments and have become an important tool in current marine resource exploration. AUVs are increasingly widely used in the field of marine resource exploration due to their advantages such as a wide operation range, strong autonomy, and high safety.

[0003] Multi-AUV cooperative systems often need to execute established action tasks, and cooperative positioning technology has become the key to determining whether the cooperative system can successfully complete the tasks. For a cooperative system, the significance of positioning lies in clarifying the absolute positions and relative position relationships of each AUV during the cooperative work process. Accurate positioning is the prerequisite for ensuring the effective completion of AUV tasks. The research on multi-AUV cooperative positioning technology mainly includes two aspects: cooperative methods and positioning algorithms. Cooperative methods include exploring the initial networking formation, formation maintenance, etc. of each AUV in the cooperative system; the positioning algorithm mainly involves the application of multiple sensors in the cooperative system and the design of information processing algorithms. The two promote each other and develop together.

[0004] Some researchers pay great attention to cooperative methods. The positioning algorithm focuses on fusing sensor information such as measurements. However, factors such as the formation structure and formation of the multi-AUV system will cause changes in the measurement information. Therefore, the positioning accuracy of the cooperative system that constructs the positioning algorithm through distance measurement will inevitably be affected.

[0005] The literature A.N. Bishop, B. Fidan, B. Anderson and P.N. Pathirana, “Optimality analysis of sensor-target localization geometries,” Automatica, vol. 46, no. 3, pp. 479–492, Mar. 2010 explores the position measurements of estimating a target by multiple noisy sensors and concludes that the relative geometry of the sensor-target will significantly affect the performance of any specific algorithm. Its research content uses mathematical methods to characterize the variance distribution of the effective estimation space, generates uncertainty ellipses, identifies and obtains the relative sensor-target geometries that minimize the uncertainty ellipses, and emphasizes the importance of the sensor-target topology on the localization performance through formal analysis results and illustrative examples. The literature W.Yan, X.Fang and J.Li, "Formation Optimization for AUV Localization With Range-Dependent Measurements Noise," in IEEE Communications Letters, vol. 18, no. 9, pp. 1579-1582, Sept. 2014, doi: 10.1109 / LCOMM.2014.2344033 conducts sensitivity tests on the separation angle and distance, etc. of the cooperative system as measurement information to analyze the impact on the localization performance of the optimal formation. The simulation results show that the localization performance is more sensitive to distance information rather than angle information.

[0006] In Patent CN109656136A, a positioning model of the cooperative system is established using the three-dimensional space state, i.e., the three-dimensional position information of the AUV, and this model only contains the distance information part; while in our method, the two-dimensional coordinates of the AUV combined with the heading angle are used to form the motion model of the system to characterize the changes in the motion states of each AUV in the cooperative system. The distance measurement model is constructed using two-dimensional coordinates, which makes it easier to obtain the graph curves and data calculations of the geometric meaning of the performance evaluation function values in the following text. Moreover, our method using the two-dimensional coordinates of the AUV is not limited to underwater systems with depth information and is also applicable to related research such as the swarm operation of land platform robots. Summary of the Invention

[0007] To solve the above technical problems, the present invention proposes a master-slave multi-AUV cooperative system formation optimization method based on the simulated annealing algorithm, effectively utilizes the distance information between the master and slave AUVs in the cooperative system, combines the positioning performance evaluation function to realize the formation optimization process, and obtains the optimal formation of the cooperative system.

[0008] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0009] A formation optimization method for a master-slave multi-AUV cooperative system based on a simulated annealing algorithm, comprising the following steps, characterized in that:

[0010] (1) Construct a motion model and a measurement model for the master-slave multi-AUV cooperative positioning system:

[0011] The motion model and measurement model of the master-slave multi-AUV cooperative positioning system described in step (1) are as follows:

[0012]

[0013] Z m,s (k + 1) 2 =(x m (k + 1)-x s (k + 1)) 2 +(y m (k + 1)-y s (k + 1)) 2 (2)

[0014] The specific meanings of the parameters in the formula are as follows:

[0015] x(k) and x(k + 1) respectively represent the x-axis coordinate values of the AUV at time k and time k + 1 in the reference coordinate, y(k) and y(k + 1) respectively represent the y-axis coordinate values of the AUV at time k and time k + 1 in the reference coordinate, θ(k) and θ(k + 1) respectively represent the heading angle information of the AUV at time k and time k + 1. The pose information of the master AUV at time k and time k + 1 is respectively written as X m (k)=[x m (k),y m (k),θ m (k)] T and X m (k + 1)=[x m (k + 1),y m (k + 1),θ m (k + 1)] T , and X s (k)=[x s (k),y s (k),θ s (k)] T and X s (k + 1)=[x s (k + 1),y s (k + 1),θ s (k + 1)] TIt represents the pose information of the AUV at times \(k\) and \(k + 1\). \(V(k)\) and \(\omega(k)\) respectively represent the velocity and angular velocity information of the AUV at time \(k\). The input quantity is \(u(k)=[V(k),\omega(k)]\). T , which are obtained by measuring with sensors such as DVL and electronic compass. Both are affected by uncorrelated Gaussian white noise interference. \(\Delta T\) is the sampling period during the discretization of the continuous system. \(Z\) m,s (k + 1) represents the distance information between the master and slave AUVs at time \(k + 1\);

[0016] After arrangement, we get:

[0017] \(X(k + 1)=f(X(k),u(k))\ (3)\)

[0018] \(Z\) m,s (k + 1)=h(X s (k + 1))+\(\omega\) Z (4)

[0019] Both \(f()\) and \(h()\) are calculation functions about the state variables. \(\omega\) Z represents the noise quantity about the measured distance;

[0020] (2) Design the positioning performance evaluation function for the master - slave multi - AUV cooperative system;

[0021] The positioning performance evaluation function for the master - slave multi - AUV cooperative system described in step (2) is:

[0022]

[0023]

[0024] The parameters in formula (5) are as follows. \(I\) Z (X s ) represents the Fisher information matrix quantity with the state of the slave AUV as the estimated quantity, is the Jacobian matrix obtained by taking the measurement value with respect to the state estimation vector of the slave AUV. \(R\) represents the noise matrix of the distance measurement. \(P\) i is the performance evaluation function value of the \(i\) - th AUV. \(P\) all is the expression of the performance evaluation function value of the entire cooperative positioning system;

[0025] (3) Design the optimization of the performance evaluation function based on the simulated annealing algorithm, that is, the formation optimization method;

[0026] The formation optimization method by optimizing the performance evaluation function based on the simulated annealing algorithm described in step (3) means transforming the problem of improving the cooperative positioning accuracy of the master - slave multi - AUV into the problem of using the simulated annealing algorithm to find the extreme value of the positioning performance evaluation function in step (2).

[0027] As a further improvement of the present invention, the specific process of the performance evaluation function optimization based on the simulated annealing algorithm, i.e., the formation optimization method, in step (3) is as follows:

[0028] For the master-slave multi-AUV cooperative positioning system:

[0029] The first step: Fix the position coordinates of all master AUVs, let T = T0, representing the initial temperature at the start of annealing, and randomly generate a set of initial positions X of the slave AUVs s,0 , and calculate the corresponding value P of the positioning performance evaluation function all,0 ;

[0030] The second step: Let T = kT, where k takes a value between 0 and 1, which is the temperature reduction rate;

[0031] The third step: Apply a random perturbation to the current set of slave AUV positions X s,t , and generate a new set of slave AUV position coordinates X s,t+1 within its neighborhood;

[0032] The fourth step: Calculate the corresponding value P of the positioning performance evaluation function all,t+1 , calculate ΔP all = P all,t+1 - P all,t ;

[0033] The fifth step: If ΔP all > 0, accept the new slave AUV position coordinates as the current optimal position, otherwise judge whether to accept the new position coordinates according to the Metropolis criterion probability ;

[0034] The sixth step: At temperature T, repeat the perturbation and acceptance process L times, that is, execute the third step to the fifth step;

[0035] The seventh step: Judge whether the temperature has reached the termination temperature level. If so, terminate the algorithm and obtain the final formation optimization result of the cooperative system. Otherwise, return to the second step.

[0036] This application has the following benefits:

[0037] This method is a formation optimization method for the master-slave multi-AUV cooperative system based on the simulated annealing algorithm. By modeling the motion and measurement of the multi-AUV cooperative system, constructing a system positioning performance evaluation function in combination with Fisher information, and using the simulated annealing algorithm for the formation optimization process. The advantages of the present invention are that the simulated annealing algorithm endows the search process with a time-varying and ultimately zero-probability mutation, thus effectively avoiding falling into local extrema, being able to probabilistically jump out and ultimately tend to the global optimum, obtaining the optimal formation for cooperative positioning, and improving the positioning accuracy of the cooperative system. Brief Description of the Drawings

[0038] Figure 1 is the flowchart of the operation of the present invention;

[0039] Figure 2 is the flowchart of the specific simulated annealing algorithm formation optimization of the present invention. Specific embodiments

[0040] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments:

[0041] The present invention proposes a method for optimizing the formation of a master-slave multi-AUV cooperative system based on a simulated annealing algorithm, aiming to provide a method for obtaining the extreme value of the positioning performance evaluation function of the cooperative system, effectively obtaining the optimal formation of the master-slave multi-AUV cooperative system, and improving the positioning accuracy during the operation of the system.

[0042] As Figure 1 shown, the present invention proposes a method for optimizing the formation of a master-slave multi-AUV cooperative system based on a simulated annealing algorithm, and the implementation steps are as follows:

[0043] (1) Construct a kinematic model and a measurement model for the master-slave multi-AUV cooperative positioning system;

[0044] (2) Design a positioning performance evaluation function for the master-slave multi-AUV cooperative system;

[0045] (3) Design an optimization method for the performance evaluation function based on the simulated annealing algorithm, that is, a formation optimization method.

[0046] The kinematic model of the cooperative system represents the motion state information of the vehicle in the reference coordinate system. Regarding the AUV as a spatial node and without considering the influence of shape and volume, a kinematic model under the dead reckoning positioning method is established. In the underwater three-dimensional space, the depth information of the AUV can be directly obtained by devices such as depth sensors. During actual navigation, the pitch angle usually does not change significantly. In the research of general AUV positioning algorithms, the motion model is simplified, and the depth information is not included in the state. The discrete kinematic model is projected from three-dimensional coordinates into a two-dimensional plane.

[0047]

[0048] The specific parameter meanings in Equation (1) are as follows: x(k) and x(k + 1) respectively represent the x-axis coordinate values of the AUV at time k and k + 1 in the reference coordinate, y(k) and y(k + 1) respectively represent the y-axis coordinate values of the AUV at time k and k + 1 in the reference coordinate, θ(k) and θ(k + 1) respectively represent the heading angle information of the AUV at time k and k + 1 in the reference coordinate, V(k), ω(k) respectively represent the speed and angular velocity information of the AUV at time k, and the input quantity is u(k) = [V(k), ω(k)] T, which can be obtained by sensors such as DVL and electronic compass. Both are affected by uncorrelated Gaussian white noise. ΔT is the sampling period during the discretization of the continuous system.

[0049] The measurement model equation is:

[0050] Z m,s (k + 1) 2 =(x m (k + 1)-x s (k + 1)) 2 +(y m (k + 1)-y s (k + 1)) 2 (2)

[0051] The specific parameter meanings in Equation (2) are as follows: The pose information of the master AUV at time k and k + 1 is represented by X m (k)=[x m (k), y m (k), θ m (k)] T and X m (k + 1)=[x m (k + 1), y m (k + 1), θ m (k + 1)] T respectively. Similarly, X s (k)=[x s (k), y s (k), θ s (k)] T and X s (k + 1)=[x s (k + 1), y s (k + 1), θ s (k + 1)] T respectively represent the pose information of the slave AUV at time k and k + 1. Z m,s (k + 1) represents the distance information between the master and slave AUVs at time k + 1;

[0052] After arrangement:

[0053] X(k + 1)=f(X(k), u(k)) (3)

[0054] Z m,s (k + 1)=h(X s (k + 1))+ω Z (4)

[0055] Both f() and h() are calculation functions regarding the state variables. ω Z represents the noise quantity regarding the measured distance;

[0056] Fisher information, also known as Fisher information number, is a concept in mathematical statistics and is often used in maximum likelihood estimation and Bayesian statistics to represent a measure of the amount of information about an unknown parameter carried by the observed data.

[0057] The FIM in the update process of the filtering and positioning algorithm for the non - linear cooperative system is expressed as follows:

[0058]

[0059] The specific parameters in Equation (5) are as follows: I Z (X s ) represents the Fisher Information Matrix (FIM) with the state of the AUV as the estimator, is the Jacobian matrix obtained by taking the measurement value with respect to the estimated vector of the AUV state, and R represents the noise matrix of the distance measurement;

[0060] Select a calculation method of taking the logarithm of the determinant of the FIM to construct an evaluation function for the positioning performance of the cooperative system. For a single slave AUV in the system, its positioning performance evaluation is as follows:

[0061] P = ln(det(I Z (X s ))) (6)

[0062] The performance evaluation function of the entire master - slave cooperative positioning system can be constructed by the summation function of the performance evaluations of individual slave AUVs:

[0063]

[0064] In the formula, i (i = 1, 2,..., N) represents the number of slave AUVs, P i is the value of the performance evaluation function of the i - th AUV, and P all is the value of the overall performance evaluation function of the cooperative system. The larger this value is, the closer the unbiased estimate of the position coordinates of the slave AUVs in the entire cooperative system is to the true value, and the better the positioning performance of the system. Therefore, obtaining the optimal formation of the cooperative system is transformed into finding a set of position coordinates of the slave AUVs that satisfy the maximum value of P all .

[0065] The optimization of the performance evaluation function based on the simulated annealing algorithm, that is, the design of the formation optimization method, is as Figure 2 shown for the master - slave multi - AUV cooperative positioning system:

[0066] Step 1: Fix the position coordinates of all master AUVs, let T = T0, which represents the initial temperature at the start of annealing, and randomly generate a set of initial positions X s,0, and calculate the corresponding positioning performance evaluation function value P all,0 ;

[0067] Step 2: Let T = kT, where k ranges from 0 to 1 and is the temperature reduction rate;

[0068] Step 3: Apply a random perturbation to the current set of AUV positions X s,t to generate a new set of AUV position coordinates X s,t+1 ;

[0069] Step 4: Calculate the corresponding positioning performance evaluation function value P all,t+1 , calculate ΔP all = P all,t+1 - P all,t ;

[0070] Step 5: If ΔP all > 0, accept the new AUV position coordinates as the current optimal position, otherwise, according to the Metropolis criterion probability judge whether to accept the new position coordinates;

[0071] Step 6: At temperature T, repeat the perturbation and acceptance process L times, that is, execute Step 3 to Step 5;

[0072] Step 7: Judge whether the temperature has reached the termination temperature level. If so, terminate the algorithm and obtain the final cooperative system formation optimization result.

[0073] The above is only a preferred embodiment of the present invention, and it is not any other form of limitation to the present invention. Any modification or equivalent change made according to the technical essence of the present invention still belongs to the scope protected by the present invention.

Claims

1. A method for optimizing the formation of a master-slave multi-AUV cooperative system based on the simulated annealing algorithm, comprising the following steps, characterized in that: (1)Construct the motion model and measurement model of the master-slave multi-AUV cooperative positioning system: The motion model and measurement model of the master-slave multi-AUV cooperative positioning system described in step (1) are as follows: ； The specific parameter meanings in the formula are as follows: and respectively represent the -axis coordinate values of the AUV at time and time in the reference coordinate system, and respectively represent the -axis coordinate values of the AUV at time and time in the reference coordinate system, and respectively represent the heading angle information of the AUV at time and time. The pose information of the master AUV at time and time is written as and respectively, while and represent the pose information of the slave AUV at time and time. respectively represent the speed and angular velocity information of the AUV at time. The input quantity is , which is measured by the DVL and electronic compass sensors. Both are disturbed by uncorrelated Gaussian white noise. is the sampling period during the discretization of the continuous system. represents the distance information between the master and slave AUVs at time After arrangement, we get: ; and are both calculation functions for state variables, represents the noise quantity regarding the measured distance; (2)Design the positioning performance evaluation function for the master-slave multi-AUV cooperative system; The construction of the positioning performance evaluation function for the master-slave multi-AUV cooperative system described in step (2) is as follows: ; The parameters in Equation (5) are as follows: represents the Fisher information matrix quantity with the AUV state as the estimator; is the Jacobian matrix obtained by taking the measurement value with respect to the AUV state estimation vector; represents the noise matrix of the distance measurement; is the performance evaluation function value of the th AUV; the expression of the performance evaluation function value of the entire cooperative positioning system; (3) Design the optimization of the performance evaluation function based on the simulated annealing algorithm, that is, the formation optimization method; The optimization of the performance evaluation function based on the simulated annealing algorithm described in step (3), that is, the formation optimization method, means transforming the problem of improving the positioning accuracy of the master-slave multi-AUV cooperative positioning into the problem of using the simulated annealing algorithm to obtain the extreme value of the positioning performance evaluation function in step (2).

2. The method for optimizing the formation of a master-slave multi-AUV cooperative system based on the simulated annealing algorithm according to claim 1, characterized in that, The specific process of the optimization of the performance evaluation function based on the simulated annealing algorithm described in step (3), that is, the formation optimization method, is as follows: For the master-slave multi-AUV cooperative positioning system: Step 1: Fix the position coordinates of all main AUVs, and let , representing the initial temperature at which annealing starts, randomly generate a set of initial positions of AUVs from , and calculate the corresponding positioning performance evaluation function value ; Step 2: Let , where ranges from 0 to 1 and is the temperature drop rate. Step 3: Apply random perturbations to the current set of slave AUV positions to generate a new set of slave AUV position coordinates within its domain ; Step 4: Calculate the corresponding positioning performance evaluation function value , calculate ; Step 5: If , accept the new AUV position coordinates as the current optimal position; otherwise, according to the Metropolis criterion probability , determine whether to accept the new position coordinates. Step 6: At temperature T , repeat the perturbation and acceptance process for L times, that is, execute Steps 3 to 5; Step 7: Judge whether the temperature reaches the termination temperature level. If so, terminate the algorithm and obtain the final formation optimization result of the cooperative system; otherwise, return to step 2.

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