Multi-unmanned aerial vehicle formation transformation control method based on auction algorithm and RVO2 algorithm

Abstract

The invention discloses a multi-unmanned aerial vehicle formation transformation control method based on an auction algorithm and an RVO2 algorithm, and belongs to the technical field of multi-unmanned aerial vehicle cooperative motion planning. The problem that an existing method is difficult to meet the real-time requirement of formation transformation control is solved. According to the method, the overall cost of formation transformation is optimized through an auction algorithm, and the probability of mutual intersection of paths of multiple unmanned aerial vehicles can be remarkably reduced in the initial stage of task allocation. In order to further ensure that the unmanned aerial vehicles do not collide with one another in the actual formation transformation process, an RVO2 algorithm is adopted to carry out real-time online calculation so as to dynamically adjust the flight path of each unmanned aerial vehicle, and compared with an existing method, the method has the advantages that the calculation complexity is remarkably reduced, the formation transformation control efficiency is improved, and the method is suitable for popularization and application. And the safety and the real-time performance of the whole formation transformation process are ensured. The method can be applied to multi-unmanned aerial vehicle formation transformation control.

Description

Technical Field

[0001] The present invention belongs to the technical field of multi - UAV collaborative motion planning, and specifically relates to a multi - UAV formation transformation control method based on the auction algorithm and the RVO2 (Reciprocal Velocity Obstacles 2) algorithm. Background Technique

[0002] The UAV formation transformation technology involves manipulating the flight trajectories and speeds of multiple UAVs to construct specific patterns, characters, or shapes in the air. This technology has extensive application potential in multiple fields, including celebrations, performances, and other occasions.

[0003] In a multi - UAV system, task planning also faces a series of challenges, which not only involve task allocation but also need to solve the problem of collision avoidance during the transformation process. Currently, the research on multi - UAV task allocation can be roughly classified into two categories: behavior - based task allocation and planning - based task allocation.

[0004] Although the planning - based task allocation method performs well in goal - oriented task execution, its computational complexity is relatively high, mainly including centralized planning methods. For example, the task allocation strategy using linear programming is an embodiment of the centralized planning method. Although such methods can theoretically provide optimal solutions, due to their high computational complexity and poor scalability, they are limited in practical applications.

[0005] In summary, due to the high computational complexity and poor scalability of existing methods, in large - scale and dense scenarios, existing methods are difficult to meet the real - time requirements of formation transformation control. Summary of the Invention

[0006] The purpose of the present invention is to solve the problem that existing methods are difficult to meet the real - time requirements of formation transformation control in large - scale and dense scenarios, and a multi - UAV formation transformation control method based on the auction algorithm and the RVO2 algorithm is proposed.

[0007] The technical solution adopted by the present invention to solve the above - mentioned technical problems is: a multi - UAV formation transformation control method based on the auction algorithm and the RVO2 algorithm, and the method specifically includes the following steps:

[0008] Step 1: Denote the set composed of all UAVs as I, and the set composed of all formation transformation target points as J, and obtain the distance matrix D according to the three - dimensional position coordinates of each UAV and the three - dimensional position coordinates of each target point;

[0009] Step 2: Use the auction algorithm and the distance matrix D to allocate the target points to each UAV respectively;

[0010] Step 3: Perform path planning for each UAV according to the allocation result in Step 2, and the controller controls each UAV according to the path planning result.

[0011] Further, obtaining the distance matrix D according to the three-dimensional position coordinates of each UAV and the three-dimensional position coordinates of each target point, the specific process is as follows:

[0012] Denote the element in the i-th row and j-th column of the distance matrix D as d ij , d ij represents the distance between the i-th UAV and the j-th target point, i = 1, 2, …, N, j = 1, 2, …, N, that is, the total number of UAVs and the total number of target points are both N.

[0013] Further, when allocating the target points to each UAV respectively, the objective function of the allocation is:

[0014]

[0015] where, g ij represents the profit obtained by allocating the j-th target point to the i-th UAV during allocation; f ij represents whether the i-th bidding UAV wins the j-th formation target point. When the i-th bidding UAV wins the j-th formation target point, f ij = 1, otherwise f ij = 0.

[0016] Further, the profit g ij is:

[0017] g ij = v ij - p ij

[0018] where, v ij represents the valuation of the j-th formation target point by the i-th bidding UAV, and p ij represents the price at which the i-th bidding UAV wins the j-th formation target point.

[0019] Further, the specific process of Step 2 is as follows:

[0020] Step 2-1: Initialize the value matrix V according to the distance matrix D. The element v ij in the i-th row and j-th column of the value matrix V is:

[0021] v ij = d thresh - d ij

[0022] where, d thresh represents the initial bid distance threshold;

[0023] Step 22: Arbitrarily initialize two sets of allocation results and record the set of allocation results as A 0 ={(i 1 ,j 1 ),(i 2 ,j 2 )},(i 1 ,j 1 ) represents the i-th 1 The target point initially assigned to each UAV is the jth 1 target points, (i 2 ,j 2 ) represents the i-th 2 The target point initially assigned to each UAV is the jth 2 target point, i 1 ,i 2 ∈{1,2,…,N},j 1 ,j 2 ∈{1,2,…,N};

[0024] Initialize the initial price of each auction target point All are 0;

[0025] Step 23: Initialize the auction round k=0;

[0026] Step 24: According to set A k Obtain all unassigned target point bidding drones, and each unassigned target point bidding drone calculates its own net profit for target point j in the kth bidding round;

[0027]

[0028] in, represents the net benefit of the i-th drone to the target point j in the k-th auction round;

[0029] Find the target point j corresponding to the maximum net profit of the i-th drone in the k-th auction round * :

[0030]

[0031] Find the next largest net profit of the i-th drone in the k-th auction round

[0032]

[0033] Among them, J\{j *} means removing target point j from set J * The target point set after

[0034] In the k-th bidding round, the i-th drone's bid for target point j * is as follows:

[0035]

[0036] where represents the valuation of the i-th bidding drone for the j-th * target point, and ε represents the slack condition threshold;

[0037] Step 25. For each target point j, find the drone i that offers the highest bid for itself in the k-th bidding round * and the highest bid

[0038]

[0039] where represents the bid of the i-th drone for target point j in Step 24;

[0040] Step 26. Adjust the price of target point j to:

[0041]

[0042] Judge whether target point j has been assigned to another drone other than drone i * :

[0043] If target point j has been assigned to another drone other than drone i * , cancel the previous assignment of target point j and assign target point j to drone i in the k-th bidding round * , and then execute Step 27;

[0044] Otherwise, directly assign target point j to drone i in the k-th bidding round * , and then execute Step 27;

[0045] Step 27. Remove the allocation relationships corresponding to the target points that have been reallocated in the k-th bidding round from set A k to obtain the updated set A' k ; k ;

[0046] And judge whether there is a target point that satisfies equal to , where represents the bid of the drone i that offered the highest bid for target point j in the (k - 1)-th bidding round * ;

[0047] If there exists a target point that satisfies equal to , the allocation result (i * , j) is added to the set A' k to obtain the set A k+1 , and then step 2-8 is executed;

[0048] If there does not exist a target point that satisfies equal to , the updated set A' k is used as the set A k+1 , and step 2-8 is continued to be executed;

[0049] Step 2-8: Determine whether the set A k+1 contains the allocation relationships of all target points;

[0050] If the set A k+1 contains the allocation relationships of all target points, the allocation process is ended;

[0051] Otherwise, let k = k + 1, and return to execute step 2-4.

[0052] Furthermore, the initial bid distance threshold d thresh = maxd ij .

[0053] Furthermore, the relaxation condition threshold ε = 0.5.

[0054] Even further, the RVO2 algorithm is used for path planning of each unmanned aerial vehicle according to the allocation result in step 2.

[0055] The beneficial effects of the present invention are:

[0056] The present invention optimizes the overall cost of formation transformation through an auction algorithm, and can significantly reduce the probability of the paths of multiple unmanned aerial vehicles crossing each other at the initial stage of task allocation. And in order to further ensure that there will be no collision between unmanned aerial vehicles during the actual formation transformation process, the RVO2 algorithm is used for real-time online calculation to dynamically adjust the flight paths of each unmanned aerial vehicle. Moreover, compared with the existing method, the method of the present invention significantly reduces the computational complexity, thereby improving the efficiency of formation transformation control and ensuring the safety and real-time performance of the entire formation transformation process. Description of the Drawings

[0057] Figure 1 is a flowchart of a multi-unmanned aerial vehicle formation transformation control method based on an auction algorithm and an RVO2 algorithm of the present invention;

[0058] Figure 2 is the overall flowchart of the auction algorithm. Detailed Implementation Modes

[0059] Detailed Implementation Mode One: Combining Figure 1 to illustrate this implementation mode. For a multi-UAV formation transformation control method based on the auction algorithm and the RVO2 algorithm described in this implementation mode, the method specifically includes the following steps:

[0060] Step 1: Denote the set composed of all UAVs as I, and the set composed of all formation transformation target points as J. Obtain the distance matrix D according to the three-dimensional position coordinates of each UAV and the three-dimensional position coordinates of each target point;

[0061] Step 2: Use the auction algorithm and the distance matrix D to allocate the target points to each UAV respectively;

[0062] Step 3: Perform path planning for each UAV according to the allocation result in Step 2. The controller (the PI controller is adopted in the present invention) controls each UAV according to the path planning result.

[0063] The auction method of the present invention allocates tasks through a negotiation mechanism, which is especially suitable for heterogeneous multi-UAV systems and can effectively achieve a task allocation effect close to the global optimum. As an advanced multi-agent path planning algorithm, the RVO2 algorithm is particularly outstanding in a dynamic environment. The main purpose is to generate a more reasonable and efficient moving path while ensuring that collisions are avoided between multiple moving bodies. This enables the multi-UAV system to complete the established tasks more safely and efficiently in a complex dynamic environment.

[0064] Detailed Implementation Mode Two: The difference between this implementation mode and Detailed Implementation Mode One is that the process of obtaining the distance matrix D according to the three-dimensional position coordinates of each UAV and the three-dimensional position coordinates of each target point is as follows:

[0065] Denote the element in the i-th row and j-th column of the distance matrix D as d ij , d ij represents the distance between the i-th UAV and the j-th target point, i = 1, 2,..., N, j = 1, 2,..., N, that is, the total number of UAVs and the total number of target points are both N.

[0066] Other steps and parameters are the same as those in Detailed Implementation Mode One.

[0067] Detailed Implementation Mode Three: The difference between this implementation mode and Detailed Implementation Mode One or Two is that when allocating the target points to each UAV respectively, the objective function of the allocation is:

[0068]

[0069] where, g ijDenote the profit obtained by assigning the j-th target point to the i-th UAV during allocation (in the present invention, one UAV is assigned to each target point, and the objective function is the sum of the profits of all UAVs); f ij Denote whether the i-th bidding UAV wins the j-th formation target point. When the i-th bidding UAV wins the j-th formation target point, f ij = 1; otherwise f ij = 0.

[0070] Other steps and parameters are the same as those in the first or second specific implementation manner.

[0071] Specific implementation manner four: The difference between this implementation manner and any one of the first to third specific implementation manners is that the profit g ij is:

[0072] g ij = v ij - p ij

[0073] where v ij denotes the valuation of the j-th formation target point by the i-th bidding UAV, and p ij denotes the price at which the i-th bidding UAV wins the j-th formation target point.

[0074] Other steps and parameters are the same as those in any one of the first to third specific implementation manners.

[0075] Specific implementation manner five: This implementation manner will be described in combination with Figure 2 . The difference between this implementation manner and any one of the first to fourth specific implementation manners is that the specific process of step two is as follows:

[0076] Step 2-1: Initialize the value matrix V according to the distance matrix D. The element v ij in the i-th row and j-th column of the value matrix V is:

[0077] v ij = d thresh - d ij

[0078] where d thresh denotes the initial bid distance threshold;

[0079] Step 2-2: Randomly initialize two sets of allocation results, and denote the set composed of the allocation results as A 0 = {(i 1 , j 1 ), (i 2 , j 2 )}, (i 1 , j 1 ) represents that the target point initially assigned to the i 1 -th UAV is the j1 A target point, (i 2 , j 2 ) represents that the j-th target point initially assigned to the i-th drone is the 2 j-th target point, where i 2 , i 1 , i 2 ∈ {1, 2, …, N} and j 1 , j 2 ∈ {1, 2, …, N};

[0080] Initialize the initial price P of each auction target point j 0 to be 0;

[0081] Step 23. Initialize the auction round k = 0;

[0082] Step 24. Obtain the auction drones for all unassigned target points according to set A k For A 0 , the auction drones for unassigned target points are all the drones among all drones except for i 1 , i 2 . Each auction drone for an unassigned target point calculates its net profit for target point j in the k-th auction round;

[0083]

[0084] Among them, represents the net profit of the i-th drone for target point j in the k-th auction round;

[0085] Find the target point j corresponding to the maximum net profit of the i-th drone in the k-th auction round * :

[0086]

[0087] Find the second-largest net profit of the i-th drone in the k-th auction round

[0088]

[0089] Among them, J\{j *} represents the set of target points after removing target point j from set J * ;

[0090] In the k-th auction round, the bid of the i-th drone for target point j * is: For:

[0091]

[0092] Among them, represents the valuation of the j-th target point by the i-th bidding drone, and ε represents the slack condition threshold; *

[0093] Step 25. For each target point j, find the drone i that offers the highest price to itself in the k-th bidding round * and the highest bid price

[0094]

[0095] Among them, represents the bid price of the i-th drone for the target point j in Step 24;

[0096] Step 26. Adjust the price of the target point j to:

[0097]

[0098] Determine whether the target point j has been assigned to other drones except the drone i * :

[0099] If the target point j has been assigned to other drones except the drone i in the previous bidding round * , cancel the previous assignment of the target point j and assign the target point j to the drone i in the k-th bidding round * , and then execute Step 27;

[0100] Otherwise, directly assign the target point j to the drone i in the k-th bidding round * , and then execute Step 27;

[0101] Step 27. Remove the allocation relationships corresponding to the target points that have been reallocated in the k-th bidding round from the set A k to obtain the updated set A'; k ; Taking A k as an example, if in the k-th bidding round, the target point j 0 is assigned to other drones except the drone i 1 , then remove the allocation relationship (i 1 , j 1 ) from the set A 1 to obtain the updated set A 0 ; 1 ;

[0102] And determine whether there exists a satisfaction equal to ​The target point (i.e., for target point j, the drones that offer the highest bids for it in the previous and next rounds are both drone i * ), where, represents the bid of drone i that offers the highest bid for target point j in the (k - 1)-th auction round * ;

[0103] If there exists a target point that satisfies equals , then add the allocation result (i * , j) to set A' k to obtain set A k+1 , and then execute Step 28;

[0104] If there does not exist a target point that satisfies equals , then use the updated set A' k as set A k+1 , and continue to execute Step 28;

[0105] Step 28: Determine whether set A k+1 already contains the allocation relationships of all target points;

[0106] If set A k+1 already contains the allocation relationships of all target points, then end the allocation process;

[0107] Otherwise, let k = k + 1, and return to execute Step 24.

[0108] Other steps and parameters are the same as those in any one of the specific embodiments 1 to 4.

[0109] The present invention uses an auction algorithm to allocate tasks, which can not only effectively reduce the overall flight path length of the UAV cluster and optimize the overall cost of formation transformation, but also naturally reduce the crossing and overlapping phenomena between the UAV flight paths when the path reaches the optimal state. This strategy significantly reduces the risk of collision between UAVs at the preliminary decision-making stage.

[0110] Specific embodiment 6: The difference between this embodiment and any one of the specific embodiments 1 to 5 is that the initial bid distance threshold d thresh = maxd ij .

[0111] Other steps and parameters are the same as those in any one of the specific embodiments 1 to 5.

[0112] Specific embodiment 7: The difference between this embodiment and any one of the specific embodiments 1 to 6 is that the relaxation condition threshold ε = 0.5.

[0113] Other steps and parameters are the same as those in any one of the specific embodiments 1 to 6.

[0114] Embodiment 8: The difference between this embodiment and any one of Embodiments 1 to 7 is that the RVO2 algorithm is used for path planning of each drone according to the allocation result in Step 2.

[0115] Other steps and parameters are the same as any one of Embodiments 1 to 7.

[0116] To ensure that no collision occurs between drones during the actual formation transformation process, the present invention uses the RVO2 algorithm for real-time online calculation to dynamically adjust the flight paths of each drone, ensuring the safety and efficiency of the entire formation transformation process.

[0117] The above examples of the present invention are only for explaining in detail the calculation model and calculation process of the present invention, rather than limiting the embodiments of the present invention. For those of ordinary skill in the art, other different forms of changes or variations can be made on the basis of the above description. It is impossible to list all the embodiments here. Any obvious changes or variations derived from the technical solutions of the present invention still fall within the protection scope of the present invention.

Claims

1. A multi-UAV formation transformation control method based on auction algorithm and RVO2 algorithm, characterized in that: The method specifically comprises the following steps: Step 1: denote the set of all drones as I, denote the set of all formation transformation target points as J, and obtain the distance matrix D according to the three-dimensional position coordinates of each drone and the three-dimensional position coordinates of each target point; Step 2: Use the auction algorithm and distance matrix D to assign the target points to each drone; Step 3: Plan the paths of each UAV according to the allocation results in step 2, and the controller controls each UAV according to the path planning results.

2. The multi-UAV formation transformation control method based on the auction algorithm and the RVO2 algorithm according to claim 1 is characterized in that: The distance matrix D is obtained according to the three-dimensional position coordinates of each drone and the three-dimensional position coordinates of each target point. The specific process is: The element in the i-th row and j-th column of the distance matrix D is recorded as d ij , d ij represents the distance between the i-th UAV and the j-th target point, i=1,2,…,N, j=1,2,…,N, that is, the total number of UAVs and the total number of target points are both N.

3. The multi-UAV formation transformation control method based on auction algorithm and RVO2 algorithm according to claim 1 is characterized in that: The target points are assigned to each UAV respectively, and the objective function of the assignment is: Among them, g ij represents the benefit obtained by allocating the jth target point to the i-th drone; f ij Indicates whether the i-th bidding drone has won the j-th formation target point. When the i-th bidding drone has won the j-th formation target point, f ij =1, otherwise f ij =0.

4. The multi-UAV formation transformation control method based on auction algorithm and RVO2 algorithm according to claim 3 is characterized in that: The income g ij for: g ij =v ij -p ij Among them, v ij represents the valuation of the i-th bidding drone for the j-th formation target point, p ij It represents the price that the i-th bidding drone bids for the j-th formation target point.

5. The multi-UAV formation transformation control method based on auction algorithm and RVO2 algorithm according to claim 2 is characterized in that: The specific process of step 2 is as follows: Step 21: Initialize the value matrix V according to the distance matrix D. The element v in the i-th row and j-th column of the value matrix V is ij for: v ij =d thresh -d ij Among them, d thresh Indicates the initial bid distance threshold; Step 22: Arbitrarily initialize two sets of allocation results and record the set of allocation results as A 0 ={(i1,j1),(i2,j2)}, (i1,j1) means that the target point initially assigned to the i1th UAV is the j1th target point, (i2,j2) means that the target point initially assigned to the i2th UAV is the j2th target point, i1,i2∈{1,2,…,N}, j1,j2∈{1,2,…,N}; Initialize the initial price of each auction target point All are 0; Step 23: Initialize the auction round k=0; Step 24: According to set A k Obtain all unassigned target point bidding drones, and each unassigned target point bidding drone calculates its own net profit for target point j in the kth bidding round; in, represents the net benefit of the i-th drone to the target point j in the k-th auction round; Find the target point j corresponding to the maximum net profit of the i-th drone in the k-th auction round * : Find the next largest net profit of the i-th drone in the k-th auction round Among them, J\{j * } means removing target point j from set J * The target point set after In the kth auction round, the i-th drone targets the target point j. * Quote for: in, represents the i-th bidding drone’s * The evaluation of the target point, ε represents the relaxation condition threshold; Step 25: For each target point j, find the drone i that has the highest bid in the kth auction round. * And the highest offer in, represents the price quoted by the i-th drone to the target point j in step 24; Step 26: Set the price of target point j Adjusted to: Determine whether the target point j has been assigned to drone i * Other drones besides: If the target point j has been assigned to a drone other than UAV i * If there are other drones other than the target point j, the previous allocation to the target point j will be cancelled, and the target point j will be allocated to drone i in the kth auction round. * , then execute step 27; Otherwise, directly assign target point j to drone i in the kth auction round * , then execute step 27; Step 27: Set A k The allocation relationship corresponding to the target points that have been reallocated in the kth auction round is from set A k Remove it from the set and get the updated set A′ k ; And determine whether there is a satisfaction equal The target point, where Indicates that in the k-1th auction round, the drone i with the highest bid for target point j * quotations; If there is a satisfying equal The target point is then assigned the result (i * ,j) Join the set A′ k Get set A k+1 , then execute step 28; If there is no satisfaction equal The target point is then the updated set A′ k As a set A k+1 , continue to step 28; Step 28: Determine set A k+1 Whether the distribution relationship of all target points is already included; If the set A k+1 If the allocation relationship of all target points is already included in , the allocation process ends; Otherwise, set k=k+1 and return to step 24.

6. The multi-UAV formation transformation control method based on auction algorithm and RVO2 algorithm according to claim 5 is characterized in that: The initial price distance threshold d thresh =maxd ij .

7. The multi-UAV formation transformation control method based on auction algorithm and RVO2 algorithm according to claim 5 is characterized in that: The relaxation condition threshold ε=0.

5.

8. The multi-UAV formation transformation control method based on auction algorithm and RVO2 algorithm according to claim 1 is characterized in that: The path planning for each UAV according to the allocation result in step 2 adopts the RVO2 algorithm.

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