A collaborative trajectory planning method for UAV swarm considering communication delay

Abstract

The present invention discloses a method for collaborative trajectory planning of a drone cluster considering communication delay, and belongs to the technical field of trajectory planning. Considering the communication delay, a "global planning-local obstacle avoidance" collaborative trajectory planning framework is constructed. In the global planning stage, the probability distribution of the positions of adjacent drones caused by random communication delay is considered, and the probability distribution of the positions of adjacent aircraft caused by the communication delay is combined with the sparse A* search algorithm, and a priority decoupling mechanism is introduced to improve the algorithm search efficiency; in the local collision avoidance stage, considering the uncertainty of the communication delay and the uncertainty of the position of the adjacent aircraft, the global trajectory still has the risk of local collision, and the optimal control problem of the distributed model predictive control is solved to realize the trajectory tracking and local adjustment of the drone in the pipeline. Based on the two-level collaborative trajectory planning, the timeliness and reliability of the collaborative trajectory planning of the drone cluster under the communication delay are ensured, and the collaborative ability of the drone cluster in the real scene is improved.

Description

Technical Field

[0001] The invention discloses a method for cooperative trajectory planning of a cluster of unmanned aerial vehicles taking communication delay into consideration, and belongs to the technical field of trajectory planning. Background Art

[0002] Collaborative trajectory planning is one of the key technologies to achieve autonomous collaboration of UAV swarms. It designs satisfactory or optimal collaborative flight trajectories by considering factors such as spatiotemporal consistency constraints, UAV performance constraints, flight mission constraints, terrain, threats, etc., and guides the UAV swarm to complete a given collaborative flight mission. However, in actual application scenarios, due to electromagnetic interference, frequent mission adjustments, etc., it is difficult for UAV swarms to ensure high-speed and reliable communication data transmission. Communication delay is a common non-ideal communication situation. The high latency characteristics of information interaction make it difficult for the trajectories planned by UAV swarms to achieve spatiotemporal coordination and consistency, increasing the risk of collisions between cluster machines, thereby reducing the ability of UAV swarms to perform collaborative tasks such as collaborative reconnaissance and target strikes, making it difficult to meet the increasingly complex needs of actual combat missions. Summary of the invention

[0003] The present invention discloses a method for cooperative trajectory planning of a UAV cluster considering communication delay. The main purpose of the method is to face the high delay characteristics of information interaction of a UAV cluster in an actual combat environment, start from the framework of "global planning-local obstacle avoidance" cooperative trajectory planning, combine the probabilistic distribution of neighboring aircraft positions caused by communication delay into the sparse A* search algorithm, and obtain a customized global pipeline sparse A* algorithm considering delay. At the same time, model predictive control is used to ensure the collision avoidance safety of the UAV cluster, enhance the timeliness and reliability of the algorithm, and improve the cooperative task capability of the UAV cluster in real scenarios.

[0004] The objective of the present invention is achieved through the following technical solutions:

[0005] The present invention discloses a method for cooperative trajectory planning of unmanned aerial vehicle clusters considering communication delay. Aiming at the communication delay problem of unmanned aerial vehicle clusters in complex application scenarios, a communication network delay model and a cooperative trajectory planning model are established. Considering the communication delay, a "global planning-local obstacle avoidance" two-level cooperative trajectory planning framework is constructed: in the global planning stage, the probability distribution of the positions of adjacent unmanned aerial vehicles caused by random communication delay is considered, and the probability distribution of the positions of adjacent aircraft caused by the communication delay is combined with the sparse A* search algorithm to obtain a customized global pipeline sparse A* algorithm considering the delay, and a priority decoupling mechanism is introduced to improve the algorithm search efficiency; in the local collision avoidance stage, considering the uncertainty of the communication delay and the uncertainty of the position of the adjacent aircraft, the global trajectory still has the risk of local collision. By solving the optimal control problem of the distributed model predictive control, the trajectory tracking and local adjustment of the unmanned aerial vehicle in the pipeline are realized. Based on the two-level cooperative trajectory planning framework, the timeliness and reliability of the cooperative trajectory planning of the unmanned aerial vehicle cluster under the communication delay are ensured, and the cooperative task capability of the unmanned aerial vehicle cluster in the real scene is improved.

[0006] The present invention discloses a method for cooperative trajectory planning of a drone cluster taking into account communication delay, comprising the following steps:

[0007] Step 1: Initialize the UAV flight performance parameter information, track constraint information and mission environment information.

[0008] Obtaining the UAV flight performance parameter information, track constraint information and mission environment information; the UAV flight performance parameter information includes the UAV flight speed, overload, maximum turning angle and minimum track segment length; the track constraint information includes the UAV flight starting point position, target point position, and safe distance between the UAV and obstacles; the mission environment information includes the position and radius of the no-fly zone.

[0009] Step 2: Considering the UAV performance constraints, mission environment constraints, network communication delay and UAV local obstacle avoidance method, a UAV trajectory planning model under communication delay is established. The UAV trajectory planning model includes a UAV kinematic model, a UAV trajectory planning problem model, a network communication delay model and a UAV local problem model.

[0010] The specific implementation method of step 2 is as follows:

[0011] (1) UAV kinematic modeling

[0012] Assuming that the UAV cluster flies at a fixed altitude, the particle kinematic model of the i-th UAV in the UAV cluster is:

[0013]

[0014] Where (x i ,yi ), V i , a i , χ i are the position coordinates, velocity, acceleration and heading angle of the i-th UAV respectively.

[0015] (2) Modeling of UAV trajectory planning problem

[0016] In the process of trajectory planning, UAVs need to consider not only the impact of terrain and various threats, but also their own performance constraints, and need to find an evaluation standard to evaluate whether the planned trajectory is the optimal trajectory. The UAV trajectory planning problem is essentially a multi-objective and multi-constraint nonlinear optimization problem, and its mathematical model is

[0017]

[0018] Where x is the trajectory of the UAV; f(x) is the cost evaluation function; g j (x) is the jth constraint.

[0019] Among them, the track cost mainly includes the distance cost and the track threat cost. The general track cost evaluation function is expressed as

[0020] J=∑(w1L i +w2D i ) (3)

[0021] Where, L i is the cost of the ith flight path, D i is the threat cost of the i-th segment, w1 and w2 are weight coefficients.

[0022] The UAV trajectory planning constraints include the UAV maneuverability constraints and the no-fly zone constraints; the maneuverability constraints include the minimum trajectory segment length and the maximum turning angle:

[0023] ① Minimum track length constraint: Due to the limitation of maneuverability, the UAV must fly a certain distance in the original direction before changing the track direction each time, that is, each track segment must not be less than the shortest direct flight distance l min , the expression of the minimum track segment length constraint is

[0024]

[0025] Among them, l k is the length of the kth track of the UAV.

[0026] ② Maximum turning angle constraint: Due to the constraints of the UAV's maneuverability, the planned trajectory needs to avoid excessive turning angles to ensure the feasibility of the trajectory. The maximum turning angle of the UAV is Δχ max , then it is required that:

[0027]

[0028] Among them, Δχ k is the turning angle of the UAV at the kth track point.

[0029] ③ No-fly zone constraints: During the flight of the drone, it is necessary to avoid the no-fly zone in the environment, that is, the drone's track is required not to intersect with the no-fly zone, which is expressed as

[0030]

[0031] Among them, s j represents the minimum distance between the drone’s track and the no-fly zone j, d safe is the safe distance between the drone and the obstacle, n NFZ is the number of no-fly zones.

[0032] (3) Network communication delay modeling

[0033] The process of UAV swarm collaborative trajectory planning requires real-time information exchange between UAVs through the communication network. In real-time network systems, information transmission inevitably has induced delays, and this delay changes with the changes in communication protocols and network load conditions, which can be modeled as a Markov chain.

[0034] Define the transmission delay at time k as d k , and m≤d k ≤n, that is, the minimum transmission delay is m and the maximum transmission delay is n, then for i,j∈S={m,m+1,…,n}, there are the following conditional probability properties without aftereffect:

[0035] P(d k+1 =j|d0,d1,…,d k =i) = P(d k+1 =j|d k =i) (7)

[0036] Defining transition probabilities

[0037] P(d k+1 =j|d k =i) =q (i-m)(j-m) (8)

[0038] Then for all i,j∈S, there is q (i-m)(j-m) ≥0 and

[0039] Introducing Markov state probability distribution

[0040] π(k)=[π0(k),π1(k),…π n-m (k)]

[0041] Then the probability distribution of adjacent delay states has the following relationship:

[0042] π(k+1)=π(k)Q M (9)

[0043] where π i (k) = P(d k =i+m)

[0044] Q M =q (i-m)(j-m)i,j∈S

[0045] The drone cluster adopts the method of equal-period synchronous sampling. In the event-driven control mode, the probability distribution of the delay of information transmission in the network is p i , where i∈S, and Then the transition probability matrix Q M The elements of are obtained as follows:

[0046]

[0047]

[0048] (4) Modeling of local problems of UAVs

[0049] In order to solve the problem of inter-machine collision that may occur in the collaboration of UAV clusters, this invention uses the UAV kinematic model on the basis of global trajectory planning, and based on the model predictive control theory, obtains the local trajectory of the UAV by solving the optimal control problem, and accurately achieves the dynamic local collision avoidance requirements of the UAV. Through the state information of the UAV under communication delay, the cost function is designed, the distributed model predictive control model is established, and the judgment criteria for inter-machine collision are proposed.

[0050] The drone state equation is as follows

[0051]

[0052] Where x = [xy V x V y ], Where (x, y), V, and a are the position coordinates, velocity, and acceleration of the UAV, respectively, corresponding to formula (1).

[0053] Define the sampling period of UAV flight control as δ, and then t k+1 =t k +δ; the communication delay time is a discrete random variable τ, which satisfies the Markov chain model of network delay, and (d-1)δ≤τ≤dδ, where d is a positive integer representing discrete communication delay. The information set of drone i is xi (t k ) is t k The position of drone i at the moment, is the location information of the neighboring drones of drone i (considering communication delay). k The cost function is:

[0054]

[0055] in is the control input, r i is its target point, T is the prediction time domain, P>0, Q>0, R>0 and they are all symmetric matrices,

[0056] The distributed model predictive control model is established as follows (DMPC Problem ):

[0057]

[0058] The reachable set of drone i at time t is calculated as follows:

[0059]

[0060] Control Input The following relations are satisfied:

[0061]

[0062] where μ j ≥0, which is called the maneuverability parameter of UAV j.

[0063] For the output set If satisfied

[0064]

[0065] but It is determined by the ellipsoid boundary Γ centered at x0, which is expressed as:

[0066] Γ={x(x-x0)′M(x-x0)≤β} (19)

[0067] Where M is a diagonalizable matrix and satisfies

[0068] M>0

[0069] M=W -1 (20)

[0070] Among them, W is the controllable Gramian matrix.

[0071] When t∈[t0,T], the reachable set of all points on the trajectory ξ(t,u0) forms a tube

[0072]

[0073] where p is the dimension of the trajectory ξ, is the radius of the reachable set at time t.

[0074] Finally, the condition to satisfy the collision avoidance constraint is

[0075] Step 3: In view of the high latency characteristics of information interaction of UAV clusters in actual combat environments, starting from the framework of "global planning-local obstacle avoidance" collaborative trajectory planning, a real-time pipeline sparse A* trajectory planning algorithm that considers the probabilistic distribution of neighboring aircraft positions is customized. That is, the probabilistic distribution of neighboring aircraft positions caused by communication delays is combined with the sparse A* search algorithm to obtain a global pipeline sparse A* algorithm that considers latency, and then the global collaborative trajectory planning of the UAV cluster is performed through the global pipeline sparse A* algorithm.

[0076] In step 3, the global pipeline sparse A* algorithm is used to perform global collaborative trajectory planning for the drone cluster. The implementation method is as follows: under the rolling planning framework, the priority decoupling mechanism is used to plan the individual drones in the drone cluster one by one, and the probability distribution of the neighboring drone positions is determined according to the delay probability distribution before the current drone starts planning. Then, the sparse A* algorithm is used to expand the pipeline to the area with low probability density of the neighboring drones, so as to realize the online rapid planning of the global collaborative trajectory for the drone cluster. The radius of the pipeline depends on the size of the communication delay and the maneuverability of the drone.

[0077] The specific implementation method of step three is:

[0078] Step 3.1: Determine whether all drones have reached the target point. If all drones have reached the target point, the algorithm ends and outputs the drone cluster track, otherwise execute step 3.2.

[0079] Step 3.2: Enter the rolling planning loop and start planning the UAV trajectory according to the priority order (predetermined planning order). If the i-th UAV reaches the target, continue to determine whether the i+1-th UAV has reached the destination until all UAVs have arrived. Otherwise, execute step 3.3.

[0080] Step 3.3: Considering the communication delay, calculate the probability distribution of the neighboring positions of the currently planned UAV according to equations (9)-(12) and update the environmental information.

[0081] Step 3.4: Using the updated information, plan the trajectory of the i-th UAV using the pipeline sparse A* search algorithm in the rolling horizon until the maximum step size is reached.

[0082] The specific implementation method of step 3.4 is as follows:

[0083] Step 3.4.1: Initialize the OPEN and CLOSED tables in the algorithm. Create the OPEN and CLOSED tables, and insert the planned starting point into the OPEN table. At this time, the CLOSED table is empty.

[0084] Step 3.4.2: Determine whether the OPEN table is empty. If the OPEN table is empty, end the search; if the OPEN table is not empty, execute step 3.4.3.

[0085] Step 3.4.3: Update the current node. Take the node with the smallest cost value from the current OPEN table as the new current node, delete the current node from the OPEN table, and put it into the CLOSED table.

[0086] Step 3.4.4: Determine whether the distance between the current node and the target point is less than or equal to the minimum track segment length l min If the distance is less than or equal to l min , then the pipeline sparse A* algorithm search is successful, and step 3.4.8 is executed; if the distance is greater than l min , then proceed to step 3.4.5.

[0087] Step 3.4.5: Determine whether the current planning step number exceeds the maximum planning step number. If the current planning step number exceeds the maximum planning step number, end the search, save the track point, and execute step 3.4.8; otherwise, execute step 3.4.6.

[0088] Step 3.4.6: Expand the new track point, generate the pipeline track segment, and calculate the node cost value. Before the current UAV starts planning, it is necessary to first determine the probability distribution of the neighboring aircraft position according to the delay probability distribution, and then expand the pipeline to the area with low probability density of the neighboring aircraft. The radius of the pipeline depends on the size of the communication delay and the maneuverability of the UAV.

[0089] The specific implementation of node cost value calculation is as follows:

[0090] The pipeline sparse A* algorithm track cost evaluation function is:

[0091]

[0092] Where, L i is the cost of the ith flight path, D iis the threat cost of the i-th segment, H(x) is the heuristic function, w1, w2, w3 are the weights of the range cost, threat cost and heuristic function respectively.

[0093] The node feasibility judgment method is as follows: considering the no-fly zone constraint and the minimum distance between aircrafts, the new extended sub-nodes are subjected to constraint checks in turn according to formula (6). Since the feasibility of the track from the starting point to the current node has been guaranteed during the extension process, it is only necessary to check the feasibility of the track segment from the current node to the extended sub-node. For new extended nodes that do not meet the constraints, they are directly discarded.

[0094] Step 3.4.7: Set the parent node of the newly extended track point as the current node, and move the newly extended node into the OPEN table. For the newly extended feasible node that meets the constraints, determine whether it is repeated with the existing nodes in the OPEN table. If there is no duplicate node, calculate the cost value of all feasible nodes and put all feasible nodes into the OPEN table; if there is a duplicate node, only keep the node with the smaller cost value.

[0095] Step 3.4.8: Backtrack the final planned trajectory. Based on the target node and the expanded nodes in the CLOSED table, use the expansion relationship between nodes to backtrack from the target node to the start node to obtain the trajectory from the start point to the target point.

[0096] Step 3.5: Repeat steps 3.1-3.4 until all drones reach the corresponding targets, thus achieving global collaborative trajectory planning for the drone cluster.

[0097] Step 4: On the basis of global trajectory planning, by solving the optimal control problem of distributed model predictive control, the trajectory tracking and adjustment of the UAV in the pipeline is realized, and reliable collision avoidance between drones in the coordinated trajectory of the UAV cluster considering the communication delay is achieved, ensuring the collision avoidance safety of the UAV cluster and improving the collaborative task capability of the UAV cluster in real scenarios.

[0098] Step 4.1: Initialize parameters, set the sampling period δ, set the two ends of the pipeline track centerline as the starting point and end point of the UAV, set k = 0, and execute step 4.4.

[0099] Step 4.2: Receive at t k-d The trajectory information of the neighboring aircraft j of the current UAV i predicted at the moment in the prediction time domain

[0100] Step 4.3: Calculate the set of inputs allowed by drone i The controllability parameter μ i , μ j The initial values ​​are set as Computational pipeline like Then μ i Reduce the fixed proportionality factor ε and repeat this process until the Record the final μ i , and calculate the allowed input set by equation (17)

[0101] Step 4.4: Measure the drone’s i at t k The exact state at the moment x i (t k ), get the drone i in t k-d All neighboring drone location information predicted at any time Generate information set of drone i

[0102] Step 4.5: Solve the distributed model predictive control problem Get the control sequence of UAV i in the prediction time domain and state sequence

[0103] Step 4.6: Send the status information of the drone i Send to its neighboring machine.

[0104] Step 4.7: In the time domain [t k ,t k+1 ] Apply control sequences to the drone i The first item.

[0105] Step 4.8: Let k = k + 1. If drone i has not reached the end point, execute step 4.2. If drone i reaches the end point, end the algorithm, output the trajectory of drone i in the pipeline, and implement the tracking and adjustment of the drone in the pipeline according to the output trajectory, so as to achieve reliable collision avoidance between drones in the coordinated trajectory of drone clusters considering communication delay, ensure the collision avoidance safety of drone clusters, and improve the collaborative task capability of drone clusters in real scenarios.

[0106] Beneficial effects:

[0107] 1. The present invention discloses a method for collaborative trajectory planning of drone clusters considering communication delay. Aiming at the communication delay problem of drone clusters in complex application scenarios, a communication network delay model and a collaborative trajectory planning model are established. Considering the communication delay, a "global planning-local obstacle avoidance" collaborative trajectory planning framework is constructed, and the probabilistic distribution of neighboring aircraft positions caused by communication delay is combined with the sparse A* algorithm node expansion, and pipeline trajectories are introduced to reduce the probability of collision between aircraft; and the pipeline sparse A* algorithm is combined with model predictive control, and through trajectory planning of local obstacle avoidance, the reliability of collaborative trajectory planning of drone clusters under communication delay is ensured, and the collaborative task capability of drone clusters in real combat scenarios is improved.

[0108] 2. The present invention discloses a collaborative trajectory planning method for UAV clusters taking communication delay into consideration. Taking communication delay into consideration, a "global planning-local obstacle avoidance" collaborative trajectory planning framework is constructed. Priority decoupling mechanism is used in global planning to reduce planning complexity. The search efficiency of the algorithm is improved through rolling planning to ensure the timeliness of collaborative trajectory planning for UAV clusters under communication delay and enhance the collaborative task capability of UAV clusters in real combat scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0109] Figure 1 This is a flow chart of a method for cooperative trajectory planning of a UAV cluster considering communication delay disclosed in the present invention;

[0110] Figure 2 This is the pipeline sparse A* algorithm flow chart;

[0111] Figure 3 This is a schematic diagram of the pipeline sparse A* algorithm node expansion;

[0112] Figure 4 The two-dimensional trajectory planning results of the pipeline sparse A* algorithm with dynamic MPC obstacle avoidance;

[0113] Figure 5 It is the minimum distance between adjacent UAVs in the two-dimensional trajectory planning result in Example 1. DETAILED DESCRIPTION

[0114] In order to better illustrate the purpose and advantages of the present invention, the present invention is further described below through an example of UAV trajectory planning in combination with accompanying drawings and tables.

[0115] Embodiment 1:

[0116] The simulation hardware is Intel Core i5-6200 CPU 2.30GHz, 8G memory, and the simulation environment is MATLABR2021b. The UAV formation performs tasks in a two-dimensional environment of 22000m×11500m. The safety distance between UAVs is set to 200m, and the safety distance between UAVs and obstacles is set to 200m.

[0117] like Figure 1 As shown, the present embodiment discloses a method for cooperative trajectory planning of a drone cluster taking into account communication delay, and the specific implementation steps are as follows:

[0118] Step 1: Obtain UAV flight performance parameter information, track constraint information and mission environment information.

[0119] Set the flight speed of the drone to 100m / s, the overload to 10g, the maximum turning angle to 45°, and the minimum track length to l. min = 1500m. The flight start / end positions of the UAV and the position and radius of the no-fly zone in the mission environment are listed in Table 1.

[0120] Table 1 Information on drones and no-fly zones

[0121] Drone Information Starting point (km) End point (km) No-fly zone information Location (km) Radius(km) Drone 1 (0,0) (22,11.5) No-fly zone 1 (4.5,7) 2.5 Drone 2 (0,3) (22,8.5) No Fly Zone 2 (13.5,2) 2 Drone 3 (0,6) (22,6) No Fly Zone 3 (13,8) 1.6 Drone 4 (0,8.5) (22,3) No Fly Zone 4 (19,5) 1 Drone 5 (0,11.5) (22,0)

[0122] Step 2: Establish the UAV trajectory planning model under communication delay, as shown in equations (23)-(37).

[0123] (1) UAV kinematic model

[0124]

[0125] (2) UAV trajectory planning model

[0126] The optimization problem of UAV trajectory planning is

[0127]

[0128] Minimum track segment length constraint:

[0129]

[0130] Maximum turning angle constraint:

[0131]

[0132] No-fly zone restrictions:

[0133]

[0134] (3) Network communication delay model

[0135] The communication delay status of the drone is

[0136] t deny =[0.5s 1s 1.5s 2s 2.5s] (29)

[0137] The corresponding Markov state initial probability distribution is

[0138] P=[0.15 0.35 0.35 0.1 0.05] (30)

[0139] The Markov probability transition matrix is

[0140]

[0141] (4) Collision avoidance method between drone clusters

[0142] The UAV system equation is as follows

[0143]

[0144] Where x = [xy V x V y ], Introducing u=v-Kx, then

[0145]

[0146] in

[0147] At this time, the poles of the system are configured as P = [-0.0513 -0.0513-1.9487-1.9487], the system is stable and controllable, and the controllable Gramian matrix is ​​W = diag{2.5 2.5 0.25 0.25}.

[0148] Considering the communication delay, if the neighboring drone j of drone i satisfies

[0149]

[0150] Then for UAV j

[0151]

[0152] Among them, through the drone i in t k The state at the moment, calculate the reachable set pipeline radius α of UAV j j,i (t) as follows

[0153]

[0154] And M = diag{m 11 m22 m 33 m 44 =W -1 .

[0155] Similarly, the reachable set pipeline of drone i can be calculated

[0156] If UAV i and UAV j do not collide, it must satisfy

[0157]

[0158] Step 3: In view of the high latency characteristics of UAV cluster information interaction in actual combat environments, starting from the framework of "global planning-local obstacle avoidance" collaborative trajectory planning, a real-time pipeline sparse A* trajectory planning algorithm is customized that takes into account the probabilistic distribution of neighboring aircraft positions (the algorithm flow chart is as follows Figure 2 As shown in the figure, the probabilistic distribution of neighboring aircraft positions caused by communication delay is combined with the sparse A* search algorithm to obtain a global pipeline sparse A* algorithm that takes delay into consideration, and then the global collaborative trajectory planning of the UAV cluster is performed through the global pipeline sparse A* algorithm.

[0159] In step 3, the global pipeline sparse A* algorithm is used to perform global collaborative trajectory planning for the drone cluster. The implementation method is as follows: under the rolling planning framework, the priority decoupling mechanism is used to plan the individual drones in the drone cluster one by one, and the probability distribution of the neighboring drone positions is determined according to the delay probability distribution before the current drone starts planning. Then, the sparse A* algorithm is used to expand the pipeline to the area with low probability density of the neighboring drones, so as to realize the online rapid planning of the global collaborative trajectory for the drone cluster. The radius of the pipeline depends on the size of the communication delay and the maneuverability of the drone.

[0160] The specific implementation method of step three is:

[0161] Step 3.1: Determine whether all drones have reached the target point. If all drones have reached the target point, the algorithm ends and outputs the drone cluster track, otherwise execute step 3.2.

[0162] Step 3.2: Enter the rolling planning loop and start planning the UAV trajectory according to the priority order (predetermined planning order). If the i-th UAV reaches the target, continue to determine whether the i+1-th UAV has reached the destination until all UAVs have arrived. Otherwise, execute step 3.3.

[0163] Step 3.3: Considering the communication delay, calculate the probability distribution of the neighboring positions of the currently planned UAV and update the environmental information.

[0164] Step 3.4: Using the updated information, plan the trajectory of the i-th UAV using the pipeline sparse A* search algorithm in the rolling horizon until the maximum step size is reached.

[0165] The specific implementation method of step 3.4 is as follows:

[0166] Step 3.4.1: Initialize the OPEN and CLOSED tables in the algorithm. Create the OPEN and CLOSED tables, and insert the planned starting point into the OPEN table. At this time, the CLOSED table is empty.

[0167] Step 3.4.2: Determine whether the OPEN table is empty. If the OPEN table is empty, end the search; if the OPEN table is not empty, execute step 3.4.3.

[0168] Step 3.4.3: Update the current node. Take the node with the smallest cost value from the current OPEN table as the new current node, delete the current node from the OPEN table, and put it into the CLOSED table.

[0169] Step 3.4.4: Determine whether the distance between the current node and the target point is less than or equal to the minimum track segment length l min If the distance is less than or equal to l min , then the pipeline sparse A* algorithm search is successful, and step 3.4.8 is executed; if the distance is greater than l min , then proceed to step 3.4.5.

[0170] Step 3.4.5: Determine whether the current planning step number exceeds the maximum planning step number. If the current planning step number exceeds the maximum planning step number, end the search, save the track point, and execute step 3.4.8; otherwise, execute step 3.4.6.

[0171] Step 3.4.6: Follow Figure 2 As shown in the figure, the new track point is extended to generate the pipeline track segment (the pipeline radius is set to 50m), and the node cost value is calculated. Before the current UAV starts planning, it is necessary to first determine the probability distribution of the neighboring aircraft position according to the delay probability distribution, and then expand the pipeline to the area with low probability density of the neighboring aircraft. The radius of the pipeline depends on the size of the communication delay and the maneuverability of the UAV.

[0172] The specific implementation of node cost value calculation is as follows:

[0173] The pipeline sparse A* algorithm track cost evaluation function is:

[0174]

[0175] Where, L i is the cost of the ith flight path, D iis the threat cost of the i-th segment, H(x) is the heuristic function, w1, w2, w3 are the weights of the range cost, threat cost and heuristic function respectively.

[0176] The node feasibility judgment method is as follows: considering the no-fly zone constraint and the minimum distance between aircrafts, the constraint check is performed on the new extended sub-nodes in turn. Since the feasibility of the track from the starting point to the current node has been guaranteed during the extension process, it is only necessary to check the feasibility of the track segment from the current node to the extended sub-node. For new extended nodes that do not meet the constraints, they are directly discarded.

[0177] Step 3.4.7: Set the parent node of the newly extended track point as the current node, and move the newly extended node into the OPEN table. For the newly extended feasible node that meets the constraints, determine whether it is repeated with the existing nodes in the OPEN table. If there is no duplicate node, calculate the cost value of all feasible nodes and put all feasible nodes into the OPEN table; if there is a duplicate node, only keep the node with the smaller cost value.

[0178] Step 3.4.8: Backtrack the final planned trajectory. Based on the target node and the expanded nodes in the CLOSED table, use the expansion relationship between nodes to backtrack from the target node to the start node to obtain the trajectory from the start point to the target point.

[0179] Step 3.5: Repeat steps 3.1-3.4 until all drones reach the corresponding target, and global collaborative trajectory planning for the drone cluster is realized.

[0180] Step 4: On the basis of global trajectory planning, by solving the optimal control problem of distributed model predictive control, the trajectory tracking and adjustment of the UAV in the pipeline is realized, and reliable collision avoidance between drones in the coordinated trajectory of the UAV cluster considering the communication delay is achieved, ensuring the collision avoidance safety of the UAV cluster and improving the collaborative task capability of the UAV cluster in real scenarios.

[0181] Step 4.1: Initialize the parameters, set the sampling period to 0.2s, set the two ends of the pipeline track centerline as the starting point and end point of the UAV, set k = 0, and execute step 4.4.

[0182] Step 4.2: Receive at t k-d The trajectory information of the neighboring aircraft j of the current UAV i predicted at the moment in the prediction time domain

[0183] Step 4.3: Calculate the set of inputs allowed by drone i The controllability parameter μ i , μ j The initial values ​​are set to 10 and 10 respectively, and the calculation pipeline like Then μ i Zoom out by 10% and repeat this process until you reach Record the final μ i , and calculate the allowed input set by equation (23)

[0184] Step 4.4: Measure the drone’s i at t k The exact state at the moment x i (t k ), get the drone i in t k-d All neighboring drone location information predicted at any time Generate information set of drone i

[0185] Step 4.5: Solve the distributed model predictive control problem Get the control sequence of UAV i in the prediction time domain and state sequence

[0186] Step 4.6: Send the status information of the drone i Send to its neighboring machine.

[0187] Step 4.7: In the time domain [t k ,t k+1 ] Apply control sequences to the drone i The first item.

[0188] Step 4.8: Let k = k + 1. If drone i has not reached the end point, execute step 4.2. If drone i reaches the end point, end the algorithm, output the trajectory of drone i in the pipeline, and implement the tracking and adjustment of the drone in the pipeline according to the output trajectory, so as to achieve reliable collision avoidance between drones in the coordinated trajectory of drone clusters considering communication delay, ensure the collision avoidance safety of drone clusters, and improve the collaborative task capability of drone clusters in real scenarios.

[0189] Simulation of pipeline sparse A* trajectory planning based on dynamic MPC obstacle avoidance Figure 4 As shown in Figure 1, the entire planning process takes 2.7580 seconds, and the planning efficiency is relatively high. The global pipeline A* trajectory planning of the drone cluster takes 0.015 seconds, and the local dynamic MPC obstacle avoidance (trajectory planning) of the drone pipeline trajectory takes 2.743 seconds. The minimum distance between adjacent drones is shown in Figure 1. Figure 5 As shown in the figure, the obstacle avoider using the dynamic MPC obstacle avoidance method has better local obstacle avoidance performance. In summary, the results show that this method can generate reliable real-time collaborative paths for drone swarms.

[0190] According to the simulation results and analysis of the aforementioned UAV trajectory planning example, it can be seen that the specified range trajectory planning method described in this embodiment can provide a feasible trajectory for the UAV cluster taking into account the communication delay, and the trajectory generation speed has a high efficiency. Therefore, the present invention has strong engineering practicality and can achieve the expected purpose of the invention.

[0191] The above specific description is a further detailed explanation of the purpose, technical solutions and beneficial effects of the invention. It should be understood that the above is only a specific implementation example of the present invention, which is only used to explain the present invention and is not used to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for cooperative trajectory planning of UAV cluster considering communication delay, characterized by: The following steps are included: Step 1: Initialize the UAV flight performance parameter information, track constraint information and mission environment information; Obtaining the UAV flight performance parameter information, track constraint information and mission environment information; the UAV flight performance parameter information includes the UAV flight speed, overload, maximum turning angle and minimum track segment length; the track constraint information includes the UAV flight starting point position, target point position, and safe distance between the UAV and obstacles; the mission environment information includes the position and radius of the no-fly zone; Step 2: Considering the UAV performance constraints, mission environment constraints, network communication delay and UAV local obstacle avoidance method, a UAV trajectory planning model under communication delay is established, wherein the UAV trajectory planning model includes a UAV kinematic model, a UAV trajectory planning problem model, a network communication delay model and a UAV local problem model; The specific implementation method of step 2 is as follows: (1) UAV kinematic modeling Assuming that the UAV cluster flies at a fixed altitude, the particle kinematic model of the i-th UAV in the UAV cluster is: Where (x i ,y i ), V i , a i , χ i are the position coordinates, velocity, acceleration and heading angle of the i-th UAV respectively; (2) Modeling of UAV trajectory planning problem In the process of trajectory planning, UAVs need to consider not only the impact of terrain and various threats, but also their own performance constraints, and need to find an evaluation criterion to evaluate whether the planned trajectory is the optimal trajectory. The UAV trajectory planning problem is essentially a multi-objective and multi-constraint nonlinear optimization problem, and its mathematical model is Where x is the trajectory of the UAV; f(x) is the cost evaluation function; g j (x) is the jth constraint; Among them, the track cost mainly includes the distance cost and the track threat cost. The track cost evaluation function is expressed as J=∑(w1L i +w2D i ) (3) Where, L i is the cost of the ith flight path, D i is the threat cost of the i-th segment, w1 and w2 are weight coefficients; The UAV trajectory planning constraints include the UAV maneuverability constraints and the no-fly zone constraints; the maneuverability constraints include the minimum trajectory segment length and the maximum turning angle: ① Minimum track length constraint: Due to the limitation of maneuverability, the UAV must fly a certain distance in the original direction before changing the track direction each time, that is, each track segment must not be less than the shortest direct flight distance l min , the expression of the minimum track segment length constraint is Among them, l k is the length of the kth track of the UAV; ② Maximum turning angle constraint: Due to the constraints of the UAV's maneuverability, the planned trajectory needs to avoid excessive turning angles to ensure the feasibility of the trajectory; the maximum turning angle of the UAV is Δχ max , then it is required that: Among them, Δχ k is the turning angle of the UAV at the kth track point; ③ No-fly zone constraints: During the flight of the drone, it is necessary to avoid the no-fly zone in the environment, that is, the drone's track is required not to intersect with the no-fly zone, which is expressed as Among them, s j represents the minimum distance between the drone’s track and the no-fly zone j, d safe is the safe distance between the drone and the obstacle, n NFZ is the number of no-fly zones; (3) Network communication delay modeling The process of UAV swarm collaborative trajectory planning requires real-time information exchange between UAVs through the communication network. In real-time network systems, information transmission inevitably has induced delays, and this delay changes with the changes in the communication protocol and the load conditions in the network, which is modeled as a Markov chain. Define the transmission delay at time k as d k , and m≤d k ≤n, that is, the minimum transmission delay is m and the maximum transmission delay is n, then for i,j∈S={m,m+1,…,n}, there are the following conditional probability properties without aftereffect: P(d k+1 =j|d0,d1,…,d k =i)=P(d k+1 =j|d k =i) (7) Defining transition probabilities P(d k+1 =j|d k =i)=q (i-m)(j-m) (8) Then for all i,j∈S, there is q (i-m)(j-m) ≥0 and Introducing Markov state probability distribution Then the probability distribution of adjacent delay states has the following relationship: π(k+1)=π(k)Q M (9) among them i (k)=P(d k (=i+m) Q M =q (i-m)(j-m)i,j∈S The drone cluster adopts the method of equal-period synchronous sampling. In the event-driven control mode, the probability distribution of the delay of information transmission in the network is p i , where i∈S, and Then the transition probability matrix Q M The elements of are obtained as follows: (4) Modeling of local problems of UAVs In order to solve the problem of inter-machine collision that may occur in the coordination of UAV clusters, on the basis of global trajectory planning, the UAV kinematic model is used. Based on the model predictive control theory, the local trajectory of the UAV is obtained by solving the optimal control problem, and the dynamic local collision avoidance requirements of the UAV are accurately achieved. Through the state information of the UAV under communication delay, the cost function is designed, the distributed model predictive control model is established, and the judgment criteria for inter-machine collision are proposed. The state equation of the drone is as follows Where x = [xy V x V y ], Where (x, y), V, and a are the position coordinates, velocity, and acceleration of the UAV, respectively, corresponding to formula (1); Define the UAV flight control sampling period as δ, and there are t k+1 =t k +δ; the communication delay time is a discrete random variable τ, which satisfies the Markov chain model of network delay, and (d-1)δ≤τ≤dδ, where d is a positive integer representing discrete communication delay; the information set of UAV i is x i (t k ) is t k The position of drone i at the moment, is the location information of the neighboring drones of drone i; drone i at time t k The cost function is: in is the control input, r i is its target point, T is the prediction time domain, P>0, Q>0, R>0 and they are all symmetric matrices, The distributed model predictive control model is established as follows: The reachable set of drone i at time t is calculated as follows: The permissible input set of UAV i is The following relations are satisfied: where μ j ≥0, called the maneuverability parameter of UAV j; For the output set If satisfied but It is determined by the ellipsoid boundary Γ centered at x0, which is expressed as: Where M is a diagonalizable matrix and satisfies M=W -1 (20) Among them, W is the controllable Gram matrix; When t∈[t0,T], the reachable set of all points on the trajectory ξ(t,u0) forms a tube where p is the dimension of the trajectory ξ, is the radius of the reachable set at time t; Finally, the condition to satisfy the collision avoidance constraint is Step 3: In view of the high latency characteristics of information interaction of UAV clusters in actual combat environments, starting from the framework of "global planning-local obstacle avoidance" collaborative trajectory planning, a real-time pipeline sparse A* trajectory planning algorithm that considers the probabilistic distribution of neighboring aircraft positions is customized. That is, the probabilistic distribution of neighboring aircraft positions caused by communication delays is combined with the sparse A* search algorithm to obtain a global pipeline sparse A* algorithm that considers latency, and then the global collaborative trajectory planning of the UAV cluster is performed through the global pipeline sparse A* algorithm; The specific implementation method of step three is: Step 3.1: Determine whether all drones have reached the target point; if all drones have reached the target point, the algorithm ends and outputs the drone cluster track, otherwise execute step 3.2; Step 3.2: Enter the rolling planning loop and start planning the UAV trajectory according to the priority order; if the i-th UAV reaches the target point, continue to determine whether the i+1-th UAV has reached the target point until all UAVs have arrived; otherwise, execute step 3.3; Step 3.3: Considering the communication delay, calculate the probability distribution of the neighboring positions of the current planned UAV according to equations (9)-(12) and update the environmental information; Step 3.4: Using the updated information, plan the trajectory of the i-th UAV using the pipeline sparse A* search algorithm in the rolling time domain until the maximum step size is reached; The specific implementation method of step 3.4 is as follows: Step 3.4.1: Initialize the OPEN table and CLOSED table in the algorithm; create the OPEN table and CLOSED table, and insert the planned starting point into the OPEN table. At this time, the CLOSED table is empty. Step 3.4.2: Determine whether the OPEN table is empty; if the OPEN table is empty, end the search; if the OPEN table is not empty, execute step 3.4.3; Step 3.4.3: Update the current node; take the node with the smallest cost value from the current OPEN table as the new current node, delete the current node from the OPEN table, and put it into the CLOSED table; Step 3.4.4: Determine whether the distance between the current node and the target point is less than or equal to the minimum track segment length l min ; If the distance is less than or equal to l min , then the pipeline sparse A* algorithm search is successful, and step 3.4.8 is executed; if the distance is greater than l min , then execute step 3.4.5; Step 3.4.5: Determine whether the current planning step number exceeds the maximum planning step number; if the current planning step number exceeds the maximum planning step number, end the search, save the track point, and execute step 3.4.8; otherwise, execute step 3.4.6; Step 3.4.6: Expand the new track point, generate the pipeline track segment, and calculate the node cost value; before the current UAV starts planning, it is necessary to first determine the probability distribution of the neighboring aircraft position according to the delay probability distribution, and then expand the pipeline to the area with low probability density of neighboring aircraft. The radius of the pipeline depends on the size of the communication delay and the maneuverability of the UAV; The specific implementation of node cost value calculation is as follows: The pipeline sparse A* algorithm track cost evaluation function is: Where, L i is the cost of the ith flight path, D i is the threat cost of the i-th segment, H(x) is the heuristic function, w1, w2, and w3 are the weights of the range cost, threat cost, and heuristic function, respectively; The node feasibility judgment method is as follows: considering the no-fly restriction zone constraint and the minimum distance between aircrafts, the constraint check is performed on the new extended sub-nodes in turn according to formula (6); since the feasibility of the track from the starting point to the current node has been guaranteed during the extension process, it is only necessary to check the feasibility of the track segment from the current node to the extended sub-node; for the new extended nodes that do not meet the constraints, they are directly discarded; Step 3.4.7: Set the parent node of the newly extended track point as the current node, and move the newly extended node into the OPEN table; for the newly extended feasible node that meets the constraints, determine whether it is repeated with the existing nodes in the OPEN table; if there is no repeated node, calculate the cost value of all feasible nodes and put all feasible nodes into the OPEN table; if there is a repeated node, only keep the node with the smaller cost value; Step 3.4.8: Backtrack the final planned trajectory; based on the target node and the expanded nodes in the CLOSED table, use the extension relationship between nodes to backtrack from the target node to the starting node to obtain the trajectory from the starting point to the target point; Step 3.5: Repeat steps 3.1-3.4 until all drones reach the corresponding target point, realizing global collaborative trajectory planning for the drone cluster; Step 4: On the basis of global trajectory planning, by solving the optimal control problem of distributed model predictive control, the trajectory tracking and adjustment of the UAV in the pipeline is realized, and reliable collision avoidance between drones in the coordinated trajectory of the UAV cluster considering the communication delay is achieved, ensuring the collision avoidance safety of the UAV cluster and improving the collaborative task capability of the UAV cluster in real scenarios.

2. The method for cooperative trajectory planning of a drone cluster considering communication delay as claimed in claim 1, characterized in that: In step three, the global pipeline sparse A* algorithm is used to perform global collaborative trajectory planning for the UAV cluster. The implementation method is as follows: under the rolling planning framework, the priority decoupling mechanism is used to plan the individual machines in the UAV cluster one by one, and the probability distribution of the neighboring machine position is determined according to the delay probability distribution before the current UAV starts planning. Then, the sparse A* algorithm is used to expand the pipeline to the area with low probability density of neighboring machines, so as to realize the online rapid planning of global collaborative trajectory for the UAV cluster; the radius of the pipeline depends on the size of the communication delay and the maneuverability of the UAV.

3. The method for cooperative trajectory planning of a drone swarm considering communication delay as claimed in claim 1, characterized in that: The implementation method of step 4 is: Step 4.1: Initialize parameters, set the sampling period δ, set the two ends of the pipeline track centerline as the starting point and end point of the UAV, set k = 0, and execute step 4.4; Step 4.2: Receive at t k-d The trajectory information of the neighboring aircraft j of the current UAV i predicted at the moment in the prediction time domain Step 4.3: Calculate the allowed input set for drone i The controllability parameter μ i , μ j The initial values ​​are set as Computational pipeline like Then μ i Reduce the fixed proportionality factor ε and repeat this process until the Record the final μ i , and calculate the allowed input set by equation (17) Step 4.4: Measure the drone’s i at t k The exact state at the moment x i (t k ), get the drone i in t k-d All neighboring drone location information predicted at any time Generate information set of drone i Step 4.5: Solve the distributed model predictive control problem Get the control sequence of UAV i in the prediction time domain and state sequence Step 4.6: Send the status information of the drone i Send to its neighboring machine; Step 4.7: In the time domain [t k ,t k+1 ] Apply control sequences to the drone i The first item of Step 4.8: Let k = k + 1; if UAV i has not reached the end point, execute step 4.2; if UAV i reaches the end point, end the algorithm and output the trajectory of UAV i in the pipeline. According to the output trajectory, the track of the UAV in the pipeline is tracked and adjusted to achieve reliable collision avoidance between drones in the coordinated trajectory of the UAV cluster considering the communication delay, ensure the collision avoidance safety of the UAV cluster, and improve the collaborative task capability of the UAV cluster in real scenarios.

Images