Distributed space-time trajectory optimization framework for unmanned aerial vehicle cluster

Abstract

The invention discloses an unmanned aerial vehicle cluster distributed spatio-temporal trajectory optimization framework, which is characterized in that an optimal control model is established and solved, a spatio-temporal trajectory of an unmanned aerial vehicle cluster is obtained, in the solving process, single unmanned aerial vehicle spatio-temporal trajectory optimization iteration and self-constraint condition iteration are carried out on any unmanned aerial vehicle, and the spatial trajectory of the unmanned aerial vehicle cluster is obtained. And communication between the unmanned aerial vehicles is carried out, global variables are obtained, and the optimal space-time trajectory of the unmanned aerial vehicles is obtained by optimizing the global variables. The unmanned aerial vehicle cluster distributed space-time trajectory optimization framework disclosed by the invention can optimize the flight trajectories of a plurality of unmanned aerial vehicles, so that the unmanned aerial vehicles avoid obstacles, the avoidance constraint among the unmanned aerial vehicles is met, and the flight time of the unmanned aerial vehicles is optimized.

Description

Technical Field

[0001] The invention relates to a distributed spatiotemporal trajectory optimization framework for an unmanned aerial vehicle cluster, and belongs to the technical field of aircraft control. Background Art

[0002] Trajectory optimization plays a vital role in enhancing the autonomy of the swarm. Trajectory optimization can be formulated as a multi-agent optimal control (MAOC) problem, which is to optimize the control history of each agent to minimize the global general performance indicator while complying with multiple nonlinear constraints.

[0003] Most MAOC problems are processed using the alternating direction method of multipliers (ADMM). Due to the strong non-convexity of the UAV cluster trajectory optimization problem, coupled with the influence of dynamic constraints, collision constraints, communication distance maintenance and other factors, ADMM is difficult to be directly applied to actual tasks. Therefore, in the prior art, the trajectory optimization of UAV clusters generally adopts distributed computing based on ADMM and a local planning framework based on DDP to solve the distributed spatiotemporal trajectory optimization problem of UAV clusters.

[0004] However, this method requires setting the terminal time for each drone in advance. However, in some actual drone cluster applications, the preset terminal time is difficult to achieve for some tasks. From the perspective of the task, time optimization is a key indicator. For example, in some tasks (such as search and rescue, express delivery), the mission duration should be shortened as much as possible.

[0005] Therefore, it is necessary to further study the existing UAV cluster trajectory optimization methods to solve the above problems. Summary of the invention

[0006] In order to overcome the above problems, the inventors conducted in-depth research and proposed a distributed spatiotemporal trajectory optimization framework for drone clusters. By establishing an optimal control model and solving the optimal control model, the spatiotemporal trajectory of the drone cluster is obtained, and the drones fly according to the obtained spatiotemporal trajectory.

[0007] In a preferred embodiment, the optimal control model is expressed as:

[0008]

[0009] Among them, i represents the number of different drones in the drone cluster, N represents the total time, represents the minimum value of the control input of UAV i at all times, represents the final flight time of drone i, t i,N represents the flight time of drone i, X i Represents the stack of state vectors of drone i at all times, Ui represents the stack of control inputs of drone i at all times, J i (X i ,U i ) represents the local objective function of the i-th UAV, st represents the constraint condition, x i,k represents the state vector of the i-th UAV at time k, u i,k represents the control vector of the ith UAV at time k, f i () represents the discrete system dynamics with nonlinear characteristics, For x i,k A safe copy variable, a i,k () is a nonlinear function used to describe path constraints, for u i,k A safe copy variable, b i,k () represents the control torque constraint function, t i,N A safe copy variable, c i,N () represents a nonlinear function, represents the set of state vectors of all neighboring drones of drone i at time k, represents the set of state constants between UAV i and its neighboring UAVs at time k, represents the set of time variables of all neighboring drones of drone i at time k, represents the set of time constraints between UAV i and its neighboring UAVs at time k, represents the set of state variables that have reached consensus, A collection of variables representing the time at which consensus is reached.

[0010] In a preferred embodiment, the solution process includes the following sub-steps:

[0011] S21. For any UAV, minimize the UAV’s own local variable x i,k 、u i,k ,t i,N The augmented Lagrangian is used to iterate the optimization of the space-time trajectory of a single UAV;

[0012] S22, for any UAV, iterating the constraint conditions of the UAV itself;

[0013] S23, each UAV communicates with all its neighboring UAVs, obtains trajectory optimization iteration results and constraint condition iteration results of its neighboring UAVs, and obtains global variables;

[0014] S24. Obtain the optimal spatiotemporal trajectory of the UAV by optimizing global variables.

[0015] In a preferred embodiment, a parameterized differential dynamic programming method is used to minimize the augmented Lagrangian and perform iterative optimization of the spatiotemporal trajectory of a single UAV.

[0016] In a preferred embodiment, in the parameterized differential dynamic programming method, the action value function is modified to change the action value function Q(x i,k ,u i,k θ i ) is modified to:

[0017]

[0018] in, represents the action value function Q at time k for x i The derivative of It represents the running cost function l for x at time k i The derivative of represents the dynamic function f at time k to x i The derivative of It represents the value function V for x at time k+1 i The derivative of represents the action value function Q at time k for u i The derivative of It represents the running cost function l for u at time k i The derivative of represents the dynamic function f at time k on u i The derivative of represents the action value function Q at time k for θ v The derivative of It represents the operating cost function l at time k for θ i The derivative of It represents the value function V for θ at time k+1 i The derivative of represents the dynamic function f at time k on θ i The derivative of represents the action value function Q at time k for x i x i The derivative of It represents the running cost function l for x at time k i x i The derivative of It represents the value function V for x at time k+1 i x i The derivative of , I represents the identity matrix, represents the action value function Q at time k for u i u i The derivative of It represents the running cost function l for u at time ki u i The derivative of represents the action value function Q at time k for θ i θ i The derivative of It represents the operating cost function l at time k for θ i θ i The derivative of It represents the value function V for θ at time k+1 i θ i The derivative of It represents the value function V for x at time k+1 i θ i The derivative of represents the action value function Q at time k for x i u i The derivative of It represents the running cost function l for x at time k i u i The derivative of

[0019] represents the action value function Q at time k for u i x i The derivative of represents the action value function Q at time k for x i θ i The derivative of It represents the running cost function l for x at time k i θ i The derivative of represents the action value function Q at time k for θ i x i The derivative of represents the action value function Q at time k for u i θ i The derivative of It represents the running cost function l for u at time k i θ i The derivative of represents the action value function Q at time k for θ i u i The derivative of .

[0020] In a preferred embodiment, in the parameterized differential dynamic programming method, the value function V(x i,N ,t i,N ) and its derivatives are obtained by the following formula:

[0021]

[0022] Among them, V xi,NRepresents the value function V for x at time N i The derivative of It represents the terminal cost function φ for x at time N i The derivative of Represents the value function V at time N for θ i The derivative of It represents the terminal cost function φ on θ at time N i The derivative of Represents the value function V for x at time N i x i The derivative of It represents the terminal cost function φ for x at time N i x i The derivative of Indicates p i The unit matrix, Represents the value function V for x at time N i θ i The derivative of It represents the terminal cost function φ for x at time N i θ i The derivative of Represents the value function V at time N for θ i x i The derivative of Represents the value function V at time N for θ i θ i The derivative of It represents the terminal cost function φ on θ at time N i θ i The derivative of 1×1 represents the 1st-order identity matrix.

[0023] In a preferred embodiment, in the parameterized differential dynamic programming method, a final time update constraint is set, which is expressed as:

[0024]

[0025] in, represents the final flight time of each drone i, t min represents the lower bound of the final time, t max Represents the upper bound of the final time.

[0026] In a preferred embodiment, in S22, the alternating direction multiplier method is used to iterate the constraints of the drone itself, and the update rule is set as:

[0027]

[0028] In a preferred embodiment, in S23, the global variable is represented as:

[0029]

[0030] in, represents the set of drones j that consider drone i as their neighbors, represents the state variable of drone i observed by neighbor drone j, represents the flight time of UAV i observed by neighbor UAV j.

[0031] In a preferred embodiment, in S24, the update rule of the global variable is set as follows:

[0032]

[0033]

[0034] Here, the superscript n indicates the nth iteration.

[0035] The beneficial effects of the present invention include:

[0036] (1) Ability to optimize the flight trajectories of multiple drones to avoid obstacles;

[0037] (2) Ability to meet avoidance constraints between drones and optimize the flight time of drones BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 A schematic diagram of a distributed spatiotemporal trajectory optimization framework for a drone swarm according to a preferred embodiment of the present invention is shown;

[0039] Figure 2 The trajectory diagram of the drone at the initial moment and after iteration in Example 1 is shown;

[0040] Figure 3 A graph showing the relationship between the number of iterations and the flight time of the drone in Example 1 is shown. DETAILED DESCRIPTION

[0041] The present invention will be further described in detail below through the accompanying drawings and embodiments. Through these descriptions, the characteristics and advantages of the present invention will become more clear and distinct.

[0042] The word "exemplary" is used exclusively herein to mean "serving as an example, embodiment, or illustration." Any embodiment described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments. Although various aspects of the embodiments are shown in the drawings, the drawings are not necessarily drawn to scale unless otherwise noted.

[0043] According to the invention, a distributed spatiotemporal trajectory optimization framework for drone swarms is provided. Figure 1 As shown, the following steps are included:

[0044] S1. Establish the optimal control model;

[0045] S2. Solve the optimal control model and obtain the spatiotemporal trajectory of the UAV cluster.

[0046] According to the present invention, after the space-time trajectory of the drone cluster is obtained, the drones fly according to the obtained space-time trajectory, and the flight control of the drones is achieved by tracking the space-time trajectory.

[0047] In S1, the optimal control model is expressed as a MACO problem that can be distributed optimized, which is used to optimize the trajectory of the drone cluster.

[0048] The optimal control model is expressed as:

[0049]

[0050] Among them, i represents the number of different drones in the drone cluster, N represents the total time, represents the minimum value of the control input of UAV i at all times, represents the final flight time of drone i, t i,N represents the flight time of drone i, X i Represents the stack of state vectors of drone i at all times, U i represents the stack of control inputs of drone i at all times, J i (X i ,U i ) represents the local objective function of the i-th UAV, st represents the constraint condition, x i,k represents the state vector of the i-th UAV at time k, u i,k represents the control vector of the ith UAV at time k, f i () represents the discrete system dynamics with nonlinear characteristics, For x i,k A safe copy variable, a i,k () is a nonlinear function used to describe path constraints, for u i,k A safe copy variable, b i,k () represents the control torque constraint function, t i,N A safe copy variable, c i,n () represents a nonlinear function, represents the set of state vectors of all neighboring drones of drone i at time k, represents the set of state constants between UAV i and its neighboring UAVs, represents the set of time variables of all neighboring drones of drone i at time k, represents the set of time constraints between UAV i and its neighboring UAVs, represents the set of state variables that have reached consensus, A collection of variables representing the time at which consensus is reached.

[0051] are all local constraints of a single UAV. is the state constant between UAVs, expressed as:

[0052]

[0053]

[0054] in, represents the state variable of neighboring drone j observed from drone i, d ij,k () represents the state constraint between drone i and its neighbor drone j, represents the flight time of neighboring drone j observed by drone i, e ij,N () represents the time constraint between UAV i and its neighbor UAV j, represents the neighbor set of UAV i excluding UAV i itself.

[0055] According to the present invention,

[0056] Among them, z j,k The state variable that represents the consensus, s j,N represents the time variable for reaching consensus, represents the neighbor set of drone i.

[0057] According to the present invention, if drone j is within the effective communication range of drone i, then drone j is the neighbor of drone i, and all neighbors of drone i and drone i together constitute the neighbor set of drone i.

[0058] Preferably, the local objective function of the i-th UAV is set as:

[0059]

[0060] Among them, l i () represents a scalar function, φ i () indicates terminal cost.

[0061] Further,

[0062]

[0063]

[0064] Right now

[0065]

[0066] In the formula, represents the expected terminal state vector of the ith UAV, R i and is the weighted diagonal matrix of the cost function. ([x i ,y i ,θ i ] T is the state variable of a single drone, [x i ,y i ] T represents the coordinates of the i-th UAV, θ i is the flight heading angle.

[0067] In S2, the solution process includes the following sub-steps:

[0068] S21. For any UAV, minimize the UAV’s own local variable x i,k 、u i,k ,t i,N The augmented Lagrangian is used to iterate the optimization of the space-time trajectory of a single UAV;

[0069] S22, for any UAV, iterating the constraint conditions of the UAV itself;

[0070] S23, each UAV communicates with all its neighboring UAVs, obtains trajectory optimization iteration results and constraint condition iteration results of its neighboring UAVs, and obtains global variables;

[0071] S24. Obtain the optimal spatiotemporal trajectory of the UAV by optimizing global variables.

[0072] In S21, the minimization of the drone's own local variable x i,k 、u i,k ,t i,N The augmented Lagrangian of is expressed as:

[0073]

[0074] Among them, x i,k represents the state vector of drone i, u i,k represents the control vector of UAV i, t i,N represents the flight time of UAV i, and the superscript n represents the number of iterations in the optimization process. represents the augmented Lagrangian function. ζ i,k, i,k 、v i,N ,y i,k , η i,N represents the dual variable of the constraint in the augmented Lagrange multiplier formula.

[0075] Furthermore, the parameterized differential dynamic programming (DDP) method is used to perform the spatiotemporal trajectory optimization iteration of a single UAV, which is expressed as:

[0076]

[0077] in, For operating costs, is the terminal cost, expressed as:

[0078]

[0079]

[0080] Among them, ρ, τ, σ represent the penalty parameters of the constraints, represents the square of the 2-norm.

[0081] According to the present invention, each UAV adopts the DDP method to perform optimization iteration respectively, thereby realizing distributed computing.

[0082] Furthermore, the parameterized differential dynamic programming method is a commonly used method in the optimal control method, and its solution process is not described in detail in the present invention.

[0083] In the parameterized differential dynamic programming method, there are action value function Q and value function V, where the action value function Q represents the expected cumulative reward that the state vector can obtain after taking the control vector; the value function V represents the expected cumulative reward that can be obtained by following the optimal strategy from the current moment to the final state when it is in state X at time t.

[0084] Preferably, in the present invention, the action value function is also modified. Specifically, the action value function Q(x i,k ,u i,k θ i ) is modified to:

[0085]

[0086] Among them, Q xi,k represents the action value function Q at time k for x i The derivative of It represents the running cost function l for x at time k i The derivative of represents the dynamic function f at time k on x i The derivative of It represents the value function V for x at time k+1 i The derivative of represents the action value function Q at time k for u i The derivative of It represents the running cost function l for u at time k i The derivative of represents the dynamic function f at time k on u i The derivative of represents the action value function Q at time k for θ i The derivative of It represents the operating cost function l at time k for θ i The derivative of It represents the value function V for θ at time k+1 i The derivative of represents the dynamic function f at time k on θ i The derivative of represents the action value function Q at time k for x i x i The derivative of It represents the running cost function l for x at time k i x i The derivative of It represents the value function V for x at time k+1 i x i The derivative of , I represents the identity matrix, represents the action value function Q at time k for u i u i The derivative of It represents the running cost function l for u at time k i u i The derivative of represents the action value function Q at time k for θ i θ i The derivative of It represents the operating cost function l at time k for θ i θ i The derivative of It represents the value function V for θ at time k+1 i θ i The derivative of It represents the value function V for x at time k+1 i θ i The derivative of represents the action value function Q at time k for x i u i The derivative of It represents the running cost function l for x at time k i u i The derivative of represents the action value function Q at time k for u i x i The derivative of represents the action value function Q at time k for x i θ i The derivative of represents the operating cost function l for x at time j i θ i The derivative of represents the action value function Q at time k for θ i x i The derivative of represents the action value function Q at time k for u i θ i The derivative of It represents the running cost function l for u at time k i θ i The derivative of represents the action value function Q at time k for θ i u i The derivative of .

[0087] Preferably, for the value function V(x i,N ,t i,N ) and its derivatives are obtained by the following formula:

[0088]

[0089] Among them, V xi,N Represents the value function V for x at time N i The derivative of It represents the terminal cost function φ for x at time N i The derivative of Represents the value function V at time N for θ i The derivative of It represents the terminal cost function φ on θ at time N i The derivative of Represents the value function V for x at time N i x i The derivative of It represents the terminal cost function φ for x at time N i x i The derivative of Indicates p i The unit matrix, Represents the value function V for x at time N i θ i The derivative of It represents the terminal cost function φ for x at time N i θ i The derivative of Represents the value function V at time N for θ i x i The derivative of Represents the value function V at time N for θ i θ i The derivative of It represents the terminal cost function φ on θ at time N i θ i The derivative of 1×1 represents the 1st-order identity matrix.

[0090] Preferably, in the parameterized differential dynamic programming method, a control constraint is also set:

[0091]

[0092] in, represents the optimal control increment, u min represents the lower boundary of the control vector, u max Represents the upper bound of the control vector.

[0093] Preferably, in the parameterized differential dynamic programming method, a final time update constraint is also set, which is expressed as:

[0094]

[0095] in, represents the final flight time of drone i, t min represents the lower bound of the final time, t max Represents the upper bound of the final time.

[0096] In S22, the alternating direction multiplier method (ADMM) is used to iterate the constraints of the UAV itself. Specifically, the update rule is set as:

[0097]

[0098] Furthermore, since the state and control variables of each UAV are decoupled, the above equation can be decomposed into M×(N+1) state sub-problems for each UAV i at each time k, which can be solved in parallel as follows:

[0099]

[0100] Similarly, the control problem can also be decomposed into M×N small problems for solving:

[0101]

[0102] And M terminal time optimization subproblems:

[0103]

[0104] in, Input constraints for control, is the terminal time boundary constraint.

[0105] In S23, the global variable is represented as:

[0106]

[0107] in, represents the set of drones j that consider drone i as their neighbors, represents the state variable of drone i observed by neighbor drone j, represents the flight time of UAV i observed by neighbor UAV j.

[0108] According to the global variables, it can be seen that the global consensus variable of drone i is a comprehensive evaluation of the state from the perspective of i’s neighbor j.

[0109] In S24, the update rule of the global variables is set as:

[0110]

[0111]

[0112] Here, the superscript n indicates the nth iteration.

[0113] Since the dual variable y i,k and η i,N As the number of iterations n increases, it will gradually become 0, so the global update gradually becomes the local average of all replica variables of drone i.

[0114] Further set the dual update as:

[0115]

[0116] According to the present invention, in S24, the DDP method can be used, and the stop criterion of the update can be determined by checking whether the original residual and the dual residual of the original variable are lower than a certain threshold, and the original residual and the dual residual are expressed as:

[0117]

[0118] in, represents the original residual, represents the dual residual, and the subscript represents the variable type of the residual. is the collection of stacks of control inputs of all drones at all times. is the set of safe replica variables corresponding to U, is the collection of state vector stacks of all drones at all times, is the set of safe copy variables corresponding to X, is the set of state vectors of all neighboring drones of all drones at all times, represents the set of time vectors of all drones at all times, represents the set of time vectors of all drones for n iterations, represents the set of state variables that all drones agree on at all times, Represents the set of time variables that all drones reach consensus on at all times.

[0119] Furthermore, the standard for setting the update to meet the stop condition is:

[0120]

[0121] Among them, ∈ abs ≥0 means absolute tolerance, ∈ rel ≥0 indicates relative tolerance, coefficient Indicates the dimension of the corresponding vector.

[0122] Various embodiments of the method described above in the present invention can be implemented in digital electronic circuit systems, integrated circuit systems, field programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), application specific standard products (ASSPs), systems on chips (SOCs), load programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various embodiments may include: being implemented in one or more computer programs, which may be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general programmable processor, which may receive data and instructions from a storage system, at least one input device, and at least one output device, and transmit data and instructions to the storage system, the at least one input device, and the at least one output device.

[0123] It should be understood that the various forms of processes shown above can be used to reorder, add or delete steps. For example, the steps recorded in the present disclosure can be executed in parallel, sequentially or in different orders, as long as the desired results of the technical solution disclosed in the present invention can be achieved, and this document is not limited here.

[0124] Example

[0125] Example 1

[0126] In the simulation experiment, each UAV in the cluster is set to fly at a constant speed in a two-dimensional plane. The kinematic model of each UAV is expressed as:

[0127]

[0128]

[0129]

[0130] [x i ,y i ,θ i ] T is the state variable of a single drone, [x i ,y i ] T represents the coordinates of the i-th UAV, θ i is the flight heading angle. The flight speed of the drone in the horizontal plane is set to a fixed value V. The drone is controlled by adjusting the turning angular velocity of the heading angle. Since the turning angular velocity of the drone is limited by physical constraints, the turning angular velocity ω i The range is set to |ω i |≤ω max , where ω max is a positive constant. In addition, min ≤t N ≤t max Set as the flight time limit for each drone.

[0131] The cluster should approach the desired terminal state while respecting the following different constraints. To this end, the quadratic cost function J for all the drones in the cluster is i (X i ,U i ) is calculated as:

[0132]

[0133] In the formula, represents the expected terminal state vector of the ith UAV, R i and is the weighted diagonal matrix of the cost function; Path constraint: obstacles in the environment during flight are regarded as circular no-fly zones, that is:

[0134]

[0135] In the formula, [x o ,y o ] T represents the center coordinate of the obstacle area, r ois the radius, and the minimum safe distance o∈O that each agent needs to maintain from the obstacle is denoted by d o , the set of obstacles in the environment is represented as O; constraints between agents: each drone in the cluster needs to maintain a safe distance from neighboring drones to avoid collision. And due to the physical limitations of the communication equipment, it also needs to maintain a certain distance from its neighbors to maintain the smooth communication link. Therefore, these constraints can be described as:

[0136] (x i,k -x j,k ) 2 +(y i,k -y j,k ) 2 ≤d col

[0137] (x i,k -x j,k ) 2 +(y i,k -y j,k ) 2 ≥d con

[0138] Where, d col Indicates the safety distance, d con Represents the maximum effective communication distance between two drones; Terminal timing constraint: It is assumed that the drones arrive at the target in sequence within the specified time interval. This constraint can be expressed mathematically as:

[0139]

[0140] In the formula, is the time interval vector, the matrix A i Represents the time series relationship between agent i and its neighbors:

[0141]

[0142] In the formula, A i The jth row of represents the temporal relationship between drone i and its neighbor j, corresponding to The j-th row of represents the preset time interval between i and j.

[0143] In the simulation experiment, the UAV uses the distributed spatiotemporal trajectory optimization framework of the UAV cluster, including:

[0144] Establish optimal control model;

[0145] Solve the optimal control model and obtain the spatiotemporal trajectory of the drone swarm.

[0146] The optimal control model is expressed as:

[0147]

[0148] The spatiotemporal trajectory acquisition process of the drone cluster includes the following steps:

[0149] The solution process consists of the following sub-steps:

[0150] S21. For any UAV, minimize the UAV’s own local variable x i,k 、u i,k ,t i,N The augmented Lagrangian is used to iterate the optimization of the space-time trajectory of a single UAV;

[0151] S22, for any UAV, iterating the constraint conditions of the UAV itself;

[0152] S23, each UAV communicates with all its neighboring UAVs, obtains trajectory optimization iteration results and constraint condition iteration results of its neighboring UAVs, and obtains global variables;

[0153] S24. Obtain the optimal spatiotemporal trajectory of the UAV by optimizing global variables.

[0154] In S21, the parameterized differential dynamic programming method is used to minimize the augmented Lagrangian and perform iterative optimization of the spatiotemporal trajectory of a single UAV. In the parameterized differential dynamic programming method, the action value function is modified to convert the action value function Q(x i,k ,u i,k θ i ) is modified to:

[0155]

[0156] In the parametric differential dynamic programming method, the value function V(x i,N ,t i,N ) and its derivatives are obtained by the following formula:

[0157]

[0158] In the parameterized differential dynamic programming method, control constraints are also set:

[0159]

[0160] A final time update constraint is also set, expressed as:

[0161]

[0162] In S22, the alternating direction multiplier method (ADMM) is used to iterate the constraints of the UAV itself. Specifically, the update rule is set as:

[0163]

[0164] In S23, the global variable is represented as:

[0165]

[0166] In S24, the update rule of the global variables is set as:

[0167]

[0168]

[0169] Here, the superscript n indicates the nth iteration.

[0170] Set the dual update to:

[0171]

[0172] Table 1 gives the conditions for the parameters of the cost function:

[0173] Table 1 Initial conditions and aerodynamics

[0174]

[0175]

[0176] During the simulation, a scenario of five drones continuously intercepting each other is set. The five drones intercept different targets in the same area from different directions, and there are position and flight path angle constraints. In addition, the drone cluster needs to intercept the target within a certain time interval. The initial time of all drones is set to 9.0s, and the collision time of all drones meets the equal interval. Constraints, the slack variables are set to 0.01s for all drones, and the neighborhood size of each drone is set to The rest of the simulation conditions are shown in Table 2.

[0177] Table 2 Initial conditions

[0178]

[0179]

[0180] The optimization results of the drone cluster are as follows: Figure 2-Figure 3 shown.

[0181] Figure 2 The dotted line represents the initial trajectory of the drone, and the solid line represents the planned trajectory of the drone after iteration. Figure 2It can be seen that the trajectories of UAV 2 and UAV 4 change from trajectories that do not meet the constraints to trajectories that avoid obstacles, and the trajectory of UAV 5 is more curved compared to the initial trajectory to meet the timing constraints.

[0182] Figure 3 The relationship between the number of iterations and the flight time of the UAV is shown in Figure 2. Figure 3 It can be seen that the flight time of the five UAVs is optimized from 9.0s with the same initial setting to 9.12s, 9.22s, 9.32s, 9.42s, and 9.53s, satisfying the continuous interception constraint of 0.1s time interval between two UAVs.

[0183] from Figure 2-3 It can be seen that this method can complete the trajectory optimization task of a UAV cluster with timing constraints through distributed spatiotemporal joint optimization, so that it can avoid obstacles and meet the avoidance constraints between UAVs, while optimizing its own flight time.

[0184] The present invention has been described above in conjunction with preferred embodiments, but these embodiments are only exemplary and serve only as an illustration. On this basis, the present invention may be subjected to a variety of substitutions and improvements, all of which fall within the scope of protection of the present invention.

Claims

1. A distributed spatiotemporal trajectory optimization framework for drone swarms, characterized by: By establishing and solving the optimal control model, the spatiotemporal trajectory of the UAV cluster is obtained, and the UAVs fly according to the obtained spatiotemporal trajectory.

2. The distributed spatiotemporal trajectory optimization framework for drone swarms according to claim 1 is characterized in that: The optimal control model is expressed as: s.t.x i，k+1 =f i (x i，k ,u i，k ) Among them, i represents the number of different drones in the drone cluster, N represents the total time, represents the minimum value of the control input of UAV i at all times, represents the final flight time of drone i, t i，N represents the flight time of drone i, X i Represents the stack of state vectors of drone i at all times, U i represents the stack of control inputs of drone i at all times, J i (X i , U i ) represents the local objective function of the i-th UAV, st represents the constraint condition, x i，k represents the state vector of the i-th UAV at time k, u i，k represents the control vector of the ith UAV at time k, fi() represents the discrete system dynamics with nonlinear characteristics, For x i，k A safe copy variable, a i，k () is a nonlinear function used to describe path constraints, for u i，k A safe copy variable, b i，k () represents the control torque constraint function, t i，N A safe copy variable, c i，N () represents a nonlinear function, represents the set of state vectors of all neighboring drones of drone i at time k, represents the set of state constants between UAV i and its neighboring UAVs at time k, represents the set of time variables of all neighboring drones of drone i at time k, represents the set of time constraints between UAV i and its neighboring UAVs at time k, represents the set of state variables that have reached consensus, A collection of variables representing the time at which consensus is reached.

3. The distributed spatiotemporal trajectory optimization framework for drone swarms according to claim 1 is characterized in that: The solution process consists of the following sub-steps: S21. For any UAV, minimize the UAV’s own local variable x i，k 、u i，k ,t i，N The augmented Lagrangian is used to iterate the optimization of the space-time trajectory of a single UAV; S22, for any UAV, iterating the constraint conditions of the UAV itself; S23, each UAV communicates with all its neighboring UAVs, obtains trajectory optimization iteration results and constraint condition iteration results of its neighboring UAVs, and obtains global variables; S24. Obtain the optimal spatiotemporal trajectory of the UAV by optimizing global variables.

4. The distributed spatiotemporal trajectory optimization framework for drone swarms according to claim 3 is characterized in that: The parameterized differential dynamic programming method is used to minimize the augmented Lagrangian and perform iterative optimization of the spatiotemporal trajectory of a single UAV.

5. The distributed spatiotemporal trajectory optimization framework for drone swarms according to claim 4 is characterized in that: In the parameterized differential dynamic programming method, the action value function is modified to change the action value function Q(x i,k ,u i,k θ i ) is modified to: in, represents the action value function Q at time k for x i The derivative of It represents the running cost function l for x at time k i The derivative of represents the dynamic function f at time k to x i The derivative of It represents the value function V for x at time k+1 i The derivative of represents the action value function Q at time k for u i The derivative of It represents the running cost function l for u at time k i The derivative of represents the dynamic function f at time k on u i The derivative of represents the action value function Q at time k for θ i The derivative of It represents the operating cost function l at time k for θ i The derivative of It represents the value function V for θ at time k+1 i The derivative of represents the dynamic function f at time k on θ i The derivative of represents the action value function Q at time k for x i x i The derivative of It represents the running cost function l for x at time k i x i The derivative of It represents the value function V for x at time k+1 i x i The derivative of , I represents the identity matrix, represents the action value function Q at time k for u i u i The derivative of It represents the running cost function l for u at time k i u i The derivative of represents the action value function Q at time k for θ i θ i The derivative of It represents the operating cost function l at time k for θ i θ i The derivative of It represents the value function V for θ at time k+1 i θ i The derivative of It represents the value function V for x at time k+1 i θ i The derivative of represents the action value function Q at time k for x i u i The derivative of It represents the running cost function l for x at time k i u i The derivative of represents the action value function Q at time k for u i x i The derivative of represents the action value function Q at time k for x i θ i The derivative of It represents the running cost function l for x at time k i θ i The derivative of represents the action value function Q at time k for θ i x i The derivative of represents the action value function Q at time k for u i θ i The derivative of It represents the running cost function l for u at time k i θ i The derivative of represents the action value function Q at time k for θ i u i The derivative of .

6. The distributed spatiotemporal trajectory optimization framework for drone swarms according to claim 4 is characterized in that: In the parametric differential dynamic programming method, the value function V(x i,N , t i，N ) and its derivatives are obtained by the following formula: Among them, V xi，N Represents the value function V for x at time N i The derivative of It represents the terminal cost function φ for x at time N i The derivative of Represents the value function V at time N for θ i The derivative of It represents the terminal cost function φ on θ at time N i The derivative of Represents the value function V for x at time N i x i The derivative of It represents the terminal cost function φ for x at time N i x i The derivative of Indicates p i The unit matrix, Represents the value function V for x at time N i θ i The derivative of It represents the terminal cost function φ for x at time N i θ i The derivative of Represents the value function V at time N for θ i x i The derivative of Represents the value function V at time N for θ i θ i The derivative of It represents the terminal cost function φ on θ at time N i θ i The derivative of 1×1 represents the 1st-order identity matrix.

7. The distributed spatiotemporal trajectory optimization framework for drone swarms according to claim 4 is characterized in that: In the parameterized differential dynamic programming method, the last time update constraint is set, which is expressed as: in, represents the final flight time of each drone i, t min represents the lower bound of the final time, t max Represents the upper bound of the final time.

8. The distributed spatiotemporal trajectory optimization framework for drone swarms according to claim 4 is characterized in that: In S22, the alternating direction multiplier method is used to iterate the constraints of the UAV itself, and the update rule is set as:

9. The distributed spatiotemporal trajectory optimization framework for drone swarms according to claim 4 is characterized in that: In S23, the global variable is represented as: in, represents the set of drones j that consider drone i as their neighbors, represents the state variable of drone i observed by neighbor drone j, represents the flight time of UAV i observed by neighbor UAV j.

10. The distributed spatiotemporal trajectory optimization framework for drone swarms according to claim 7, characterized in that: In S24, the update rule of the global variables is set as: Here, the superscript n indicates the nth iteration.

Images