A parafoil UAV trajectory optimization method based on differential evolution

Abstract

The present invention discloses a parafoil UAV trajectory optimization method based on differential evolution improvement, comprising: establishing a reduced-order particle model of the parafoil in a wind-fixed coordinate system and a model of mountain obstacles in the parafoil flight area; determining the initial state of the parafoil and the expected state of landing, determining the position (x0, y0, h0) and heading angle ψ0 of the parafoil at the initial time t0 of airdrop, and the landing time t f The expected position (x f ,y f ,h f ) and the desired heading angle ψ f , the maximum downward pull of the parafoil control rope u max ; Establish the objective function of parafoil trajectory planning; divide the parafoil flight time interval; use the improved differential evolution algorithm to solve the optimal heading angle and optimal trajectory of the parafoil in each time period. The planned trajectory obtained by the trajectory optimization method of the present invention has an accurate landing point position, headwind landing, low trajectory energy consumption, a small change in the control amount when the parafoil returns, provides control amount redundancy, and a smooth trajectory for easy tracking.

Description

Technical Field

[0001] The invention relates to the fields of image processing, trajectory planning and machine learning, and in particular to a parafoil UAV trajectory optimization method based on differential evolution improvement. Background Art

[0002] The parafoil is a flexible aircraft made of textile materials. After the parachute is opened, air enters the air chamber through the incision on the leading edge of the parafoil, forming stagnation pressure in the air chamber, which enables the parafoil to maintain a relatively stable wing shape and generate lift and drag. Therefore, the parafoil has a high lift-to-drag ratio, excellent gliding performance and controllability. Pulling the trailing edge of the canopy can adjust the parafoil's flight direction and speed, achieving precise landing, overcoming the shortcomings of traditional circular parachutes that the flight trajectory drifts with the wind and the landing points are widely scattered. At the same time, the parafoil can land non-destructively in a bird-like manner when landing, and has broad application prospects in the fields of precise airdrop of battlefield supplies, precise airdrop of natural disaster relief supplies, and spacecraft recovery.

[0003] Planning a suitable homing trajectory for the parafoil is one of the prerequisites for achieving accurate airdrops. It largely determines the landing accuracy and homing control method of the parafoil. Only on the basis of a suitable planned trajectory can a suitable trajectory tracking controller be designed. Therefore, trajectory planning is of great significance for achieving accurate parafoil airdrops. Parafoil trajectory planning refers to planning a homing trajectory from the initial airdrop point to the target point that meets specific performance indicators based on the parafoil dynamic constraints. Early homing was mainly radial homing and conical homing. Due to its low homing accuracy, it is now less used. The main parafoil trajectory planning methods are the optimal control homing method and the segmented homing method.

[0004] The most similar invention "CN 103529851 A" "A subdivided and segmented parafoil homing control method" discloses a method of subdividing the segmented homing method, focusing on rationally planning the homing path of the low-altitude parafoil according to the real-time altitude, position and other information of the airdrop system, formulating corresponding control strategies, and reducing the adverse effects of environmental factors such as low-altitude wind on the system control accuracy.

[0005] "CN 111897362 A" "A method for combined trajectory planning of parafoils in complex environments" discloses a method for combined trajectory planning of parafoils in complex environments, which divides the parafoil airdrop area into an obstacle area with obstacles and a circular landing area with the target point as the center and which is open and flat; a fast search random tree path planning algorithm is used in the obstacle area to quickly search for feasible trajectories, and the termination condition of the search is that the horizontal distance between the position to which the path extends and the target landing point is less than or equal to the radius of the circular landing area, and only obstacle avoidance tasks are considered in the obstacle area; the termination state of the trajectory search in the obstacle area is used as the initial state of the trajectory planning in the circular landing area, and a segmented homing planning design is used in the circular landing area to complete the parafoil height control and headwind alignment tasks.

[0006] "CN 115964895 A" "A state estimation method, device, computer equipment and storage medium for parafoil trajectory reconstruction" discloses a trajectory planning reconstruction method: obtaining the parafoil process equation and the parafoil observation data, obtaining the parafoil observation equation, and obtaining the linear Kalman state transfer equation to obtain the prior estimation and the posterior estimation equation; according to the linear Kalman state transfer equation, the prior estimation and the posterior estimation equation, the prior state error and the posterior state error are obtained, and the Kalman gain equation is obtained; the error covariance matrix and the prior error covariance matrix are defined, the Kalman gain equation is solved, and the Kalman gain and the undetermined coefficient matrix of the Kalman gain equation are obtained; according to the posterior estimation equation, the Kalman gain and the undetermined coefficient matrix, the state reconstruction result of the parafoil state is obtained. The trajectory reconstruction and planning are completed.

[0007] The optimization function of the segmented return algorithm generally does not include energy consumption indicators, so the segmented return method does not have an advantage in terms of energy consumption. In addition, the obtained track contains multiple transitional turning sections with the smallest radius. At this time, the control rope needs to be suddenly pulled down to the maximum amount, and then restored to a smaller control amount in a short time, which puts higher requirements on the actual control of the parafoil. The above technology does not consider the requirements of headwind landing and low track energy consumption in the parafoil track planning, making it difficult to implement in engineering. Even if the goal of precise landing against the wind can be achieved, the control energy consumption is relatively large. Summary of the invention

[0008] Purpose of the invention: In order to overcome the shortcomings of the above-mentioned prior art, the present invention proposes a parafoil UAV trajectory optimization method based on differential evolution improvement; the planned trajectory obtained by this method has an accurate landing point position, headwind landing, low trajectory energy consumption, and can bypass obstacles such as mountains. At the same time, the control amount change amplitude of the parafoil when returning is small, which provides control amount redundancy for the system, and the trajectory is smooth and easy to track.

[0009] Technical solution: The improved parafoil UAV trajectory optimization method based on differential evolution of the present invention comprises the following steps:

[0010] (1) Establish a reduced-order particle model of the parafoil in a wind-fixed coordinate system:

[0011]

[0012] Where: x, y, h are the position components of the parafoil in the wind-fixed coordinate system; in the three-dimensional space coordinate system: u s is the horizontal speed of the parafoil; u z is the vertical velocity; ψ is the heading angle, which belongs to the xy plane in the three-dimensional space coordinate system; the position component of x is the cosine value of the heading angle ψ in the horizontal xy plane and the horizontal velocity u s The position component y is the sine value of the heading angle ψ in the horizontal xy plane and the horizontal velocity u s product of; speed is the heading angular rate; u is the control value corresponding to the asymmetric downward deflection of the parafoil;

[0013] (2) Establish a model of mountain obstacles in the parafoil flight area:

[0014]

[0015] Where h(x,y) is the height of the mountain obstacle at the horizontal coordinate (x,y); m is the number of mountain obstacles in the parafoil flight area, and h i is the peak height of the i-th mountain obstacle, (x 0i ,y 0i ) is the center coordinate of the ith mountain obstacle, x si is the slope related quantity of the ith mountain obstacle along the x-axis, y si is the slope-related quantity of the ith mountain obstacle along the y-axis; in the trajectory planning process, the corresponding h(x, y) is used at time t through Get the radius value of the current parafoil position from the i-th mountain.

[0016] (3) Determine the initial state of the parafoil and the desired state of landing, and then determine the position (x0, y0, h0) and heading angle ψ0 of the parafoil at the initial time t0 of the airdrop, and the parafoil position at the landing time t f The expected position (x f ,y f ,h f ) and the desired heading angle ψ f , the maximum downward pull of the parafoil control rope u max ; The above expected position is determined in the three-dimensional coordinate system as (x f ,yf ,h f )=(0,0,0), the desired heading angle is ψ f =π or -π satisfies headwind landing to reduce landing impact.

[0017] (4) Establish the objective function of parafoil trajectory planning: J = f1J1+f2J2+f3J3+f4J4;

[0018] Where J1=(x(t f )-x f ) 2 +(y(t f )-y f ) 2 is the horizontal position error index of the landing point; J2 = cos(ψ(t f ))+1, is the landing point heading error indicator; To control energy consumption indicators; is the safety obstacle avoidance index; f1, f2, f3 and f4 are weighting factors; x(t f ) is the horizontal x-coordinate of the parafoil on the planned flight path at the time of landing, y(t f ) is the horizontal y-direction coordinate of the parafoil on the planned flight path at the time of landing, ψ(t f ) is the heading angle of the parafoil on the planned flight path at the time of landing. Among them, d i (t) is the distance between the parafoil and the obstacle surface of the ith mountain at time t; R safe It is the preset safe distance between the parafoil and the mountain obstacle surface.

[0019] (5) Divide the flight time intervals of the parafoil;

[0020] (6) The improved differential evolution algorithm is used to solve the optimal heading angle of the parafoil in each time period. First, a population of size N is obtained by randomly initializing u(t). The output population of the current generation is obtained through mutation and crossover operations. Finally, the optimal solution in the population is obtained through selection operations, that is, the heading angle x of the six time intervals corresponding to the optimal planning trajectory. G,best From the reduced-order particle model, we can get x=u s *cosψ, where ψ represents x G,best The heading angle of a certain period of time in the , and x(t) = x(t-1) + x, when t is 1, x(t) represents the x value x0 of the set starting position, and the x(t) in the optimal track is derived. The reduced-order particle model shows that y = u s *sinψ, where ψ represents x G,bestThe heading angle of a certain period of time, and y(t) = y(t-1) + y, when t is 1, y(t) represents the y value y0 of the set starting position, and y(t) in the optimal track is derived; from the reduced-order particle model, h = u z And h(t)=h(t-1)-h. Since the parafoil homing is a descending process, the unit displacement value in the vertical direction is negative. When t is 1, h(t) represents the h value h0 of the set starting position, and then h(t) in the optimal track is derived. Finally, the optimal track path(t)=(x(t),y(t),h(t)),t∈[t0,t f ]. Among them, t f is the set starting height h and vertical descent speed u z x(t) is the position information of the parafoil flying along the x-axis in three-dimensional space, y(t) is the position information of the parafoil flying along the y-axis in three-dimensional space, and h(t) is the position information of the parafoil flying along the z-axis in three-dimensional space. The three types of position information are combined to form a complete trajectory operation process.

[0021] In step (5), the parafoil flight period [t0, t f ] is divided into n adjacent time intervals, and u(t) takes a constant value in each sub-interval to control the parafoil.

[0022] In step (6), the process of using the improved differential evolution algorithm is as follows:

[0023] (6.1) In the first iteration of the improved differential evolution algorithm, N individuals X representing six time intervals are generated by a random generator. j i,0 The expression is as follows:

[0024]

[0025] Among them, rand(0,1) represents a random number between 0 and 1, x j max Represents the maximum boundary value of the heading angle, x j min Represents the minimum boundary value of the heading angle, thereby generating a random heading angle within the set range.

[0026] (6.2) In the first generation of the improved differential evolution algorithm, the population N is divided into three parts, and mutation is performed using the three mutation operators "DE / rand / 1", "DE / best / 1" and "DE / rand-to-best / 1". In the other iterations of the algorithm, the mutation strategy of the current generation is constructed, and the optimal solution X of the parent generation target vector is selected. best,gThe mutation operator used constructs the mutation strategy, that is, 2 / 3 of the individuals in the population are assigned the same mutation operator as the optimal solution, and the remaining individuals are randomly divided into two parts and assigned the remaining two mutation operators.

[0027] (6.3) Adopting the adaptive crossover strategy, the population obtained in step (6.2) is adaptively crossovered according to the following formula:

[0028]

[0029] Among them, u j i,g =Ξu j-1 i,g It means that the j-th dimension is crossed in the same way as the j-1-th dimension. p is the dynamic crossover length and its initial value is set to 0.

[0030] (6.4) The obtained u j i,g Compared with the first generation X j i,0 Substitute the value into the parafoil's objective function for track comparison. The smaller the value, the better the obstacle avoidance effect and the lower the energy consumption. Finally, find the N individuals with the best effect in the two populations to form a new population.

[0031] (6.5) If the current iteration does not reach the termination condition G max , then substitute the new population into step (6.2) to continue iterative optimization. If the termination condition is reached, stop the iteration and output the optimal solution.

[0032] In step (6.3), if the dynamic continuous crossover length p≠0, continuous crossover is performed.

[0033] In step (6.3), during the crossover process, when the test vector U i,g From the target vector X i,g When getting an element, p is set to:

[0034]

[0035] When the test vector U i,g From the mutation vector V i,g When getting an element, p is set to:

[0036]

[0037] Where A represents the event used for judgment in the Bernoulli trial, the number n in A(n) represents the probability of success of the event is 1 / 3, 1 / 2 or 1 / 3, and p represents the cumulative length from the segment where event A succeeds to the segment where event A fails. A(n) refers to A(1 / 3), A(1 / 2) and A(2 / 3) in the formula.

[0038] From the reduced-order particle model, we can get x = u s *cosψ, where ψ represents x G,best The heading angle in a certain time period, x(t)=x(t-1)+x, when t is 1, x(t) represents the x value x0 of the set starting position, and then the x(t) in the optimal track is derived.

[0039] In step (6), the following difference strategy is used for differential mutation:

[0040] DE / rand / 1: V i,g =X r1,g +F×(X r2,g -X r3,g )

[0041] Among them, r1, r2, r3 represent mutually exclusive integers randomly generated in the range [1, N]; F∈[0,1] is the mutation factor; X best,g is the individual vector with the best fitness value in the g-th generation population; K is a random number in the range of [0,1].

[0042] In step (6), the following difference strategy is used for differential mutation:

[0043] DE / best / 1: V i,g =X best,g +F×(X r1,g -X r3,g )

[0044] V i,g =X best,g +F×(X r1,g -X r3,g )

[0045] Among them, r1, r2, r3 represent mutually exclusive integers randomly generated in the range [1, N]; F∈[0,1] is the mutation factor; X best,g is the individual vector with the best fitness value in the g-th generation population; K is a random number in the range of [0,1].

[0046] In step (6), the following difference strategy is used for differential mutation:

[0047] DE / rand-to-best / 1: V i,g =X i,g +K×(X best,g -X i,g )+F×(X r1,g -X r2,g )

[0048] Among them, r1, r2, r3 represent mutually exclusive integers randomly generated in the range [1, N]; F∈[0,1] is the mutation factor; X best,g is the individual vector with the best fitness value in the g-th generation population; K is a random number in the range of [0,1].

[0049] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0050] (1) The present invention parameterizes the heading angle in the optimization process into a series of piecewise constants while taking into account the initial value constraints of the parafoil, the final end point headwind precise landing constraints, the control constraints and the obstacle avoidance constraints. Under the constraints of the reduced-order particle model, the mutation strategy of the current generation is constructed by adopting the mutation strategy of the optimal solution of the parent generation, thereby achieving a balance between global exploration and local development.

[0051] (2) The present invention uses an improved differential evolution method to optimize the weighted and minimum control quantities of the horizontal position error of the parafoil, the heading error of the landing point, the control energy consumption, and the safe obstacle avoidance error, thereby obtaining a planned track. The planned track obtained by the present invention meets the requirements of precise and headwind landing, and achieves detour around obstacles. At the same time, the track energy consumption is lower. The control quantity is composed of the heading angles of six time intervals, which simplifies the control of the parafoil when returning to the home position. At the same time, the value of the control quantity varies within a small range, providing the system with control quantity redundancy, which is beneficial to the deviation correction during track tracking control. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 This is a flow chart of the improved differential evolution algorithm used in the present invention;

[0053] Figure 2 This is a diagram showing the effect of the variation strategy improvement adopted by the present invention;

[0054] Figure 3 This is a diagram showing the improvement effect of the crossover strategy in the front, middle and back periods of the present invention;

[0055] Figure 4 A three-dimensional graph comparing the trajectory of the flight path planning of the present invention;

[0056] Figure 5 This is a comparison chart of the fitness values ​​of the optimal trajectory for the track planning of the present invention;

[0057] Figure 6 It is a box plot comparing the fitness values ​​of the optimal trajectory for the track planning of the present invention. DETAILED DESCRIPTION

[0058] like Figure 1As shown, when the present invention adopts the improved differential evolution algorithm, the parent population is generated by random generation, and different mutation and crossover operations are adopted in different iteration generations, so that the global exploration requirements are better met in the early stage, the requirements of more balanced global exploration and convergence ability are met in the middle stage, and the requirements of better convergence ability are met in the later stage of the algorithm. Finally, the optimal population is obtained through selection.

[0059] like Figure 2 As shown, in the early stage of the improved differential evolution algorithm, 2 / 3 of the population individuals use the "DE / rand / 1" formula to mutate to meet the needs of global exploration. In the middle stage, the "DE / rand-to-best / 1" formula is used to mutate to meet the needs of global exploration and convergence ability. In the later stage, the "DE / best / 1" formula is used for mutation operator mutation to meet the needs of convergence ability in the later stage of the algorithm, so as to obtain the optimal trajectory.

[0060] The improved parafoil UAV trajectory optimization method based on differential evolution of the present invention comprises the following steps:

[0061] (1) Establish a reduced-order particle model of the parafoil in a wind-fixed coordinate system:

[0062]

[0063] Where: x, y, h are the position components of the parafoil in the wind-fixed coordinate system; in the three-dimensional space coordinate system: u s is the horizontal speed of the parafoil; u z is the vertical velocity; ψ is the heading angle, which belongs to the xy plane in the three-dimensional space coordinate system; the position component of x is the cosine value of the heading angle ψ in the horizontal xy plane and the horizontal velocity u s The position component y is the sine value of the heading angle ψ in the horizontal xy plane and the horizontal velocity u s Product of. Speed is the heading angular rate; u is the control quantity corresponding to the asymmetric downward deflection of the parafoil.

[0064] (2) Establish a model of mountain obstacles in the parafoil flight area:

[0065] In battlefield environments or complex terrain conditions, there are enemy fire or mountain obstacles in the parafoil flight area, so these obstacles are bypassed when planning the flight path. The present invention uniformly models mountain obstacles or local fire threats as the following mountain obstacles:

[0066]

[0067] Where h(x,y) is the height of the mountain obstacle at the horizontal coordinate (x,y); m is the number of mountain obstacles in the parafoil flight area, and hi is the peak height of the i-th mountain obstacle, (x 0i ,y 0i ) is the center coordinate of the ith mountain obstacle, x si is the slope related quantity of the ith mountain obstacle along the x-axis, y si is the slope related quantity of the ith mountain obstacle along the y-axis direction; during the parafoil descent, the parafoil flight height h(t) decreases with time t, and the mountain radius increases accordingly. To simplify the calculation, it is assumed that the slope of each mountain obstacle along the two axes is the same, that is, x si =y si , and then find the radius of the i-th peak at the parafoil flight height h(t) at time t:

[0068]

[0069] Where H represents the parafoil altitude at the current moment.

[0070] (3) Determine the initial state of the parafoil and the expected landing state, which is used to determine the position (x0, y0, h0) and heading angle ψ0 of the parafoil at the initial time t0 of the airdrop, and the parafoil at the landing time t f The expected position (x f ,y f ,h f ) and the desired heading angle ψ f , the maximum downward pull of the parafoil control rope u max .

[0071] Determine the desired landing position of the parafoil, and the desired heading angle ψf of the parafoil meets the requirements for headwind landing, that is, ψ f is the opposite direction of the wind direction at the landing target point. Assuming that the wind direction at the landing point is consistent with the positive direction of the X-axis, that is, ψ f =180°, or ψf = -180°, then the headwind landing condition is converted to cosψ f =-1, at this time, if the control ropes on both sides of the parafoil are pulled down quickly, the parafoil can be dropped against the wind.

[0072] (4) Establish the objective function of parafoil trajectory planning: J = f1J1+f2J2+f3J3+f4J4;

[0073] Where J1=(x(t f )-x f ) 2 +(y(t f )-y f ) 2 , is the landing point horizontal position error index J2 = cos(ψ(t f ))+1, is the landing point heading error indicator; To control energy consumption indicators; is the safety obstacle avoidance index; f1, f2, f3 and f4 are weighting factors; x(t f ) is the horizontal x-coordinate of the parafoil on the planned flight path at the time of landing, y(t f ) is the horizontal y-direction coordinate of the parafoil on the planned flight path at the time of landing, ψ(t f ) is the heading angle of the parafoil on the planned flight path at the time of landing. Among them, d i (t) is the distance between the parafoil and the obstacle surface of the ith mountain at time t; R safe It is the preset safe distance between the parafoil and the mountain obstacle surface.

[0074] (5) The parafoil flight time interval is divided into the parafoil flight time interval [t0, t f ] is divided into 6 adjacent intervals, and u(t) takes a constant value in each sub-interval to control the parafoil.

[0075] (6) Perform trajectory optimization: set the maximum number of iterations G, the population size NP, set the dimension to the flight interval n, the scale factor F, F∈[0,1] controls the degree of mutation, and evenly distribute the same number of populations to perform the three mutation processes of "DE / rand / 1", "DE / best / 1" and "DE / rand-to-best / 1";

[0076] The mutated population is used to calculate the objective function. Each individual has n dimensions representing n time zones. If the heading angle is <-π at a certain moment, 2π is added. If it is >π, 2π is subtracted to complete the angle correction.

[0077] If the optimal solution of the current parent population is derived from the mutation of "DE / rand / 1", 2 / 3NP individuals of this population are allocated and 1 / 6 individuals of the remaining population are allocated, and it is called the main population.

[0078] The probability of a Bernoulli event during the crossover process is p, the main population is assigned the largest p, and the other two populations are assigned smaller p.

[0079] Determine whether the maximum number of iterations has been reached. If the current number of iterations is g≤G, continue iterating. If the current number of iterations is g>G, stop the loop and output the optimal solution x that minimizes J. G,best .x G,best A six-dimensional vector consisting of six heading angles in six time periods in step (5).

[0080] Example: The present invention compares the improved differential evolution algorithm ADE-PC with the Gaussian pseudo-spectral method, the segmented return method, the trajectory planning method in a complex environment, and the trajectory reconstruction method. The initial point position of the parafoil airdrop is set to (1500, 1000, 2000), the expected horizontal position of the landing point is (0, 0), the speed of the parafoil is set to v = 10m / s, and the initial heading angle is set to 45°. Then v is decomposed into the horizontal speed vs = 9.5m / s, the vertical speed vz = 3.1m / s, the glide ratio is about 3.1, and u max =0.18. In this embodiment, the influence of the constant wind is regarded as the initial position offset of the airdrop, and the flight period [t0,t f ] is set to 6 segments, △σk=0.002, learning rate λ is set to 0.01, maximum number of iterations is set to 6000, and objective function coefficients f1, f2 and f3 are set to 0.01, 16 and 4 respectively.

[0081] The improvement effect of the cross strategy in the early, middle and late periods is as follows Figure 3 As shown. Figure 3 It can be seen that in the early stage of crossover, the population tends to obtain crossover information from the parent individuals, which meets the requirements of the algorithm for global optimization in the early stage. In the middle stage of the algorithm, the population evenly obtains mutation information from the parent and mutant populations, which meets the requirements of the algorithm for global optimization and rapid convergence in the middle stage. In the late stage of the algorithm, the population prefers to obtain genetic information from the mutant population, which meets the requirements of the algorithm for rapid convergence to the optimal solution in the late stage.

[0082] The trajectory planning results are as follows: Figure 4 As shown. Figure 4 It can be seen that the Gaussian pseudospectral method, the segmented return method, the trajectory planning method and the trajectory reconstruction method in complex environments, and the improved differential evolution algorithm ADE-PC of the present invention can all plan feasible trajectories for the parafoil. Starting from the same initial point, the five methods can reach the same target point through different trajectories, and at the same time meet the requirements of precise landing against the wind.

[0083] In the Gaussian pseudo-spectral method and the track reconstruction method, the parafoil reaches the landing point through two large loops, resulting in a large energy consumption. In the segmented homing track and the track planning method in a complex environment, the parafoil passes through the target approach segment, the energy control segment and the headwind landing segment to reach the target point, but the offset is defective. In the planned track of the improved differential evolution algorithm ADE-PC in this embodiment, the parafoil consumes altitude through a roundabout turn with a smaller radius and then lands at the target point. The offset and energy consumption are better than the other comparison methods. The planned target point position is (2.17e-12, 5.02e-13), achieving accurate homing.

[0084] from Figure 5It can be seen that the improved differential evolution algorithm ADE-PC has a greater advantage in finding the optimal planning trajectory than the other four methods, showing that the improved differential evolution algorithm plays a role in the problems of terminal headwind precision landing constraints, control constraints and obstacle avoidance constraints.

[0085] from Figure 6 It can be seen that the improved differential evolution algorithm ADE-PC has stronger optimization ability in different iterative generations than the other four methods, avoiding the dilemma of falling into local optimality and having strong convergence.

Claims

1. A parafoil UAV trajectory optimization method based on differential evolution, characterized in that: The following steps are involved: (1) Establish a reduced-order particle model of the parafoil in a wind-fixed coordinate system: Where: x, y, h are the position components of the parafoil in the wind-fixed coordinate system; u s is the horizontal speed of the parafoil; u z is the vertical velocity; ψ is the heading angle; is the heading angular rate; u is the control value corresponding to the asymmetric downward deflection of the parafoil; (2) Establish a model of mountain obstacles in the parafoil flight area: Where h(x,y) is the height of the mountain obstacle at the horizontal coordinate (x,y); m is the number of mountain obstacles in the parafoil flight area, and h i is the peak height of the i-th mountain obstacle, (x 0i ,y 0i ) is the center coordinate of the ith mountain obstacle, x si is the slope related quantity of the ith mountain obstacle along the x-axis, y si is the slope related quantity of the ith mountain obstacle along the y-axis; (3) Determine the initial state of the parafoil and the desired landing state, and then determine the position (x0, y0, h0) and heading angle ψ0 of the parafoil at the initial time t0 of the airdrop, and the parafoil at the landing time t f The expected position (x f ,y f ,h f ) and the desired heading angle ψ f , the maximum downward pull of the parafoil control rope u max ; (4) Establish the objective function of parafoil trajectory planning: J = f1J1+f2J2+f3J3+f4J4; Where J1=(x(t f )-x f ) 2 +(y(t f )-y f ) 2 is the horizontal position error index of the landing point; J2 = cos(ψ(t f ))+1, is the landing point heading error indicator; To control energy consumption indicators; is the safety obstacle avoidance index; f1, f2, f3 and f4 are weighting factors; x(t f ) is the horizontal x-coordinate of the parafoil on the planned flight path at the time of landing, y(t f ) is the horizontal y-direction coordinate of the parafoil on the planned flight path at the time of landing, ψ(t f ) is the heading angle of the parafoil on the planned flight path at the time of landing; Among them, d i (t) is the distance between the parafoil and the obstacle surface of the ith mountain at time t; R safe The preset safe distance between the parafoil and the mountain obstacle surface; (5) Divide the flight time intervals; (6) The improved differential evolution algorithm is used to solve the optimal heading angle of the parafoil in each time period. First, a population of size N is obtained by randomly initializing u(t). The output population of the current generation is obtained through mutation and crossover. Finally, the optimal solution in the population is obtained, that is, the heading angle x of the time period corresponding to the optimal planning trajectory. G,best , and then derive the optimal path path(t)=(x(t),y(t),h(t)),t∈[t0,t f ]; Step (6) comprises the following steps: (6.1) Generate N individuals X representing six time intervals j i,0 ; The expression is as follows: Where rand(0,1) means randomly generating a number between 0 and 1, x j max Represents the maximum boundary value of the heading angle, x j min Represents the minimum boundary value of the heading angle; (6.2) The population N is randomly divided into three parts and mutation is performed using the mutation operator; (6.3) The population obtained in step (6.2) is subjected to adaptive crossover according to the following formula: Among them, u j i,g =Ξu j-1 i,g Indicates that the j-th dimension is cross-linked in the same way as the j-1-th dimension, p is the dynamic continuous cross-link length, where the initial value is set to 0; If the dynamic continuous crossover length p≠0, continuous crossover is performed; In the crossover process, when the trial vector U i,g From the target vector X i,g When getting an element, p is set to: Among them, A represents the event used for judgment in the Bernoulli trial, and p represents the cumulative length from the segment where event A succeeds to the segment where event A fails; When the test vector U i,g From the mutation vector V i,g When getting an element, p is set to: Among them, A represents the event used for judgment in the Bernoulli trial, and p represents the cumulative length from the segment where event A succeeds to the segment where event A fails; The following difference strategies are used for differential mutation: V i,g =X r1,g +F×(X r2,g -X r3,g ) Among them, r1, r2, r3 represent mutually exclusive integers randomly generated in the range [1, N]; F∈[0,1] is the mutation factor; X best,g is the individual vector with the best fitness value in the g-th generation population; K is a random number in the range of [0,1]; (6.4) The obtained u j i,g Compared with the first generation X j i,0 Substitute it into the parafoil objective function to compare the tracks, and finally find the N individuals with the best effect in the two populations to form a new population; (6.5) If the current iteration does not reach the termination condition G max , then the new population is brought into (6.2) for iterative optimization. If the termination condition is reached, the iteration is stopped and the optimal solution is output.

Images