CN111694375B - Parafoil system track planning method and system, and track tracking control method and system - Google Patents
Parafoil system track planning method and system, and track tracking control method and system Download PDFInfo
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- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
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Abstract
The invention discloses a parafoil system track planning method, which comprises the following steps: 1. establishing a parafoil reduced order particle model under a wind fixed coordinate system; 2. determining the initial moment t of air-drop of a parafoil system0Position and heading angle of, landing time tfDesired position and desired heading angle of, maximum pull-down u of the parafoil steering linemax(ii) a 3. Establishing a target function of a flight path planning of a parafoil system; 4. flying parafoil for a time period t0,tf]Dividing the space into n adjacent spaces, and measuring a constant value in each subinterval to control the parafoil system; 5. solving the optimal control quantity of each interval in the flight period of the parafoil to make the objective function value take the minimum value; 6. and deducing a planned flight path according to the optimal control quantity sequence and the initial state and speed of the parafoil. The planned flight path obtained by the method meets the requirements of accuracy and upwind landing, the energy consumption of the flight path is low, the control of the parafoil during the navigation is simple, the variation amplitude of the control quantity is small, greater control quantity redundancy is provided for the system, the flight path is smooth and reasonable, and the tracking is convenient.
Description
Technical Field
The invention belongs to the technical field of parafoil track planning and tracking control, and particularly relates to a track planning method and system of a parafoil system, and a method and system for tracking and planning a track.
Background
The ram-type parafoil is a flexible aircraft made of textile material, and after parachute opening, air enters an air chamber from a front edge notch of the parafoil, and stagnation pressure is formed in the air chamber, so that the parafoil can keep a stable wing shape and generate lift force and resistance, and the parafoil has high lift-drag ratio and excellent gliding performance and controllability. The flying direction and speed of the parafoil can be adjusted by pulling the rear edge of the canopy, accurate landing is realized, the defects that the flying track of the traditional circular parachute is floated along with wind and the landing point is greatly dispersed are overcome, meanwhile, the parafoil can be landed in a sparrow landing mode in a nondestructive mode, and the parafoil has wide application prospects in the fields of battlefield material accurate airdrop, natural disaster relief material accurate airdrop, spacecraft recovery and the like, and is paid attention by many researchers at home and abroad. The method has the advantages that the planning of the proper homing track for the parafoil system is one of the prerequisites whether the precise air-drop can be realized, the landing precision and the homing control mode of the parafoil are determined to a great extent, and the proper track tracking controller can be designed only on the basis of the proper planned track, so that the track planning has important significance for realizing the precise air-drop of the parafoil.
The parafoil system track planning refers to planning a homing track which is from an initial air drop point to a target point and meets a specific performance index for the parafoil system on the basis of parafoil dynamic constraint. The early homing is mainly radial homing and conical homing, and the homing precision is low, so that the homing is less adopted, and the current main flight path planning method of the parafoil system is an optimal control homing method and a sectional homing method.
The optimal control homing method takes accuracy, safety, small control energy and the like as optimization targets, and a solving algorithm mainly comprises an indirect method and a direct method, wherein the literature: the dynamics and homing scheme research of the parafoil system [ D ] of the national defense science and technology university, 2005, the optimal flight path planning problem of the parafoil system is solved by adopting an indirect method, the optimal control problem is converted into a two-point boundary value problem by utilizing a minimum value principle and then solved, but the method needs to perform forward integration on a state equation and then perform reverse integration on a collaborative equation, and the process is complex. The literature: the method comprises the steps of designing a parafoil system homing track fault-tolerant design [ J ] based on a pseudo-spectrum method, controlling theory and application, 2013(06), 702- & ltSUB & gt 708, the parafoil system complex multi-constraint track planning [ J ] based on a Gaussian pseudo-spectrum method, aviation science report, 2017(03), 220- & ltSUB & gt 230 and the like, solving an optimum control homing track planning problem of the parafoil by using a direct method, mainly converting the optimum control track planning problem into a nonlinear planning problem by using the pseudo-spectrum method, and solving the problem by using a sequence quadratic planning algorithm. The literature: a Multi-object trajectory optimization method of partial base on a partial search algorithm [ C ]//2019Chinese Control Conference (CCC),27-30July 2019 solves a parafoil flight path planning problem by using a pseudospectral method, determines a Pareto optimization point by using a PSO method, and further improves the flight path planning effect. The method is characterized in that the method comprises the following steps of directly utilizing a PSO algorithm to realize the Robust Guidance of the Parafoil, wherein the method is used for solving the problems of the conventional Optimization of the parachute, such as simple weather for Robust Guidance [ C ]//2018AIAA Guidance, Navigation, and Control reference, 8-12 January2018. The literature: designing a homing track of a parafoil system with constraint based on a genetic algorithm [ J ]. school report of the university of the south and the middle (Nature science version), 2017(02), converting an optimal control track planning problem into a parameter optimization problem of a B spline basis function control vertex in 404-410, and then performing target function optimization by adopting intelligent algorithms such as a genetic algorithm or a quantum genetic algorithm. The literature: a sensitivity analysis method [ J ] of the optimal homing trajectory design of the parafoil system comprises the steps of (2015), (08) and (1003) 1011. converting a flight path planning problem into a series of parameter optimization problems by utilizing an optimization algorithm combining control variable parameterization and time scale based on the sensitivity analysis method and then carrying out numerical solution. It should be noted that the optimal control quantity obtained by such optimal control track planning methods is often continuous and is not easy to implement in engineering.
The segmented homing method is practically applied to systems such as X-38 and the like due to simple operation process and strong robustness. The literature is as follows: 11-16, based on genetic algorithm, researches the design problem of the subsection homing track of the parafoil system, the planned track is divided into a target approach section, an energy control section and an upwind landing section, the target approach section and the upwind main section mainly implement gliding movement, and the energy management section mainly implements spiral line descending turning movement. The literature is as follows: a parafoil system segmented homing design and simulation [ J ] space control based on energy constraint, 2011,29(5):43-47 designs a parafoil system segmented homing track based on an improved particle swarm algorithm, and simulation shows that the designed homing track is simple and practical and meets the requirement of drop point precision. Zhengcheng improved genetic algorithm based on IAGA effectively solves the problem of segmented homing trajectory, the proposed algorithm can effectively prevent precocity, the convergence speed is faster, and the planned flight path meets the requirements of fixed point and upwind landing. The homing control [ J ] of the parafoil system in a larger wind field, a control theory and application, 2016(12), 1630 and 1638, optimizes a segmented homing track based on a particle swarm algorithm, corrects the track by adopting an LADRC controller, and a simulation result shows that the homing control can improve the wind resistance and the homing precision. The literature: based on IAFSA, the four-degree-of-freedom parafoil segmented homing design [ J ] fire power and command control, 2017(02):64-68. based on an artificial fish swarm algorithm, parameter optimization is carried out on a segmented track objective function, the proposed algorithm can accelerate the convergence speed of the algorithm, and a planned track meets the requirements of accurate landing point and upwind landing. The objective functions adopted by the segmented homing algorithm are different in size, and the flight path planning problem is converted into an optimization problem of an Entry Point (Entry Point) parameter, although the adopted algorithms have different convergence speeds, the obtained results are approximately the same, and the accurate landing and headwind landing requirements can be met. It should be noted that the optimization function of the segmented homing algorithm generally does not include an energy consumption index, so that the segmented homing method is not superior in energy consumption, and in addition, the obtained flight path includes a plurality of transition turning sections with the minimum radius, the control rope is required to be suddenly pulled down to the maximum amount at the moment, and then is required to be restored to a smaller control amount in a short time, and the higher requirement is provided for the actual control of the parafoil.
Disclosure of Invention
The invention aims to: aiming at the problems in the prior art, the invention provides a flight path planning method of a parafoil system, the planned flight path obtained by the method meets the requirements of accurate and upwind landing, the flight path energy consumption is lower, the parafoil is simple to operate and control during navigation, the variation range of the control quantity is smaller, greater control quantity redundancy is provided for the system, the flight path is smooth and reasonable, and the tracking is convenient.
The technical scheme is as follows: the invention discloses a parafoil system track planning method on one hand, which comprises the following steps:
s11, establishing a parafoil reduced order particle model under a wind fixed coordinate system:
wherein (x, y, h) are the position components of the parafoil system in the horizontal plane x direction, y direction and vertical direction in the wind fixed coordinate system respectively, and vsFor horizontal direction velocity, v, of parafoil systemszIs the vertical direction velocity, psi is the heading angle,
is the course angular rate, u is the control quantity corresponding to the asymmetric downward deflection of the parafoil;
s12, determining the initial airdrop time t of the parafoil system0Position (x) of0,y0,h0) And heading angle psi0Parafoil system at landing time tfDesired position (x)f,yf,hf) And desired heading angle psifMaximum pull-down quantity u of parafoil control ropemax；
S13, establishing an objective function of the parafoil system track planning: j ═ f 1J1+f2J2+f3J3；
Wherein J1＝(x(tf)-xf)2+(y(tf)-yf)2A landing point horizontal position error target; j. the design is a square2＝cos(ψ(tf) +1, which is the landing point course error target;
to control energy consumption goals; f. of1、f2And f3Is a weighting factor; x (t)f)、y(tf)、ψ(tf) Coordinates and course angles of the parafoil on the planned flight path in the x direction and the y direction of the horizontal plane at the landing time are respectively;
s14, flying time of parafoil [ t0,tf]Dividing into n adjacent intervals, and taking constant value for u (t) in each subinterval to control the parafoil system, namely:
wherein:
denote u (t) as the sequence [ sigma ]k]，k＝1,…,n；
S15, solving the optimal control quantity sigma of each interval in the flight period of the parafoilkTaking the minimum value of the objective function value J to obtain the optimal control quantity sequence
S16, deriving a planned flight path (t) (x (t), y (t), h (t)) according to the optimal control quantity sequence and the initial state and speed of the parafoil, and t e [ t ]0,tf]；
Wherein:
h(t)＝h0+vzt，
in step S15, the optimal control quantity sequence of the parafoil in the flight period is solved by using a gradient descent method, which specifically includes:
s151, setting a learning rate lambda, an allowable error e, a maximum iteration number L and a control quantity step size delta sigmak(ii) a Randomly initializing a control quantity sequence within the upper and lower bounds of the control quantity of each subinterval as
According to
Calculating an initial value J of the objective function0(ii) a Initializing the number of iterations l to 0, initializing the negative gradient of each subinterval 
S152, updating the control quantity of each subinterval
If it is not
Then order
If it is not
Then order
According to the updated control quantity sequence
Calculating the value of the objective function Jl+1；
Calculate the negative gradient for the current iteration:
s153, judging whether an iteration ending condition is reached, wherein the iteration ending condition is as follows: the current iteration time L is more than or equal to L or the variation of the objective function value | Jl+1-Jl|<e; if the iteration end condition is reached, the control quantity sequence
For controlling the order of magnitude optimallyEnding iteration; if the iteration end condition is not satisfied, let the iteration number l be l +1, and jump to step S152 to continue the next iteration.
According to a sequence of control quantities [ sigma ]k]The steps of calculating the objective function value J are as follows:
calculating the flight time of the parafoil:
obtaining a course angle and a horizontal plane position of the parachute-flying system on the planned flight path at the landing time according to the particle model:
wherein
Calculating a landing point horizontal position error target value J1And landing site course error target value J2；
According to the flight time period t of the parafoil0,tf]The control quantity u (t) of the inner parafoil is calculated to control the energy consumption target value J3；
Calculating the value of the objective function J ═ f1J1+f2J2+f3J3。
On the other hand, the invention also discloses a track tracking control method, which comprises the following steps:
s21, obtaining the planned flight path P of the parafoil according to the flight path planning method of the parafoil system ref(t)，t∈[t0,tf]；
S22, calculating the position deviation vector of the parafoil system and the planned flight path in the horizontal plane at the time t
Calculating the lateral offset distance of the parafoil:
calculating course angle deviation of parafoil
Calculating the deviation of the glide angle of the parafoil: gamma rayerror(t)＝γref(t)-γ0(t)
Calculating the height error of the parafoil:
wherein P isref(t).x、Pref(t) y is the coordinate value of x direction and y direction in the horizontal plane at the moment t on the planning track; x is the number oft、ytIs the actual position of the parafoil system at time t;
the course angle at the moment t on the planned flight path;
is composed of
The angle with the x-axis;
is composed of
And planning track point Pref(t) the included angle of the tangent;
the actual course angle of the parafoil system at the moment t; gamma rayref(t) is a planning track point PrefA roll-down angle at (t); gamma ray0(t) is the glide angle of the piloting parafoil in the parafoil system at time t;
s23, calculating the horizontal plane tracking control quantity and the vertical tracking control quantity at the time t:
wherein u is1The horizontal plane tracking control quantity of the parafoil system is used for controlling the horizontal turning angle rate of the parafoil through asymmetric pull-down so as to realize horizontal plane course adjustment; u. of2The longitudinal height adjustment is realized by controlling the glide angle rate of the parafoil through symmetrical pull-down for the longitudinal tracking control quantity of the parafoil system; u. of1maxAnd u2maxIs the maximum value, k, of asymmetric and symmetric pull-down of the parafoil respectively1、k2、k3、k4The coefficient of lateral deviation, the coefficient of course angle deviation, the coefficient of height error and the coefficient of glide angle deviation.
During the flight of the parafoil, the steps S22 and S23 are executed in a loop until the parafoil system lands.
The invention also discloses a system for realizing the flight path planning method of the parafoil system, which comprises the following steps:
the parafoil reduced price point model establishing module 11 is used for establishing a parafoil reduced price point model under a wind fixed coordinate system:
wherein (x, y, h) are the position components of the parafoil system in the horizontal plane x direction, y direction and vertical direction in the wind fixed coordinate system respectively, and vsFor the horizontal direction velocity, v, of the parafoil systemzIs the vertical direction velocity, psi is the heading angle,
is the course angular rate, u is the control quantity corresponding to the asymmetric downward deflection of the parafoil;
parafoil system initial state and landing expectation state determining moduleBlock 12 for determining the initial moment t of aerial delivery of the parafoil system0Position (x) of0,y0,h0) And heading angle psi0Parafoil system at landing time tfDesired position (x)f,yf,hf) And desired heading angle psifMaximum pull-down quantity u of parafoil control ropemax；
An objective function establishing module 13, configured to establish an objective function for a flight path planning of a parafoil system: j ═ f1J1+f2J2+f3J3；
Wherein J1＝(x(tf)-xf)2+(y(tf)-yf)2A landing point horizontal position error target; j. the design is a square2＝cos(ψ(tf) +1, which is the landing point course error target;
to control energy consumption goals; f. of1、f2And f3Is a weighting factor; x (t) f)、y(tf)、ψ(tf) Coordinates and course angles of the parafoil on the planned flight path in the x direction and the y direction of the horizontal plane at the landing time are respectively;
a flight time interval division module 14 for dividing the flight time interval t of the parafoil0,tf]Dividing into n adjacent intervals, and taking constant value for u (t) in each subinterval to control the parafoil system, namely:
wherein:
denote u (t) as the sequence [ sigma ]k]，k＝1,…,n；
An optimal control quantity calculation module 15 for solving the optimal control quantity sigma of each interval in the flight period of the parafoilkTaking the minimum value of the objective function value J to obtain the optimal control quantity sequence
A planning track derivation module 16, configured to derive a planned track path (t) (x (t), y (t), h (t)), and te [ t ] (t) according to the optimal control quantity sequence and the initial state and speed of the parafoil0,tf]。
The invention also discloses a system for realizing the track tracking control method, which comprises the following steps:
a track planning module 21, configured to obtain a planned track P of the parafoil according to the parafoil system track planning methodref(t)，t∈[t0,tf]；
A deviation calculation module 22 for calculating the position deviation vector of the parafoil system and the planned flight path in the horizontal plane at the moment t
Parafoil offset distance Lxy(t) course angle deviation
Glide angle deviation gamma of parafoilerror(t) height error of parafoil Herror(t)；
And a tracking control amount calculation module 23, configured to calculate a horizontal plane tracking control amount and a vertical tracking control amount at time t.
Has the advantages that: compared with the prior art, the parafoil system track planning method disclosed by the invention has the advantages that under the condition of considering parafoil initial value constraint, terminal upwind accurate landing constraint and control constraint, the control variables are parameterized into a series of sectional constant values, and under the constraint of parafoil particle model state equation, the weighted sum of horizontal position error, landing point course error and control energy consumption of the parafoil system and the minimum control quantity are solved through a gradient descent method, so that the planned track is obtained. The planned flight path obtained by the method can meet the requirements of accurate and upwind landing, the energy consumption of the flight path is lower, the controlled variable is composed of a segmented constant value, the control of the parafoil during the navigation is simplified, and meanwhile, the value of the controlled variable is changed in a smaller range, so that greater controlled variable redundancy is provided for the system, and the deviation correction during the flight path tracking control is facilitated.
Drawings
FIG. 1 is a flow chart of a method for planning a flight path of a parafoil, which is disclosed by the invention;
FIG. 2 is a sectional constant control diagram of the flight period;
FIG. 3 is a schematic diagram illustrating a comparison of planned flight paths according to an embodiment;
FIG. 4 is a schematic diagram illustrating a comparison of planned track course angles according to an embodiment;
FIG. 5 is a control quantity versus control quantity diagram according to an embodiment;
FIG. 6 is a diagram illustrating the variation of the objective function value with the number of iterations according to a first embodiment;
FIG. 7 is a schematic diagram of the components of a parafoil track planning system in accordance with one embodiment;
FIG. 8 is a flowchart of a track following control method disclosed in the second embodiment;
FIG. 9 is a schematic diagram of the velocity variation of the parafoil after the superposition of random gust disturbances according to the second embodiment;
FIG. 10 is a schematic diagram showing the result of track following at the horizontal plane of the parafoil in the second embodiment;
FIG. 11 is a schematic diagram showing the longitudinal track following result of a parafoil in the second embodiment;
FIG. 12 is a graph showing a lateral error during the course of track following the parafoil in the second embodiment;
FIG. 13 is a longitudinal error curve diagram during the course of track tracking of the parafoil in the second embodiment;
FIG. 14 is a graph showing a change in control amount during track following of the parafoil in the second embodiment;
fig. 15 is a schematic composition diagram of a track following control system disclosed in the second embodiment.
Detailed Description
The invention is further elucidated with reference to the drawings and the detailed description.
Example 1:
as shown in fig. 1, the invention discloses a method for planning a flight path of a parafoil system, which comprises the following steps:
s11, establishing a parafoil reduced order particle model under a wind fixed coordinate system:
wherein (x, y, h) are the position components of the parafoil system in the horizontal plane x direction, y direction and vertical direction in the wind fixed coordinate system respectively, and v sFor horizontal direction velocity, v, of parafoil systemszIs the vertical direction velocity, psi is the heading angle,
is the course angular rate, u is the control quantity corresponding to the asymmetric downward deflection of the parafoil;
s12, determining the initial airdrop time t of the parafoil system0Position (x) of0,y0,h0) And heading angle psi0Parafoil system at landing time tfDesired position (x)f,yf,hf) And desired heading angle psifMaximum pull-down quantity u of parafoil control ropemax；
The expected landing position of the parafoil system is determined according to the landing requirement, and the expected heading angle psi of the parafoil systemfThe requirement for headwind landing, i.e. psifIn the opposite direction to the landing target wind direction, the landing point wind direction is assumed to coincide with the X-axis forward direction, i.e.' psi f180 deg. or psifThe headwind landing condition may be converted to cos psifIf the control ropes on the two sides of the parafoil are pulled down rapidly at the moment, the parafoil can be descended against the wind.
S13, establishing an objective function of the parafoil system track planning:
J＝f1J1+f2J2+f3J3 (2)
wherein J1＝(x(tf)-xf)2+(y(tf)-yf)2A landing point horizontal position error target; j. the design is a square2＝cos(ψ(tf) +1, which is the landing point course error target;
to control energy consumption goals; f. of1、f2And f3As weighting factors, different values can be selected according to different emphasis points of different tasks; x (t)f)、y(tf)、ψ(tf) Coordinates and course angles of the parafoil on the planned flight path in the x direction and the y direction of the horizontal plane at the landing time are respectively;
S14, flying parafoil for a time period t0,tf]Dividing into n adjacent intervals, and taking constant value in each subinterval u (t) to control the parafoil system, as shown in figure 2, namely:
wherein:
denote u (t) as the sequence [ sigma ]k]，k＝1,…,n；
S15, solving the optimal control quantity sigma of each interval in the flight period of the parafoilkTaking the minimum value of the objective function value J to obtain the optimal control quantity sequence
Step S14 discretizes the control quantity, then the flight path planning is converted into the control sequence optimization selection problem, and the invention adopts the gradient descent method to solve the optimal control quantity sequence of the parafoil flight period. The gradient direction of the function J (u (t)) at a certain value u (t) is the direction in which J descends fastest, the gradient descent method is simple in theory, and programming is easy to achieve. When the minimum value of the objective function is calculated, starting from any initial point in the defined domain, the minimum value point can be reached as fast as moving along the negative gradient direction. The method specifically comprises the following steps S151-S153:
s151, setting a learning rate lambda, an allowable error e, a maximum iteration number L and a control quantity step size delta sigmak(ii) a Randomly initializing a control quantity sequence within the upper and lower bounds of the control quantity of each subinterval as
According to
Calculating an initial value J of the objective function0(ii) a Initializing the number of iterations l to 0, initializing the negative gradient of each subinterval 
S152, updating the control quantity of each subinterval
If it is used
Then make it give
If it is used
Then make it give
According to the updated control quantity sequence
Calculating an objective function value Jl+1；
Calculating the negative gradient of the current iteration:
s153, judging whether an iteration ending condition is reached, wherein the iteration ending condition is as follows: the current iteration time L is more than or equal to L or the variation of the objective function value | Jl+1-Jl|<e; if the iteration end condition is reached, the control quantity sequence
For optimal controlMeasuring the sequence, and ending the iteration; if the iteration end condition is not satisfied, let the iteration number l be l +1, and jump to step S152 to continue the next iteration.
S16, deriving a planned flight path (t) (x (t), y (t), h (t)) according to the optimal control quantity sequence and the initial state and speed of the parafoil, and t e [ t ]0,tf]；
Wherein:
h(t)＝h0+vzt，
in step S15, the control quantity sequence [ sigma ] is usedk]The steps of calculating the objective function value J are as follows:
calculating the flight time of the parafoil:
obtaining a course angle and a horizontal plane position of the parachute-flying system on the planned flight path at the landing time according to the particle model:
wherein
Calculating a landing point horizontal position error target value J1And landing site course error target value J2；
According to the flight time period t of the parafoil0,tf]The control quantity u (t) of the inner parafoil is calculated to control the energy consumption target value J3；
Calculating the value of the objective function J ═ f1J1+f2J2+f3J3。
The embodiment simulates the flight path planning method and is based on Gaussian pseudo-spectrum The optimal control homing algorithm of the method and the segmented homing algorithm based on the genetic algorithm are compared. The pseudo-spectrum-based optimal track algorithm references documents: (1) fault-tolerant design of homing trajectory of parafoil system based on pseudo-spectral method [ J ] for high sea, Zhang Li Min, Sunwiln, etc]Control theory and application 2013(06), 702 and 708; (2) winged umbrella system complex multi-constraint trajectory planning based on Gauss pseudo-spectrum method [ J)]The aviation bulletin 2017(03) 220-. The segmented track algorithm based on the genetic algorithm references the literature: (1) optimized design of Sesbania Uralensis, Qinzhong, Chengdong, and the like pteromalus system sectional homing trajectory [ J]Space return and remote sensing 2004(03):11-16., (2) Zhengcheng, Wuqingxiang, Jiangsheng, etc. IAGA-based optimization of parafoil system segmented homing trajectory [ J]Photoelectric and control, 69-72, (3) Taojin, Sunwilk, Chen-reinforce, etc. homing control of parafoil system in larger wind field [ J]Control theory and application 2016(12) 1630-]Aviation computing technology 2017(06): 55-59. When the position of the initiation point of the parachute airdrop is (1500, 1000, 2000), the desired horizontal position of the landing point is (0,0), the velocity of the parachute is set to v 10m/s, the initial heading angle is 45 °, v can be decomposed into a horizontal velocity v s9.5m/s, velocity v in vertical directionz3.1m/s, a glide ratio of about 3.1, umax0.18. In the embodiment, the influence of the constant wind is regarded as the deviation of the initial position of the air-drop, and the flight time period t0,tf]Is set to 6, delta sigmak0.002, learning rate λ was set to 0.01, maximum number of iterations was set to 6000, and objective function coefficient f was set to1、f2And f3The obtained path planning results are shown in fig. 3, in which fig. 3- (a) is a horizontal plane path comparison and fig. 3- (b) is a three-dimensional path comparison. As can be seen from FIG. 3, the segmented flight path algorithm based on the genetic algorithm, the optimal control flight path algorithm based on the Gaussian pseudo-spectrum method and the optimal segmented constant flight path algorithm based on the gradient descent method disclosed by the invention can effectively plan feasible flight paths for the parafoil system, and the three go from the same initial point and go through different flight pathsCan reach the same target point and simultaneously meet the requirement of accurate landing against the headwind. In the segmented homing flight path, the parafoil passes through a target approach segment, an energy control segment and an upwind landing segment to reach a target point; in the optimal flight path of the Gaussian pseudo-spectrum method, the parafoil flies to the far end firstly, consumes a certain height and then turns to a target point to fly; in the planned flight path of the embodiment, the parafoil consumes height through a roundabout turn with a larger radius and then lands on a target point, and the planned target point is (0.0990, 0.2542), so that accurate homing is realized.
FIG. 4 is a schematic diagram of a comparison of the course heading angle of a planned flight path; it can be seen from the above that, starting from the same initial course angle of 45 degrees, the course angles of the segmented homing, the optimal homing and the homing algorithm in the text are all about 180 degrees basically when landing, and the goal of landing against the wind at an angle of 180 degrees is realized. FIG. 5 is a control quantity versus comparison diagram; as can be seen from the change curve of the control quantity in the figure, the control quantity of the parafoil under 3 flight path planning algorithms is smaller than the maximum value allowed, and the planned flight path meets the parafoil control characteristic and is flyable. The optimal control homing landing precision is high, the control amount is small, but the control process is a continuously changing curve, the control motor needs to be continuously adjusted to realize the control target, and the control difficulty is high; the control quantity of the sectional homing is a sectional constant value, mainly relates to a plurality of simple operations such as turning, gliding, sparrow descending and the like, the control operation is simpler than the optimal homing, the sectional homing mode is easier to realize than the optimal control homing mode from the aspect of engineering practicability, however, it can be found that the segmented homing control amount is large, and in addition, in the initial direction adjustment segment, the transition segment between the target approach segment and the energy management segment, and the transition segment between the energy management segment and the upwind landing segment, the parafoil needs to be suddenly increased from a small control amount to a maximum control amount, and then decreases again from the maximum control amount to a smaller control amount, which increases the difficulty of maneuvering, while due to the greater lag in parafoil control, when the control is not yet fully effected, the control amount is quickly reduced from the maximum control amount to the smaller control amount again, and such a manipulation brings about a large tracking error. Compared with the two previous track planning algorithms, the track planning algorithm of the embodiment combines the advantages of the optimal control track planning algorithm and the segmented track planning algorithm, firstly, the two previous algorithms are the same, the planned track landing precision is high, and the accurate landing is realized; secondly, the energy consumption is controlled; the control is a sectional constant value, and the operation is easy; finally, as can be seen from fig. 5, the control quantity designed by the algorithm of the present invention mainly changes around the reference value, and the change is not large, which provides greater control quantity redundancy for subsequent track tracking. Fig. 6 shows the variation of the objective function with the number of iterations in this embodiment, and it can be seen that the gradient descent method has almost completely converged when the number of iterations is about 1200, and the minimum value of the objective function of the gradient descent method is 0.3092.
TABLE 1 track planning Algorithm index comparison
| Serial number | Homing mode | Deviation of distance | Upwind error | Energy consumption | Target sum |
| 1 | Genetic segmentation | 1.34 |
0 | 1.8521 | 7.4083 |
| 2 | |
0 | 0 | 0.1976 | 0.7904 |
| 3 | Optimal segmentation | 0.2727 | 0.0015 | 0.0706 | 0.3092 |
The table 1 further shows the comparison of the planning index results of the three track planning algorithms, and as can be seen from the data in the table, the segmented homing only requires that the control quantity is within the constraint range, so that the segmented homing energy consumption is larger compared with the optimal homing track; the optimal control track planning algorithm has the best performance in the aspects of landing distance deviation and upwind landing, and the total energy consumption value of optimal homing control is smaller than that of segmented homing by one order of magnitude, because the optimal homing control takes the minimum control energy as one of the design indexes of a target function; the optimal segmentation constant homing provided by the invention has a compromise in the aspects of distance deviation and upwind landing, but the energy consumption is minimum, and the total value of the target function of the flight path planning method provided by the invention is the lowest from the view point of the total target value.
As shown in fig. 7, a system for implementing the above-mentioned flight path planning method includes:
the parafoil reduced price particle model establishing module 11 is used for establishing a parafoil reduced order particle model under a wind fixed coordinate system;
A parafoil system initial state and landing expectation state determination module 12 for determining the parafoil system at the airdrop initial time t0Position (x) of0,y0,h0) And heading angle psi0Parafoil system at the moment of landingtfDesired position (x)f,yf,hf) And desired heading angle psifMaximum pull-down quantity u of parafoil control ropemax；
An objective function establishing module 13, configured to establish an objective function for a flight path planning of a parafoil system: j ═ f1J1+f2J2+f3J3；
Wherein J1＝(x(tf)-xf)2+(y(tf)-yf)2A landing point horizontal position error target; j. the design is a square2＝cos(ψ(tf) +1, which is the landing point course error target;
to control energy consumption goals; f. of1、f2And f3Is a weighting factor; x (t)f)、y(tf)、ψ(tf) Coordinates and course angles of the parafoil on the planned flight path in the x direction and the y direction of the horizontal plane at the landing time are respectively;
a flight time interval division module 14 for dividing the flight time interval t of the parafoil0,tf]Dividing into n adjacent intervals, and taking constant value for u (t) in each subinterval to control the parafoil system, namely:
wherein:
denote u (t) as the sequence [ sigma ]k]，k＝1,…,n；
An optimal control quantity calculating module 15, configured to solve the optimal control quantity σ of each interval in the parafoil flight period according to steps 151-153kTaking the minimum value of the objective function value J to obtain the optimal control quantity sequence
A planning track derivation module 16 for deriving a sequence of optimal control quantities and a parafoil The planned track path (t) (x (t), y (t), h (t)) is derived, t e [ t ]0,tf]。
The second embodiment:
the embodiment discloses a method for tracking and controlling a planned flight path in the first embodiment, as shown in fig. 8, the method includes:
s21, obtaining the planning track P of the parafoil according to the parafoil system track planning method in the first embodimentref(t)，t∈[t0,tf]；
S22, calculating the position deviation vector of the parafoil system and the planned flight path in the horizontal plane at the time t
Calculating the lateral offset distance of the parafoil:
calculating course angle deviation of parafoil
Calculating the deviation of the glide angle of the parafoil: gamma rayerror(t)＝γref(t)-γ0(t)
Calculating the height error of the parafoil:
wherein P isref(t).x、Pref(t) y is the coordinate value of x direction and y direction in the horizontal plane at the moment t on the planning track; x is the number oft、ytIs the actual position of the parafoil system at time t;
for planning course angle at time t on track；
Is composed of
The angle with the x-axis;
is composed of
And planning track point Pref(t) the included angle of the tangent;
the actual course angle of the parafoil system at the moment t; gamma rayref(t) is a planning track point PrefA roll-down angle at (t); gamma ray0(t) is the glide angle of the piloting parafoil in the parafoil system at time t;
s23, calculating the horizontal plane tracking control quantity and the vertical tracking control quantity at the time t:
wherein u is1For the horizontal plane tracking control quantity of the parafoil system, controlling the horizontal turning angle rate of the parafoil through asymmetric pull-down to realize horizontal plane course adjustment; u. of 2The longitudinal height adjustment is realized by controlling the glide angle rate of the parafoil through symmetrical pull-down for the longitudinal tracking control quantity of the parafoil system; u. u1maxAnd u2maxIs the maximum value, k, of asymmetric and symmetric pull-down of the parafoil respectively1、k2、k3、k4The coefficient of lateral deviation, the coefficient of course angle deviation, the coefficient of height error and the coefficient of glide angle deviation.
And circularly executing the steps S22 and S23 until the parafoil system lands during the flight of the parafoil.
The present embodiment simulates the above-described track following control method. The specifically adopted model is a parafoil 6 degree of freedom model, and the model parameters are as shown in the following table 2.
TABLE 2 parafoil parameters
| Parameter(s) | Load mass (kg) | Parafoil mass (kg) | Exhibition length (m) | Chord length (m) | Thickness (m) | Length of umbrella rope (m) |
| Value of | 135 | 13 | 7 | 3 | 0.3 | 7.5 |
The actual initial free-cast position of the parafoil is (1550, 950, 2050), the initial heading angle is 50 °, and compared with the planned initial drop position (1500, 1000, 2000), there is an initial position error of 50m in each direction of the xyz three axes, and an angle error of 5 ° with the planned initial heading angle of 45 °. In order to verify the wind resistance of the track following control method, the embodiment also adds gust interference between 100 seconds and 200 seconds, since the wind resistance is constantWind interference is considered as the offset of the initial planned position, so that in this embodiment, after the influence of constant wind is removed, random gust is modeled as a gaussian random process with an average value of 0 and a standard deviation of 1m/s, and the gust interference obtained after the gust interference is superimposed on the flight speed of the parafoil is shown in fig. 9. In the presence of the above-mentioned initial position error, heading angle error and random gust disturbance, a tracking controller is provided, which comprises two channels, horizontal and longitudinal, and which is defined as equation (4) at time t. In this example, the parameter k in the formula (4) 1、k2、k3、k45/57.3, 3, 2/57.3 and 2 respectively, and the parafoil track tracking results shown in figure 10 and figure 11 are obtained. From fig. 10 and fig. 11, under the action of the track tracking controller, the parafoil continuously adjusts the moving direction after starting from the initial launching point, quickly approaches to the planned track, and then lands to the target point along the planned track exactly against the wind. Fig. 12 and fig. 13 are divided into a lateral error and a longitudinal error in the track tracking process of the parafoil, and it can be seen from fig. 12 and fig. 13 that the parafoil has a large error in both the lateral direction and the longitudinal direction at the beginning, but the track tracking error rapidly converges to a stable state, and in addition, because random gust interference exists between 100 seconds and 200 seconds, there is a certain fluctuation in the lateral direction and the height direction errors during this period, but the total trend of the lateral error and the longitudinal error is still rapidly reduced, which shows that the track tracking control method disclosed by the present invention has a strong interference suppression capability, and the calculation amount is small, so that the implementation is easy.
FIG. 14 is a process of control variation during the course of parafoil track tracking, where symmetrical control is used to correct for altitude errors; the asymmetric control amount, i.e., the differential control amount, is used to correct the lateral error. Comparing the optimal piecewise constant control quantity in fig. 5 with the actual differential control quantity in fig. 14, it can be found that the two trends are consistent, the control quantity is substantially constant, the differential control quantity is just started to be positive, which indicates that the parafoil is just started to continuously deflect leftwards, in the process, the control quantity is gradually increased in a step shape, which indicates that the turning radius is gradually decreased, then the control quantity is changed to be negative, and at this time, the parafoil deflects rightwards, and finally lands at the target point by 180 ° against the wind.
The embodiment also discloses a system for implementing the track following control, as shown in fig. 15, including:
a track planning module 21, configured to obtain a planned track P of the parafoil according to the parafoil system track planning method in the first embodimentref(t)，t∈[t0,tf]；
A deviation calculation module 22 for calculating the position deviation vector of the parafoil system and the planned flight path in the horizontal plane at the moment t
Parafoil offset distance Lxy(t) course angle deviation
Glide angle deviation gamma of parafoilerror(t) height error of parafoil Herror(t)；
And the tracking control quantity calculating module 23 is used for calculating the horizontal tracking control quantity and the longitudinal tracking control quantity at the time t according to the formula 4.
Claims (8)
1. The parafoil system flight path planning method is characterized by comprising the following steps:
s11, establishing a parafoil reduced order particle model under a wind fixed coordinate system:
wherein (x, y, h) are the position components of the parafoil system in the horizontal plane x direction, y direction and vertical direction in the wind fixed coordinate system respectively, and vsFor horizontal direction velocity, v, of parafoil systemszIs the vertical direction velocity, psi is the heading angle,
is the course angular rate, u is the control quantity corresponding to the asymmetric downward deflection of the parafoil;
s12, determining parafoil systemThe system is at the initial time t of air drop0Position (x) of0,y0,h0) And heading angle psi0Parafoil system at landing time t fDesired position (x)f,yf,hf) And desired heading angle psifMaximum pull-down quantity u of parafoil control ropemax；
S13, establishing an objective function of the parafoil system track planning: j ═ f1J1+f2J2+f3J3；
Wherein J1＝(x(tf)-xf)2+(y(tf)-yf)2A landing point horizontal position error target; j. the design is a square2＝cos(ψ(tf) +1, which is the landing point course error target;
to control energy consumption goals; f. of1、f2And f3Is a weighting factor; x (t)f)、y(tf)、ψ(tf) Coordinates and course angles of the parafoil on the planned flight path in the x direction and the y direction of the horizontal plane at the landing time are respectively;
s14, flying time of parafoil [ t0,tf]Dividing into n adjacent intervals, and taking constant value for u (t) in each subinterval to control the parafoil system, namely:
wherein:
denote u (t) as the sequence [ sigma ]k]，k＝1,…,n；
S15, solving the optimal control quantity sigma of each interval in the flight period of the parafoilkTaking the minimum value of the objective function value J to obtain the optimal control quantity sequence
S16, deriving a planned flight path (t) (x (t), y (t), h (t)) according to the optimal control quantity sequence and the initial state and speed of the parafoil, and t e [ t ]0,tf]；
Wherein:
h(t)＝h0+vzt，
2. the parafoil system track planning method of claim 1, wherein the step S15 of solving the optimal control quantity sequence of the parafoil in the flight time period by using a gradient descent method specifically comprises:
s151, setting a learning rate lambda, an allowable error e, a maximum iteration number L and a control quantity step size delta sigma k(ii) a Randomly initializing a control quantity sequence within the upper and lower bounds of the control quantity of each subinterval as
According to
Calculating an initial value J of the objective function0(ii) a Initializing the number of iterations l to 0, initializing the negative gradient of each subinterval
S152, updating the control quantity of each subinterval
If it is not
Then order
If it is not
Then order
According to the updated control quantity sequence
Calculating the value of the objective function Jl+1；
Calculate the negative gradient for the current iteration:
s153, judging whether an iteration ending condition is reached, wherein the iteration ending condition is as follows: the current iteration time L is more than or equal to L or the variation of the objective function value | Jl+1-Jl|<e; if the iteration end condition is reached, the control quantity sequence
Ending iteration for the optimal control quantity sequence; if the iteration end condition is not satisfied, let the iteration number l equal to l +1, jump to step S152 and continue the next iteration.
3. A parafoil system track planning method according to claim 2 in which the control quantity sequence [ σ ] is based onk]The steps of calculating the objective function value J are as follows:
calculating the flight time of the parafoil:
obtaining a course angle and a horizontal plane position of the parachute-flying system on the planned flight path at the landing time according to the particle model:
wherein
Calculating a landing point horizontal position error target value J1And landing site course error target value J 2；
According to the flight time period t of the parafoil0,tf]The control quantity u (t) of the inner parafoil is calculated to control the energy consumption target value J3；
Calculating the value of the objective function J ═ f1J1+f2J2+f3J3。
4. The track tracking control method is characterized by comprising the following steps:
s21, obtaining the planning track P of the parafoil according to the parafoil system track planning method of any one of claims 1 to 3ref(t)，t∈[t0,tf]；
S22, calculating the position deviation vector of the parafoil system and the planned flight path in the horizontal plane at the moment t
Calculating the lateral offset distance of the parafoil:
calculating course angle deviation of parafoil
Calculating the deviation of the glide angle of the parafoil: gamma rayerror(t)＝γref(t)-γ0(t)
Calculating the height error of the parafoil:
wherein P isref(t).x、Pref(t) y is the coordinate value of x direction and y direction in the horizontal plane at the moment t on the planning track; x is the number oft、ytIs the actual position of the parafoil system at time t;
the course angle at the moment t on the planned flight path;
is composed of
The angle with the x-axis;
is composed of
And planning track point Pref(t) the included angle of the tangent;
the actual course angle of the parafoil system at the moment t; gamma rayref(t) is a planning track point PrefA roll-down angle at (t); gamma ray0(t) is the glide angle of the piloting parafoil in the parafoil system at time t;
s23, calculating the horizontal plane tracking control quantity and the vertical tracking control quantity at the time t:
wherein u is1The horizontal plane tracking control quantity of the parafoil system is used for controlling the horizontal turning angle rate of the parafoil through asymmetric pull-down so as to realize horizontal plane course adjustment; u. of 2For the longitudinal tracking control quantity of the parafoil system, the gliding angle rate of the parafoil is controlled by symmetrical downward pulling to realize longitudinal height adjustment; u. u1maxAnd u2maxIs the maximum value, k, of asymmetric pull-down and symmetric pull-down of the parafoil respectively1、k2、k3、k4Respectively is a lateral deviation coefficient, a course angle deviation coefficient, a height error coefficient and a glide angle deviation coefficient,
and circularly executing the steps S22 and S23 until the parafoil system lands during the flight of the parafoil.
5. Parafoil system track planning system characterized in that includes:
the parafoil reduced price particle model establishing module (11) is used for establishing a parafoil reduced order particle model under a wind fixed coordinate system:
wherein (x, y, h) are the position components of the parafoil system in the horizontal plane x direction, y direction and vertical direction in the wind fixed coordinate system respectively, and vsFor horizontal direction velocity, v, of parafoil systemszIs the vertical direction velocity, psi is the heading angle,
is the course angular rate, u is the control quantity corresponding to the asymmetric downward deflection of the parafoil;
a parafoil system initial state and landing expectation state determination module (12) for determining the parafoil system at the airdrop initial time t0Position (x) of0,y0,h0) And heading angle psi0Parafoil system at landing time tfDesired position (x)f,yf,hf) And desired heading angle psifMaximum pull-down quantity u of parafoil control rope max；
An objective function establishing module (13) for establishing an objective function of the flight path planning of the parafoil system: j ═ f1J1+f2J2+f3J3；
Wherein J1＝(x(tf)-xf)2+(y(tf)-yf)2A landing point horizontal position error target; j. the design is a square2＝cos(ψ(tf) +1, which is the landing point course error target;
to control energy consumption goals; f. of1、f2And f3Is a weighting factor; x (t)f)、y(tf)、ψ(tf) Coordinates and course angles of the parafoil on the planned flight path in the x direction and the y direction of the horizontal plane at the landing time are respectively;
a flight time interval division module (14) for dividing the flight time interval [ t ] of the parafoil0,tf]Dividing into n adjacent intervals, and taking constant value for u (t) in each subinterval to control the parafoil system, namely:
wherein:
denote u (t) as the sequence [ sigma ]k]，k＝1,…,n；
An optimal control quantity calculation module (15) for solving the optimal control quantity sigma of each interval in the flight period of the parafoilkTaking the minimum value of the objective function value J to obtain the optimal control quantity sequence
A planning track derivation module (16) for deriving a sequence of optimal control variables and an initialization of the parafoilState and speed, deriving planned path (t) (x (t), y (t), h (t)), t e [ t ∈ t [ ((t)) ]0,tf]。
6. The parafoil system track planning system according to claim 5, wherein the optimal control quantity calculation module (15) adopts a gradient descent method to solve the optimal control quantity sequence of the parafoil in the flight period, and specifically comprises:
S151, setting a learning rate lambda, an allowable error e, a maximum iteration number L and a control quantity step size delta sigmak(ii) a Randomly initializing a controlled quantity sequence of upper and lower bounds of the controlled quantity of each subinterval as
According to
Calculating an initial value J of the objective function0(ii) a Initializing the number of iterations l to 0, initializing the negative gradient of each subinterval
S152, updating the control quantity of each subinterval
If it is not
Then order
If it is not
Then order
According to the updated control quantity sequence
Calculating the value of the objective function Jl+1；
Calculate the negative gradient for the current iteration:
s153, judging whether an iteration ending condition is reached, wherein the iteration ending condition is as follows: the current iteration time L is more than or equal to L or the variation of the objective function value | Jl+1-Jl|<e; if the iteration end condition is reached, the control quantity sequence
Ending iteration for the optimal control quantity sequence; if the iteration end condition is not satisfied, let the iteration number l be l +1, and jump to step S152 to continue the next iteration.
7. Parafoil system track planning system according to claim 6, characterized in that the optimal control quantity calculation module (5) is based on a sequence of control quantities [ σ [ σ ] ]k]The steps of calculating the objective function value J are as follows:
calculating the flight time of the parafoil:
obtaining a course angle and a horizontal plane position of the parachute-flying system on the planned flight path at the landing time according to the particle model:
Wherein
Calculating a landing point horizontal position error target value J1And landing point course error target value J2；
According to the flight time period t of the parafoil0,tf]The control quantity u (t) of the inner parafoil is calculated to control the energy consumption target value J3；
Calculating the value of the objective function J ═ f1J1+f2J2+f3J3。
8. A track following control system, comprising:
a flight path planning module (21) for obtaining a planned flight path P of a parafoil according to the method for planning a flight path of a parafoil system according to any one of claims 1 to 3ref(t)，t∈[t0,tf]；
A deviation calculation module (22) for calculating the position deviation vector of the parafoil system and the planned flight path in the horizontal plane at the moment t
Parafoil offset distance Lxy(t) course angle deviation
Glide angle deviation gamma of parafoilerror(t) height error of parafoil Herror(t)；
And the tracking control quantity calculation module (23) is used for calculating the horizontal tracking control quantity and the longitudinal tracking control quantity at the moment t.
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