CN115270313A - Umbrella-machine combination modeling method, device, server and storage medium - Google Patents

Umbrella-machine combination modeling method, device, server and storage medium Download PDF

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CN115270313A
CN115270313A CN202211178271.7A CN202211178271A CN115270313A CN 115270313 A CN115270313 A CN 115270313A CN 202211178271 A CN202211178271 A CN 202211178271A CN 115270313 A CN115270313 A CN 115270313A
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parachute
unmanned aerial
aerial vehicle
establishing
umbrella
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肖奔
刘松
沈洋
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Xian Lingkong Electronic Technology Co Ltd
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Abstract

The application discloses a modeling method, a device, a server and a storage medium for an umbrella-machine combination. The method comprises the following steps: acquiring a first initial condition of a parachute, a second initial condition of an unmanned aerial vehicle and an initial state quantity of a parachute-machine assembly; circularly executing the modeling simulation step until the simulation result of the umbrella-machine combination model is consistent with the preset motion rule; the modeling simulation step comprises: establishing a kinetic equation of the parachute based on the first initial condition of the parachute; based on a kinetic equation of the parachute, a parachute six-degree-of-freedom model is established; establishing a six-degree-of-freedom model of the unmanned aerial vehicle based on a second initial condition of the unmanned aerial vehicle; establishing a dynamic equation of the hanging system as a constraint model; obtaining an umbrella-machine combination model based on a parachute, an unmanned aerial vehicle six-degree-of-freedom model and a constraint model; and simulating the umbrella-machine combination model based on the initial state quantity of the umbrella-machine combination. The invention can carry out umbrella-machine combination modeling by a proper and accurate modeling method.

Description

Modeling method, device, server and storage medium for umbrella-machine combination
Technical Field
The application relates to the technical field of modeling of parachuting unmanned aerial vehicles, in particular to a modeling method, a device, a server and a storage medium for an parachute-unit combination.
Background
Along with the development of unmanned aerial vehicle technique, unmanned aerial vehicle's range of application is more and more extensive. For example, in military applications, drones may serve as aerial reconnaissance platforms and weapons platforms for performing a variety of missions, attacks, blockages, jamming, relaying, and damage assessment. In civilian aspect, unmanned aerial vehicle can be used to aerial photography, meteorological detection, topography survey and drawing and rescue and relief work etc..
The radius of operation, the cruise time of unmanned aerial vehicle usually can receive factors such as self size, fuel and restrict. In order to increase the effective combat radius and cruise time of the unmanned aerial vehicle, the small unmanned aerial vehicle which is thrown to a target area through the throwing platform is delivered. At present, the mainly applied throwing platforms comprise various artilleries, rocket projectiles, large-scale loaders and the like. In order to adapt to various launching environments, the small unmanned aerial vehicle is often transported to a target area in the form of a shot, a carrying box and the like and then is changed into an unmanned aerial vehicle form so as to execute a predetermined task. Due to the influence of the launching platform, the initial working state of the unmanned aerial vehicle in the launching process has great uncertainty, so that the reference motion state cannot be established like a conventional aircraft. In order to make this type of unmanned aerial vehicle that releases enter into controllable flight state, use the method of parachute stabilized unmanned aerial vehicle, parachuting unmanned aerial vehicle is proposed promptly.
The specific launching process of the parachute landing type unmanned aerial vehicle is as follows: firstly, the small unmanned aerial vehicle is arranged in the protective cover in a shot shape and hung below the parachute to be thrown into a free falling body. Then the parachute is opened, and small-size unmanned aerial vehicle slows down, subtracts to revolve under the effect of parachute with the shot form to fall perpendicularly. Later, when unmanned aerial vehicle falling speed is stable and the rotational speed reduces to a certain scope, unmanned aerial vehicle is under wing, fin deployment mechanism's effect, and it becomes the unmanned aerial vehicle form of conventional overall arrangement by the shot form, and unmanned aerial vehicle's the aircraft nose at this moment points to ground to at the uniform velocity whereabouts under the effect of parachute. Finally, parachuting unmanned aerial vehicle throws off the parachute, and unmanned aerial vehicle dives downwards, changes unmanned aerial vehicle from the state of diving downwards into the state of flying on level through automatic control system to it flies the task to prepare to carry out.
In order to accurately simulate the movement of a parachute-unmanned aerial vehicle launching system of a parachuting unmanned aerial vehicle and provide a theoretical basis for a subsequent unmanned aerial vehicle to enter a controllable state, the parachute-unmanned aerial vehicle assembly needs to be modeled in the unmanned aerial vehicle launching process. Currently, related modeling research mainly focuses on the field of manned space missions, and particularly, most of the research is about dynamic modeling of a parachute-reentry module system, and mainly researches are about the parachute opening process of a large parachute and related problems of parachute technology. However, the large parachute system has a complex structure and a plurality of working procedures, and is not completely suitable for a parachute-unmanned aerial vehicle delivery system because the prolonged inflation time is long. And when the unmanned aerial vehicle is changed into an unmanned aerial vehicle with a conventional layout in the launching process, wings and empennages need to be unfolded, and the steps are not needed by the returning capsule, so that the modeling method of the parachute-returning capsule system cannot be applied to the movement of the parachute-unmanned aerial vehicle system. At present, no proper and accurate modeling method exists for modeling the umbrella-machine combination in the unmanned aerial vehicle launching process.
Disclosure of Invention
The embodiment of the application provides a modeling method, a device, a server and a storage medium for an parachute-unmanned aerial vehicle combination, and can solve the problem that no proper and accurate modeling method exists for modeling the parachute-unmanned aerial vehicle combination in the launching process of the parachute-unmanned aerial vehicle at present, so that the motion of a parachute-unmanned aerial vehicle launching system of the parachute-unmanned aerial vehicle is accurately simulated, and a theoretical basis is provided for a follow-up unmanned aerial vehicle to enter a controllable state.
In a first aspect, an embodiment of the present invention provides a modeling method for an umbrella-machine assembly, including:
acquiring a first initial condition of a parachute, a second initial condition of an unmanned aerial vehicle and an initial state quantity of a parachute-machine assembly;
circularly executing the modeling simulation step until the simulation result of the umbrella-machine combination model is consistent with the preset motion rule; wherein the parachute-aircraft assembly comprises the parachute and the unmanned aerial vehicle connected by a suspension system;
wherein the modeling simulation step comprises:
establishing a parachute dynamics equation under a parachute body coordinate system based on the first initial condition of the parachute;
establishing a parachute six-degree-of-freedom model based on the kinetic equation of the parachute;
establishing an unmanned aerial vehicle six-degree-of-freedom model under an unmanned aerial vehicle body coordinate system based on the second initial condition of the unmanned aerial vehicle;
establishing a dynamic equation of the hanging system as a constraint model;
obtaining an umbrella-machine combination model based on the parachute six-degree-of-freedom model, the unmanned aerial vehicle six-degree-of-freedom model and the constraint model;
simulating the umbrella-machine combination model based on the initial state quantity of the umbrella-machine combination.
With reference to the first aspect, in a possible implementation manner, the establishing a dynamical equation of the parachute in a parachute body coordinate system based on the first initial condition of the parachute includes:
calculating a generalized quality matrix for the parachute based on the first initial condition;
under a parachute body coordinate system, establishing a first resultant force and a first resultant moment equation which are received by the parachute, wherein the first resultant force comprises a cross-connection point of the hanging system to the constraint force of the parachuteF c1 The first resultant moment comprises a restraining moment of the cross connecting point to the parachuteM c1 ；
And establishing a dynamic equation of the parachute under a parachute body coordinate system according to the generalized mass matrix of the parachute, the first resultant force and the first resultant moment equation.
With reference to the first aspect, in a possible implementation manner, the calculating a generalized quality matrix of the parachute based on the first initial condition includes:
obtaining the additional mass of the parachute based on the additional mass coefficient, the atmospheric density, the characteristic volume of the parachute and the moment of inertia generated by the gas of the discharging part, and obtaining an additional mass matrix of the parachute;
calculating a generalized inertia matrix of the parachute;
determining a generalized quality matrix for the parachute; wherein the generalized mass matrix is a sum of the additional mass matrix and the generalized inertia matrix.
With reference to the first aspect, in a possible implementation manner, the establishing a six-degree-of-freedom model of the unmanned aerial vehicle in a body coordinate system of the unmanned aerial vehicle based on the second initial condition of the unmanned aerial vehicle includes:
under the coordinate system of the unmanned aerial vehicle body, a second resultant force and a second resultant moment equation which are received under the folding state of the unmanned aerial vehicle and a third resultant force and a third resultant moment equation which are received under the unfolding state of the unmanned aerial vehicle are respectively established, wherein the second resultant force and the third resultant force both comprise the restraining force of the cross connection point of the hanging system on the unmanned aerial vehicleF c2 And the second resultant moment and the third resultant moment both comprise the constraint moment of the intersection point to the unmanned aerial vehicleM c2 ；
And establishing an unmanned aerial vehicle kinetic equation, and establishing a six-degree-of-freedom model of the unmanned aerial vehicle based on the unmanned aerial vehicle kinetic equation.
With reference to the first aspect, in one possible implementation manner, a parachute kinematics equation is obtained based on an unmanned aerial vehicle kinematics model and a mutual mapping relationship between an unmanned aerial vehicle body coordinate system and a parachute body coordinate system;
the parachute-aircraft combination model comprises the unmanned aerial vehicle kinematics model and the parachute kinematics model.
With reference to the first aspect, in one possible implementation manner, the establishing a dynamic equation of the suspension system includes:
and analyzing the connecting points of the hanging system by a balance point method, and establishing a dynamic model of the hanging system based on zero resultant force borne by the connecting points.
With reference to the first aspect, in one possible implementation manner, the dynamical equation of the suspension system is further obtained based on the number of the umbrella ropes, the number of the hanging straps, and the position vector of the intersection point.
In a second aspect, another embodiment of the present invention provides an apparatus for modeling an umbrella-machine combination, comprising:
the acquisition module is used for acquiring a first initial condition of a parachute, a second initial condition of the unmanned aerial vehicle and an initial state quantity of the parachute-machine assembly;
the execution module is used for circularly executing the modeling simulation step until the simulation result of the umbrella-machine combination model is consistent with the preset motion rule; wherein the parachute-aircraft assembly comprises the parachute and the unmanned aerial vehicle connected by a suspension system;
wherein the execution module comprises:
the first establishing submodule is used for establishing a kinetic equation of the parachute under a parachute body coordinate system based on the first initial condition of the parachute;
the second establishing submodule is used for establishing a parachute six-degree-of-freedom model based on the kinetic equation of the parachute;
the third establishing submodule is used for establishing a six-degree-of-freedom model of the unmanned aerial vehicle under the unmanned aerial vehicle body coordinate system based on the second initial condition of the unmanned aerial vehicle;
the fourth establishing submodule is used for establishing a dynamic equation of the hanging system to serve as a constraint model;
an obtaining submodule for obtaining an umbrella-machine combination model based on the parachute six-degree-of-freedom model, the unmanned aerial vehicle six-degree-of-freedom model and the constraint model;
a simulation submodule for simulating the umbrella-machine combination model based on the initial state quantity of the umbrella-machine combination.
In a third aspect, another embodiment of the present invention provides a server, including: a memory and a processor;
the memory is to store program instructions;
the processor is configured to execute program instructions in a server, so that the server executes the umbrella-machine combination modeling method according to any one of the above.
In a fourth aspect, another embodiment of the present invention provides a computer-readable storage medium, where executable instructions are stored, and when the executable instructions are executed by a computer, the method for modeling an umbrella-machine combination according to any one of the above embodiments can be implemented.
One or more technical solutions provided in the embodiments of the present invention have at least the following technical effects or advantages:
the modeling method of the umbrella-machine combination provided by the embodiment of the invention comprises the following steps: the method comprises the steps of obtaining a first initial condition of a parachute, a second initial condition of the unmanned aerial vehicle and an initial state quantity of the parachute-unit assembly. And circularly executing the modeling simulation step until the simulation result of the umbrella-machine combination model is consistent with the preset motion rule. Wherein, the umbrella-unit combination includes parachute and unmanned aerial vehicle that connects through the suspension system. Wherein, the modeling simulation step comprises: and establishing a kinetic equation of the parachute under a parachute body coordinate system based on the first initial condition of the parachute. And establishing a six-degree-of-freedom model of the parachute based on a kinetic equation of the parachute. And establishing a six-degree-of-freedom model of the unmanned aerial vehicle under the unmanned aerial vehicle body coordinate system based on the second initial condition of the unmanned aerial vehicle. And establishing a dynamic equation of the hanging system as a constraint model. And obtaining an umbrella-machine combination model based on the parachute six-degree-of-freedom model, the unmanned aerial vehicle six-degree-of-freedom model and the constraint model. And simulating the umbrella-machine combination model based on the initial state quantity of the umbrella-machine combination.
According to the modeling method of the parachute-unmanned aerial vehicle combination, the parachute and the unmanned aerial vehicle are modeled by the six-degree-of-freedom model respectively, mass center motion in the parachute landing process of the unmanned aerial vehicle can be subjected to simulation analysis, postures of the parachute and the unmanned aerial vehicle and stress conditions of the hanging strips of the parachute can be simulated and evaluated, and the accuracy of the modeling model is improved. The constraint model for building the umbrella-unit combination comprises two stages of the folding state of the wings and the unfolding state of the wings of the unmanned aerial vehicle in the real launching process, the motion process of the unmanned aerial vehicle from launching to the launching of the parachute is simulated more truly, data support is provided for the control of the subsequent unmanned aerial vehicle, the times of physical tests are reduced, and the design research and development cost is saved. The embodiment of the invention realizes that the parachute-unmanned aerial vehicle assembly modeling is carried out by a proper and accurate modeling method in the parachute landing unmanned aerial vehicle launching process so as to accurately simulate the movement of a parachute-unmanned aerial vehicle launching system of the parachute landing unmanned aerial vehicle and provide a theoretical basis for the subsequent unmanned aerial vehicle to enter a controllable state.
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In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments of the present invention will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a block flow diagram of a method for modeling an umbrella-aircraft combination provided by an embodiment of the present application;
FIG. 2 is a schematic structural diagram of a modeling apparatus for an umbrella-mechanism combination provided by an embodiment of the present application;
fig. 3 is a schematic structural diagram of an execution module according to an embodiment of the present disclosure;
FIG. 4 is a schematic view of a coordinate system of an umbrella-mechanism combination provided by an embodiment of the present application;
fig. 5 is a schematic view of an umbrella-aircraft combination provided in an embodiment of the present application in a wing-deployed state of an unmanned aerial vehicle;
fig. 6 is a schematic view of an umbrella-unit assembly in a wing folded state of the drone provided by an embodiment of the present application;
FIG. 7 is a schematic view of longitudinal force analysis of the parachute-mechanism combination parachute landing process provided in the embodiments of the present application;
fig. 8 is a pitch angle variation curve of the unmanned aerial vehicle provided in the embodiment of the present application;
FIG. 9 is a variation curve of the pitch angle of the parachute provided in the embodiment of the present application;
FIG. 10 is a graph of the total tension of the harness provided by an embodiment of the present application;
fig. 11 is unmanned aerial vehicle three-dimensional velocity variation curve that this application embodiment provided.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. It should be apparent that the described embodiments are only some of the embodiments of the present invention, and not all of them. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, an embodiment of the present invention provides a modeling method for an umbrella-machine combination, including steps 101 to 102:
the parachute-aircraft assembly is a combination of a parachute and an aircraft, and as shown in fig. 4 to 6, includes a parachute 1 and an unmanned aerial vehicle 2 connected with each other (as shown in fig. 5, a schematic view of the parachute-aircraft assembly in an unmanned aerial vehicle wing unfolding state, a wing 21 is in an unfolding state). The parachute 1 comprises a canopy 11, a parachute cord 12 and a suspender 13 m Representing the centre of mass of the parachute.
The modeling method of the umbrella-machine combination provided by the embodiment of the invention carries out condition simplification before modeling, and comprises the following steps:
performing dynamic modeling for a parachute in a full-open state, making the following simplifying assumptions:
1) The parachute is a rigid body with six degrees of freedom, the shape of the canopy is regarded as a combined body of the hemisphere and the frustum of cone in the inflating process, the elastic deformation of the canopy rope is ignored, and the shape of the canopy is fixed in the stable descending stage after the canopy is full. 2) The position of the center of mass of the umbrella cover is fixed relative to the bottom edge in the inflation process, namely the position of the center of mass of the umbrella cover is not changed in the inflation process and is superposed with the pneumatic pressure center. 3) The fluid additional force and the additional moment generated by the unsteady motion of the parachute are partially represented by the additional mass. 4) The sling is a thread elastic material and can only withstand tensile deformation. 5) The effect of the hanging unmanned aerial vehicle wake on the umbrella is negligible. 6) The planar geodetic assumption.
Step 101: and acquiring the first initial condition of the parachute, the second initial condition of the unmanned aerial vehicle and the initial state quantity of the parachute-machine assembly.
Wherein, the first initial condition of the parachute comprises the parameters of the parachute: canopy mass m of parachute c Mass m of parachute line s To lowerMass m of hanging strip of falling umbrella r Additional mass coefficient k ii And k jj Aerodynamic damping coefficient in the X-axis direction of a parachute body coordinate systemm dx Aerodynamic damping coefficient in the Y-axis direction of the parachute body coordinate systemm dy Aerodynamic damping coefficient in the Z-axis direction of the parachute body coordinate systemm dz Center of mass C of parachute m To the origin of the parachute body coordinate systemO 1 Distance d of c Moment of inertia of the parachute about three coordinate axes of the parachute body coordinate system
Figure 404750DEST_PATH_IMAGE001
Canopy projection diameter D p Axial coefficient of force C of parachute T Axial force coefficient C of parachute at balanced angle of attack of 0 T0 Parameter C of axial force coefficient of parachute to angle of attack Tα Normal force coefficient of parachuteC N Parameter C of parachute Normal force coefficient vs. Angle of attack Nα Angle of attack of parachute α, modulus of elasticity of suspender E BA Initial length of slingL A Modulus of elasticity E of umbrella cord BO Initial length of umbrella cordL 0 。
The second initial condition of the drone includes: aerodynamic lift coefficient C of unmanned aerial vehicle in unfolding state L Coefficient of resistance C D Coefficient of lateral force C y Pitching moment coefficient C m Rolling moment coefficient C l Yaw moment coefficient C n Mass, moment of inertia in the deployed state of the drone, reference chord length C of the drone A Reference span length b of wing and wing reference areaS w And the position vector of the mass center of the unmanned aerial vehicle under the unmanned aerial vehicle body coordinate system in the unmanned aerial vehicle unfolding stateρ c3 Whereinρ c3 calculated, the rest are known quantities. Unmanned aerial vehicle folded state inertia and resistance area S D Coefficient of resistance C Dz Coefficient of resistance moment C Mz Distance d from aerodynamic focus to center of gravity z When the unmanned aerial vehicle is folded, the mass center of the unmanned aerial vehicle isPosition vector under unmanned aerial vehicle body coordinate systemρ c2 Wherein, in the process,ρ c2 calculated, the remainder being known amounts.
Initial state quantity of umbrella-unit assembly: the values are assigned, for example, an initial position [0, -8000], an initial velocity [238, 0], and an initial attitude [ 0-60/57.3 ].
Step 102: and circularly executing the modeling simulation step.
The modeling simulation step comprises steps 1021-1026:
step 1021: and establishing a kinetic equation of the parachute under a parachute body coordinate system based on the first initial condition of the parachute.
Further, step 1021 includes steps 10211 through 10213.
Step 10211: a generalized quality matrix for the parachute is calculated based on the first initial condition.
Step 10211 includes steps 102111 to 102113.
Step 102111: and obtaining the additional mass of the parachute based on the additional mass coefficient, the atmospheric density, the characteristic volume of the parachute and the moment of inertia generated by the gas of the discharging part, and obtaining an additional mass matrix of the parachute.
In practice, the additional mass is calculated by the canopy volume, the additional mass of the parachute is divided into two parts, the included mass and the apparent mass, the additional mass matrix is a 6 × 6 symmetric matrix with 21 independent components, the parachute studied in the present application is a typical axisymmetric body, and the number of the non-zero independent additional masses is 4, namely, alpha 11 、α 22 =α 33 、α 55 =α 66 、α 26 =-α 35 The correlation experiment shows that when the origin of the coordinate system of the parachute body is coincident with the canopy pressure center, the additional mass component alpha 26 =-α 35 =0, only three additional mass components α need be determined 11 、α 22 =α 33 、α 55 =α 66， The parachute add-on mass is generally calculated as follows:
Figure 826504DEST_PATH_IMAGE002
wherein alpha is ii Representing the mass part, α, of the mass matrix jj Representing the moment of inertia part, k, in a mass matrix ii And k is jj Each represents an additional mass coefficient of magnitude which is the ratio of the sum of the intrinsic mass and the apparent mass to the intrinsic mass, p represents the atmospheric density,
Figure 826821DEST_PATH_IMAGE003
the characteristic volume (the inner volume of the canopy, namely the hemispherical volume of the hemispherical canopy after being inflated is adopted in the calculation),
Figure 701236DEST_PATH_IMAGE004
the moment of inertia generated by exhausting part of gas is shown, namely the moment of inertia generated after the part of gas is exhausted from the inner part of the canopy under the external pressure on the surface of the canopy.
Figure 812411DEST_PATH_IMAGE004
Can be expressed as a characteristic volume
Figure 823093DEST_PATH_IMAGE003
Relation to projected diameter:
Figure 56628DEST_PATH_IMAGE005
wherein D is p Representing the canopy projected diameter, i.e., the diameter of the plane of the inflated hemispherical canopy. Obtaining the additional mass matrix phi of the parachute F Comprises the following steps:
Figure 608219DEST_PATH_IMAGE006
step 102112: calculating generalized inertia matrix phi of parachute B1 。
Figure 585403DEST_PATH_IMAGE007
Wherein,d c representing parachute mass center C m To the origin of the parachute body coordinate systemO 1 The distance of (a) to (b),m p the mass of the parachute is shown,I X1X1 、I Y1Y1 、I Z1Z1 (ii) moment of inertia about three coordinate axes of the parachute body coordinate system, respectivelyI X1X1 、I Y1Y1 、I Z1Z1 Known volume, supplied by the parachute manufacturer).
Step 102113: determining a generalized quality matrix of the parachute; and the generalized mass matrix is the sum of the additional mass matrix and the generalized inertia matrix.
Calculating generalized mass matrix phi of parachute 1 Comprises the following steps:
Figure 919432DEST_PATH_IMAGE008
step 10212: under a parachute body coordinate system, a first resultant force and a first resultant moment equation which are borne by the parachute are established, wherein the first resultant force comprises a restraining force of a cross connecting point of a hanging system on the parachuteF c1 The first resultant moment includes the restraining moment of the cross-connecting point to the parachuteM c1 。
The method specifically comprises the following steps of establishing a first resultant force and a first resultant moment equation which are applied to the parachute.
And establishing a parachute body coordinate system by taking the geometric central position of the canopy as an origin. Specifically, as shown in FIG. 4, the geometric center of the canopy is shownO 1 As an origin point, points to the convergence point of the umbrella ropes along the symmetry axis of the canopyO 1 X 1 The shaft is provided with a plurality of axial holes,O 1 Y 1 shaft andO 1 Z 1 the axial direction is determined according to the initial conditions, in particular, the umbrellaThe parachute landing type unmanned aerial vehicle is thrown obliquely sometimes and is thrown straightly sometimes, and the initial throwing position of the parachute landing type unmanned aerial vehicle is determinedO 1 Y 1 Shaft andO 1 Z 1 in the axial direction, andO 1 X 1 the axes form a right-hand coordinate system, and a parachute body coordinate system is establishedO 1 X 1 Y 1 Z 1 。
Further, as shown in FIG. 4, the points of intersection of the umbrella cords are continued to be referred toO 3 Is taken as the origin of the original point,O 3 X 3 the shaft points to the other end of the hanging strip along the direction of the stretched hanging strip,O 3 Y 3 shaft andO 3 Z 3 the axial direction is determined according to the initial conditions, andO 3 X 3 the axes jointly form a right-hand coordinate system, and a coordinate system of the hanging system body is establishedO 3 X 3 Y 3 Z 3 . In FIG. 4, the geodetic coordinate systemO E X E Y E Z E Adopts a local north-east coordinate system,O E X E a shaft,O E Y E Shaft andO E Z E the axial directions point to the north, the sky and the east of the local area respectively. The world coordinate system is a right-hand coordinate system.
Parachute body coordinate systemO 1 X 1 Y 1 Z 1 Coordinate system of suspension systemO 3 X 3 Y 3 Z 3 And the geodetic coordinate systemO E X E Y E Z E Any two coordinate systems can rotate corresponding Euler angles around the coordinate axis to carry out mutual conversion.
In practice, the parachute can receive gravity, aerodynamic force and suspender constraint force effect in the motion process, and the first resultant force and the first resultant moment of the parachute are calculated according to the following formula under a parachute body coordinate system:
Figure 323869DEST_PATH_IMAGE009
wherein,F 1 indicating the first resultant force to which the parachute is subjected,M 1 representing the first resultant moment to which the parachute is subjected,G 1 which represents the weight of the parachute,F a1 showing the aerodynamic force of the parachute,F c1 shows the restraint force of the connecting point of the suspension system of the parachute on the parachute,M c1 indicating the restraining moment (restraining force) of the cross-point to the parachuteF c1 And restraining momentM c1 Given by a constraint equation, the solution needs to be coupled with a dynamic equation of the unmanned aerial vehicle, specifically, a constraint model is built at the joint of a parachute and the unmanned aerial vehicle by adopting a balance point method, and then constraint force is appliedF c1 And restraining torqueM c1 The six-degree-of-freedom models of the unmanned aerial vehicle and the parachute are respectively introduced, so that in the simulation motion process of each step, the connection point is in a static balance state to solve and obtain the constraint forceF c1 And restraining momentM c1 Then apply a restraining forceF c1 And a restraining momentM c1 And substituting the motion state of the whole system into the respective six-degree-of-freedom model. )ρ c1 The position vector of the center of mass of the parachute under the parachute body coordinate system is shown (formed by the center of mass C of the parachute m To the origin of the parachute body coordinate systemO 1 Distance d of c Determined),M d1 representing the aerodynamic damping matrix of the parachute.
Aerodynamic force of parachuteF a1 In the parachute body coordinate system, the calculation expression is as follows:
Figure 844980DEST_PATH_IMAGE010
wherein,X s representF a1 The component in the X-axis direction of the parachute body coordinate system,Y s representF a1 The component in the Y-axis direction of the parachute body coordinate system,Z s to representF a1 The component in the Z-axis direction of the parachute body coordinate system,ρwhich is indicative of the density of the atmosphere,V c the core-pressing speed of the parachute is shown,V cx indicating the core-pressing speed of the parachuteV c The component along the X-axis in the parachute body coordinate system,V cy indicating the core-pressing speed of the parachuteV c Component along the Y-axis in the parachute body coordinate system: (V c 、V cx 、V cy Output from the kinetic equation of the parachute established by newton-euler equation),C N the normal force coefficient of the parachute is represented,C T the axial force coefficient of the parachute is represented,A 0 the nominal canopy area, i.e. the frontal area of the canopy, is given by assigning a first initial condition.
Coefficient of normal forceC N And coefficient of axial forceC T A quadratic equation with parachute angle of attack α as argument is represented:
Figure 625854DEST_PATH_IMAGE011
wherein,
Figure 814390DEST_PATH_IMAGE012
a parameter representing the normal force coefficient of the parachute versus angle of attack,
Figure 389728DEST_PATH_IMAGE013
represents the axial force coefficient of the parachute when the equilibrium attack angle is 0,
Figure 194873DEST_PATH_IMAGE014
parameters representing the axial force coefficient of the parachute versus the angle of attack,
Figure 700809DEST_PATH_IMAGE015
given by assigning a first initial condition,
Figure 806168DEST_PATH_IMAGE016
indicating the equilibrium angle of attack of the parachute (equilibrium angle of attack of the parachute)
Figure 490091DEST_PATH_IMAGE016
Characteristic parameters of the parachute itself, provided by the parachute manufacturer or obtained through wind tunnel test), angle of attack of the parachute
Figure 313690DEST_PATH_IMAGE017
The calculation model of (a) is:
Figure 108471DEST_PATH_IMAGE018
wherein,V cx indicating the core-pressing speed of the parachuteV c The component along the X-axis in the parachute body coordinate system,V cy indicating the core-pressing speed of the parachuteV c The component along the Y-axis in the parachute body coordinate system,V cz indicating the core-pressing speed of the parachuteV c Component along the Z-axis in the parachute body coordinate system: (V c 、V cx 、V cy 、V cz The kinetic equation of the parachute established by newton-euler equation is output).
Pneumatic damping matrix for parachuteM d1 The component expression under the parachute body coordinate system is as follows:
Figure 333916DEST_PATH_IMAGE019
wherein,M dx to representM d1 The component in the X-axis direction of the parachute body coordinate system,M dy representM d1 The component in the Y-axis direction of the parachute body coordinate system,M dz representM d1 The component in the Z-axis direction of the parachute body coordinate system,m dx the aerodynamic damping coefficient in the X-axis direction of the parachute body coordinate system is expressed,m dy the aerodynamic damping coefficient in the Y-axis direction of the parachute body coordinate system is expressed,m dz represents the aerodynamic damping coefficient in the Z-axis direction of the parachute body coordinate system (m dx 、m dy 、m dz The damping parameter of the parachute itself, which is a known quantity),qdenotes dynamic pressure: (
Figure 188739DEST_PATH_IMAGE020
Wherein
Figure 968477DEST_PATH_IMAGE021
in order to be at the density of the atmosphere,V c indicating the core pressure velocity of the parachute), L indicating the characteristic length of the parachute (intrinsic characteristics of the parachute, known quantity), S indicating the characteristic area of the parachute (intrinsic characteristics of the parachute, known quantity),V Cm the centre of mass velocity of the parachute is represented,ω x representing the component of the angular velocity of the parachute in the X-axis direction in the parachute body coordinate system,ω y representing the component of the angular velocity of the parachute in the Y-axis direction in the parachute body coordinate system,ω z representing the component of the angular velocity of the parachute in the Z-axis direction in the parachute body coordinate system.
Centre of mass velocity of parachuteV Cm Expressed as:
Figure 629265DEST_PATH_IMAGE022
in the above formula, the first and second carbon atoms are,
Figure 896167DEST_PATH_IMAGE023
wherein,V cx indicating the core-pressing speed of the parachuteV c The component along the X-axis in the parachute body coordinate system,V cy indicating the core-pressing speed of the parachuteV c The component along the Y-axis in the parachute body coordinate system,V cz indicating the core-pressing speed of the parachuteV c Component along the Z-axis in the parachute body coordinate system: (V c 、V cx 、V cy 、V cz Output from the kinetic equation of the parachute established by newton-euler equation), as shown in figure 4,d c representing parachute mass center C m To the origin of the parachute body coordinate systemO 1 The distance between them.
Step 10213: and establishing a parachute dynamic equation under a parachute body coordinate system according to the generalized mass matrix, the first resultant force and the first resultant moment equation of the parachute.
Wherein Newton-Euler equation in the form of a rotation through rigid body motion in an ideal fluid
Figure 984209DEST_PATH_IMAGE024
And establishing a kinetic equation of the parachute.
The kinetic equation for an inflatable parachute can be expressed as:
Figure 454505DEST_PATH_IMAGE025
wherein m is p Representing the total mass of the parachute, m p =m c +m s +m r ，m c Represents the canopy mass, m s Represents the mass of the parachute line, m r Representing sling mass;
Figure 918984DEST_PATH_IMAGE026
the components of the external force and the external moment borne by the parachute in the parachute body coordinate system are respectively;
Figure 791125DEST_PATH_IMAGE027
the components of the speed and the angular speed of the parachute in the parachute body coordinate system are respectively;
Figure 784489DEST_PATH_IMAGE028
the components of the acceleration and the angular acceleration of the parachute in a parachute body coordinate system are respectively;
Figure 804397DEST_PATH_IMAGE029
representing parachute mass center C m To the origin O of the parachute body coordinate system 1 The distance of (a);
Figure 10251DEST_PATH_IMAGE030
respectively representing the moment of inertia of the parachute around three coordinate axes of the parachute body coordinate system.
Figure 799215DEST_PATH_IMAGE031
5 components representing the additional mass of the parachute respectively;
Figure 416010DEST_PATH_IMAGE032
respectively representing the rate of change of 5 components of additional mass during the parachute inflation process.
Step 1022: and establishing a six-degree-of-freedom model of the parachute based on a kinetic equation of the parachute.
In practice, the six-degree-of-freedom model of the parachute is also required to be established through the first weight, the first moment of inertia, the first resultant force and the first resultant moment of the parachute.
Wherein the first moment of inertia of the parachute is represented by the moments of inertia of the three parts of canopy, cord and harness:
Figure 923215DEST_PATH_IMAGE033
wherein I represents the first moment of inertia of the parachute, I c.x Representing the moment of inertia of the canopy about the X-axis, I s.x Representing moment of inertia of the parachute line about the X-axis, I r.x Representing the moment of inertia of the strap about the X-axis, I c.y Representing moment of inertia of the canopy about the Y-axis, I s.y Representing moment of inertia of the parachute line about the Y-axis, I r.y Representing the moment of inertia of the sling about the Y-axis, I c.z Representing moment of inertia of the canopy about the Z-axis, I s.z Representing moment of inertia of the parachute line about the Z-axis, I r.z Representing the moment of inertia of the sling about the Z-axis, I c.x 、I s.x 、I r.x 、I c.y 、I s.y 、I r.y 、I c.z 、I s.z 、I r.z Are characteristic values of the parachute itself, known quantities.
Step 1023: and establishing a six-degree-of-freedom model of the unmanned aerial vehicle under an unmanned aerial vehicle body coordinate system based on a second initial condition of the unmanned aerial vehicle.
Step 1023 includes steps 10231 to 10232.
Step 10231: respectively establishing a second resultant force and a second resultant moment equation which are received by the unmanned aerial vehicle in a folded state and a third resultant force and a third resultant moment equation which are received by the unmanned aerial vehicle in an unfolded state under an unmanned aerial vehicle body coordinate system, wherein the second resultant force and the third resultant force both comprise restraining forces of a suspension system cross connection point to the unmanned aerial vehicleF c2 The second resultant torque and the third resultant torque both comprise the restraint torque of the cross-connecting point to the unmanned aerial vehicleM c2 。
Specifically, an unmanned aerial vehicle body coordinate system is established by using the mass center of the unmanned aerial vehicle as an origin. As shown in fig. 4, the center of mass of the drone is used as the origin, and the direction parallel to the longitudinal symmetry axis of the drone and directed to the bottom of the drone isO 3 X 3 The shaft is provided with a plurality of axial grooves,O 3 Y 3 the axis lies in a longitudinal plane of symmetry,O 3 Z 3 the axis is perpendicular to the longitudinal plane of symmetry, anO 3 X 3 、O 3 Y 3 AndO 3 Z 3 coordinate axes jointly form a right-hand coordinate system, and an unmanned aerial vehicle body coordinate system is establishedO 3 X 3 Y 3 Z 3 。
Parachute body coordinate systemO 1 X 1 Y 1 Z 1 Unmanned aerial vehicle body coordinate systemO 3 X 3 Y 3 Z 3 Coordinate system of body of suspension systemO 3 X 3 Y 3 Z 3 And the geodetic coordinate systemO E X E Y E Z E Any two coordinate systems can rotate corresponding Euler angles around the coordinate axis to carry out mutual conversion.
In practice, can receive gravity, aerodynamic drag and the effect of suspender restraint power under the unmanned aerial vehicle fold condition, can receive gravity, aerodynamic drag and the effect of suspender restraint power under the unmanned aerial vehicle wing expansion state, the second that receives under the unmanned aerial vehicle fold condition is calculated according to the following formula under unmanned aerial vehicle body coordinate system and is resumeed the moment with the second to and the third that receives under the expansion state is resumeed the moment with the third and is closed the moment:
Figure 667180DEST_PATH_IMAGE034
wherein,F 2 representing a second resultant force experienced by the drone in the folded condition,M 2 the second resultant moment received by the unmanned aerial vehicle in the folded state is shown,G b which represents the weight of the drone,F D the aerodynamic resistance of the unmanned aerial vehicle in the folded state is shown,F c2 shows the restraining force of the connecting point B (shown in figures 5 and 6) of the hanging system on the unmanned aerial vehicle,M c2 the constraint torque and the constraint force of the intersection point B on the unmanned aerial vehicle are representedF c2 And restraining torqueM c2 Given by constraint equation, it needs to be coupled with parachute dynamics equation to solve (constraint force)F c2 And a restraining momentM c2 The solution method is the same as the above-mentioned constraint forceF c1 And a restraining momentM c1 ），ρ c2 A position vector of the center of mass of the unmanned aerial vehicle in the second coordinate system in the folded state of the unmanned aerial vehicle is represented (given by assigning the second initial condition),M d2 the pneumatic damping moment of the unmanned aerial vehicle in the folded state is shown,F 3 representing the third resultant force experienced by the drone in the deployed state,M 3 the third resultant moment received by the unmanned aerial vehicle in the unfolding state is shown,F a2 representing the aerodynamic forces to which the drone is subjected in the deployed state,ρ c3 a position vector of the center of mass of the unmanned aerial vehicle in the second coordinate system in the unfolding state of the unmanned aerial vehicle is represented (given by assigning a second initial condition),M a2 and the pneumatic damping moment of the unmanned aerial vehicle in the unfolding state is represented.
Pneumatic resistance that receives under unmanned aerial vehicle fold conditionF D AndM d2 the expression in the unmanned aerial vehicle body coordinate system is as follows:
Figure 310651DEST_PATH_IMAGE035
wherein,
Figure 911397DEST_PATH_IMAGE036
representing the speed of the unmanned aerial vehicle in a folded state under an unmanned aerial vehicle body coordinate system;
Figure 578001DEST_PATH_IMAGE037
respectively assigning the resistance area, the resistance coefficient and the resistance moment coefficient of the folded state of the unmanned aerial vehicle to a second initial condition;
Figure 187974DEST_PATH_IMAGE038
indicate the distance from the pneumatic focus to the center of gravity under the folding state of the unmanned aerial vehicleAssigning a given value to the second initial condition;
Figure 623635DEST_PATH_IMAGE039
is at atmospheric density.
Aerodynamic force that receives under unmanned aerial vehicle expandes stateF a2 The expression in the unmanned aerial vehicle body coordinate system is as follows:
Figure 660861DEST_PATH_IMAGE040
wherein,XrepresentF a2 The component in the X-axis direction of the unmanned aerial vehicle body coordinate system,Yto representF a2 The component in the Y-axis direction of the coordinate system of the drone body,ZrepresentF a2 The component in the Z-axis direction of the unmanned aerial vehicle body coordinate system, rho represents the atmospheric density,V b representing the speed of the unmanned aerial vehicle in an unmanned aerial vehicle body coordinate system in an unfolding state;S w representing a reference area of the wings of the unmanned aerial vehicle;C D representing the pneumatic resistance coefficient of the unmanned aerial vehicle in the unfolding state;C y representing the lateral force coefficient of the unmanned aerial vehicle in the unfolding state;C L shows the lift coefficient of the unmanned aerial vehicle in the unfolding state (C D 、C y 、C L By assigning a value to the second initial condition).
Pneumatic damping torque of unmanned aerial vehicle in unfolding stateM a2 The expression in the unmanned aerial vehicle body coordinate system is as follows:
Figure 61100DEST_PATH_IMAGE041
wherein,lrepresentM a2 The component in the X-axis direction of the unmanned aerial vehicle body coordinate system,mto representM a2 The component in the Y-axis direction of the coordinate system of the drone body,nto representM a2 Component in Z-axis direction of unmanned aerial vehicle body coordinate systemAnd p represents the density of the atmosphere,V b representing the speed of the unmanned aerial vehicle in the unmanned aerial vehicle body coordinate system in the unfolding state; s w Representing a reference area of the wings of the unmanned aerial vehicle, and giving the reference area by assigning a second initial condition; c l Showing the roll moment coefficient, C m Representing the coefficient of pitching moment, C n Expressing a yaw moment coefficient, and assigning and giving a pneumatic moment coefficient of the unmanned aerial vehicle through a second initial condition; c A A reference chord length representing the UAV, b a reference span length of the UAV wing, C l 、C m 、C n 、C A B is given by assigning a second initial condition.
Step 10232: and establishing an unmanned aerial vehicle kinetic equation, and establishing an unmanned aerial vehicle six-degree-of-freedom model based on the unmanned aerial vehicle kinetic equation.
In practice, the six-degree-of-freedom model of the drone is established by the second weight, the second moment of inertia (an inherent characteristic of the drone, which is a known quantity), the second resultant force, and the second resultant moment of the drone.
A six-degree-of-freedom model of the unmanned aerial vehicle is generally established in a six-degree-of-freedom module of a visual simulation mould Simulink. The six-degree-of-freedom module is directly adopted for modeling the unmanned aerial vehicle body, so that the model is simpler and more convenient on the basis of meeting the precision, and the engineering application calculation efficiency is met.
Step 1024: and establishing a dynamic equation of the hanging system as a constraint model. A constraint model of the umbrella-machine combination is generally built in a visual simulation mould Simulink.
Specifically, a dynamic equation of the hanging system is established, and the dynamic equation comprises the following steps:
and analyzing the connecting points of the hanging system by a balance point method, and establishing a dynamic model of the hanging system based on zero resultant force borne by the connecting points.
Further, the kinetic equation of the hanging system is also obtained based on the number of the umbrella ropes, the number of the hanging belts and the position vector of the intersection point.
As shown in fig. 5 and 6, the core of the balance point method is to ensure that the tensions of the two ropes OB and BA are equal in each simulation time step, that is, the following constraint model is obtained:
Figure 209184DEST_PATH_IMAGE042
tension of OB section ropeT BO I.e. the restraining force of the connecting point on the parachuteF c1 Tension of rope of BA sectionT BA Namely the constraint force of the connecting point on the unmanned aerial vehicleF c2 WhereinT BO 、T BA can be represented as:
Figure 764930DEST_PATH_IMAGE043
wherein,
Figure 707479DEST_PATH_IMAGE044
wherein,N BO number of ropes for umbrella ropes of BO section, N BA Number of ropes, L, representing suspender of BA section 0 Indicating the initial length of the parachute line, L A Indicating the initial length of the harness, E BO The modulus of elasticity (an intrinsic characteristic of the cord, a known amount) of the cord, E BA Denotes the modulus of elasticity (the intrinsic characteristic of the strap, a known quantity) of the strap ε BO Represents the average strain amount epsilon of each umbrella rope section BA The average strain of each length of the hanging strip is shown,
Figure 410992DEST_PATH_IMAGE045
the average strain rate of each section of the parachute cord is shown (the average strain amount epsilon of each section of the parachute cord is shown BO Derived) is obtained,
Figure 300451DEST_PATH_IMAGE046
Shows the average strain rate of each sling (through the average strain amount epsilon of each sling) BA Derived by derivation),
Figure 773021DEST_PATH_IMAGE047
representing O points in the geodetic coordinate systemA position vector (obtained by obtaining the displacement X, Y and Z of the parachute in a geodetic coordinate system through a translation motion equation of the parachute),
Figure 89733DEST_PATH_IMAGE048
a position vector representing the intermediate free point B (obtained by the constraint equation equilibrium point method),
Figure 280542DEST_PATH_IMAGE049
the position vector of the connecting point on the unmanned aerial vehicle body (obtained by obtaining the displacement X, Y and Z of the unmanned aerial vehicle in the geodetic coordinate system through the translation motion equation of the unmanned aerial vehicle), B BO Shows the tension damping coefficient, B, of each segment of the parachute cord BA The tension damping coefficient of each sling is expressed as:
Figure 504850DEST_PATH_IMAGE050
wherein, B 0 Represents the tension damping constant (unit: s) -1 ) And the value range is [0 (undamped) to 0.5 (critical damping)]。m i Indicating the mass of the individual lengths of umbrella cord/harness, E i Representing the modulus of elasticity (as a known quantity), ρ, of each segment of the umbrella cord/harness i The linear density (in known quantities) of each length of the umbrella cord/sling is shown.
ObtainingF c1 AndF c2 rear end，Obtaining the restraining moment of the connecting point to the parachute based on the product of the force and the momentM c1 And the connecting point is used for restraining the unmanned aerial vehicleM c2 And the components of each moment in the directions of three coordinate axes under the respective body coordinate system.
The dynamic modeling is carried out on the suspender-umbrella rope system at the suspender-umbrella rope system (namely, a hanging system) connecting point B through a balance point method, so that the attitude change of the parachute and the unmanned aerial vehicle and the stress condition of the suspender can be reflected more truly, the accuracy of an analysis result is improved, and an initial attitude basis is provided for the control of the subsequent parachute throwing and horizontal flying of the unmanned aerial vehicle.
The inertia force of the intersection particle can be ignored in the equation solving process, and the effect of the strap restraining force is still considered, namely the intersection particle is always in a static balance state.
Step 1025: and obtaining an umbrella-machine combination model based on the parachute six-degree-of-freedom model, the unmanned aerial vehicle six-degree-of-freedom model and the constraint model.
Wherein, the umbrella-machine combination model comprises an unmanned aerial vehicle kinematics model and a parachute kinematics model.
And obtaining the kinematics modeling of the unmanned aerial vehicle based on the visual simulation mould Simulink. And obtaining the parachute kinematics model based on the unmanned aerial vehicle kinematics model and the mutual mapping relation of the unmanned aerial vehicle body coordinate system and the parachute body coordinate system.
Specifically, the kinematic modeling of the parachute includes a translational kinematic equation establishment and a rotational kinematic equation establishment.
Establishing a translational kinematic equation: mutually mapping a parachute body coordinate system and an unmanned aerial vehicle body coordinate system of the unmanned aerial vehicle body coordinate system according to the following corresponding relation to establish a translational kinematic equation in MATLAB:
Figure 284456DEST_PATH_IMAGE051
that is to say that
Figure 568807DEST_PATH_IMAGE052
U, V, w in the expression of (a) are respectively V x 、V y 、V z The value of (b) replaces, among other things,
Figure 184596DEST_PATH_IMAGE053
representing the velocity component of the parachute in a geodetic coordinate system, and integrating the velocity component to obtain the displacement X, Y and Z of the parachute in the geodetic coordinate system;θ、ϕ、Ψthe euler angle of the parachute in the parachute body coordinate system can be obtained through the following rotational kinematics.
Rotational kinematic equation:
Figure 478174DEST_PATH_IMAGE054
that is to say, the
Figure 863019DEST_PATH_IMAGE055
P, q, r in the expression of (1) are represented by ω x 、ω y 、ω z The value of (c) is replaced. Wherein,
Figure 583851DEST_PATH_IMAGE056
representing the amount of change in the euler angle of the parachute.
The translational kinematic equation and the rotational kinematic equation are both in the form of equations in a geodetic coordinate system.
The parachute body coordinate system and the unmanned aerial vehicle body coordinate system are mapped with each other according to the corresponding conversion relation, the kinematics equation of the parachute can be directly obtained based on the kinematics equation of the unmanned aerial vehicle, the existing kinematics module of the unmanned aerial vehicle of the visual simulation mould Simulink is effectively utilized, the flow field analysis and the flexible body modeling process can be removed under the condition of ensuring the physical reality, and the estimation simulation efficiency is improved.
Step 1026: the umbrella-machine combination model is simulated based on the initial state quantity of the umbrella-machine combination.
Step 1027: until the simulation result of the umbrella-machine combination model is consistent with the preset motion rule; wherein the umbrella-unit assembly comprises the parachute and the unmanned aerial vehicle connected by a suspension system.
Fig. 7 shows a schematic diagram of the force analysis of the folded unmanned aerial vehicle and the force analysis of the parachute, and in fig. 7,F D represents the aerodynamic resistance suffered by the unmanned aerial vehicle in a folded state,X as indicating the aerodynamic drag (aerodynamic forces include aerodynamic drag) experienced by the parachute, T and T' indicating the pulling force provided by the parachute lines,G b which represents the weight of the drone,G 1 which represents the weight of the parachute,M d2 the pneumatic damping moment of the unmanned aerial vehicle in the folding state is shown,M c2 represents the restraining moment of the connecting point B to the unmanned aerial vehicle,M G the gravity moment of the unmanned aerial vehicle in the folded state is shown,
Figure 421357DEST_PATH_IMAGE057
the pitch angle of the airframe is shown, theta is the track inclination angle, and alpha is the angle of attack.
The umbrella-machine combination is simulated by utilizing the steps, and the following results are obtained: fig. 8 is a pitch angle variation curve of the unmanned aerial vehicle provided in the embodiment of the present application. Fig. 9 is a parachute pitch angle variation curve provided in the embodiments of the present application. As can be seen from fig. 8 and 9, at 30s the wings of the drone are deployed, the aerodynamic lift increases, and a head-up moment is generated. Fig. 10 is a graph showing the total tension of the harness according to the embodiment of the present application. Fig. 11 is unmanned aerial vehicle three-dimensional speed change curve that this application embodiment provided. As can be seen from figures 10 and 11, eventually at the deceleration of the parachute, the parachute-unit combination tends to fall at a steady speed, and the harness tension tends to be constant.
According to the modeling method of the parachute-unmanned aerial vehicle combination, the parachute and the unmanned aerial vehicle are modeled by the six-degree-of-freedom model respectively, mass center motion in the parachute landing process of the unmanned aerial vehicle can be subjected to simulation analysis, postures of the parachute and the unmanned aerial vehicle and stress conditions of the hanging strips of the parachute can be simulated and evaluated, and the accuracy of the modeling model is improved. The constraint model for building the umbrella-machine combination comprises two stages of the folding state of the wings of the unmanned aerial vehicle and the unfolding state of the wings of the unmanned aerial vehicle in the real launching process, the motion process of the unmanned aerial vehicle from launching to throwing off parachute access control is simulated more truly, data support is provided for the control of the subsequent unmanned aerial vehicle, the times of physical tests are reduced, and the design research and development cost is saved. The embodiment of the invention realizes that the parachute-unmanned aerial vehicle combined modeling is carried out by a proper and accurate modeling method in the unmanned aerial vehicle launching process so as to accurately simulate the movement of a parachute-unmanned aerial vehicle launching system of the parachute landing type unmanned aerial vehicle and provide a theoretical basis for the subsequent unmanned aerial vehicle to enter a controllable state.
According to the embodiment of the invention, the parachute and the unmanned aerial vehicle are respectively modeled by six degrees of freedom, and the balance point method is adopted at the intersection point B of the sling-umbrella rope system, so that the attitude changes of the parachute and the unmanned aerial vehicle and the stress condition of the sling can be reflected more truly, the accuracy of an analysis result is improved, and an initial attitude basis is provided for the control of the subsequent parachute throwing and horizontal flying of the unmanned aerial vehicle.
Another embodiment of the present invention provides a modeling apparatus for an umbrella-machine combination, as shown in fig. 2, including:
an obtaining module 201, configured to obtain a first initial condition of a parachute, a second initial condition of the unmanned aerial vehicle, and an initial state quantity of the parachute-aircraft assembly.
The execution module 202 is used for circularly executing the modeling simulation steps until the simulation result of the umbrella-machine combination model is consistent with the preset motion rule; wherein, the umbrella-machine combination comprises a parachute and an unmanned aerial vehicle which are connected through a hanging system.
As shown in fig. 3, the execution module 202 includes:
the first establishing submodule 2021 is configured to establish a dynamical equation of the parachute in the parachute body coordinate system based on the first initial condition of the parachute.
Specifically, the first building submodule 2021 includes:
and the computing unit is used for computing the generalized quality matrix of the parachute based on the first initial condition.
Specifically, the calculation unit includes:
and the acquisition subunit is used for acquiring the additional mass of the parachute based on the additional mass coefficient, the atmospheric density, the characteristic volume of the parachute and the moment of inertia generated by the gas of the discharging part and acquiring an additional mass matrix of the parachute.
And the calculating subunit is used for calculating the generalized inertia matrix of the parachute.
The determining subunit is used for determining a generalized quality matrix of the parachute; and the generalized mass matrix is the sum of the additional mass matrix and the generalized inertia matrix.
The first establishing unit is used for establishing a first resultant force and a first resultant moment equation which are applied to the parachute under the parachute body coordinate system, wherein the first resultant force comprises a restraining force of a cross connecting point of the hanging system to the parachuteF c1 The first resultant moment includes the restraining moment of the cross-connecting point to the parachuteM c1 。
And the second establishing unit is used for establishing a dynamic equation of the parachute under the parachute body coordinate system according to the generalized mass matrix, the first resultant force and the first resultant moment equation of the parachute.
And the third establishing unit is used for establishing a six-degree-of-freedom model of the parachute based on the kinetic equation of the parachute.
And the second establishing submodule 2022 is used for establishing a parachute six-degree-of-freedom model based on a parachute kinetic equation.
And the third establishing submodule 2023 is configured to establish a six-degree-of-freedom model of the unmanned aerial vehicle in the unmanned aerial vehicle body coordinate system based on the second initial condition of the unmanned aerial vehicle.
Wherein the third establishing sub-module 2023 includes:
the fourth establishing unit is used for respectively establishing a second resultant force and a second resultant moment equation which are received by the unmanned aerial vehicle in a folded state and a third resultant force and a third resultant moment equation which are received by the unmanned aerial vehicle in an unfolded state under the coordinate system of the unmanned aerial vehicle body, wherein the second resultant force and the third resultant force both comprise the restraining force of the intersection point of the hanging system on the unmanned aerial vehicleF c2 The second resultant torque and the third resultant torque both comprise the restraint torque of the cross-connecting point to the unmanned aerial vehicleM c2 ；
And the fifth establishing unit is used for establishing an unmanned aerial vehicle kinetic equation and establishing an unmanned aerial vehicle six-degree-of-freedom model based on the unmanned aerial vehicle kinetic equation.
And the fourth establishing submodule 2024 is used for establishing a dynamic equation of the hanging system to serve as a constraint model.
The fourth establishing sub-module 2024 is specifically configured to analyze the intersection point of the suspension system by a balance point method, and establish a dynamic equation of the suspension system based on the fact that the resultant force applied to the intersection point is zero.
Further, the fourth establishing sub-module 2024 is further configured to obtain a dynamic equation of the suspension system based on the number of the umbrella ropes, the number of the suspension belts, and the position vector of the intersection point.
The obtaining submodule 2025 is used for obtaining an umbrella-machine combination model based on the parachute six-degree-of-freedom model, the unmanned aerial vehicle six-degree-of-freedom model and the constraint model.
Wherein, the umbrella-machine combination model comprises an unmanned aerial vehicle kinematics model and a parachute kinematics model. And obtaining the parachute kinematics model based on the unmanned aerial vehicle kinematics model and the mutual mapping relation between the unmanned aerial vehicle body coordinate system and the parachute body coordinate system.
The simulation submodule 2026 is configured to simulate the umbrella-machine combination model based on the initial state quantity of the umbrella-machine combination.
Another embodiment of the present invention provides a server, including: a memory and a processor.
The memory is for storing program instructions.
The processor is configured to execute program instructions in the server to cause the server to perform the above-described umbrella-mechanism combination modeling method.
Another embodiment of the present invention provides a computer-readable storage medium, which stores executable instructions, and when the computer executes the executable instructions, the computer can implement the above method for modeling an umbrella-machine combination.
The storage medium includes, but is not limited to, a Random Access Memory (RAM), a Read-Only Memory (ROM), a Cache, a Hard Disk (Hard Disk Drive), or a Memory Card (HDD). The memory may be used to store computer program instructions.
Although the present application provides method steps as in an embodiment or a flowchart, more or fewer steps may be included based on conventional or non-inventive labor. The sequence of steps recited in this embodiment is only one of many steps performed and does not represent a unique order of execution. When the device or the client product in practice executes, it can execute sequentially or in parallel according to the method shown in the embodiment or the figures (for example, in the context of parallel processors or multi-thread processing).
The apparatuses, modules or units illustrated in the above embodiments may be implemented by a computer chip or an entity, or implemented by a product with certain functions. For convenience of description, the above devices are described as being divided into various modules by functions, which are described separately. The functionality of the modules may be implemented in the same one or more software and/or hardware implementations of the present application. Of course, a module that implements a certain function may be implemented by a plurality of sub-modules or sub-units in combination.
The methods, apparatus or modules herein may be implemented in computer readable program code means for a server implemented in any suitable manner, for example, the server may take the form of, for example, a microprocessor or processor and computer readable medium storing computer readable program code (e.g., software or firmware) executable by the (micro) processor, logic gates, switches, application Specific Integrated Circuits (ASICs), programmable logic servers and embedded microservers, examples of which include, but are not limited to, the following: ARC 625D, atmel AT91SAM, microchip PIC18F26K20, and Silicone Labs C8051F320. Those skilled in the art will also appreciate that, in addition to implementing the server operations as pure computer readable program code, the same functions may be implemented entirely by logically programming method steps such that the server functions in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers and the like. Such a server may therefore be considered as a hardware component, and the means included therein for implementing the various functions may also be considered as a structure within the hardware component. Or even means for performing the functions may be regarded as being both a software module for performing the method and a structure within a hardware component.
Some of the modules in the apparatus of the present application may be described in the general context of computer-executable instructions, such as program modules, being executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, classes, etc. that perform particular tasks or implement particular abstract data types. The application may also be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules may be located in both local and remote computer storage media including memory storage devices.
From the above description of the embodiments, it is clear to those skilled in the art that the present application can be implemented by software plus necessary hardware. Based on such understanding, the technical solutions of the present application may be embodied in the form of software products or in the implementation process of data migration, which essentially or partially contributes to the prior art. The computer software product may be stored in a storage medium such as ROM/RAM, magnetic disk, optical disk, etc. and includes instructions for causing a computer device (which may be a personal computer, mobile terminal, server, or network device, etc.) to perform the methods of the various embodiments or portions of embodiments of the present application.
The embodiments in the present specification are described in a progressive manner, and the same or similar parts among the embodiments may be referred to each other, and each embodiment focuses on the differences from the other embodiments. All or portions of the present application are operational with numerous general purpose or special purpose computing system environments or configurations. For example: personal computers, server computers, hand-held or portable devices, tablet-type devices, mobile communication terminals, multiprocessor systems, microprocessor-based systems, programmable electronic devices, network PCs, minicomputers, mainframe computers, distributed computing environments that include any of the above systems or devices, and the like.
The above embodiments are only used to illustrate the technical solutions of the present application, and are not intended to limit the present application; although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications or substitutions do not depart from the spirit and scope of the present disclosure.

Claims (10)

1. A method of modeling an umbrella-machine combination, comprising:
acquiring a first initial condition of a parachute, a second initial condition of the unmanned aerial vehicle and an initial state quantity of a parachute-machine assembly;
circularly executing the modeling simulation step until the simulation result of the umbrella-machine combination model is consistent with the preset motion rule; wherein the parachute-aircraft assembly comprises the parachute and the unmanned aerial vehicle connected by a suspension system;
wherein the modeling simulation step comprises:
establishing a kinetic equation of the parachute under a parachute body coordinate system based on the first initial condition of the parachute;
establishing a six-degree-of-freedom model of the parachute based on the kinetic equation of the parachute;
establishing a six-degree-of-freedom model of the unmanned aerial vehicle under the unmanned aerial vehicle body coordinate system based on the second initial condition of the unmanned aerial vehicle;
establishing a dynamic equation of the hanging system as a constraint model;
obtaining an umbrella-machine combination model based on the parachute six-degree-of-freedom model, the unmanned aerial vehicle six-degree-of-freedom model and the constraint model;
and simulating the umbrella-machine combination model based on the initial state quantity of the umbrella-machine combination.
2. The method for modeling an umbrella-machine combination according to claim 1, wherein said establishing a parachute dynamics equation in a parachute body coordinate system based on said parachute's first initial conditions comprises:
calculating a generalized quality matrix for the parachute based on the first initial condition;
under a parachute body coordinate system, establishing a first resultant force and a first resultant moment equation which are received by the parachute, wherein the first resultant force comprises a cross-connection point pair of the hanging systemRestraint of umbrellaF c1 The first resultant moment comprises a restraining moment of the cross connecting point to the parachuteM c1 ；
And establishing a dynamic equation of the parachute under a parachute body coordinate system according to the generalized mass matrix of the parachute, the first resultant force and the first resultant moment equation.
3. The method of claim 2, wherein the calculating the generalized quality matrix for the parachute based on the first initial condition comprises:
obtaining the additional mass of the parachute based on the additional mass coefficient, the atmospheric density, the characteristic volume of the parachute and the moment of inertia generated by the gas of the opening part, and obtaining an additional mass matrix of the parachute;
calculating a generalized inertia matrix of the parachute;
determining a generalized quality matrix for the parachute; wherein the generalized mass matrix is a sum of the additional mass matrix and the generalized inertia matrix.
4. The method of claim 1, wherein the establishing a six-degree-of-freedom model of the drone in a drone body coordinate system based on the second initial condition of the drone comprises:
respectively establishing a second resultant force and a second resultant moment equation which are received by the unmanned aerial vehicle in a folded state and a third resultant force and a third resultant moment equation which are received by the unmanned aerial vehicle in an unfolded state under an unmanned aerial vehicle body coordinate system, wherein the second resultant force and the third resultant force both comprise a restraining force of a suspension system intersection point to the unmanned aerial vehicleF c2 And the second resultant moment and the third resultant moment both comprise the constraint moment of the intersection point to the unmanned aerial vehicleM c2 ；
And establishing an unmanned aerial vehicle kinetic equation, and establishing a six-degree-of-freedom model of the unmanned aerial vehicle based on the unmanned aerial vehicle kinetic equation.
5. The method of claim 1, wherein the parachute-aircraft combination is modeled based on a kinematics model of the drone and a mutual mapping relationship of a body coordinate system of the drone and a body coordinate system of the parachute;
the parachute-aircraft combination model comprises the unmanned aerial vehicle kinematics model and the parachute kinematics model.
6. The method of claim 1, wherein the establishing a kinetic equation for the suspension system comprises:
and analyzing the cross-connection point of the hanging system by a balance point method, and establishing a dynamic equation of the hanging system based on zero resultant force borne by the cross-connection point.
7. The method of claim 6, wherein the suspension system equations are further derived based on the number of parachute lines, the number of harnesses, and the location vectors of the intersection points.
8. An apparatus for modeling an umbrella-machine combination, comprising:
the acquisition module is used for acquiring a first initial condition of a parachute, a second initial condition of the unmanned aerial vehicle and an initial state quantity of the parachute-machine assembly;
the execution module is used for circularly executing the modeling simulation step until the simulation result of the umbrella-machine combination model is consistent with the preset motion rule; wherein the parachute-aircraft assembly comprises the parachute and the unmanned aerial vehicle connected by a suspension system;
wherein the execution module comprises:
the first establishing submodule is used for establishing a kinetic equation of the parachute under a parachute body coordinate system based on the first initial condition of the parachute;
the second establishing submodule is used for establishing a parachute six-degree-of-freedom model based on the kinetic equation of the parachute;
the third establishing submodule is used for establishing a six-degree-of-freedom model of the unmanned aerial vehicle under an unmanned aerial vehicle body coordinate system based on a second initial condition of the unmanned aerial vehicle;
the fourth establishing submodule is used for establishing a kinetic equation of the hanging system to serve as a constraint model;
an obtaining submodule for obtaining an umbrella-machine combination model based on the parachute six-degree-of-freedom model, the unmanned aerial vehicle six-degree-of-freedom model and the constraint model;
and the simulation submodule is used for simulating the umbrella-machine combination model based on the initial state quantity of the umbrella-machine combination.
9. A server, comprising: a memory and a processor;
the memory is to store program instructions;
the processor is used for executing program instructions in a server to enable the server to execute the modeling method of the umbrella-machine combination as claimed in any one of claims 1 to 7.
10. A computer-readable storage medium, characterized in that the computer-readable storage medium stores executable instructions, and when the computer executes the executable instructions, the computer can realize the modeling method of the umbrella-machine combination according to any one of claims 1 to 7.
CN202211178271.7A 2022-09-27 2022-09-27 Umbrella-machine combination modeling method, device, server and storage medium Pending CN115270313A (en)

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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116011142A (en) * 2023-01-03 2023-04-25 中国电力工程顾问集团有限公司 Dynamic modeling method and modeling device for high-altitude wind power generation device
CN117669275A (en) * 2024-02-02 2024-03-08 东方空间(江苏)航天动力有限公司 Method, device and equipment for performing simulation integration on dynamics of space vehicle
CN117902055A (en) * 2024-03-19 2024-04-19 四川腾盾科技有限公司 Design method of parachute opening steel rope load of air-drop unmanned aerial vehicle and parachute opening device

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106446442A (en) * 2016-10-12 2017-02-22 北京理工大学 Parachute unfolding process stability assessment method of Mars parachute bag combination
US20200055608A1 (en) * 2017-02-20 2020-02-20 Beijing Jingdong Shangke Information Technology Co., Ltd. Parachute system, safety protection method and device of unmanned aerial vehicle

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106446442A (en) * 2016-10-12 2017-02-22 北京理工大学 Parachute unfolding process stability assessment method of Mars parachute bag combination
US20200055608A1 (en) * 2017-02-20 2020-02-20 Beijing Jingdong Shangke Information Technology Co., Ltd. Parachute system, safety protection method and device of unmanned aerial vehicle

Non-Patent Citations (5)

* Cited by examiner, † Cited by third party
Title
吴翰等: "基于凯恩方程的无人机伞降回收动力学建模与仿真", 《北京航空航天大学学报》 *
吴翰等: "无人机伞降回收十二自由度模型建立与仿真", 《西北工业大学学报》 *
唐乾刚等: "伞弹系统九自由度动力学模型", 《兵工学报》 *
宁雷鸣等: "无人机伞降回收过程动力学建模与仿真", 《航天返回与遥感》 *
杜坤明等: "无人机前开伞式降落过程动力学建模与仿真", 《航天返回与遥感》 *

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116011142A (en) * 2023-01-03 2023-04-25 中国电力工程顾问集团有限公司 Dynamic modeling method and modeling device for high-altitude wind power generation device
CN116011142B (en) * 2023-01-03 2024-06-07 中国电力工程顾问集团有限公司 Dynamic modeling method and modeling device for high-altitude wind power generation device
CN117669275A (en) * 2024-02-02 2024-03-08 东方空间(江苏)航天动力有限公司 Method, device and equipment for performing simulation integration on dynamics of space vehicle
CN117669275B (en) * 2024-02-02 2024-04-26 东方空间(江苏)航天动力有限公司 Method, device and equipment for performing simulation integration on dynamics of space vehicle
CN117902055A (en) * 2024-03-19 2024-04-19 四川腾盾科技有限公司 Design method of parachute opening steel rope load of air-drop unmanned aerial vehicle and parachute opening device
CN117902055B (en) * 2024-03-19 2024-06-11 四川腾盾科技有限公司 Design method of parachute opening steel rope load of air-drop unmanned aerial vehicle and parachute opening device

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Application publication date: 20221101