Method for constructing dynamics model of tensegrity unmanned aerial vehicle based on lagrange equation

Abstract

The application discloses a tensioned whole unmanned aerial vehicle dynamics model construction method based on Lagrange equation, relates to the field of robots, and can accurately describe the movement of a tensioned whole unmanned aerial vehicle in two environments of ground and air. The technical scheme is as follows: the tensioned whole unmanned aerial vehicle dynamics model construction method based on Lagrange equation, the tensioned whole unmanned aerial vehicle is a six-pole tensioned whole unmanned aerial vehicle, and the specific steps include the following steps. Step one: taking the position and attitude of a central four-rotor unmanned aerial vehicle in a tensioned whole unmanned aerial vehicle system and the pole end nodes not directly connected with the central four-rotor unmanned aerial vehicle as research objects, a node matrix and a connection matrix are used to construct the spatial configuration of the six-pole tensioned whole unmanned aerial vehicle. Step two: based on the spatial configuration in step one, the total kinetic energy, the total potential energy and the constraint equation of the tensioned whole unmanned aerial vehicle are calculated, and a collision contact model is combined to finally obtain the tensioned whole unmanned aerial vehicle dynamics model.

Description

Technical Field

[0001] This invention relates to the field of robotics, and more specifically to a method for constructing a dynamic model of a tensioned integral unmanned aerial vehicle based on the Lagrange equation. Background Technology

[0002] In complex and confined environments, ordinary drones are vulnerable to collisions and impaired mobility due to limitations in communication, positioning, and obstacle detection capabilities. Current impact-resistant drones suffer from incomplete protection, high cost, poor maneuverability, and insufficient payload capacity. Therefore, designing a novel buffer structure that provides structural protection for drones and enables them to perform controlled rolling motion on the ground and take off again is of significant practical importance.

[0003] Inspired by the impact resistance, lightweight, and flexibility of tensioned monolithic structures, the tensioned monolithic UAV is a novel UAV structure that integrates a six-bar tensioned monolithic structure with a quadcopter UAV. Compared to ordinary UAVs, this structure combines the flexibility and high maneuverability of aerial vehicles with the safety of ground robots, effectively avoiding direct collisions between the UAV's propulsion structure and obstacles. It offers significant advantages in complex environments where obstacles are difficult to detect and avoid. However, currently, there is no mathematical model for tensioned monolithic UAVs, making it impossible to precisely control their rolling motion.

[0004] Therefore, obtaining a dynamic model of the tensioning unmanned aerial vehicle is very important. Summary of the Invention

[0005] In view of this, the present invention provides a method for constructing a dynamic model of a tensioned integral unmanned aerial vehicle based on the Lagrange equation, which accurately describes the motion of the tensioned integral unmanned aerial vehicle in both ground and air environments.

[0006] To achieve the above objectives, the technical solution of this invention is: a method for constructing a dynamic model of a tensioned integral UAV based on the Lagrange equation, wherein the tensioned integral UAV is a six-bar tensioned integral UAV, and the specific steps include:

[0007] Step 1: Taking the position and attitude of the central quadcopter UAV in the tensioned integral UAV system, and the rod end nodes that are not directly connected to the central quadcopter UAV as the research objects, the spatial configuration of the six-rod tensioned integral UAV is constructed using the node matrix and connection matrix.

[0008] Step 2: Based on the spatial configuration of Step 1, calculate the total kinetic energy, total potential energy, and constraint equations of the tensioned integral UAV. Combined with the collision contact model, the dynamic model of the tensioned integral UAV is finally obtained.

[0009] Specifically, the six-bar tensioned integrated drone has an overall frame consisting of: 6 rigid pressure bars, 24 elastic cables, and a quadcopter drone placed at the center of the six-bar tensioned integrated structure; two of the parallel rigid pressure bars are directly connected to the central quadcopter drone, and the other four rigid pressure bars are flexibly connected to the central quadcopter drone through elastic cable components.

[0010] Furthermore, in step one, the specific steps for constructing the spatial configuration of the six-bar tensioned integral UAV are as follows:

[0011] Vector n i =[n ix n iy n iz ] T This represents the position coordinates of the end nodes of the four rigid compression members not directly connected to the central quadcopter UAV in the world coordinate system, where i represents the i-th end node, i = 1, ..., 8, and the end node matrix is ​​denoted as N. b :N b =[n1 n1…n8]

[0012] The position vector of the central quadcopter UAV in the world coordinate system is ξ = [x0 y0 z0]. T The attitude angle of the central quadcopter UAV in the world coordinate system in, θ and ψ represent the roll angle, pitch angle, and yaw angle, respectively; the positions of the other four rod end nodes are determined based on the geometric relationship between the central quadcopter UAV and the rigid pressure bar directly connected to the central quadcopter UAV.

[0013] Specifically, the position coordinates of the four rod end nodes corresponding to the two rigid pressure rods directly connected to the central quadcopter UAV in the world coordinate system are n, respectively. d1 n d2 n d3 n d4 :

[0014]

[0015] The node velocities at the rod ends are respectively

[0016]

[0017] Where R is the rotation matrix corresponding to the attitude angle of the central quadrotor UAV at any time, ω is the angular velocity vector of the central quadrotor UAV, and r1, r2, r3, and r4 are the relative distance vectors between the four end nodes of the two rigid pressure rods directly connected to the central quadrotor UAV and the center of the UAV in the body coordinate system.

[0018] make:

[0019] N = [n1 n2…n8 ξ η]

[0020] N s =[n1 n2…n8 n d1 n d2 n d3 n d4 ]

[0021] Wherein, the coordinates in N are the generalized coordinates of the dynamic model of the tensioned integral UAV system. The pose of the entire tensioned integral UAV system is uniquely determined by N. s The node matrix of the system;

[0022] In a six-bar tensioned monolithic structure, both the rigid compression members and the elastic cable members are composed of connections at the end nodes of each bar. A connection matrix C is established for each rigid compression member. b Connection matrix C of elastic cable members s ;

[0023] The rigid compression member matrix B and the elastic cable member matrix S of the six-bar tensioned integrated UAV are obtained:

[0024]

[0025]

[0026] The kth column b of the rigid compression member matrix B k The vector representing the k-th rigid compression member is s. Similarly, the k'-th column s of the elastic cable member matrix S is s. k' Represents the k'-th elastic cable vector;

[0027] Define column vectors Let α be a 4-dimensional real vector. k The k-th element is 1, and the rest are 0. Given a 24-dimensional real vector, in vector β k' The k'-th element is 1, and the rest are 0;

[0028] The vector form of N is constructed as q = VEC(N), where N s The vector form is q s =VEC(N) s The vectors of rigid compression members and elastic cable members are represented as follows:

[0029]

[0030] in, Let X be the coordinates of the centroid of the k-th rigid compression member in the world coordinate system. k, Y k' All correspond to b k , and s k' The coefficient matrices are as follows:

[0031]

[0032] Where I3 is the identity matrix.

[0033] Further, step two: Based on the spatial configuration of step one, calculate the total kinetic energy, total potential energy, and constraint equations of the tensioned integral UAV. Combined with the collision contact model, the final dynamic model of the tensioned integral UAV is obtained. The specific steps are as follows:

[0034] The total kinetic energy of the tensioned drone assembly includes: the kinetic energy T of the rigid pressure struts in the six-strut tensioned assembly that are not directly connected to the central quadcopter drone. b The kinetic energy T of the central quadcopter drone and its directly connected rigid pressure bar as a whole. db :

[0035] The kinetic energy T of the four rigid compression struts in the six-strut tensioned system that are not directly connected to the central quadcopter drone. b for:

[0036]

[0037] in, For the k-th rigid compression bar b k quality, ω bk For the k-th rigid compression bar b k angular velocity, h k For the k-th rigid compression bar b k angular momentum, I bk For the k-th rigid compression bar b k Moment of inertia, For the k-th rigid compression bar b k Length, For the k-th rigid compression bar b k speed, The first derivative of q;

[0038] If we consider the central quadcopter drone and the two rigid pressure bars directly connected to it as a whole A, then the kinetic energy T of this whole A is... db for:

[0039]

[0040] Where, m db Let I be the total mass of system A, and let I be the moment of inertia matrix of system A. Let ξ be the first derivative. λ is the first derivative of η. d1 , λ d2 They are respectively:

[0041]

[0042]

[0043] The total kinetic energy of the six-bar tensioning integrated unmanned aerial vehicle system is:

[0044]

[0045] Where M(q) represents the mass matrix of the six-bar tensioned overall UAV system;

[0046] The total potential energy of the tensioned unmanned aerial vehicle (UAV) system includes: the elastic potential energy V of the elastic cable in the tensioned UAV system. s and the system's gravitational potential energy V g ;

[0047] The original length of the k'th elastic cable is The current length is ||s k' The elastic modulus of the elastic cable is K. k' The elastic potential energy V of the elastic cable in the tensioned overall unmanned aerial vehicle system s for:

[0048]

[0049] Where K = [K1…K 24 ], σ k' Let I be the force density of the k'-th elastic cable. 36 It is a 36×36 identity matrix, and:

[0050]

[0051] The gravitational potential energy V of the tensioning integrated unmanned aerial vehicle system g for:

[0052]

[0053] Where g = [0 0 -9.806] T G is the gravity vector of the system.

[0054] The total potential energy of the six-bar tensioning integrated unmanned aerial vehicle system is:

[0055] V = V s +V g

[0056] The constraint equations for the tensioning integrated unmanned aerial vehicle system include: the length constraints of the four rigid compression members.

[0057] In the six-bar tensioned integral UAV structure, the specific constraints of the system are: the length constraints of the four rigid compression members, namely:

[0058]

[0059] The collision contact model of the tensioned integral UAV system is as follows: During the ground rolling motion of the tensioned integral UAV, the external forces acting on the system mainly include propeller thrust and the collision force and friction force generated by the contact between the rod end nodes and the external environment; for rod end node i, the collision contact force acting on this node in the world coordinate system is f. i =[f ix f iy f iz ] T Then the total contact forces acting on the system are:

[0060]

[0061] The resultant force of the collision on the four end nodes of the two rigid compression rods fixedly connected to the drone is f. ct =f n1 +f n2 +f n3 +f n4 f n1 f n2 f n3 f n4 The collision forces acting on the four end nodes of the two rigid compression rods fixedly connected to the drone, and the resultant moment about the center of the drone, are: The updated collision contact force of the system is then expressed as f c :

[0062]

[0063] The thrust generated by the four propellers is f d1 f d2 f d3 f d4 The straight-line distance between the center of each propeller motor and the center of mass of the quadcopter UAV is... Let c be the proportionality coefficient between the thrust and torque generated by the motor rotation; then the resultant torque τ generated by the propeller thrust on the center of the UAV is... d for:

[0064]

[0065] The force exerted by the central quadcopter UAV on the rod end node is expressed as:

[0066]

[0067]

[0068]

[0069]

[0070] The Lagrangian function of the tensioned overall unmanned aerial vehicle system is:

[0071]

[0072] Where λ is the Lagrange multiplier; further, the system dynamics equations are:

[0073]

[0074] make Including the tension of the elastic cable, gravity, and impact contact force.

[0075] The overall dynamic model of the tensioning UAV is as follows:

[0076]

[0077] Beneficial effects:

[0078] 1. This invention discloses a method for constructing a dynamic model of a tensioned integral unmanned aerial vehicle (UAV) based on the Lagrange equation. This model takes the pose of the central quadrotor UAV and the coordinates of the detached rod-end nodes as the research objects. It uses node coordinate matrices and connection matrices to characterize the spatial configuration of the tensioned integral UAV, and calculates the system's kinetic energy, potential energy, constraints, and external forces. Finally, combined with a collision contact model, a cross-domain integrated dynamic model of the tensioned integral UAV across ground and air is obtained. This invention's method for constructing a dynamic model of a tensioned integral UAV based on the Lagrange equation fills a gap in the dynamic model of tensioned integral UAVs. This model possesses rapid response capabilities and small positional deviations, and can accurately describe the motion of the tensioned integral UAV in both ground and air environments.

[0079] 2. This invention optimizes the generalized coordinates of the system, adjusting them to the pose of the central quadcopter UAV and the rod end nodes not connected to the UAV. The dynamic model is general and can intuitively reflect the influence of external forces on the motion state of the internal UAV, accurately describing the motion of the tensioned whole UAV in both ground and air environments, and can more accurately control the rolling motion of the tensioned whole UAV. Attached Figure Description

[0080] Figure 1 A schematic diagram of the nodes of the tensioning integral UAV of the present invention is shown;

[0081] Figure 2 The flowchart of the numerical simulation solution program based on MATLAB of this invention is shown;

[0082] Figure 3 The figure shows a comparison between the numerical solution and the coordinate changes of node 6 in the physical object during the motion of the tensioning UAV. Detailed Implementation

[0083] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0084] This invention provides a method for constructing a dynamic model of a tensioned overall unmanned aerial vehicle based on the Lagrange equation, the detailed implementation of which is as follows:

[0085] Step 1: Representation of the system's spatial configuration:

[0086] Figure 1 A schematic diagram of the nodes of the tensioning integral UAV of the present invention is shown. For example... Figure 1 As shown, the overall frame of the six-bar tensioned monolithic UAV includes: 6 rigid pressure bars, 24 elastic cables, and a quadcopter UAV placed at the center of the six-bar tensioned monolithic structure. The UAV is connected to two parallel rigid pressure bars, and the other four rigid pressure bars in the six-bar tensioned monolithic structure are flexibly connected to the UAV through elastic cable members. Vector n i =[n ix n iy n iz ] T This indicates the position of the end nodes of the four rigid compression members not directly connected to the central quadcopter drone in the coordinate system. Let N be the position coordinates of the link end node, where i (i = 1, ..., 8) represents the i-th link end node. Let N be the link end node matrix. b :

[0087]

[0088] Furthermore, the vector ξ = [x0 y0 z0] T and These represent the coordinates of the central quadcopter UAV in the coordinate system. The position and attitude angles in the middle, where, θ and ψ represent the roll angle, pitch angle, and yaw angle, respectively. Based on the geometric relationship between the UAV and the rigid struts directly connected to it, the positions of the other four strut end nodes can be determined. Specifically, the four strut end nodes corresponding to the two rigid struts directly connected to the UAV are located in the coordinate system... The position coordinates in are nd1 n d2 n d3 n d4 :

[0089]

[0090] The node velocities at the rod ends are respectively

[0091]

[0092] Where R is the rotation matrix corresponding to the attitude angle of the central quadrotor UAV at any given time, ω is the angular velocity vector of the central quadrotor UAV, and r1, r2, r3, and r4 are the coordinate systems of the body coordinate system, respectively. The relative distance vectors between the four end nodes of the two rigid pressure bars directly connected to the center quadcopter drone and the center of the drone;

[0093] Let l db Given the lengths of the two rigid compression bars directly connected to the drone, then:

[0094]

[0095] make:

[0096] N = [n1 n2…n8 ξ η]

[0097] N s =[n1 n2…n8 n d1 n d2 n d3 n d4 ]

[0098] In this context, the coordinates in N represent the generalized coordinates of this cross-domain integrated dynamics model. N uniquely determines the pose and attitude of the entire six-bar tensioned unmanned aerial vehicle system. s This is the node matrix of the system.

[0099] In a six-bar tensioned monolithic structure, both the rigid compression members and the elastic cable members are connected by nodes at each end of the bars. Therefore, we establish connection matrices for the rigid compression members separately. Connection matrix of elastic cable members If the k-th component is formed by connecting the end nodes i and j (i,j=1,…,8,d1,…,d4,i≠j), then each element of the connection matrix is:

[0100]

[0101] In summary, we can obtain the rigid compression member matrix B and the elastic cable member matrix S of the six-bar tensioned integrated UAV:

[0102]

[0103]

[0104] Where the kth column b of the rigid compression member matrix B k The vector representing the k-th rigid compression member is s. Similarly, the k'-th column s of the elastic cable member matrix S is s. k' This represents the k'th elastic cable vector.

[0105] Define column vectors Let α be a 4-dimensional real vector. k The k-th element is 1, and the rest are 0. Given a 24-dimensional real vector, in vector β k' The k'th element is 1, and the rest are 0.

[0106] The vector form of N is constructed as q = VEC(N), where N s The vector form is q s =VEC(N) s The vectors of rigid compression members and elastic cable members are represented as follows:

[0107]

[0108] in, Let X be the coordinates of the centroid of the k-th rigid compression member in the world coordinate system. k X k Y k' All correspond to b k , and s k' The coefficient matrices are as follows:

[0109]

[0110] Where I3 is the identity matrix.

[0111] Step 2: Derivation of the system dynamics model:

[0112] For the six-bar tensioned integrated UAV as the research object, neglecting the mass of the elastic cable and the change in the moment of inertia of the elastic cable caused by deformation, and equating the elastic cable to a point mass, the kinetic energy of the system includes: the translational and rotational kinetic energy of the rigid pressure bar, the translational and rotational kinetic energy of the central quadcopter UAV, and the translational kinetic energy of the elastic cable. This invention mainly calculates the kinetic energy of the UAV and the rigid pressure bar.

[0113] The total kinetic energy of the tensioned drone assembly includes: the kinetic energy T of the rigid pressure struts in the six-strut tensioned assembly that are not directly connected to the central quadcopter drone.b The kinetic energy T of the central quadcopter drone and its directly connected rigid pressure bar as a whole. db .

[0114] The kinetic energy of the rigid compression strut in the six-strut tensioning system that is not directly connected to the drone is:

[0115]

[0116] in, For rigid compression bar b k quality For b k angular velocity, h k For b k angular momentum, For b k Moment of inertia, For b k Length, For b k The speed.

[0117] If we consider the drone and the rigid pressure bar directly connected to it as a whole A, then the kinetic energy of this subsystem is:

[0118]

[0119] Where, m db Let I be the total mass of the UAV and the two rigid pressure bars, and let I be the rotational inertia matrix of the subsystem.

[0120]

[0121]

[0122] The total kinetic energy of the six-bar tensioning integrated unmanned aerial vehicle system is:

[0123]

[0124] in, The mass matrix of the tensioning overall unmanned aerial vehicle system.

[0125] The total potential energy of the tensioned unmanned aerial vehicle (UAV) system includes: the elastic potential energy V of the elastic cable in the tensioned UAV system. s and the system's gravitational potential energy V g .

[0126] Let the original length of the k'-th elastic cable be... The current length is ||s k' The elastic modulus of the elastic cable is K. k' The elastic potential energy of the elastic cable in the system is:

[0127]

[0128] Where K = [K1…K 24 ], σ k' Let I be the force density of the k'-th elastic cable. 36 It is a 36×36 identity matrix, and:

[0129]

[0130] The gravitational potential energy of the system is:

[0131]

[0132] Where g = [0 0 -9.806] T G is the gravity vector of the system.

[0133] The total potential energy of the six-bar tensioning integrated unmanned aerial vehicle system is:

[0134]

[0135] The constraint equations for the tensioning integrated unmanned aerial vehicle system include: the length constraints of the four rigid compression members.

[0136] In the six-bar tensioned integral UAV structure, the specific constraints of the system are: the length constraints of the four rigid compression members, namely:

[0137]

[0138]

[0139] During the ground rolling motion of the tensioned unmanned aerial vehicle (UAV), the external forces acting on the system mainly include propeller thrust and the collision and friction forces generated by the contact between the rod end nodes and the external environment. For rod end node i, let it be in the coordinate system... The collision contact force acting on this node is f i =[f ix f iy f iz ] T Then the total contact forces acting on the system are:

[0140]

[0141] Let f be the resultant force of the collision force on the four end nodes of the two rigid compression rods fixedly connected to the drone. ct =f n1 +f n2 +f n3 +f n4The resultant torque about the center of the drone is The collision contact force of the system can then be expressed as:

[0142]

[0143] Let f be the magnitude of the thrust generated by the four propellers. d1 f d2 f d3 f d4 The center of each propeller motor and the coordinate system of the fuselage middle The straight-line distance between the axes is l, and the proportionality coefficient between the thrust and torque generated by the motor rotation is c; then the resultant torque τ generated by the propeller thrust on the center of the UAV is... d for:

[0144]

[0145] Furthermore, the force exerted by the central quadcopter UAV on the rod end node can be expressed as:

[0146]

[0147]

[0148]

[0149]

[0150] In summary, the Lagrangian function of the system can be obtained as follows:

[0151]

[0152] Where λ is a Lagrange multiplier. Furthermore, the system dynamics equations can be obtained:

[0153]

[0154] make Including the elastic cable tension, gravity, and collision contact force, the system dynamics equations can be simplified to:

[0155]

[0156] Furthermore, by calculating the second derivative of the constraint equations with respect to time, the general form of the system dynamics model is obtained:

[0157]

[0158] remember:

[0159]

[0160] It can be further organized as follows:

[0161]

[0162] like Figure 2 The diagram shows the flowchart for numerical simulation of the dynamic model of a tensioned integral UAV in MATLAB. The steps are as follows:

[0163] Step 1: Define the initial position of each node.

[0164] Step 2: Define the connection method for each node.

[0165] Step 3: Define the physical parameters of the rigid bar and the elastic cable.

[0166] Step 4: Specify the simulation duration T.

[0167] Step 5: Determine if time t > T is true. If yes, end the process; otherwise, proceed to step 6.

[0168] Step 6: Calculate the resultant force of the spring on each node.

[0169] Step 7: Calculate the force exerted by the ground surface on the ground contact node.

[0170] Step 8: Calculate the magnitude of acceleration at each node.

[0171] Step 9: Increase the node movement time by Δt, then return to step 5.

[0172] The tensioning drone is placed horizontally and rotated around the coordinate system. The "x" axis is rotated by a certain angle, after which the tensioning drone will move under the action of gravity and collide with the ground, recording the coordinate changes of each node. Figure 3 The figure shows a comparison between the numerical solution and the coordinate changes of node 6 in the physical experiment when the entire UAV is in motion. It can be seen that the trend of node coordinate changes in the physical experiment is basically consistent with the trend of node coordinate changes in the numerical simulation.

[0173] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for constructing a dynamic model of a tensioned integral unmanned aerial vehicle (UAV) based on the Lagrange equation, wherein the tensioned integral UAV is a six-bar tensioned integral UAV, characterized in that... The specific steps include: Step 1: Taking the position and attitude of the central quadcopter UAV in the tensioned integrated UAV system, and the rod end nodes not directly connected to the central quadcopter UAV as the research objects, the spatial configuration of the six-rod tensioned integrated UAV is constructed using a node matrix and a connection matrix; the specific steps for constructing the spatial configuration of the six-rod tensioned integrated UAV in Step 1 are as follows: vector This represents the position coordinates of the end nodes of the four rigid compression members not directly connected to the central quadcopter UAV in the world coordinate system, where i represents the i-th end node, i=1,…,8, and the end node matrix is ​​denoted as . : The position vector of the central quadcopter UAV in the world coordinate system is The attitude angle of the central quadcopter UAV in the world coordinate system ,in, , , These represent the roll angle, pitch angle, and yaw angle, respectively; based on the geometric relationship between the central quadcopter UAV and the rigid pressure bar directly connected to the central quadcopter UAV, the positions of the other four bar end nodes are determined; Specifically, the position coordinates of the four rod end nodes corresponding to the two rigid pressure rods directly connected to the central quadcopter UAV in the world coordinate system are as follows: : The node velocities at the rod ends are respectively : in, Let be the rotation matrix corresponding to the attitude angle of the central quadcopter UAV at any given time. It is the angular velocity vector of the central quadcopter UAV. These are the relative distance vectors between the four end nodes of the two rigid pressure bars directly connected to the center quadcopter UAV in the body coordinate system and the center of the UAV. make: in, The coordinates in the model are generalized coordinates of the overall tensioned unmanned aerial vehicle system dynamics model, obtained through... The only way to determine the pose of the entire tensioning unmanned aerial vehicle system The node matrix of the system; In a six-bar tensioned monolithic structure, both the rigid compression members and the elastic cable members are composed of connections at the end nodes of each bar. Connection matrices for the rigid compression members are established separately. Connection matrix of elastic cable members ; Obtain the rigid compression member matrix of the six-bar tensioned integral UAV. Elastic cable component matrix : The rigid compression member matrix The kth column Represents the vector of the k-th rigid compression member; similarly, the matrix of the elastic cable member... The List Representing the Root elastic cable vector; Define column vectors It is a 4-dimensional real vector. The k-th element is 1, and the rest are 0. A 24-dimensional real vector, in the vector The Middle One element is 1, and the rest are 0; Build The vector form is , The vector form is The vectors of rigid compression members and elastic cable members are represented as follows: in, Let be the coordinates of the centroid of the k-th rigid compression member in the world coordinate system. , , All are corresponding , and The coefficient matrix, For the k-th rigid compression member, the members are as follows: in, It is the identity matrix; Step 2: Based on the spatial configuration of Step 1, calculate the total kinetic energy, total potential energy, and constraint equations of the tensioned integral UAV. Combined with the collision contact model, the dynamic model of the tensioned integral UAV is finally obtained.

2. The method for constructing a dynamic model of a tensioned integral unmanned aerial vehicle based on the Lagrange equation as described in claim 1, characterized in that, The six-bar tensioned integrated UAV has an overall frame comprising: 6 rigid pressure bars, 24 elastic cables, and a quadcopter UAV placed at the center of the six-bar tensioned integrated structure; two of the parallel rigid pressure bars are directly connected to the central quadcopter UAV, and the other four rigid pressure bars are flexibly connected to the central quadcopter UAV through elastic cable components.

3. The method for constructing a dynamic model of a tensioned integral unmanned aerial vehicle based on the Lagrange equation as described in claim 1, characterized in that, Step two: Based on the spatial configuration of step one, calculate the total kinetic energy, total potential energy, and constraint equations of the tensioned integral UAV. Combined with the collision contact model, the final dynamic model of the tensioned integral UAV is obtained. The specific steps are as follows: The total kinetic energy of the tensioning assembly drone includes: the kinetic energy of the rigid pressure bars in the six-bar tensioning assembly that are not directly connected to the central quadcopter drone. The kinetic energy of the central quadcopter drone and its directly connected rigid pressure bar as a whole. : The kinetic energy of the four rigid compression struts in the six-strut tensioned system that are not directly connected to the central quadcopter drone. for: in, For the k-th rigid compression bar quality For the k-th rigid compression bar angular velocity, For the k-th rigid compression bar angular momentum, For the k-th rigid compression bar Moment of inertia, For the k-th rigid compression bar Length, For the k-th rigid compression bar speed, for The first derivative; If we consider the central quadcopter drone and the two rigid pressure bars directly connected to it as a whole A, then the kinetic energy of this whole A is... for: in, The total mass of component A, Let A be the rotational inertia matrix of the entire system A. for The first derivative, for The first derivative, , They are respectively: The total kinetic energy of the six-bar tensioning integrated unmanned aerial vehicle system is: in, This represents the mass matrix of a six-bar tensioned unmanned aerial vehicle (UAV) system. The total potential energy of the tensioned unmanned aerial vehicle (UAV) system includes the elastic potential energy of the elastic cable in the tensioned UAV system. and the system's gravitational potential energy ; No. The original length of the root elastic cord is The current length is The elastic modulus of the elastic cable is The elastic potential energy of the elastic cable in the tensioned overall unmanned aerial vehicle system for: in, , , , For the first Force density of the root elastic cable It is a 36×36 identity matrix, and: Gravitational potential energy of the overall unmanned aerial vehicle system for: in, , The gravity vector of the system; The total potential energy of the six-bar tensioning integrated unmanned aerial vehicle system is: The constraint equations for the tensioning integrated unmanned aerial vehicle system include: the length constraints of the four rigid compression members. ; In the six-bar tensioned integral UAV structure, the specific constraints of the system are: the length constraints of the four rigid compression members, namely: The collision contact model of the tensioned integral UAV system is as follows: During the ground rolling motion of the tensioned integral UAV, the external forces acting on the system include propeller thrust and the collision force and friction force generated by the contact between the rod end nodes and the external environment; for rod end node i, the collision contact force acting on this node in the world coordinate system is: Then the total contact forces acting on the system are: The resultant force of the collision on the four end nodes of the two rigid compression rods fixedly connected to the drone is , The collision forces acting on the four end nodes of the two rigid compression rods fixedly connected to the drone, and the resultant moment about the center of the drone, are: The system's collision contact force update is then expressed as: : The thrust generated by the four propellers is The straight-line distance between the center of each propeller motor and the center of mass of the quadcopter UAV is... The proportionality coefficient between the thrust and torque generated by the rotation of the motor is The resultant torque generated by the propeller thrust on the center of the UAV; for: The force exerted by the central quadcopter UAV on the rod end node is expressed as: The Lagrangian function of the tensioned overall unmanned aerial vehicle system is: in These are Lagrange multipliers; further, the system dynamics equations are: make This includes the tension of the elastic cable, gravity, and impact contact force. The dynamic model of the tensioning integral UAV is as follows: 。

Images