A Control Method for Unmanned Aerial Vehicle (UAV) Suspension System Based on Input Shaping and Differential Flatness

Abstract

This invention provides a control method for a UAV sling system based on input shaping and differential flatness, belonging to the field of UAV control. The method includes the following steps: First, dynamic modeling of the UAV sling system is performed; then, differential flatness is determined for the UAV sling system based on its state variables and input variables, thereby determining the UAV's reference trajectory according to the desired sling load trajectory and the UAV's yaw angle; further, zero-vibration and differential input shaping are used to process the input signals of the control system, and the UAV trajectory is controlled by the processed input signals, thereby achieving rapid balancing and attenuation of the sling load oscillations. This invention can reduce high-frequency, high-speed load oscillations caused by strong coupling between the UAV and the suspended load, improving the overall motion performance of the system.

Description

Technical Field

[0001] This invention belongs to the field of unmanned aerial vehicle (UAV) control technology, specifically relating to a control method for a UAV sling system based on input shaping and differential flatness. Background Technology

[0002] In recent years, with the development of technologies such as new materials, inertial navigation, and microelectromechanical systems (MEMS), low-cost, miniaturized unmanned aerial vehicles (UAVs), represented by rotorcraft, have increasingly emerged and are being applied, with UAV payload transportation being particularly prominent in both civilian and military fields. However, traditional UAV systems are typical underactuated systems, making it quite difficult to achieve UAV position control while suppressing the oscillation of the sling load's swing angle. The basic control objective of UAV sling load systems is to design cooperative control algorithms to achieve cooperative transportation of UAV sling load systems under physical constraints. Currently, for UAV sling load systems under a composite control framework, the stable control of the sling load remains a challenge due to the coupling effect between the sling load and the UAV. How to plan and track the trajectory of the sling load so that it completes a specific transportation task with minimal residual oscillation is a problem that urgently needs to be solved. Summary of the Invention

[0003] The purpose of this invention is to solve the problems mentioned in the background art and provide a control method for a UAV sling system based on input shaping and differential flatness, which can effectively reduce high-frequency and high-speed load oscillations caused by strong coupling between the UAV and the suspended load, and improve the overall motion performance of the system.

[0004] To achieve the above-mentioned technical objectives, the technical solution adopted by the present invention is as follows:

[0005] A control method for a UAV sling system based on input shaping and differential flattening includes the following steps:

[0006] S1. Establish a dynamic model of the UAV sling system; The UAV sling system includes the UAV, the suspension rope, and the sling load. The suspension rope is fixedly connected to the middle of the lower side of the UAV, and the sling load is fixed to the lower end of the suspension rope; Based on the positional relationship between the UAV and the sling load when the suspension rope is tensioned, establish a dynamic model of the UAV sling system.

[0007] S2. Verify the differential flatness of the UAV mounting system and derive the flat output variable;

[0008] S3. Filter the trajectory of the suspended load using an input shaper; use the flat output variable derived in step S2 as the input variable of the input shaper, and use the input variable processed by the input shaper as a new input command to input into the control system, thereby controlling the trajectory of the UAV and achieving rapid balancing oscillation attenuation of the suspended load.

[0009] As a preferred option, the state variables of the UAV hoisting system are: Where r is the UAV position, R is the UAV rotation matrix, Ω is the UAV angular velocity, and p is the unit vector from the center of mass of the suspended load to the center of mass of the UAV; the input variable of the UAV sling system is u = [f, M]T, where f is the total lift of the UAV and M is the torque of the UAV.

[0010] As a preferred option, the Euler-Lagrange equations are used to establish the dynamic model of the UAV sling system in step S1. The specific process is as follows:

[0011] First, establish an inertial coordinate system {E}, a body coordinate system {B}, and a load coordinate system {S} for the UAV sling system;

[0012] An inertial coordinate system {E} is fixed on the Earth's surface, with its origin O. E The takeoff point of the drone is fixed on the ground, O E X E The axis points in the direction of the drone's forward flight, O E Z E The axis is vertically upward, O E Y E The axis is perpendicular to O E X E Y E For planes, the right-hand rule applies.

[0013] The body coordinate system {B} is fixed on the body of the UAV and moves with the UAV; the origin O B At the center of mass of the drone, O B X B The axis lies within the plane of symmetry of the UAV, parallel to the line connecting the front and rear rotors, and points in the forward flight direction; O B Y B The axis is parallel to the line connecting the left and right rotors, with the positive direction being to the right; O B Z B Shaft and O B X B Y B The plane is perpendicular, and the direction is determined according to the right-hand rule;

[0014] The load coordinate system {S} is fixed on the center of mass of the suspended load and moves with the suspended load; the origin O S At the center of gravity of the suspended load, O S X S Pointing in the forward swing direction of the suspended load; O S Y S The direction of the load's left and right swing is indicated by pointing to the left, with left pointing being the positive direction; O S Z S With O S X S Y SThe plane is perpendicular, and the direction is determined according to the right-hand rule;

[0015] When the suspension rope is taut, the positional relationship between the drone and the suspended load is as follows:

[0016] r L =r+lp(1)

[0017] In formula (1), Let {E} be the position of the suspended load relative to the inertial coordinate system. Let {E} be the position of the UAV relative to the inertial coordinate system {E}. The length of the suspension rope. Let be the unit vector from the center of mass of the suspended load to the center of mass of the UAV;

[0018] The unit vector p is obtained by rotating it twice around the ZE axis.

[0019]

[0020] In formula (2), φ L For suspension ropes wrapped around O E X E The swing angle of the axis, θ L For suspension ropes wrapped around O E Y E The swing angle of the shaft, Let R(φ) be the rotation matrix from the body coordinate system {B} to the load coordinate system {S}. L ) and R(θ L ) and respectively, the load coordinate system {S} around O E X E Shaft and O E Y E The rotation matrix of the axis;

[0021] The dynamic model of the UAV sling load system is established using the Euler-Lagrange equations as follows:

[0022]

[0023] In formula (3), These are the velocity and acceleration of the suspended load relative to the inertial coordinate system {E}, respectively. These are the drone's mass and the mass of the load it carries, respectively. It is the acceleration due to gravity; R∈SO(3) is the total lift of the UAV; R∈SO(3) is the rotation matrix from the inertial coordinate system {E} to the body coordinate system {B}; e z =[0 0 1]; J is the angular velocity of the suspended load relative to the inertial coordinate system {E}. Q ∈R 3×3Let be the inertial matrix of the UAV relative to the inertial coordinate system {E}; Let be the angular velocity of the UAV relative to the body coordinate system {B}; For the torque of the drone.

[0024] As a preferred option, the specific process of step S2 is as follows:

[0025] Taking the nth-order differential of formula (1), we can derive:

[0026] r (n) =r L (n) -lp (n) (4)

[0027] According to the equation of motion of the suspended load:

[0028]

[0029] And unit vectors:

[0030]

[0031] We can obtain:

[0032]

[0033] In formulas (5) and (6), T refers to the tension of the suspension rope;

[0034] According to the dynamic model of the UAV hoisting system, i.e., formula (3), we can obtain:

[0035]

[0036] Therefore:

[0037]

[0038]

[0039] in The UAV is parallel to the body coordinate system {B}O B Z B The unit vector of the axis;

[0040] To obtain the rotation matrix from the body coordinate system {B} to the inertial coordinate system {E} definition

[0041]

[0042] Assuming the body coordinate system {B} rotates to the inertial coordinate system {E} in the order of Z-axis - Y-axis - X-axis, c y -b z plane and by -b z Since the planes are the same, the remaining two unit vectors of the organism can be found:

[0043]

[0044]

[0045] in The UAV is parallel to the body coordinate system {B}O B X B The unit vector of the axis; The UAV is parallel to the body coordinate system {B}O B Y B The unit vector of the axis;

[0046] Therefore, the rotation matrix R is:

[0047]

[0048] Taking the first derivative of formula (8), we get:

[0049]

[0050] Formula (15) in unit vectors The projection on is:

[0051]

[0052] Substituting formula (16) into formula (15) and rearranging, we get:

[0053]

[0054] Therefore, the angular velocity of the UAV relative to the body coordinate system {B} The components are as follows:

[0055]

[0056] in The roll rate is angular velocity. The pitch angular velocity, Yaw angular velocity;

[0057]

[0058] Therefore, the angular acceleration of the UAV relative to the body coordinate system {B} The components are as follows:

[0059]

[0060] in This is the roll acceleration. For pitch acceleration, It is the pitch acceleration;

[0061] Taking the derivative with respect to the unit vector p, we get:

[0062]

[0063] Therefore there is

[0064]

[0065] Taking the cross product p on both sides of formula (7), we get:

[0066]

[0067] According to formula (7), the unit vector p(n) depends on rL(n+2), that is, the unit vector p depends on Therefore, by combining formula (4), it can be further seen that the position r(n) of the UAV depends on rL(n+2);

[0068] According to formula (9), f depends on and According to formulas (10)-(14), R also depends on and According to step S21, It depends on rL(4), that is, both f and R depend on rL(4);

[0069] According to formula (20), the angular velocity Ω of the UAV depends on rL (5). Combining this with formulas (3)-(6), the torque M depends on...

[0070] According to formula (23), ω depends on

[0071] Therefore, the UAV mounting system possesses differential flatness, and its flat output variable is z, z = [r L ,ψ] T .

[0072] Preferably, the input forming device in step S3 is a zero-vibration and differential input forming device, namely ZVD.

[0073] As a preferred option, the formula model for ZVD is:

[0074]

[0075] In formula (24), T d =2π / ω d For the damping period,

[0076] In the UAV sling system, drag is treated as an external disturbance and compensated for; therefore, the damping coefficient ξ = 0. Simultaneously, the natural frequency ω of the load balancing oscillation is considered. n The natural frequency ω of the system is determined to be... d , and formula

[0077]

[0078] That is, the natural frequency ω d The expression.

[0079] The beneficial effects of this invention are:

[0080] 1. By adopting a zero-vibration and differential input shaper (ZVD) as a feedforward mechanism, the hanging load can be effectively balanced and oscillated without the need for additional devices such as sensors, making it more convenient and effective in practical applications.

[0081] 2. First, the differential flatness of the UAV hoisting system was verified, which allows the optimal trajectory to be planned in a flat output space, and then rise back to the initial state and input space. This reduces the dimension of the optimal control problem to a number that can be calculated in real time in practical applications, avoiding lengthy and extensive calculations when controlling multi-dimensional variables. This not only improves the efficiency of system control, but also avoids errors that are prone to occur in large-scale calculations, thus improving the control effect.

[0082] 3. By combining zero vibration and differential input shaper with differential flatness, the efficiency and effectiveness of system control are improved, while the high-frequency and high-speed load oscillations caused by strong coupling between the UAV and the suspended load are effectively reduced, thereby improving the overall motion performance of the system and making the entire control method efficient and reliable. Attached Figure Description

[0083] Figure 1 This is a schematic diagram of the configuration framework of a drone mounting system;

[0084] Figure 2 A schematic diagram of the input shape;

[0085] Figure 3 This is a schematic diagram of the control method of the present invention;

[0086] Figure 4 This diagram illustrates the change in the position of the drone and its suspended load over time.

[0087] Figure 5 A trajectory optimization diagram for a drone sling system using input shaping technology;

[0088] Figure 6This is a schematic diagram illustrating the change of the suspension rope's swing angle over time.

[0089] Figure 7 A quantitative performance comparison chart for three different configurations.

[0090] Label name in the image:

[0091] 1. Drones, 2. Suspension ropes, 3. Load-bearing devices. Detailed Implementation

[0092] The embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0093] It should be noted that the terms such as "upper", "lower", "left", "right", "front", and "back" used in the invention are only for clarity of description and are not intended to limit the scope of the invention. Changes or adjustments to their relative relationships, without substantially altering the technical content, should also be considered within the scope of the invention.

[0094] like Figure 1 As shown, this invention provides a control method for a UAV sling system based on input shaping and differential flattening, comprising the following steps:

[0095] S1. A dynamic model of the UAV sling system is established using the Euler-Lagrange equations. The UAV sling system includes a UAV 1, a suspension rope 2, and a sling load 3. The suspension rope 2 is fixedly connected to the lower middle of the UAV 1, and the sling load 3 is fixed to the lower end of the suspension rope 2. Based on the positional relationship between the UAV 1 and the sling load 3 when the suspension rope 2 is tensioned, a dynamic model of the UAV sling system is established. The specific process is as follows:

[0096] The drone-borne system is itself a complex control system, and accurately modeling it mathematically is quite difficult. To facilitate the establishment of its dynamic model, the system makes the following assumptions:

[0097] (1) Both the UAV 1 and the suspended load 3 are rigid bodies, and their elastic deformation is ignored. The mass is uniformly distributed and the structure of the UAV 1 is symmetrical.

[0098] (2) Ignore the mass of suspension rope 2 and assume that suspension rope 2 is always taut, that is, the rope has no elastic deformation and its length does not change;

[0099] (3) Ignore the aerodynamic effects on the suspension rope 2 and the suspended load 3.

[0100] First, establish an inertial coordinate system {E}, a body coordinate system {B}, and a load coordinate system {S} for the UAV sling system;

[0101] An inertial coordinate system {E} is fixed on the Earth's surface, with its origin O. EThe takeoff point of UAV 1, fixed on the ground, O E X E The axis points in the forward flight direction of UAV 1, O E Z E The axis is vertically upward, O E Y E The axis is perpendicular to O E X E Y E For planes, the right-hand rule applies.

[0102] The body coordinate system {B} is fixed on the body of UAV 1 and moves with UAV 1; the origin O B At the center of mass of the drone, O B X B The axis lies in the plane of symmetry of UAV 1, parallel to the line connecting the front and rear rotors of UAV 1, and points in the forward flight direction; O B Y B The axis is parallel to the line connecting the left and right rotors, with the positive direction being to the right; O B Z B Shaft and O B X B Y B The plane is perpendicular, and the direction is determined according to the right-hand rule;

[0103] The load coordinate system {S} is fixed on the center of mass of the suspended load 3 and moves with the suspended load 3; the origin O S At the center of mass of the suspended load 3, O S X S Pointing to the forward swing direction of the suspended load 3; O S Y S The direction of the swing of the suspended load 3 is indicated by left and right swing, with left pointing being the positive direction; O S Z S With O S X S Y S The plane is perpendicular, and the direction is determined according to the right-hand rule;

[0104] When suspension rope 2 is taut, the positional relationship between drone 1 and suspended load 3 is as follows:

[0105] r L =r+lp(1)

[0106] In formula (1), Let be the position of the suspended load 3 relative to the inertial coordinate system {E}. Let be the position of UAV 1 relative to the inertial coordinate system {E}. The length of the suspension rope is 2. Let be the unit vector from the center of mass of the suspended load (3) to the center of mass of the UAV (1).

[0107] The unit vector p passes through continuous loops around Z. E Obtained by rotating the axis twice

[0108]

[0109] In formula (2), φ L For suspension rope 2 wrapped O E X E The swing angle of the axis, θ L For suspension rope 2 wrapped O E Y E The swing angle of the shaft, Let R(φ) be the rotation matrix from the body coordinate system {B} to the load coordinate system {S}. L ) and R(θ L ) and respectively, the load coordinate system {S} around O E X E Shaft and O E Y E The rotation matrix of the axis;

[0110] The dynamic model of the UAV sling load system can be expressed using the Euler-Lagrange equations as follows:

[0111]

[0112] Where L = γ - U is the Lagrangian function, γ is the system kinetic energy, U is the system potential energy, and q = [x, y, z, θ] L ,φ L ] T Let x, y, and z be the generalized coordinates of the system, and let φ be the three-dimensional coordinates of UAV 1 in the inertial coordinate system. L For suspension rope 2 wrapped O E X E The swing angle of the axis, θ L For suspension rope 2 wrapped O E Y E The swing angle of the shaft; in For the system's generalized velocity, These represent the velocities of UAV 1 in each of the three-dimensional coordinate directions in the inertial coordinate system; For suspension rope 2 wrapped O E X E The angular velocity of the shaft's oscillation. For suspension rope 2 wrapped O E Y E The angular velocity of the shaft's oscillation; F ext =[F x ,F y ,F z ,0,0] T For the generalized force of the system, F x ,F y ,Fz These are the forces in the x, y, and z directions, respectively.

[0113] The generalized kinetic energy γ of the UAV 1 sling system is expressed as:

[0114] γ=γ t +γ r (4)

[0115] Among them, translational kinetic energy rotational kinetic energy

[0116] The generalized potential energy U of the system (with the ground as the zero potential energy surface) is:

[0117] U = m Q ge z +m L lg(e z -lcosθ L cosφ L (5)

[0118] Substituting equations (4) and (5) into equation (3), we obtain the dynamic equation of the UAV mounting system as follows:

[0119]

[0120] in, These represent the inertia matrix, centripetal force matrix, and gravity vector of the composite system, respectively. The generalized forces acting on the system are as follows:

[0121] The dynamic equations of the UAV mounting system are as follows:

[0122]

[0123] in,

[0124]

[0125] Where M is the mass of the UAV, m is the mass of the suspended load, and l is the length of the suspension rope.

[0126]

[0127] In equation (A-3),

[0128]

[0129]

[0130]

[0131]

[0132]

[0133] Combining the formulas (A-1)-(A-4), we get:

[0134]

[0135] Expanding equation (6), we can obtain the dynamic model of the UAV 1 sling system as follows:

[0136]

[0137] In formula (7), These are the velocity and acceleration of the suspended load relative to the inertial coordinate system {E}, respectively. These are the drone's mass and the mass of the load it carries, respectively. It is the acceleration due to gravity; R∈SO(3) is the total lift of the UAV; R∈SO(3) is the rotation matrix from the inertial coordinate system {E} to the body coordinate system {B}; e z =[0 0 1]; J represents the angular velocity of the suspended load 3 relative to the inertial coordinate system {E}. Q ∈R 3×3 Let be the inertial matrix of UAV 1 relative to the inertial coordinate system {E}; Let be the angular velocity of UAV 1 relative to the body coordinate system {B}; For the torque of the drone.

[0138] S2. Verify the differential flatness of the UAV 1 suspension system and derive the flat output variable;

[0139] The state variables of the UAV 1 hoisting system are Where r is the UAV position, R is the UAV rotation matrix, Ω is the UAV angular velocity, and p is the unit vector from the suspended load 3 to the UAV's center of mass; the input variables of the UAV sling system are u = [f, M]. T Where f is the total lift of the UAV and M is the torque of the UAV;

[0140] Specifically, the following steps are included:

[0141] Taking the nth-order differential of formula (1), we can derive:

[0142] r (n) =r L (n) -lp (n) (8)

[0143] According to the motion equation of the suspended load 3:

[0144]

[0145] And unit vectors:

[0146]

[0147] We can obtain:

[0148]

[0149] In formulas (9) and (10), T refers to the tension of the suspension rope 2;

[0150] According to the dynamic model of the UAV hoisting system, i.e., formula (7), we can obtain:

[0151]

[0152] Therefore:

[0153]

[0154]

[0155] in The UAV is parallel to the body coordinate system {B}O B Z B The unit vector of the axis;

[0156] To obtain the rotation matrix from the body coordinate system {B} to the inertial coordinate system {E} definition

[0157]

[0158] Assuming the body coordinate system {B} rotates to the inertial coordinate system {E} in the order of Z-axis - Y-axis - X-axis, c y -b z plane and b y -b z Since the planes are the same, the remaining two unit vectors of the organism can be found:

[0159]

[0160]

[0161] in The UAV is parallel to the body coordinate system {B}O B X B The unit vector of the axis; The UAV is parallel to the body coordinate system {B}O B Y B The unit vector of the axis;

[0162] Therefore, the rotation matrix R is:

[0163]

[0164] Taking the first derivative of formula (12), we get:

[0165]

[0166] Formula (19) in unit vectors The projection on is:

[0167]

[0168] Substituting formula (20) into formula (19) and rearranging, we get:

[0169]

[0170] Therefore, the angular velocity of the UAV relative to the body coordinate system {B} The components are as follows:

[0171]

[0172] in The roll rate is angular velocity. The pitch angular velocity, Yaw angular velocity;

[0173]

[0174] Therefore, the angular acceleration of the UAV relative to the body coordinate system {B} The components are as follows:

[0175]

[0176] in This is the roll acceleration. For pitch acceleration, It is the pitch acceleration;

[0177] Taking the derivative with respect to the unit vector p, we get:

[0178]

[0179] Therefore there is

[0180]

[0181] Taking the cross product p on both sides of formula (11), we get:

[0182]

[0183] The unit vector p is obtained according to formula (11). (n) Depends on r L (n+2) That is, the unit vector p depends on Therefore, by combining formula (8), we can further see the position r of the UAV. (n) Depends on r L (n+2) That is, the drone's position r and its derivative r (n) It can be represented by a flat output and its finite-order differential;

[0184] According to formula (13), f depends on and According to formulas (14)-(18), R also depends on and According to step S21, Depends on r L (4) That is, both f and R depend on r. L (4) That is, the UAV rotation matrix R and lift f can be represented by a flat output and its finite-order differential.

[0185] According to formula (24), the angular velocity Ω of the UAV depends on r. L (5) Furthermore, combining formulas (7)-(10), it can be concluded that the torque M depends on... That is, the angular velocity Ω and torque M of the UAV can be represented by a flat output and its finite-order differential.

[0186] According to formula (27), ω depends on That is, the unit vector p and the angular velocity ω can be represented by the flat output and its finite-order differential.

[0187] In summary, the state variables of the UAV hoisting system And the input variable u = [f, M] T All can be determined by the suspended load position r L The yaw angle ψ of the UAV and its finite-order differential are expressed, so the position r of the suspended load is... L The yaw angle ψ of the UAV is the flat output variable z, i.e., z = [r L ,ψ] T Therefore, the drone mounting system has differential flatness.

[0188] S3. Filter the trajectory of the suspended load 3 using a zero-vibration and differential input shaper (ZVD); The flat output variable derived in step S2 (i.e., the desired suspended load position r) is then used to... LThe yaw angle ψ of the UAV is used as the input variable of the input shaper. The input variable processed by the input shaper is used as a new input command to input the control system, thereby controlling the trajectory of the UAV 1 and thus realizing the rapid balance and oscillation attenuation of the suspended load 3.

[0189] Input shaping refers to a technique where a new instruction, formed by convolving a pulse sequence with a desired input command, is used as the system input. This allows the system to complete rigid body motion without inducing, or only inducing, engineering-acceptable residual vibrations. The pulse sequence is called the input shaper, and its duration and amplitude are determined based on the system's modal frequencies and damping ratios. A simplified diagram of input shaping is shown below. Figure 2 As shown.

[0190] When a multi-pulse sequence of input shaper is applied to the system, the residual vibration amplitude of the system at the time of the last pulse is...

[0191]

[0192] in,

[0193] When the last pulse ends, the system vibration is eliminated.

[0194]

[0195] To minimize the time delay, the first pulse should occur at time zero.

[0196] t1=0 (29)

[0197] At the same time, to ensure that the motion of the rigid body system is consistent before and after forming, constraint equations are added:

[0198]

[0199] From the constraint equations (29)-(30), a zero residual vibration input shaper with first-order robustness can be obtained, called the ZVD input shaper, and its expression is as follows:

[0200]

[0201] In formula (31), T d =2π / ω d For the damping period,

[0202] In the UAV 1 sling system, drag is treated as an external disturbance and compensated for; therefore, the damping coefficient ζ = 0. Simultaneously, the natural frequency ω of the oscillation of the sling load 3 is balanced. n The natural frequency ω of the system is determined to be... d ,

[0203]

[0204] The natural frequency is specified using the drone 1 and the payload quality.

[0205] like Figure 3 As shown, the control principle of this invention is as follows:

[0206] By using ZVD as a feedforward mechanism, the control input signals of the UAV 1 sling system (i.e., the sling load position rL and the UAV yaw angle ψ, which are used as input signals based on the differential flatness verification of the UAV sling system) are convolved to obtain new input signals, which are then input into the control system to control the flight trajectory of UAV 1. This allows UAV 1 to fly in a favorable manner to stabilize the sling load 3, reduce the high-frequency, high-speed load oscillations caused by the strong coupling between UAV 1 and the sling load 3, and improve the overall motion performance of the system.

[0207] like Figure 4 , 5 As shown, a ZVD input forming experiment was conducted:

[0208] To verify the impact of ZVD input shaping technology on trajectory generation, the initial state of the suspended load 3 is defined as r. L = [0, 0, -l], the target state is r L =[2,2,1], UAV yaw angle ψ:0→60°. Input forming parameter settings are shown in Table 2.

[0209] Table 2 Input Forming Parameter Settings

[0210]

[0211] The system applies ZVD input forming technology, and the positions of the UAV 1 and the suspended load 3 are as follows: Figure 4 As shown in the figure (the left side of the figure represents the position of UAV 1, and the right side represents the position of the suspended load 3), it can be seen that the initial desired trajectories of both UAV 1 and suspended load 3 exhibit slight braking when they reach the halfway point of their ascent time, directly causing system oscillations. After applying ZVD input shaping technology, it can be observed that the ZVD filter causes a certain angle of tilt in the trajectory, thus allowing for early prediction of the acceleration and deceleration of the system motion at the beginning and end of the trajectory. ZVD input shaping technology accelerates the slight decay of the system's transient response. The trajectory optimization diagram of the UAV 1 suspended system using input shaping technology is shown below. Figure 5 As shown, without ZVD input shaping technology, UAV 1 exhibits greater maneuverability during mission execution, resulting in noticeable oscillations in its flight trajectory. When a ZVD filter is applied, UAV 1's flight trajectory becomes closer to a straight line.

[0212] like Figure 6-7 As shown, a suspension load 3 swing reduction experiment was conducted.

[0213] To evaluate the performance of the control scheme proposed in this invention, a comparative analysis was conducted among three different configurations:

[0214] Configuration I: Given a drone trajectory

[0215] Configuration II: Given an input-shaped UAV trajectory

[0216] Configuration III: Given a suspended load 3-track based on the differential flatness of the input shaping

[0217] Three different configurations are applied, with the suspension rope swing angle as follows: Figure 6 As shown. Analyzing the oscillation attenuation of the suspended load 3 from the perspective of the suspension rope's swing angle is more significant. From configuration I, it can be seen that φ L The resulting oscillation angle reached a maximum of 600 degrees, causing severe oscillations of the suspended load 3 and significantly impacting the stability of the entire UAV 1 suspension system. When ZVD input forming technology (Configuration II) and a differential flattening model (Configuration III) were applied, the oscillations of the suspended load 3 were significantly suppressed. Furthermore, the equilibrium oscillations of the suspended load 3 in Configuration III became much milder.

[0218] Furthermore, in order to quantitatively compare the performance of the three different configurations, the following parameters are given to measure the system performance.

[0219]

[0220] Where, γ RMS β represents the average position error of the UAV. RMS For the tilt angle of the drone fuselage, when β RMS A larger α value means a larger roll and yaw angle for the drone, and a longer flight time; RMS The load oscillation level is zero in the ideal state; f RMS This represents the degree of oscillation in the attitude angular frequency of the UAV.

[0221] like Figure 7 The figure shows a quantitative performance comparison of three different configurations. It can be observed from the figure that in configuration I (i.e., without a clearly defined load oscillation attenuation strategy), the UAV fuselage tilt angle β... RMS and load oscillation degree α RMS Both are maximum. Configuration III exhibits the smallest positional error and load oscillation, demonstrating the effectiveness of the input-shaped differential flattening model.

[0222] This invention provides a control method for a UAV sling system based on input shaping and differential flatness, enabling the suspended load to achieve minimal residual oscillation with the fastest possible motion. First, the differential flatness of the UAV sling system is verified, allowing the determination of the UAV's reference trajectory based on the desired load trajectory and the UAV's yaw angle. Second, ZVD input shaping technology is applied to the UAV sling system, determining the natural frequency of the suspended load's balancing oscillation as the system's natural frequency, thereby achieving rapid oscillation decay of the suspended load.

[0223] Simulation experiments were designed to perform ZVD input shaping and suspended load sway reduction experiments, and three different configurations were set up to analyze and illustrate the system. Experimental results show that ZVD input shaping technology can predict the acceleration and deceleration of the system motion at the beginning and end of the trajectory in advance, accelerating the slight decay of the system's transient response. Furthermore, configuration III, which provides a suspended load trajectory based on the differential flatness of input shaping, has the smallest position error and load oscillation degree, thus verifying the effectiveness of the trajectory generation strategy.

[0224] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A control method for a UAV sling system based on input shaping and differential flattening, characterized in that, Includes the following steps: S1. Establish a dynamic model of the UAV sling system; The UAV sling system includes the UAV, the suspension rope, and the sling load. The suspension rope is fixedly connected to the middle of the lower side of the UAV, and the sling load is fixed to the lower end of the suspension rope; Based on the positional relationship between the UAV and the sling load when the suspension rope is tensioned, establish a dynamic model of the UAV sling system. S2. Verify the differential flatness of the UAV mounting system and derive the flat output variable; S3. Filter the trajectory of the suspended load using the input shaper; use the flat output variable derived in step S2 as the input variable of the input shaper, and use the input variable processed by the input shaper as a new input command to input into the control system to control the trajectory of the UAV.

2. The UAV sling system control method based on input shaping and differential flatness according to claim 1, characterized in that: The state variables of the drone hoisting system are Where r is the UAV position, R is the UAV rotation matrix, Ω is the UAV angular velocity, and p is the unit vector from the center of mass of the suspended load to the center of mass of the UAV; the input variables of the UAV sling system are u = [f, M]. T , where f is the total lift of the UAV and M is the torque of the UAV.

3. The UAV sling system control method based on input shaping and differential flatness according to claim 2, characterized in that: In step S1, the Euler-Lagrange equations are used to establish the dynamic model of the UAV sling system. The specific process is as follows: First, establish an inertial coordinate system {E}, a body coordinate system {B}, and a load coordinate system {S} for the UAV sling system; An inertial coordinate system {E} is fixed on the Earth's surface, with its origin O. E The takeoff point of the drone is fixed on the ground, O E X E The axis points in the direction of the drone's forward flight, O E Z E The axis is vertically upward, O E Y E The axis is perpendicular to O E X E Y E For planes, the right-hand rule applies. The body coordinate system {B} is fixed on the body of the UAV and moves with the UAV; the origin O B At the center of mass of the drone, O B X B The axis lies within the plane of symmetry of the UAV, parallel to the line connecting the front and rear rotors, and points in the forward flight direction; O B Y B The axis is parallel to the line connecting the left and right rotors, with the positive direction being to the right; O B Z B Shaft and O B X B Y B The plane is perpendicular, and the direction is determined according to the right-hand rule; The load coordinate system {S} is fixed on the center of mass of the suspended load and moves with the suspended load; the origin O S At the center of gravity of the suspended load, O S X S Pointing in the forward swing direction of the suspended load; O S Y S The direction of the load's left and right swing is indicated by pointing to the left, with left pointing being the positive direction; O S Z S With O S X S Y S The plane is perpendicular, and the direction is determined according to the right-hand rule; When the suspension rope is taut, the positional relationship between the drone and the suspended load is as follows: r L ＝r+lp(1) In formula (1), Let {E} be the position of the suspended load relative to the inertial coordinate system. Let {E} be the position of the UAV relative to the inertial coordinate system {E}. The length of the suspension rope. Let be the unit vector from the center of mass of the suspended load to the center of mass of the UAV; The unit vector p passes through continuous loops around Z. E Obtained by rotating the axis twice In formula (2), φ L For suspension ropes wrapped around O E X E The swing angle of the axis, θ L For suspension ropes wrapped around O E Y E The swing angle of the shaft, Let R(φ) be the rotation matrix from the body coordinate system {B} to the load coordinate system {S}. L ) and R(θ L ) and respectively, the load coordinate system {S} around O E X E Shaft and O E Y E The rotation matrix of the axis; The dynamic model of the UAV sling load system is established using the Euler-Lagrange equations as follows: In formula (3), These are the velocity and acceleration of the suspended load relative to the inertial coordinate system {E}, respectively. These are the drone's mass and the mass of the load it carries, respectively. It is the acceleration due to gravity; R∈SO(3) is the total lift of the UAV; R∈SO(3) is the rotation matrix from the inertial coordinate system {E} to the body coordinate system {B}; e z =[0 0 1]; Let ω be the angular velocity of the suspended load relative to the inertial coordinate system {E}. Let be the inertial matrix of the UAV relative to the inertial coordinate system {E}; Let be the angular velocity of the UAV relative to the body coordinate system {B}; For the torque of the drone.

4. The UAV sling system control method based on input shaping and differential flatness according to claim 3, characterized in that, The specific process of step S2 is as follows: Taking the nth-order differential of formula (1), we can derive: r (n) ＝r L (n) -lp (n) (4) According to the equation of motion of the suspended load: And unit vectors: We can obtain: In formulas (5) and (6), T refers to the tension of the suspension rope; According to the dynamic model of the UAV hoisting system, i.e., formula (3), we can obtain: Therefore: in The UAV is parallel to the body coordinate system {B}O B Z B The unit vector of the axis; To obtain the rotation matrix from the body coordinate system {B} to the inertial coordinate system {E} definition Assuming the body coordinate system {B} rotates to the inertial coordinate system {E} in the order of Z-axis - Y-axis - X-axis, c y -b z plane and b y -b z Since the planes are the same, the remaining two unit vectors of the organism can be found: in The UAV is parallel to the body coordinate system {B}O B X B The unit vector of the axis; The UAV is parallel to the body coordinate system {B}O B Y B The unit vector of the axis; Therefore, the rotation matrix R is: Taking the first derivative of formula (8), we get: Formula (15) in unit vectors The projection on is: Substituting formula (16) into formula (15) and rearranging, we get: Therefore, the angular velocity of the UAV relative to the body coordinate system {B} The components are as follows: in The roll rate is angular velocity. The pitch angular velocity, Yaw angular velocity; Therefore, the angular acceleration of the UAV relative to the body coordinate system {B} The components are as follows: in This is the roll acceleration. For pitch acceleration, It is the pitch acceleration; Taking the derivative with respect to the unit vector p, we get: Therefore there is Taking the cross product p on both sides of formula (7), we get: According to formula (7), the unit vector p is obtained. (n) Depends on r L (n+2) That is, the unit vector p depends on Therefore, by combining formula (4), we can further see the position r of the UAV. (n) Depends on r L (n+2) ; According to formula (9), f depends on and According to formulas (10)-(14), R also depends on and According to step S21, Depends on r L (4) That is, both f and R depend on r. L (4) ; According to formula (20), the angular velocity Ω of the UAV depends on r. L (5) Furthermore, combining formulas (3)-(6), it can be concluded that the torque M depends on... According to formula (23), ω depends on Therefore, the UAV mounting system possesses differential flatness, and its flat output variable is z, z = [r L ,ψ] T .

5. The UAV sling system control method based on input shaping and differential flatness according to claim 4, characterized in that: In step S3, the input forming device adopts a zero-vibration and differential input forming device, namely ZVD.

6. The UAV sling system control method based on input shaping and differential flatness according to claim 5, characterized in that: The formula model of ZVD is In formula (24), T d =2π / ω d For the damping period, In the UAV mounting system, drag is treated as an external disturbance and compensated for; therefore, the damping coefficient ζ = 0. Simultaneously, the natural frequency ω of the load balancing oscillation is considered. n The natural frequency ω of the system is determined to be... d , and formula That is, the natural frequency ω d The expression.

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