A robust control method for mass load of cooperative lifting points of a swarm of rotary-wing UAVs

Abstract

The present invention relates to a robust control method for the coordinated lifting point mass load of a cluster of rotorcraft drones, comprising the following steps: establishing a dynamic model of a four-rotor drone cluster coordinated lifting system including disturbances based on Lagrangian mechanics and the Hamilton principle; constructing a robust controller for the coordinated lifting point mass load based on the dynamic model using the backstepping method, sequentially controlling the load position, cable direction, and drone attitude; at the same time, introducing a saturation function to ensure that the rotorcraft drone thrust is bounded relative to the load position error and velocity error; introducing a disturbance estimator and embedding it into the control input of each rotorcraft drone; and determining an update method for the disturbance estimator through a projection function to obtain the desired thrust and the drone's angular velocity, thereby controlling the point mass load to stably move in the presence of disturbances. Compared with the prior art, the present invention has strong robustness, ensuring that the load can track a predetermined trajectory with high precision in an interference environment.

Description

Technical Field

[0001] The present invention relates to the field of automatic control of load transportation, and in particular to a robust control method for cooperative lifting point mass loads of a cluster of rotary-wing unmanned aerial vehicles. Background Art

[0002] A key application area for rotary-wing drones is logistics. Compared to traditional logistics, rotary-wing drones offer low costs, convenience, efficiency, and flexible dispatch. They can quickly and easily reach locations inaccessible by road or water, opening up a wide range of supply and rescue opportunities. For example, when an earthquake disrupts transportation networks, they can be used to quickly deliver medical supplies and relief aid. Following a tsunami or severe storm, they can also be used to quickly transport materials and supplies to offshore oil rigs. Notably, major e-commerce companies such as JD.com and Amazon, leveraging their respective platforms' technological advantages, have begun deploying rotary-wing drones for autonomous, rapid short-distance delivery. Currently, this delivery model is primarily based on a "fixed" delivery model. However, this fixed delivery model has the following limitations: 1) strict requirements on payload weight and shape limit its application scenarios; and 2) the payload itself significantly impacts the rotary-wing drone's flexibility.

[0003] The rotor UAV lifting system can break the limitations of the UAV fixed delivery system. Especially for the delivery mission scenarios of larger or heavier loads, multiple rotor UAVs can be used to transport them through coordinated suspension with cables. In some emergency response fields, such as emergency fire rescue and rapid delivery of military equipment, rotorcraft lifting and transportation systems also have important application needs. Rotor UAV lifting systems can be divided into single-machine lifting systems and multi-machine collaborative lifting systems. Single-machine lifting systems are suitable for small-light load transportation scenarios. For large-heavy loads, single-machine lifting is no longer applicable. In this case, multi-machine collaborative lifting becomes a better choice. However, due to the introduction of the "bond" of the load, strong mutual constraints between the internal systems (rotor UAV-cable-load-cable-rotor UAV) are added, such as Figure 1 As shown in the figure, more nonlinear and uncertain coupling terms are introduced, which complicates the overall mathematical motion model of the system and leads to problems such as difficulty in coordination between UAVs and difficulty in controlling the position of payloads. Summary of the Invention

[0004] The purpose of the present invention is to provide a robust control method for the collaborative lifting of point mass loads by a cluster of rotorcraft UAVs, simplify the control architecture, ensure strong robustness, ensure that the load can track the predetermined trajectory with high precision, and realize the collaborative lifting of heavier point mass loads by a cluster of rotorcraft UAVs in an interference environment.

[0005] The purpose of the present invention can be achieved by the following technical solutions:

[0006] A robust control method for cooperatively lifting mass loads of a cluster of rotary-wing UAVs comprises the following steps:

[0007] S1: Based on Lagrangian mechanics and Hamilton's principle, a dynamic model of a quadcopter swarm collaborative lifting system with disturbances is established. In this system, the quadcopter and the point mass load are connected by an inelastic cable.

[0008] S2: Based on the dynamic model, the backstepping method is used to construct a robust controller for the coordinated lifting point mass load, which controls the load position, cable direction and drone attitude in turn. At the same time, a saturation function is introduced to ensure that the thrust of the rotor drone is bounded relative to the load position error and velocity error. A disturbance estimator is introduced and embedded into the control input of each rotor drone, and the update method of the disturbance estimator is determined by the projection function to obtain the desired thrust and angular velocity of the drone, so that the control point mass load can move stably in the presence of disturbances.

[0009] The model of the point mass load is a mass point with two degrees of freedom.

[0010] Said S1 comprises the following steps:

[0011] S11: Consider a body coordinate system {B i}, the position and velocity of the i-th quadrotor drone are expressed as p i 、v i ; The attitude and angular velocity of the i-th quadrotor drone are Ω i ; The position and velocity of the load are p L v L ; The direction and angular velocity of the i-th cable are q i 、ω i , the rope length is l i The kinematic equation of the multi-machine collaborative lifting system is:

[0012]

[0013]

[0014]

[0015] The position and speed relationship between the i-th UAV and the payload is:

[0016] p i =p L -l i q i #(4)

[0017] v i =vL -l i S(ω i )q i #(5)

[0018] S12: Determine the total kinetic energy and gravitational potential energy of the system:

[0019]

[0020]

[0021] Among them, m i is the mass of the i-th UAV;

[0022] S13: Determine the Lagrangian mechanics of the entire hoisting system:

[0023] S14: Neglecting the quadrotor rotational kinetic energy, the entire system is subjected to the rotor thrust f i =-T i R i c3 and the upper-limit unknown constant external disturbance d of the payload and the UAV respectively L d i , the virtual work done by these forces is:

[0024]

[0025] Among them, δp i and δp L is the arbitrary virtual displacement of the i-th UAV and payload;

[0026] According to D'Alembert's principle, the dynamics of the system satisfies:

[0027]

[0028] Using the method of integration by parts, we can derive the following Euler-Lagrange equation:

[0029]

[0030]

[0031] S15: Determine the dynamic model of the system from the above equations:

[0032]

[0033]

[0034] in, is a symmetric positive definite matrix.

[0035] By and q i consistent direction Independent control, and By and Force control in two directions. Since the quadrotor UAV system is under-actuated, the rotor thrust T i Direction-R i c3 cannot be set arbitrarily. By controlling the angular velocity, the attitude of the aircraft can be controlled, so f i Aim at the desired direction and finally achieve trajectory tracking. We first need to design a virtual force Decompose it into two components that are perpendicular to each other and These two components are used to control the position of the load and the direction of the cable. In order to eliminate the error in the thrust direction, in the last step of the backstepping process, the angular velocity Ω of the quadrotor is set i Make the actual thrust direction -r i With the expected thrust direction consistent.

[0036] The controller design process is divided into three parts: payload position control, cable direction control, and drone attitude control.

[0037] The load position control is:

[0038] Define the position and velocity errors of the load:

[0039] e p =p L -p d #(14)

[0040]

[0041] Define the Lyapunov function V1:

[0042]

[0043] where e=k1(e p +βe v ) is the coupling error, k1 and β are the positive gain;

[0044] The saturation function is defined as

[0045] Taking the derivative of V1, we get:

[0046]

[0047] By transformation we get:

[0048]

[0049] Where W1 is positive definite, the expression is W1: = βσ T (e)σ(e)+k2(βσ(e)+e v ) T σ(βσ(e)+e v );

[0050] In order to eliminate the influence of external disturbance on the system, the estimation of disturbance amount is introduced The estimated error is Will Rewrite it as follows:

[0051]

[0052] Write the known quantity in the above formula as ζ, but:

[0053]

[0054] design To eliminate the known quantity ζ, the expected for:

[0055]

[0056] The component u i With q i The direction is consistent, and

[0057] Define the matrix Q = [q1, q2, ..., q n ],get:

[0058] u i =-c i，n Q T (QQ T ) -1 ζq i #(twenty two)

[0059] Substituting into formula (18) we get The final form is:

[0060]

[0061] The cable direction control is:

[0062] Define the third error:

[0063]

[0064] in is a smooth curve representing the desired direction of the i-th cable in the inertial system, assuming that at least three desired directions are linearly independent of each other;

[0065] Define the second Lyapunov function as:

[0066]

[0067] By derivatizing and transforming the Lyapunov function, we obtain the following expression:

[0068]

[0069] The next step in the backstepping process is to eliminate the third term in the above equation. To simplify the mathematical expression, the fourth error is defined as:

[0070]

[0071] After introducing the new error, the third Lyapunov function is defined as:

[0072]

[0073] The derivative of V3 is:

[0074]

[0075] definition After transformation, we get:

[0076]

[0077] in is a positive definite term;

[0078] definition To eliminate The second item in:

[0079]

[0080] Will Substituting into formula (28), since get:

[0081]

[0082] The expected thrust of the rotary wing UAV is The direction of the desired thrust is

[0083] The UAV attitude control is:

[0084] Define the directional error between the actual thrust and the expected thrust of the drone:

[0085]

[0086] The thrust of the i-th UAV is:

[0087]

[0088] Will Decomposed into i Parallel and vertical parts At the same time and T i Substituting into formula (30), we get:

[0089]

[0090] Introducing new errors Then, define the fourth Lyapunov function as:

[0091]

[0092] Taking the derivative of V4 we get:

[0093]

[0094] To eliminate The second item in sets the angular velocity of the drone to:

[0095]

[0096] where ψ i and is the actual and expected yaw angle of the i-th UAV;

[0097] eliminate After the second term in , we add the perturbation estimator to obtain the final Lyapunov function and its derivative:

[0098]

[0099]

[0100] in The updating rule of the disturbance estimator is:

[0101]

[0102]

[0103] The final form of the derivative of the Lyapunov function is:

[0104]

[0105] Compared with the prior art, the present invention has the following beneficial effects:

[0106] The present invention takes the payload as the direct controlled object and reversely designs the controller of each rotorcraft, simplifies the control architecture, takes into account the impact of external interference on the overall system, and embeds the estimated value of the unknown interference into the control input of each rotorcraft, thereby resisting the influence of external interference and ensuring that the heavier mass payload can track the predetermined trajectory with high precision in an interference environment, with strong robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0107] Figure 1 This is a schematic diagram of the mutual constraints of the multi-machine collaborative lifting system;

[0108] Figure 2 This is a schematic diagram of a multi-machine collaborative lifting system;

[0109] Figure 3 Flow chart of the method of the present invention. DETAILED DESCRIPTION

[0110] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0111] This embodiment provides a robust control method for the mass load of a coordinated lifting point of a cluster of rotary-wing UAVs. Figure 3 As shown, the following steps are included:

[0112] S1: Based on Lagrangian mechanics and Hamilton principle, a dynamic model of a four-rotor UAV cluster cooperative lifting system with disturbance is established. In the system, the UAVs and point mass loads are connected by inelastic cables, such as Figure 2 At the same time, determine the physical parameters of the system, such as the weight of the drone and payload, the length of the cable, etc.

[0113] S2: Based on the dynamic model, the backstepping method is used to construct a robust controller for the coordinated lifting point mass load. The load position, cable direction, and UAV attitude are controlled in sequence. At the same time, a saturation function is introduced to ensure that the thrust of the rotor UAV is bounded relative to the load position error and velocity error. A disturbance estimator is introduced and embedded in the control input of each rotor UAV. The update method of the disturbance estimator is determined by the projection function to obtain the desired thrust and angular velocity of the UAV, and the control point mass load moves stably in the presence of disturbances.

[0114] The process of establishing the controller in this embodiment is described in detail in the Summary of the Invention section and will not be repeated here.

[0115] In the actual control process, S2 includes the following steps:

[0116] S21: Obtain the status information of each rotorcraft and point mass payload through sensors and feed it back to the ground station.

[0117] S22: Given the desired transport trajectory, the rotorcraft UAV cluster is controlled to collaboratively perform the task of lifting the mass load according to the collaborative lifting point mass load robust controller in S2.

[0118] The expected delivery trajectory function determined in this embodiment is as follows:

[0119]

[0120] in

[0121]

[0122] During the simulation, this embodiment selects 4 rotor UAVs (ie, n=4); the mass of each rotor UAV is m i =0.21kg; the mass of the load is m L =0.06kg; the length of the cable is l1=l3=0.6m, l2=0.8m, l4=1.0m; the control parameters are β=0.5, k1=3, k2=2, k q =10,k ω =4,k r =300,h q =10,h ω =1,h r =50, When conducting simulation verification, it is also necessary to adjust parameters according to actual conditions to prepare for experimental verification.

[0123] S23: The point mass load is transported to the destination along the desired trajectory, completing the collaborative lifting task in the interference environment.

[0124] The above describes in detail the preferred embodiments of the present invention. It should be understood that those skilled in the art can make numerous modifications and variations based on the concepts of the present invention without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.

Claims

1. A robust control method for the mass load of a coordinated lifting point of a cluster of rotary-wing UAVs, characterized by: The following steps are involved: S1: Based on Lagrangian mechanics and Hamilton's principle, a dynamic model of a quadcopter swarm collaborative lifting system with disturbances is established. In this system, the quadcopter and the point mass load are connected by an inelastic cable. S2: Based on the dynamic model, a robust controller for the coordinated lifting point mass load is constructed using backstepping. The controller sequentially controls the load position, cable direction, and UAV attitude. A saturation function is introduced to ensure that the rotor UAV thrust is bounded relative to the load position error and velocity error. A disturbance estimator is introduced and embedded into the control input of each rotor UAV. The disturbance estimator is updated using a projection function to obtain the desired thrust and UAV angular velocity. This ensures stable motion of the control point mass load in the presence of disturbances. The model of the point mass load is a mass point with two degrees of freedom; Said S1 comprises the following steps: S11: Consider a body coordinate system {B i }, the position and velocity of the i-th quadrotor drone are expressed as p i 、v i ; The attitude and angular velocity of the i-th quadrotor drone are Ω i ; The position and velocity of the load are p L v L ; The direction and angular velocity of the i-th cable are q i 、ω i , the rope length is l i The kinematic equation of the multi-machine collaborative lifting system is: The position and speed relationship between the i-th UAV and the payload is: p i =p L -l i q i v i =v L -l i S(ω i )q i S12: Determine the total kinetic energy and gravitational potential energy of the system: Among them, m i is the mass of the i-th UAV; S13: Determine the Lagrangian mechanics of the entire hoisting system: S14: Neglecting the quadrotor rotational kinetic energy, the entire system is subjected to the rotor thrust f i =-T i R i c3 and the upper-limit unknown constant external disturbance d of the payload and the UAV respectively L d i , the virtual work done by these forces is: Among them, δp i and δp L is the arbitrary virtual displacement of the i-th UAV and payload; According to D'Alembert's principle, the dynamics of the system satisfies: Using the method of integration by parts, we can derive the following Euler-Lagrange equation: S15: Determine the dynamic model of the system: in, is a symmetric positive definite matrix.

2. The robust control method for mass load of a coordinated lifting point of a swarm of rotary-wing UAVs according to claim 1 is characterized in that: In the kinetic model, By and q i consistent direction Independent control, By and Force control in two directions; since the quadrotor UAV system is under-actuated, the rotor thrust T i Direction-R i c3 cannot be set arbitrarily. By controlling the angular velocity to control the attitude of the aircraft, f i Aim at the desired direction and finally achieve trajectory tracking.

3. The robust control method for the mass load of the coordinated lifting point of a cluster of rotary-wing UAVs according to claim 1 is characterized in that: A virtual force is introduced in S2 Decompose it into two components that are perpendicular to each other and These two components are used to control the position of the load and the orientation of the cable, respectively.

4. The robust control method for mass load of a coordinated lifting point of a swarm of rotary-wing UAVs according to claim 1 is characterized in that: In order to eliminate the error in the thrust direction in S2, in the last step of the backstepping method, the angular velocity Ω of the quadrotor drone is set i Make the actual thrust direction -r i With the expected thrust direction consistent.

5. The robust control method for mass load of a coordinated lifting point of a swarm of rotary-wing UAVs according to claim 1 is characterized in that: The controller design process is divided into three parts: payload position control, cable direction control and UAV attitude control. In the payload position control, the disturbance estimator and saturation function are introduced.

6. The robust control method for mass load of a coordinated lifting point of a cluster of rotary-wing UAVs according to claim 5 is characterized in that: The load position control is: Define the position and velocity errors of the load: e p =p L -p d Define the Lyapunov function V1: where e=k1(e p +βe v ) is the coupling error, k1 and β are the positive gain; The saturation function is defined as Taking the derivative of V1, we get: By transformation we get: Where W1 is positive definite, the expression is In order to eliminate the influence of external disturbance on the system, the estimation of disturbance amount is introduced The estimated error is Will Rewrite it as follows: Write the known quantity in the above formula as ζ, but: design To eliminate the known quantity ζ, the expected for: The component u i With q i The direction is consistent, and Define the matrix Q = [q1,q2,···,q n ],get: u i =-c i,n Q T (QQ T ) -1 ζq i Thus we get The final form is:

7. The robust control method for mass load of a coordinated lifting point of a cluster of rotary-wing UAVs according to claim 6 is characterized in that: The cable direction control is: Define the third error: in is a smooth curve representing the desired direction of the i-th cable in the inertial system, assuming that at least three desired directions are linearly independent of each other; Define the second Lyapunov function as: By derivatizing and transforming the Lyapunov function, we obtain the following expression: The next step in the backstepping process is to eliminate the third term in the above equation. To simplify the mathematical expression, the fourth error is defined as: After introducing the new error, the third Lyapunov function is defined as: The derivative of V3 is: definition After transformation, we get: in is a positive definite term; definition To eliminate The second item in: Will Substitute the derivative expression of the third Lyapunov function, since get: The expected thrust of the rotary wing UAV is The direction of the desired thrust is 8. The robust control method for mass load of a coordinated lifting point of a cluster of rotary-wing UAVs according to claim 7 is characterized in that: The UAV attitude control is: Define the directional error between the actual thrust and the expected thrust of the drone: The thrust of the i-th UAV is: Will Decomposed into i Parallel and perpendicular parts At the same time and T i Substitution Transforming the derivative, we get: Introducing new errors Then, define the fourth Lyapunov function as: Taking the derivative of V4 we get: To eliminate The second item in sets the angular velocity of the drone to: where ψ i and is the actual and expected yaw angle of the i-th UAV; eliminate After the second term in , we add the perturbation estimator to obtain the final Lyapunov function and its derivative: in The updating rule of the disturbance estimator is: The final form of the derivative of the Lyapunov function is:

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