Layout and control collaborative design method of multi-unmanned aerial vehicle collaborative transportation system

Abstract

The invention belongs to the field of cooperative control algorithms and structural design, and particularly relates to a layout and control cooperative design method for a multi-unmanned-aerial-vehicle cooperative transportation system, and the method comprises the steps: building a dynamic model and a control model of the multi-unmanned-aerial-vehicle cooperative transportation system; carrying out comprehensive modeling on the physical layout and the control strategy of the multi-unmanned aerial vehicle cooperative transportation system, and then defining a comprehensive performance index and quantifying the comprehensive performance index into a model-optimizable objective function; performing parameterization processing on the layout position of the unmanned aerial vehicle, and describing the distribution position of the unmanned aerial vehicle around the load by using an angle parameter; meanwhile, the layout position of the unmanned aerial vehicle and controller parameters serve as optimization variables, and joint optimization is carried out; and applying the optimized layout position and controller parameters to an actual multi-unmanned aerial vehicle cooperative transportation system, and carrying out flight control and performance testing. According to the invention, the anti-disturbance capability, the stability and the tracking precision of the system are improved, and the transportation capability and the robustness of the system in a complex environment are remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the fields of cooperative control algorithms and structural design, and particularly relates to a collaborative design method for the layout and control of a multi-UAV cooperative transportation system. Background Art

[0002] Multi-UAV cooperative transportation systems have shown great application potential in multiple fields. In the logistics field, they can quickly and flexibly complete the tasks of goods distribution and transportation, especially suitable for the last-mile delivery in urban environments. In the construction field, multi-UAV systems can cooperate to carry building materials, accelerate the construction progress, and improve the construction efficiency. In terms of load lifting, multi-UAVs working together can lift large or heavy objects, expanding the possibilities of UAVs in industrial applications.

[0003] Current multi-UAV cooperative transportation systems face some challenges in layout and control. Unreasonable layout may lead to increased interference between UAVs, reducing transportation efficiency and even posing a collision risk. Insufficient control accuracy will affect the stability and accuracy of the system, especially in complex environments or in the face of external disturbances. In addition, existing technologies also have certain limitations in load capacity and robustness, restricting the application of multi-UAV systems in a wider range of scenarios. Summary of the Invention

[0004] In order to solve the above technical problems existing in the prior art, the present invention proposes a collaborative design method for the layout and control of a multi-UAV cooperative transportation system, and its specific technical solutions are as follows:

[0005] A collaborative design method for the layout and control of a multi-UAV cooperative transportation system, comprising:

[0006] By establishing the dynamic model and control model of the multi-UAV cooperative transportation system, comprehensively modeling the physical layout and control strategy of the multi-UAV cooperative transportation system, and then defining a comprehensive performance index and quantifying it as an objective function that can be optimized by the model;

[0007] Parametrize the layout positions of the UAVs, and use angular parameters to describe the distribution positions of the UAVs around the load;

[0008] At the same time, take the layout positions of the UAVs and the controller parameters as optimization variables and perform joint optimization;

[0009] Apply the optimized layout positions and controller parameters to the actual multi-UAV cooperative transportation system for flight control and performance testing.

[0010] Furthermore, the multi-UAV collaborative transportation system includes a payload and multi-rotor UAVs. Considering the system as a rigid body and describing the system motion state through a state vector, random Gaussian noise is introduced in the derivation of the dynamic model to simulate external disturbances.

[0011] Furthermore, the payload is geometric in shape, and the layout position parameters of the multi-rotor UAVs are parameterized as the attachment position angle variables θ = [θ i ,..., θ N T on the mid-plane of the payload, where θ i represents the attachment position of the i-th UAV on the curve Γ at the center of gravity of the payload shape;

[0012] The state vector x is defined as:

[0013]

[0014] where p and respectively represent the position and velocity of the payload center of gravity relative to the global world reference frame, γ represents the Roll-Pitch-Yaw triple, which defines the orientation of the local body frame, and ω represents the angular velocity relative to the local body frame; each rotor provides four thrust inputs, so if there are N rotors, the thrust input vector has a total of 4×N dimensions;

[0015] Based on Newton's laws of motion and Euler's rigid body dynamics equations, the dynamic model of the system is derived:

[0016]

[0017] where m and J respectively represent the total mass and inertia matrix of the system, g = [0, 0, -9.81] T is the gravitational acceleration vector, R is the rotation matrix, e3 is the third vector of the standard Euclidean basis, is the total thrust generated by all rotors, and τ is the total torque vector in the local frame;

[0018] The dynamic model is linearized in the hover configuration, and the thrust input vector is decomposed into where is the feedforward thrust, u′ is the first-order component of the linearized model. At the same time, the state vector x is decomposed into

[0019] The disturbance vector acting on the system is modeled as random Gaussian noise where and respectively represent the disturbing force and torque acting on the origin of the local body reference frame;

[0020] The continuous-time linearized dynamics equation is as follows:

[0021]

[0022] where, is obtained by taking the Jacobian matrix of the state vector x under hover conditions, and are obtained by taking the Jacobian matrices of the thrust input vector u and the disturbance vector d respectively, and these matrices depend on θ directly or through the system inertia.

[0023] Furthermore, applying optimal control theory to the integrated modeling of the physical layout and control strategy of a multi-UAV cooperative transportation system, the optimization objective is to minimize the system performance index, specifically including:

[0024] First, define the auxiliary variables:

[0025] z = Cx′ + Du′ (4)

[0026] where, x′ is the disturbance component of the state vector, u′ is the disturbance component of the thrust input, and C and D are weight matrices;

[0027] The aim is to find the feedback gain such that:

[0028] u′ = -K * (θ)x′ (5)

[0029] and minimize the integral control cost of :

[0030] J = ∫0 ∞ z T z dt (6)

[0031] According to optimal control theory, the optimal linear feedback controller that minimizes the cost function J is:

[0032] K * (θ) = (D T D) -1 B(θ) T S1(θ) (7)

[0033] where, B(θ) is the input matrix, and S1(θ) is the solution of the algebraic Riccati equation:

[0034] A T S1 + S1A - S1B(D T D) -1 B T S1 + C TC = 0 (8)

[0035] Among them, S1 is the solution of the algebraic Riccati equation, A is the dynamic matrix, and B is the input matrix;

[0036] The optimal cost function obtained by solving is:

[0037]

[0038] Among them, B d is the perturbation influence matrix, T represents the matrix transpose, and trace represents the trace of the matrix.

[0039] Furthermore, the Mahalanobis distance is used to quantify the distance between the thrust saturation hyperplane and the thrust input distribution, so that the thrust input is within the feasible region, specifically including:

[0040] Calculate the closed-loop state covariance S2(θ) of the system of the optimal linear feedback controller, which is affected by the same white noise disturbance d, and use the optimal continuous-time state observer theory to calculate, so as to obtain the equation:

[0041]

[0042] Among them, A f (θ) = A - B(θ)K * (θ) is the dynamic matrix of the closed-loop system, and B d is the perturbation influence matrix; the solution S2(θ) of this equation approximately represents the covariance after the system state is linearized under white noise disturbance;

[0043] The feedforward thrust value calculated from the hover equilibrium condition is obtained through formula (10), and the covariance matrix ∑ of the input obtained through the feedback law u = K * (θ) T S2(θ)K * (θ), and the goal is to maximize the probability of the feasible input;

[0044] Set the low saturation of the thrust to u l = u l 1 4N , and the high saturation is set to u h = u h 1 4N Among them, 1 4N represents a 4n-dimensional vector with all elements being 1. At this time, the optimization problem to be solved becomes:

[0045]

[0046] Among them, F(·) is the cumulative distribution on the thrust input, and its mean and covariance depend on θ;

[0047] The Mahalanobis distance is used to quantify the margin between the feedforward thrust and the thrust saturation. The Mahalanobis distance from point u to a distribution with mean and covariance ∑ u is defined as:

[0048]

[0049] By minimizing the Mahalanobis distance, the thrust input is made to be within the feasible region and far from the saturation boundary;

[0050] Based on the fact that each input component has a low saturation and a high saturation, and each quadcopter has four thrust inputs, there are 8N different hyperplanes in the input space. At this time, the goal of maximizing the probability of the feasible input in formula (11) is transformed into maximizing the Mahalanobis distance between the thrust saturation hyperplane and the input distribution. The optimization problem is formulated as:

[0051]

[0052] Find the optimal UAV layout parameter θ * to maximize the minimum Mahalanobis distance between the thrust saturation hyperplane and the feedforward thrust.

[0053] Furthermore, the joint optimization of the UAV layout position and the controller parameters specifically includes the following steps:

[0054] 1) Initialize parameters: Set the number of multi-rotor UAVs N = 4, the inertial parameters of the UAVs, the inertial parameters of the loads, the shape of the loads is a geometric rectangle, and the weight matrices C and D are selected according to the system performance requirements;

[0055] 2) Initial guess: Make an initial guess for the attachment position angle θ of the multi-rotor UAVs;

[0056] 3) System inertia calculation: Calculate the inertia matrix J of the entire system according to the current attachment position angle θ;

[0057] 4) System matrix calculation: Calculate the matrices A, B(θ) and B d (θ) in the system dynamics model according to the system inertia matrix J, as well as the feedforward thrust

[0058] 5) Solve the algebraic Riccati equation: Solve the algebraic Riccati equation using formula (8) to obtain the solution S1(θ);

[0059] 6) Feedback gain calculation: Calculate the optimal feedback gain matrix K * (θ) according to formula (7) using the obtained S1(θ) and the system matrix B(θ);

[0060] 7) State covariance calculation: According to formula (10), using the feedback gain matrix K * (θ) and the system dynamic matrix A f (θ), calculate the state covariance matrix S2(θ) of the closed-loop system;

[0061] 8) Input covariance calculation: According to the feedback law, calculate the covariance matrix ∑ of the input u = K * (θ) T S2(θ)K * (θ);

[0062] 9) Mahalanobis distance initialization: Initialize the minimum Mahalanobis distance to a relatively large value;

[0063] 10) Mahalanobis distance update: For each thrust input component u k and each thrust saturation value u a : u l or u h , solve the quadratic programming problem, calculate the Mahalanobis distance d′, and update the minimum Mahalanobis distance

[0064] 11) Layout update: Using the Nelder-Mead simplex method, update the attachment position angle θ of the quadrotor UAV according to the calculated minimum Mahalanobis distance ;

[0065] 12) Repeated iteration: Repeat steps 3) to 11) until the optimization is completed to obtain the optimal layout parameter θ of the quadrotor UAV * .

[0066] Furthermore, the outer loop of the controller uses the Nelder-Mead simplex method to optimize the layout parameters, and the inner loop of the controller solves the saturation constraint boundaries of each input channel through linear quadratic programming LQR.

[0067] Furthermore, the controller includes:

[0068] State estimator: By fusing data from sensors, use the filtering algorithm to estimate the estimated state of the system in real time

[0069] LQR controller: Based on the estimated state and the desired state x d , the LQR controller calculates the optimal thrust input u by minimizing the weighted sum of the state deviation and the control input;

[0070] Communication channel: Responsible for distributing the thrust input u calculated by the LQR controller to each rotor. Through N parallel communication channels, each rotor can receive an independent thrust command, thereby achieving individual control of each rotor.

[0071] Rotor control unit: Responsible for controlling each rotor according to the received thrust command, converting the thrust command into a motor control signal, and driving the rotor to generate the required thrust to achieve control of the system's movement.

[0072] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0073] The method of the present invention jointly solves the layout design and control synthesis problems through an optimization routine inspired by control theory. The optimization framework of the present invention allows the system to accommodate different payload shapes, inertias, and the number of quadcopters. The selection of the weight matrices C and D represents the degree of freedom for control designers to obtain the desired performance. The present invention is a co-design tool that uses the idea of robust control to calculate the optimal layout of the thrust modules around the payload.

[0074] Specifically, the present invention proposes a novel cost function that can capture the robustness of the multi-UAV system to disturbances, and proposes an effective procedure for optimizing this cost function with respect to the layout variables, and verifies the effectiveness of the proposed method through experiments. The experimental results show that the optimized layout and control strategy can significantly improve the stability and anti-disturbance ability of the system, especially in the case of loads with different shapes and masses.

[0075] In summary, through an innovative co-design method, the present invention combines the physical layout of the multi-UAV system with the optimization of the control strategy, and uses advanced optimization algorithms and simulation verification means to improve the anti-disturbance ability, stability, and tracking accuracy of the system, and significantly enhances the transportation ability and robustness of the system in complex environments. Description of the Drawings

[0076] Figure 1 Schematic diagram of the payload of the quadcopter UAV for collaborative transportation of a single panel in an embodiment of the present invention;

[0077] Figure 2 Schematic diagram of the geometric shape of the payload and its midplane in an embodiment of the present invention. The intersection of the payload and the side is the curve Γ;

[0078] Figure 3 Schematic diagram of the quadcopter UAV attached along the curve Γ in an embodiment of the present invention, including the positions θ i (i = 1,..., 4) of the attachment points, the position of the center of mass of the rigid body reference frame (the center of Γ), and the action point t d of the disturbing force f​d ;

[0079] Figure 4 This is a two-dimensional example diagram of the minimum Mahalanobis distance for input saturation in an embodiment of the present invention. In the figure, the random variables u1 and u2 are in the interval [u l , u h , centered at the point (u1, u2), showing the contour lines of the Mahalanobis distance. These contour lines represent the distance from the point to the distribution and determine the minimum distance through the tangent of the ellipse;

[0080] Figure 5 This is a block diagram of the control architecture in an embodiment of the present invention;

[0081] Figure 6 This is the optimal layout optimization flow chart in an embodiment of the present invention. Detailed implementation manners

[0082] In order to make the objectives, technical solutions and technical effects of the present invention clearer, the following further elaborates on the present invention in detail in conjunction with the specification drawings and embodiments.

[0083] This embodiment discloses a collaborative design method for the layout and control of a multi-UAV collaborative transportation system, including:

[0084] First, comprehensively model the physical layout and control strategy of the multi-UAV collaborative transportation system as shown in Figure 1 , and analyze and optimize the two as a whole. By establishing the dynamic model and control model of the system, clarify the influence mechanism of the layout parameters and controller parameters on the system performance. Then define a comprehensive performance index to quantify the performance requirements in multiple aspects such as the stability, response speed, and load adaptability of the system into an optimizable objective function.

[0085] Parametrize the layout positions of the UAVs, and use angular parameters to describe the distribution positions of the UAVs around the load. At the same time, use controller parameters such as the weight matrix elements of LQR as optimization variables to ensure that the optimization algorithm can comprehensively search the feasible solution space. Select the Nelder-Mead simplex method as the optimization algorithm to jointly optimize the UAV layout and controller parameters to find the optimal combination scheme.

[0086] The Nelder-Mead simplex method is a direct search method suitable for multi-dimensional unconstrained optimization problems and can effectively find the global optimal solution. During the optimization process, take the layout positions of the UAVs and the controller parameters as optimization variables, and gradually approach the optimal solution by iteratively updating the vertices of the simplex.

[0087] Through real aircraft verification and performance evaluation, conduct virtual tests on the optimized collaborative design scheme to ensure its effectiveness and robustness in the simulation environment.

[0088] Finally, apply the optimized layout and control parameters to the actual multi - UAV collaborative transportation system for flight control and performance testing. By verifying under different working conditions, such as different load masses, shapes, and flight environments, collect the response data of the system and analyze its stability and adaptability. Further fine - tune and improve the optimization scheme according to the comparison results to ensure that the system can achieve the expected robust performance in practical applications and realize efficient and stable collaborative transportation tasks.

[0089] To simplify the optimization problem and improve the computational efficiency, in this embodiment, the UAV layout position is parameterized as an angular variable on the mid - plane of the load. This parameterization method not only reduces the number of variables in the optimization problem but also can flexibly adapt to loads of different shapes and sizes, while ensuring the accuracy and efficiency of system modeling. By parameterizing the layout position of the multi - rotor UAV, it is more convenient to carry out system dynamics modeling and control law design, thereby achieving precise control and optimization of the entire multi - rotor UAV - load system.

[0090] The dynamic model takes into account the geometric shape, mass characteristics of the load, and the thrust input of the UAV, and specifically includes the following:

[0091] (1) Load geometric assumption: Assume that the load is in the shape of a straight prism with known mass characteristics and shape. This assumption simplifies the subsequent mathematical derivations and covers common load types, such as packages, boxes, etc.

[0092] (2) UAV layout parameterization: Parameterize the layout position of the multi - rotor UAV as the attachment position angle θ = [θ i ,..., θ N on the mid - plane of the load, where θ T represents the attachment position of the i - th UAV on the curve Γ at the center of gravity of the load shape. See i and Figure 2 and Figure 3 for details. This parameterization method reduces the number of variables in the optimization problem and can flexibly adapt to loads of different shapes and sizes.

[0093] (3) System modeling: Consider the overall system including the multi - rotor UAV and the load as a rigid body, and its state vector x is defined as:

[0094]

[0095] where p and respectively represent the position and velocity of the load center of gravity with respect to the global world reference frame, γ represents the Roll-Pitch-Yaw triple, which defines the orientation of the local frame, and ω represents the angular velocity with respect to the local body frame. Each rotor provides four inputs, so if there are N rotors, the thrust input vector has a total of 4×N dimensions. Assume that each thrust component is restricted to the interval [u l , u h .

[0096] (4) Derivation of the dynamic model: Based on Newton's laws of motion and Euler's rigid body dynamics equations, the dynamic model of the system is derived:

[0097]

[0098] where m and J respectively represent the total mass and inertia matrix of the system, g = [0, 0, -9.81] T is the gravitational acceleration vector, R is the rotation matrix, e3 is the third vector of the standard Euclidean basis, is the total thrust generated by all rotors, and τ is the total torque vector in the local body frame.

[0099] Linearize the rigid body dynamic model in the hover configuration and decompose the input into where is the feedforward thrust and u′ is the first-order component of the linearized model. At the same time, decompose the state vector x into

[0100] (5) Linearization and perturbation modeling: Model the perturbation applied to the system as random Gaussian noise where and respectively represent the disturbing force and torque acting on the origin of the local body reference frame.

[0101] The continuous-time linearized dynamic equation is:

[0102]

[0103] where, is obtained by taking the Jacobian matrix of the state vector x under the hover condition, and are obtained by taking the Jacobian matrix of the thrust input u and the perturbation vector d respectively, and these matrices depend on θ directly or through the system inertia that is itself a function of θ.

[0104] To minimize the performance metrics of the system and achieve an optimal layout and control, in this embodiment, preferably, the layout optimization and control optimization of the multi-UAV cooperative transportation system are regarded as a unified optimization problem. The optimization objective is to minimize the performance metrics of the system, which are inspired by control theory and are used to measure the robustness of the system under random perturbations.

[0105] First, define the auxiliary variables:

[0106] z = Cx′ + Du′ (4)

[0107] where x′ is the perturbation component of the state vector, u′ is the perturbation component of the thrust input, and C and D are weight matrices.

[0108] The aim is to find the feedback gain such that:

[0109] u′ = -K * (θ)X′ (5)

[0110] and minimize the integral control cost of:

[0111] J = ∫0 ∞ z T z dt (6)

[0112] According to optimal control theory, the optimal linear feedback controller that minimizes the cost function J is:

[0113] K * (θ) = (D T D) -1 B(θ) T S1(θ) (7)

[0114] where B(θ) is the input matrix and S1(θ) is the solution of the algebraic Riccati equation:

[0115] A T S1 + S1A - S1B(D T D) -1 B T S1 + C T C = 0 (8)

[0116] where S1 is the solution of the algebraic Riccati equation, A is the dynamic matrix, B is the input matrix, D is the weight matrix, and C is the weight matrix.

[0117] The optimal cost function obtained by solving is:

[0118]

[0119] Among them, S1 is the solution of the algebraic Riccati equation, and B d is the perturbation influence matrix, T represents the matrix transpose, and trace represents the trace of the matrix.

[0120] As Figure 4 shown, in order to ensure that the thrust input is within the feasible region and improve the robustness and reliability of the system, in this embodiment, the optimization cost function uses the Mahalanobis distance to quantify the distance between the input distribution and the saturation.

[0121] By calculating the system closed-loop state covariance S2(θ) of the optimal feedback controller, it is subject to the same white noise interference d. Using the optimal continuous-time state observer theory to calculate, the equation can be obtained:

[0122]

[0123] Among them, A f (θ) = A - B(θ)K * (θ) is the dynamic matrix of the closed-loop system, and B d is the perturbation influence matrix. The solution S2(θ) of this equation approximately represents the covariance after the system state is linearized under white noise interference.

[0124] From formula (10), the feedforward thrust value calculated from the hover equilibrium condition can be obtained, as well as the covariance matrix ∑ of the input obtained through the feedback law u = K * (θ) T S2(θ)K * (θ). The goal is to maximize the probability of the feasible input. Set the low saturation of the thrust to u l = u l 1 4N , and the high saturation to u h = u h 1 4N , where 1 4N represents a 4n-dimensional vector with all elements being 1. At this time, the optimization problem to be solved becomes:

[0125]

[0126] Among them, F(·) is the cumulative distribution on the thrust input, and its mean and covariance depend on θ. Use the Mahalanobis distance to quantify the margin between the average (feedforward thrust) and the thrust saturation. The Mahalanobis distance from the point u to the distribution with mean and covariance ∑ u is defined as:

[0127]

[0128] This distance metric takes into account the mean and covariance of the input, and can more accurately reflect the relative position between the thrust input and the saturation boundary. By minimizing this distance, it can be ensured that the thrust input is within the feasible region and as far away from the saturation boundary as possible, thereby improving the robustness and reliability of the system.

[0129] Since each input component has a low saturation u l and a high saturation u h , and each quadcopter has four thrust inputs, there are 8N different hyperplanes to consider in the input space. At this time, the goal of maximizing the probability of the feasible input in formula (11) is transformed into maximizing the Mahalanobis distance between the thrust saturation hyperplane and the input distribution. The optimization problem can be formulated as:

[0130]

[0131] Find the optimal θ * to maximize the minimum Mahalanobis distance between the thrust saturation hyperplane and the feedforward thrust. This minimum Mahalanobis distance is calculated by evaluating it separately on each saturation hyperplane. Therefore, this minimization step is component-wise and is performed on the two saturations [u l , u h . The inner minimization on u is necessary because the point with the minimum distance from needs to be found on each hyperplane.

[0132] To achieve the precise control and optimization of the multi-UAV cooperative transportation system, in this embodiment, preferably, the entire multi-UAV-load system is regarded as a single rigid body for control. Through the calculation of the LQR linear quadratic regulator gain, the unified control of the entire system is realized. A hierarchical control structure is adopted, where the estimator is used to obtain the motion state of the entire system, and the controller generates thrust commands for each UAV according to this state information.

[0133] As Figure 5 shown, the controller architecture includes a state estimator for estimating the overall motion state of the system, and sending thrust commands to each rotor through N parallel communication channels. The specific controller architecture includes the following parts:

[0134] State estimator: This part is responsible for estimating the overall motion state of the system based on the measurement data of the system. The state estimator fuses the data from the sensors and uses filtering algorithms to estimate the estimated state of the system in real time to provide accurate state information for subsequent control.

[0135] LQR controller: Based on the estimated state obtained and the desired state x d, the LQR controller calculates the optimal control input. The LQR controller determines the control input u by minimizing the weighted sum of the state deviation and the control input, enabling the system to respond quickly and stably to the state deviation while considering the limitations of the control input.

[0136] Communication channel: This part is responsible for distributing the control input u calculated by the LQR controller to each rotor. Through N parallel communication channels, each rotor can receive independent thrust commands, thus achieving individual control of each rotor.

[0137] Rotor control unit: Responsible for controlling each rotor according to the received thrust command. The rotor control unit converts the thrust command into specific motor control signals to drive the rotor to generate the required thrust for precise control of the system movement.

[0138] The entire multi-UAV-load system is regarded as a single rigid body for control. Through the calculation of LQR (Linear Quadratic Regulator) gains, unified control of the entire system is achieved. A hierarchical control structure is adopted, where the estimator is used to obtain the motion state of the entire system, and the controller generates thrust commands for each UAV based on this state information.

[0139] To achieve the optimal layout and control of the multi-UAV collaborative transportation system, in this embodiment, the optimization process is based on The control theory uses an improved Nelder-Mead simplex algorithm.

[0140] As Figure 6 shown, the specific steps of the optimization solution include:

[0141] 1) Initialize parameters: Set the number of quadrotor UAVs N = 4, the inertial parameters of the UAVs, the inertial parameters of the load, the shape of the load is rectangular, and the weight matrices C and D are selected according to the system performance requirements.

[0142] 2) Initial guess: Make an initial guess for the attachment position angle θ of the quadrotor UAVs, for example, uniformly distributed around the load.

[0143] 3) System inertia calculation: Calculate the inertia matrix J of the entire system according to the current attachment position angle θ.

[0144] 4) System matrix calculation: Calculate the matrices A, B(θ) and B d (θ) in the system dynamics model according to the inertia matrix J of the system and other parameters, as well as the feedforward thrust

[0145] 5) Solve the algebraic Riccati equation: Solve the algebraic Riccati equation using formula (8) to obtain the solution S1(θ).

[0146] 6) Feedback gain calculation: According to Equation (7), using the obtained S1(θ) and the system input matrix B(θ), calculate the optimal feedback gain matrix K * (θ).

[0147] 7) State covariance calculation: According to Equation (10), using the feedback gain matrix K * (θ) and the system dynamic matrix A f (θ), calculate the state covariance matrix S2(θ) of the closed-loop system.

[0148] 8) Input covariance calculation: According to the feedback law, calculate the covariance matrix ∑ u = K * (θ) T S2(θ)K * (θ).

[0149] 9) Mahalanobis distance initialization: Initialize the minimum Mahalanobis distance to a relatively large value.

[0150] 10) Mahalanobis distance update: For each thrust input component u k and each thrust saturation value u a : u l or u h , solve the quadratic programming problem, calculate the Mahalanobis distance d′, and update the minimum Mahalanobis distance

[0151] 11) Layout update: Using the Nelder-Mead simplex algorithm, update the attachment position angle variable θ of the quadrotor UAV according to the calculated minimum Mahalanobis distance .

[0152] 12) Repeated iteration: Repeat steps 3) to 11) until the optimization is completed to obtain the optimal quadrotor UAV layout parameter θ * .

[0153] To verify the effectiveness of the proposed method and ensure the actual performance of the multi-UAV cooperative transportation system, in this embodiment, preferably, the experimental verification includes a hover experiment, a reference step response experiment, a trajectory tracking experiment, and a disturbance rejection experiment.

[0154] The effectiveness of the proposed method is verified through experiments in the present invention. Based on the optimized layout and control parameters, an actual multi-UAV collaborative transportation experimental platform is built. Appropriate models of UAVs are selected and equipped with necessary sensors, communication modules, and control units to ensure the stable operation of the system. At the same time, reasonable experimental scenarios and test procedures are designed to comprehensively evaluate the actual performance of the system. Different-shaped and -mass loads are used in the experiments, including square panels, concave square panels, and L-shaped panels, as well as 3 or 4 quadrotor UAVs with different quantities.

[0155] The experimental equipment includes quadrotor UAVs, load panels, motion capture systems, radio communication equipment, etc. The experimental process includes: Hover experiment: Hover tests are carried out under windless and windy (1 m / s) conditions, and data such as the displacement deviation and attitude angle of the system are recorded. Position reference step response experiment: A 1-m position reference step change is applied when the system is in the hover state, and the transient response of the system is recorded. Trajectory tracking experiment: Using an L-shaped panel, a circular trajectory tracking experiment is carried out. In a horizontal plane with a circular diameter of 2 m and a height of 2 m, the reference speed is 0.5 m / s. Disturbance rejection test: During flight, a disturbance mass is attached below the load by magnetic adsorption, and the response and recovery of the system to the disturbance are recorded.

[0156] During the experiment, the response data of the system, including position, velocity, attitude, angular velocity, thrust input, etc., are collected using a motion capture system and other sensors. The collected data are analyzed to evaluate the stability and adaptability of the system, with a focus on analyzing performance indicators such as the displacement deviation, attitude change, and control input of the system.

[0157] As described above, it is only the preferred implementation case of the present invention and does not impose any form of limitation on the present invention. Although the implementation process of the present invention has been described in detail above, for those familiar with the field, they can still modify the technical solutions recorded in the foregoing examples or make equivalent replacements for some of the technical features. Any modifications, equivalent replacements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A co - design method for the layout and control of a multi - UAV collaborative transportation system, characterized in that, Including: By establishing the dynamic model and control model of the multi-UAV cooperative transportation system, comprehensively modeling the physical layout and control strategy of the multi-UAV cooperative transportation system, and then defining a comprehensive performance index and quantifying it as an objective function that can be optimized by the model; Parametrize the layout positions of the UAVs, and use angular parameters to describe the distribution positions of the UAVs around the load; At the same time, take the layout positions of the UAVs and the controller parameters as optimization variables for joint optimization; Apply the optimized layout positions and controller parameters to the actual multi-UAV cooperative transportation system for flight control and performance testing.

2. The co - design method for the layout and control of the multi - UAV collaborative transportation system according to claim 1, characterized in that, The multi-UAV cooperative transportation system includes a load and multi-rotor UAVs. The system is regarded as a rigid body, and the system motion state is described by a state vector. Random Gaussian noise is introduced in the derivation of the dynamic model to simulate external disturbances.

3. The co - design method for the layout and control of the multi - UAV collaborative transportation system according to claim 2, wherein The load is in a geometric shape, and the layout position of the multi-rotor UAV is parameterized by the attachment position angle variable θ = [θ i ,..., θ N T , where θ i represents the attachment position of the i-th UAV on the curve Γ at the centroid of the load shape;​ The state vector x is defined as: where p and respectively represent the position and velocity of the payload center of gravity relative to the global world reference frame, γ represents the Roll-Pitch-Yaw triple that defines the orientation of the local body frame, and ω represents the angular velocity relative to the local body frame; each rotor provides four thrust inputs, so if there are N rotors, the thrust input vector has a total of 4×N dimensions; According to Newton's laws of motion and Euler's rigid body dynamics equations, the dynamic model of the system is derived: where \(m\) and \(J\) denote the total mass and the inertia matrix of the system respectively, \(g = [0, 0, -9.81]\) T is the gravitational acceleration vector, \(R\) is the rotation matrix, \(e_3\) is the third vector of the standard Euclidean basis, is the total thrust generated by all the rotors, and \(\tau\) is the total torque vector in the local frame; Linearize the dynamic model in hover configuration and decompose the thrust input vector into where is the feedforward thrust, u′ is the first-order component of the linearized model. Meanwhile, decompose the state vector x into The vector of disturbances applied to the system for modeling is random Gaussian noise where and represent the disturbing force and moment acting on the origin of the local body reference frame, respectively; Then the continuous-time linearized dynamic equation is: where, is obtained by taking the Jacobian matrix of the state vector x under hover conditions, and are obtained by taking the Jacobian matrices of the thrust input vector u and the disturbance vector d, respectively, and these matrices depend on θ directly or through the system inertia.

4. The collaborative design method for the layout and control of the multi-UAV collaborative transportation system according to claim 3, characterized in that, Apply the optimal control theory to the integrated modeling of the physical layout and control strategy of a multi-UAV cooperative transportation system. The goal of optimization is to minimize the system's performance metrics, specifically including: First, define auxiliary variables: z = Cx′ + Du′ (4) where x′ is the perturbation component of the state vector, u′ is the perturbation component of the thrust input, and C and D are weight matrices; The purpose is to find the feedback gain such that: u′ = -K * (θ)x′ (5) and minimize the integral control cost: According to the optimal control theory, the optimal linear feedback controller that minimizes the cost function J is: K * (θ) = (D T D) -1 B(θ) T S1(θ) (7) where B(θ) is the input matrix, and S1(θ) is the solution of the algebraic Riccati equation: A T S1+S1A-S1B(D T D) -1 B T S1+C T C = 0 (8) where S1 is the solution of the algebraic Riccati equation, A is the dynamic matrix, and B is the input matrix; The optimal cost function is obtained by solving: Among them, B d is the perturbation influence matrix, T represents the matrix transpose, and trace represents the trace of the matrix.

5. The collaborative design method for the layout and control of the multi-UAV collaborative transportation system according to claim 4, wherein Quantify the distance between the thrust saturation hyperplane and the thrust input distribution through the Mahalanobis distance to keep the thrust input within the feasible region, specifically including: Calculate the system closed-loop state covariance S2(θ) of the optimal linear feedback controller, which is subject to the same white noise disturbance d, and use the optimal continuous-time state observer theory to calculate, thus obtaining the equation: where, A f (θ) = A - B(θ)K * (θ) is the dynamic matrix of the closed-loop system, and B d is the disturbance influence matrix; the solution S2(θ) of this equation approximately represents the covariance after the system state is linearized under white noise interference; The feedforward thrust value calculated from the hovering equilibrium condition is obtained through Equation (10), and the covariance matrix ∑ of the input is obtained through the feedback law u = K * (θ) T S2(θ)K * (θ), and the goal is to maximize the probability of the feasible input; Set the low saturation of the thrust to u l = u l 1 4N , and the high saturation is set to u h = u h 1 4N , where 1 4N represents a 4n-dimensional vector with all elements being 1. At this time, the optimization problem to be solved becomes: where F(·) is the cumulative distribution on the thrust input, and its mean and covariance depend on θ; The Mahalanobis distance is used to quantify the margin between the feedforward thrust and the thrust saturation. The Mahalanobis distance of point u from a distribution with mean and covariance ∑ u is defined as: By minimizing the Mahalanobis distance, the thrust input is kept within the feasible region and away from the saturation boundary; Based on the fact that each input component has a low saturation and a high saturation, and each quadcopter has four thrust inputs, there are 8N different hyperplanes in the input space. At this time, the goal of maximizing the feasible input probability in formula (11) is transformed into maximizing the Mahalanobis distance between the thrust saturation hyperplane and the input distribution, and the optimization problem is expressed as: Find the optimal UAV layout parameter θ * Maximize the minimum Mahalanobis distance between the thrust saturation hyperplane and the feedforward thrust.

6. The collaborative design method for the layout and control of the multi-UAV collaborative transportation system according to claim 5, characterized in that The joint optimization of the UAV layout positions and controller parameters specifically includes the following steps: 1) Initialize parameters: Set the number of multi-rotor UAVs N = 4, the inertial parameters of the UAVs, the inertial parameters of the load, the shape of the load is a geometric rectangle, and the weight matrices C and D are selected according to the system performance requirements; 2) Initial guess: Make an initial guess for the attachment position angle θ of the multi-rotor UAVs; 3) System inertia calculation: Calculate the inertia matrix J of the entire system according to the current attachment position angle θ; 4) System matrix calculation: Based on the inertia matrix J of the system, calculate matrices A, B(θ), and B d (θ) in the system dynamics model, as well as the feedforward thrust 5) Solve the algebraic Riccati equation: Use formula (8) to solve the algebraic Riccati equation to obtain the solution S1(θ); 6) Feedback gain calculation: According to formula (7), using the obtained S1(θ) and system matrix B(θ), calculate the optimal feedback gain matrix K * (θ); 7) State covariance calculation: According to formula (10), using the feedback gain matrix K * (θ) and the system dynamic matrix A f (θ), calculate the state covariance matrix S2(θ) of the closed-loop system; 8) Input covariance calculation: According to the feedback law, calculate the covariance matrix ∑ of the input u = K * (θ) T S2(θ)K * (θ); 9) Mahalanobis distance initialization: Initialize the minimum Mahalanobis distance to a relatively large value; 10) Mahalanobis distance update: For each thrust input component u k and each thrust saturation value u a : u l or u h , solve the quadratic programming problem, calculate the Mahalanobis distance d′, and update the minimum Mahalanobis distance 11) Layout update: Using the Nelder-Mead simplex method, update the attachment position angle θ of the quadrotor drone according to the calculated minimum Mahalanobis distance ​ 12) Repeated iteration: Repeat steps 3) to 11) until the optimization is completed to obtain the optimal layout parameters θ of the quadrotor UAV * .

7. The co - design method for the layout and control of the multi - UAV collaborative transportation system according to claim 6, characterized in that The outer loop of the controller optimizes the layout parameters using the Nelder-Mead simplex method, and the inner loop of the controller solves the saturation constraint boundaries of each input channel through linear quadratic regulator (LQR).

8. The co - design method for the layout and control of the multi - UAV collaborative transportation system according to claim 7, characterized in that The controller includes: State estimator: By fusing data from sensors, it uses a filtering algorithm to estimate the estimated state of the system in real time LQR Controller: Based on the estimated state and the desired state x d , the LQR controller calculates the optimal thrust input u by minimizing the weighted sum of the state deviation and the control input; Communication channels: responsible for distributing the thrust input u calculated by the LQR controller to each rotor. Through N parallel communication channels, each rotor can receive an independent thrust command, thereby achieving individual control of each rotor; Rotor control units: responsible for controlling each rotor according to the received thrust command, converting the thrust command into a motor control signal, and driving the rotor to generate the required thrust to achieve control of the system motion.

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