Multi-state multi-target model prediction control method for unmanned aerial vehicle-load suspension system

Abstract

The invention relates to a flight control technology of an unmanned aerial vehicle suspension load system, and provides a multi-target nonlinear model prediction control method for an unmanned aerial vehicle-load suspension system, so as to realize accurate track tracking, active suppression of lifting rope swinging and collaborative optimization of flight smoothness. According to the multi-state multi-target model prediction control method for the unmanned aerial vehicle-load suspension system, firstly, a nonlinear model prediction control equation is constructed; discretizing the continuous kinetic model by adopting a fourth-order Runge-Kutta method to obtain a high-precision state transition equation under discrete time as a dynamic constraint; forming an optimal control function of a flight nonlinear model predictive control equation of the unmanned aerial vehicle-load suspension system; adding thrust amplitude constraint and moment boundary constraint as inequality constraint conditions of a nonlinear model predictive control equation; and finally, multi-target optimal control of the unmanned aerial vehicle-load suspension system is realized. The method is mainly applied to design and manufacturing occasions of unmanned aerial vehicle hanging load systems.

Description

Technical Field

[0001] The present invention relates to the flight control technology of an unmanned aerial vehicle (UAV) suspension load system. Specifically, it relates to a non-linear model predictive control method based on multi-objective and multi-state optimization for realizing the flight control of a UAV-load suspension system. The present invention proposes a multi-state multi-objective model predictive control method for a UAV-load suspension system. Background Art

[0002] In recent years, UAVs, especially those with high mobility and load capacity, have been widely used in fields such as logistics transportation, agricultural spraying, and disaster rescue. Among them, suspension transportation operation is one of the typical applications of UAVs. According to the different connection forms between the load and the UAV, the UAV-load suspension system can be divided into two categories: rigid connection and flexible connection. Among them, due to the limitations of the load size and connection rigidity of the rigid connection, it is difficult to adapt to complex transportation requirements; while the flexible rope connection improves the adaptability and versatility, but introduces the UAV-load-rope coupling dynamics problem, resulting in enhanced system non-linearity and increased control degrees of freedom, which poses higher requirements for the robustness and multi-objective coordination ability of the control strategy. Especially in a dynamic environment or a high-precision transportation task, it is often necessary to meet multiple flight objectives such as UAV trajectory tracking, load trajectory tracking, load swing suppression, and flight attitude stability, which poses a severe challenge to the model construction accuracy and multi-objective optimization ability of the control algorithm.

[0003] For the flexible-connected UAV-payload suspension system, researchers have developed various control strategies to achieve flight control. In terms of traditional control algorithms, Akhtar et al. designed a nonlinear feedback controller to cope with the nonlinear characteristics of the UAV-payload suspension system and achieved the tracking control of the payload along the desired trajectory (Journal: IEEE Transactions on Control Systems Technology; Authors: Akhtar, Adeel and Saleem, Sajid and Shan, Jinjun; Publication Date: 2022; Article Title: Path Invariant Controllers for a Quadrotor With a Cable-Suspended Payload Using a Global Parameterization; Pages: 2002-2017). Xia et al. linearized the dynamic model of the UAV-payload suspension system and designed a feedback control method to achieve the tracking control of the UAV along the desired trajectory (Conference: 2023 IEEE International Conference on Mechatronics and Automation; Authors: Xia, Tianqi and Dong, Enzeng and Yang, Sen and Tong, Jigang and Du, Shengzhi; Publication Date: 2023; Article Title: Modeling and Control Design for Quadrotor Transporting System With a Cable-Suspended Rigid Payload; Pages: 2247-2252). In addition, Lv et al. proposed a nonlinear cascaded controller to achieve the exponentially stable control of the UAV-payload suspension system, and its control objectives include UAV attitude, cable swing angle, and payload velocity. (Journal: IEEE Transactions on Vehicular Technology; Authors: Lv, Zong-Yang and Wu, Yuhuan and Rui, Wang; Publication Date: 2020; Article Title: Nonlinear Motion Control for a Quadrotor Transporting a Cable-Suspended Payload; Pages: 8192-8206).Ren et al. designed an adaptive controller for an unmanned aerial vehicle (UAV)-payload slung system considering input saturation, achieving suppression of payload swing during flight (Journal: IEEE Transactions on Aerospace and Electronic Systems; Authors: Ren, Yong and Liu, Zhijie and Zhao, Zhijia and Lam, Hak-Keung; Publication Date: 2024; Article Title: Adaptive Active Anti-Vibration Control for a 3-D Helicopter Flexible Slung-Load System With Input Saturations and Backlash; Pages: 320-333).

[0004] In addition to the above traditional control algorithms, in recent years, the nonlinear model predictive control method has achieved good results in the flight control of unmanned aerial vehicles (UAVs), attracting extensive attention. Sun et al. demonstrated that the nonlinear model predictive controller has superior performance in dynamic trajectory tracking compared to the feedback controller they designed (Journal: IEEE Transactions on Robotics; Authors: Sun, Sihao and Romero, Angel and Foehn, Philipp and Kaufmann, Elia and Scaramuzza, Davide; Publication Date: 2022; Article Title: A Comparative Study of Nonlinear MPC and Differential-Flatness-Based Control for Quadrotor Agile Flight; Pages: 3357-3373). By introducing the nonlinear model predictive control technology into the UAV-payload suspension system, Lan et al. achieved synchronous payload trajectory tracking and suspension cable swing suppression flight control (Conference: 2023 9th International Conference on Control Science and Systems Engineering; Authors: Lan, Xuejing and Gong, Lei and Zheng, Lifeng and Liu, Siyuan and Xu, Wenbiao; Publication Date: 2023; Article Title: Anti-Swing Strategy of a Quadrotor with Suspended Payload Based on Model Predictive Control; Pages: 20-25).

[0005] From the above research, it can be seen that the core objectives of the flight of the UAV-load suspension system can be summarized into three points: UAV trajectory tracking, load trajectory tracking, and reduction of the swing of the load suspension rope. Although certain progress has been made in the control of the UAV trajectory suspension system in existing research, the following problems still exist: First, existing methods mostly focus on a single system state or partial system states, such as separately tracking the UAV or load trajectory, or controlling the load trajectory and the swing of the suspension rope, but there are deficiencies in the multi-state control effect; Second, many methods use approximate methods such as linearization of the dynamic model to deal with the complex dynamic coupling relationship between the UAV, the load, and the suspension rope, making it difficult for the controller to handle the coupling effects between multiple state variables; Finally, in addition to trajectory tracking, the current methods do not fully consider the flight objectives of the UAV-load suspension system. For example, less consideration is given to flight objectives such as the smoothness of the UAV flight attitude and energy conservation. Summary of the Invention

[0006] To overcome the deficiencies of the existing technology, the present invention aims to propose a multi-objective nonlinear model predictive control method for the UAV-load suspension system to achieve the collaborative optimization of accurate trajectory tracking of the UAV-load system, active suppression of the swing of the suspension rope, and flight smoothness. To this end, based on the nonlinear model predictive control framework, the present invention designs a multi-objective optimal control algorithm for the UAV-load suspension system. The multi-state multi-objective model predictive control method for the UAV-load suspension system of the present invention: First, construct a nonlinear model predictive control equation; construct a continuous dynamic model including the coupling relationship between the UAV, the load, and the suspension rope, and use the fourth-order Runge-Kutta method to discretize the continuous dynamic model to obtain a high-precision state transition equation under discrete time as the dynamic constraint of the nonlinear model predictive control equation, ensuring that the control output conforms to the physical motion law of the UAV; design a composite loss function covering the UAV expected position and velocity tracking loss function, the load position and velocity tracking loss function, the suspension rope swing direction and velocity suppression loss function, the UAV attitude smoothness and attitude angular velocity minimization loss function, and the thrust and torque minimization loss function, and set the weights occupied by each loss function through a weight matrix to form the optimal control function of the nonlinear model predictive control equation for the flight of the UAV-load suspension system, and determine the flight objectives of the UAV-load suspension system; add thrust amplitude constraints and torque boundary constraints as the inequality constraint conditions of the nonlinear model predictive control equation to ensure that the obtained optimal control output conforms to the physical characteristics of the actuator; finally, achieve the multi-objective optimal control of the UAV-load suspension system.

[0007] The specific steps are as follows:

[0008] Step 1) Definition of system state variables and model predictive control problem

[0009] This invention focuses on the multi-objective flight control problem of the UAV-load suspension system. The system state vector is defined to include the UAV position, velocity, attitude, angular velocity, load position, velocity, the cable direction and its derivative, as shown in Equation (1):

[0010]

[0011] Each state variable in Equation (1) is a 3D vector, and the overall system state is a 24D vector. Among them, p Q is the UAV position vector, v Q is the UAV velocity vector, R Q is the UAV attitude rotation matrix, ω Q is the UAV angular velocity vector, p L is the load position vector, v L is the load velocity vector, ρ is the cable direction vector, is the cable direction change velocity vector. The superscript T represents the transpose of a vector or matrix; in addition, the system control variable is defined as u = [f τ T T , where f is the lift scalar generated by four rotors, and τ is the three-dimensional moment vector generated by rotor differential. The model predictive control problem is defined as shown in Equation (2):

[0012] subject to:

[0013] where J k is the loss function, subject to indicates the constraints that the variables need to satisfy, x k+1 = f(x k ,u k ) is the system discrete dynamics constraint, x0 = x m is the initial state constraint, and are the feasible region constraints of the system state and input variables;

[0014] Step 2) Dynamics model derivation and discrete dynamics constraint construction

[0015] To obtain the dynamics model of the UAV-load suspension system, based on the Lagrange-D'Alembert principle, the continuous dynamics equation is derived, and the motion equations of the UAV-load suspension system are obtained as Equations (3) to (8)

[0016]

[0017] In Equation (4), m Q represents the UAV mass, m L ​Denote the load mass, \(e_3\) denote the unit vector pointing in the positive direction of the z-axis, \(l\) denote the rope length, \(\omega\) in Equation (5) denote the angular velocity of the suspension rope swing, and \(J\) in Equation (8) Q denote the moment of inertia of the UAV. In order to further obtain the differential dynamic equation of the state variables in Equation (1), it is first necessary to eliminate the UAV angular velocity and derive the second-order differential component in the direction of the suspension rope After arranging the above equation, Equation (9) is obtained

[0018]

[0019] By analyzing the forces on the system, the expression of the suspension rope tension is shown in Equation (10)

[0020]

[0021] Finally, the complete UAV dynamic equation for the state variables in Equation (1) is obtained, as shown in Equation (11)

[0022]

[0023] Equation (11) shows the continuous differential dynamic equation of the system state. However, according to Equation (2), a discrete UAV dynamic equation \(x\) k+1 = f(x k , u k ) is required as a conditional constraint. First, Equation (11) is abbreviated as and the fourth-order Runge-Kutta method with high precision and high stability is used to discretize this differential equation;

[0024] Step 3) Construction of the multi-objective composite loss function

[0025] To meet the multi-objective requirements during the flight of the UAV-load suspension system, within the framework of Equation (2), multiple task objective functions for different flight process requirements are designed to solve the problems of simultaneous tracking and smooth flight of the UAV-load trajectory. Since all the following loss functions are evaluated at the same time step, the time subscript \(k\) will be omitted for a more concise expression;

[0026] The tracking flight of the UAV trajectory is one of the basic objectives of this control algorithm, mainly considering the tracking of the desired position and velocity of the UAV. The corresponding tracking loss functions are shown in Equations (12) and (13):

[0027]

[0028] Equations (12) and (13) respectively encourage the actual position \(p\) of the UAV Q to approach the desired position \(p\) of the UAV Qd , and the actual velocity \(v\) of the UAVQ Approaching the desired speed v of the UAV Qd . Q pQ And Q vQ is the weight adjustment matrix of the UAV trajectory tracking loss function;

[0029] Design the load position and speed tracking loss functions as shown in Eqs. (14) and (15)

[0030]

[0031] The loss functions (14) and (15) respectively encourage the actual position p of the load L to approach the desired position p of the load Ld , and the actual speed v of the load L to approach the desired speed v of the load Ld , Q pL And Q vL represents the weight adjustment matrix of the load trajectory tracking loss function;

[0032] First, design the sling swing direction loss function as shown in Eq. (16)

[0033] J ρ =(ρ T -[00 - 1]) T Q ρ (ρ - [00 - 1] T ) (16)

[0034] The loss function (16) encourages the sling direction to approach the desired direction. The sling direction is defined as the normalized relative position vector of the load pointing to the UAV, and the desired direction is [00 - 1] T indicates that the desired load direction is directly below the UAV with no relative displacement in the xy plane. Q ρ represents the weight adjustment matrix of the sling direction loss function;

[0035] In addition to the sling direction constraint, suppressing the sling swing speed can effectively eliminate the fast high - frequency swing of the sling during flight and increase the flight stability of the UAV - load suspension system. Design the sling swing speed suppression loss function as shown in Eq. (17)

[0036]

[0037] Eq. (17) encourages the sling swing speed to approach the 0 vector, that is, to minimize the sling swing speed, represents the weight adjustment matrix of the sling swing speed loss function;

[0038] Design the UAV attitude stability loss function as shown in Eq. (18)

[0039]

[0040] Among them, the expected attitude of the UAV is set to the stable hovering attitude of the UAV, and R Qd = I3 is the three-dimensional identity matrix. Equation (18) encourages the UAV to maintain a stable attitude during flight, reduces the inclination angle of the UAV flight attitude, reduces the redundant acceleration in the xy plane, and improves the flight stability. Q RQ represents the weight adjustment matrix of the UAV attitude loss function;

[0041] The UAV attitude angular velocity minimization loss function is shown in Equation (19)

[0042]

[0043] Equation (19) encourages the UAV angular velocity to approach the 0 vector, that is, encourages the minimization of the angular velocity, represents the weight adjustment matrix of the suspension rope direction loss function;

[0044] The control quantity is divided into two parts. Among them, the thrust minimization loss function is:

[0045] J f = q f (f - (m Q + m L )g) 2 (20)

[0046] Among them, m Q and m L are the masses of the UAV and the load respectively, g is the acceleration due to gravity, f = (m Q + m L )g is the minimum lift required to maintain the stable hovering of the UAV-load suspension system. Therefore, Equation (20) encourages the minimization of the lift during the flight of the UAV, and q f is the weight adjustment amount of the thrust loss function. In addition, the UAV moment minimization loss function is shown in Equation (21)

[0047] J τ = (τ T - [0 0 0]) T Q τ (τ - [0 0 0] T ) (21)

[0048] Equation (21) encourages the UAV moment to approach the 0 vector, that is, encourages the minimization of the UAV moment, and Q τ is the weight matrix of the UAV moment loss function;

[0049] The overall loss function is shown in Equation (22).

[0050]

[0051] Step 4) Control quantity constraint construction

[0052] Considering the actual situation of the UAV-load suspension system, the upper limit of thrust and the upper and lower limits of torque of the control quantity are restricted to ensure the safe operation of the actuator. The restrictions on the control quantity are shown in Eqs. (23) and (24):

[0053] 0 ≤ f ≤ f u (23)

[0054] τ l ≤ τ i ≤ τ u , i = x, y, z (24)

[0055] where f u is the set upper limit of thrust, and τ l and τ u are the set lower and upper limits of torque;

[0056] According to Eq. (2), the design of the loss function, discrete dynamic constraints, and control quantity feasible region in the model predictive control algorithm has been completed so far.

[0057] The features and beneficial effects of the present invention are as follows:

[0058] 1. Considering the augmented UAV-load suspension state quantity, a comprehensive UAV-load suspension kinematic model including multiple states is proposed. This model can achieve multi-state trajectory tracking of the UAV state, load state, and suspension rope state, and has better versatility and scalability.

[0059] 2. Aiming at the flight requirements during the UAV-load suspension flight, considering flight objectives including trajectory tracking, swing suppression, UAV attitude stability, and minimization of input, a multi-objective loss function including multiple penalty terms is designed. Through multi-dimensional optimization of the flight trajectory, good flight performance is achieved.

[0060] 3. The effectiveness of the algorithm is verified by simulation. The trajectory tracking experiment proves that this method has the ability of fast and accurate tracking, and the ablation experiment confirms that the proposed loss function can significantly improve the optimality of the control law. Description of the Drawings

[0061] Figure 1 is a three-dimensional trajectory diagram of the 8-shaped desired trajectory tracking flight of the UAV using the proposed algorithm;

[0062] Figure 2 is the x, y, and z axis trajectory diagrams of the 8-shaped desired trajectory tracking flight of the UAV using the proposed algorithm;

[0063] Figure 3It is a three-dimensional trajectory graph of the complex spiral-shaped desired trajectory tracking flight of the UAV using the proposed algorithm;

[0064] Figure 4 It is the x, y, and z axis trajectory graphs of the complex spiral-shaped desired trajectory tracking flight of the UAV using the proposed algorithm;

[0065] Figure 5 It is a three-dimensional trajectory graph of the figure-eight-shaped desired trajectory tracking flight of the load using the proposed algorithm;

[0066] Figure 6 It is the x, y, and z axis trajectory graphs of the figure-eight-shaped desired trajectory tracking flight of the load using the proposed algorithm;

[0067] Figure 7 It is a three-dimensional trajectory graph of the complex spiral-shaped desired trajectory tracking flight of the load using the proposed algorithm;

[0068] Figure 8 It is the x, y, and z axis trajectory graphs of the complex spiral-shaped desired trajectory tracking flight of the load using the proposed algorithm;

[0069] Figure 9 It is a comparison graph of the sling direction during the trajectory tracking process using the algorithm with / without the swing suppression term;

[0070] Figure 10 It is a comparison graph of the UAV attitude during the trajectory tracking process using the algorithm with / without the flight stability term;

[0071] Figure 11 It is a comparison graph of the UAV control quantity during the trajectory tracking process using the algorithm with / without the flight stability term;

[0072] Figure 12 It is a schematic diagram of the calculation process of the NMPC algorithm. Specific implementation manner

[0073] The technical problem to be solved by the present invention is: the multi-state control of the UAV, load, and sling of the UAV-load suspension system, and the multi-objective control including load swing reduction, stable flight of the UAV, and minimum energy consumption flight.

[0074] Based on the above non-linear model predictive control framework, through the specific design of the objective function, state transition equation, and control constraints, a multi-objective optimal control method for the UAV-load suspension system is realized. Specifically, it includes the following points:

[0075] a Considering the actual flight requirements of the UAV-load suspension system, a composite loss function including multiple loss functions is designed, enabling the system to achieve multi-objective optimal control effects such as minimizing the trajectory tracking error, suppressing the swing energy, and improving the control smoothness.

[0076] b The dynamic model of the UAV-load suspension system is derived, and it is transformed into a discrete state transition equation using the fourth-order Runge-Kutta method, ensuring that the control method output conforms to the physical characteristics of the UAV-load suspension system's motion.

[0077] c Based on the control input of the UAV-load suspension system, the feasibility constraints of the control quantity are defined, ensuring that the control output calculated by the algorithm meets the actual conditions of the system.

[0078] Multi-state multi-objective model predictive control method for UAV-load suspension system: First, construct the nonlinear model predictive control equation; build a continuous dynamic model including the coupling relationship of the UAV, load, and suspension rope, and discretize the continuous dynamic model using the fourth-order Runge-Kutta method to obtain a high-precision state transition equation at discrete time as the dynamic constraint of the nonlinear model predictive control equation, ensuring that the control output conforms to the physical motion law of the UAV; design a composite loss function covering the UAV's desired position and velocity tracking loss function, load position and velocity tracking loss function, suspension rope swing direction and velocity suppression loss function, UAV attitude stability and attitude angular velocity minimization loss function, thrust and torque minimization loss function, and set the weights occupied by each loss function through a weight matrix to form the optimal control function of the UAV-load suspension system's flight nonlinear model predictive control equation, determining the flight target of the UAV-load suspension system; add thrust amplitude constraints and torque boundary constraints as the inequality constraint conditions of the nonlinear model predictive control equation to ensure that the obtained optimal control output conforms to the physical characteristics of the actuator; finally, achieve a multi-objective optimal control applicable to the UAV-load suspension system.

[0079] Among them, the nonlinear model predictive control framework of the UAV-load suspension system is given in Equation (2), and the continuous dynamic model is defined in Equation (11). The UAV's desired position and velocity tracking loss function is defined in Equations (12) and (13); the load position and velocity tracking loss function is defined in Equations (14) and (15); the suspension rope swing direction and velocity suppression loss function is defined in Equations (16) and (17); the UAV attitude stability and attitude angular velocity minimization loss function is defined in Equations (18) and (19); the thrust and torque minimization loss function is defined in Equations (20) and (21); finally, Equation (22) shows the composite loss function. The thrust amplitude constraint is defined in Equation (23), and the torque boundary constraint is defined in Equation (24).

[0080] The specific steps are as follows:

[0081] Step 1) System state variables and model predictive control problem definition

[0082] This invention focuses on the multi-objective flight control problem of the UAV-load suspension system. Define the system state vector to include the UAV position, velocity, attitude, angular velocity, load position, velocity, cable direction and its derivative, as shown in Equation (1):

[0083]

[0084] In Equation (1), each state variable is a 3D vector, and the overall system state is a 24D vector. Among them, p Q is the UAV position vector, v Q is the UAV velocity vector, R Q is the UAV attitude rotation matrix, ω Q is the UAV angular velocity vector, p L is the load position vector, v L is the load velocity vector, ρ is the cable direction vector, is the cable direction change velocity vector. The superscript T represents the transpose of a vector or matrix; in addition, define the system control quantity as u = [f τ T T , where f is the lift scalar generated by four rotors, τ is the three-dimensional torque vector generated by rotor differential, and the model predictive control problem is defined as shown in Equation (2):

[0085] subject to:

[0086] where J k is the loss function, subject to indicates the constraints that the variables need to satisfy, x k+1 = f(x k ,u k ) is the system discrete dynamics constraint, x0 = x m is the initial state constraint, and are the feasible region constraints of the system state and input quantity;

[0087] Step 2) Dynamics model derivation and discrete dynamics constraint construction

[0088] To obtain the dynamics model of the UAV-load suspension system, based on the Lagrange-D'Alembert principle, the continuous dynamics equation is derived, and the motion equations of the UAV-load suspension system are obtained as Equations (3) to (8)

[0089] ​

[0090] In Equation (4), m Q represents the mass of the UAV, and m L represents the mass of the load. e3 represents the unit vector pointing in the positive direction of the z-axis, l represents the length of the rope. In Equation (5), ω represents the angular velocity of the rope swing. In Equation (8), J Q represents the moment of inertia of the UAV. To further obtain the differential dynamic equation of the state variables in Equation (1), it is first necessary to eliminate the angular velocity of the UAV and derive the second-order differential component in the direction of the rope After organizing the above equation, Equation (9) is obtained

[0091]

[0092] By analyzing the forces on the system, the expression of the rope tension is shown in Equation (10)

[0093]

[0094] Finally, the complete dynamic equation of the UAV for the state variables in Equation (1) is obtained, as shown in Equation (11)

[0095]

[0096] Equation (11) shows the continuous differential dynamic equation of the system state. However, according to Equation (2), a discrete dynamic equation of the UAV x k+1 = f(x k , u k ) is required as a conditional constraint. First, Equation (11) is abbreviated as and the fourth-order Runge-Kutta method with high precision and high stability is used to discretize this differential equation;

[0097] Step 3) Construction of the multi-objective composite loss function

[0098] To meet the multi-objective requirements during the flight of the UAV-load suspension system, within the framework of Equation (2), multi-task objective functions for different flight process requirements are designed to solve the problems of simultaneous tracking and smooth flight of the UAV-load trajectory. Since all the following loss functions are evaluated at the same time step, the time subscript k will be omitted for a more concise expression;

[0099] The tracking flight of the UAV trajectory is one of the basic objectives of this control algorithm, mainly considering the tracking of the desired position and velocity of the UAV. The corresponding tracking loss functions are shown in Equations (12) and (13):

[0100]

[0101] Equations (12) and (13) respectively encourage the actual position p of the UAVQ Approaching the desired position p of the drone Qd , and the actual speed v of the drone Q Approaching the desired speed v of the drone Qd . Q pQ And Q vQ is the weight adjustment matrix of the drone trajectory tracking loss function;

[0102] Design the load position and speed tracking loss functions as in Equations (14) and (15)

[0103]

[0104] The loss functions (14) and (15) respectively encourage the actual position p of the load L to approach the desired position p of the load Ld , and the actual speed v of the load L to approach the desired speed v of the load Ld , Q pL and Q vL represent the weight adjustment matrix of the load trajectory tracking loss function;

[0105] First, design the sling swing direction loss function as shown in Equation (16)

[0106] J ρ =(ρ T -[00 - 1]) T Q ρ (ρ - [00 - 1] T ) (16)

[0107] The loss function (16) encourages the sling direction to approach the desired direction. The sling direction is defined as the normalized relative position vector of the load pointing to the drone, and the desired direction is [00 - 1] T indicating that the desired load direction is directly below the drone with no relative displacement in the xy plane. Q ρ represents the weight adjustment matrix of the sling direction loss function;

[0108] In addition to the sling direction constraint, suppressing the sling swing speed can effectively eliminate the fast high - frequency swing of the sling during flight and increase the flight stability of the drone - load suspension system. Design the sling swing speed suppression loss function as shown in Equation (17)

[0109]

[0110] Equation (17) encourages the sling swing speed to approach the 0 vector, that is, to minimize the sling swing speed, represents the weight adjustment matrix of the sling swing speed loss function;

[0111] Design the UAV attitude stability loss function as shown in Equation (18).

[0112]

[0113] Among them, the expected attitude of the UAV is set to the stable hovering attitude of the UAV, and R Qd =I3 is the three-dimensional identity matrix. Equation (18) encourages the UAV to maintain a stable attitude during flight, reduces the inclination angle of the UAV flight attitude, reduces the redundant acceleration in the xy plane, and improves the flight stability. Q RQ represents the weight adjustment matrix of the UAV attitude loss function;

[0114] The UAV attitude angular velocity minimization loss function is shown in Equation (19).

[0115]

[0116] Equation (19) encourages the UAV angular velocity to approach the 0 vector, that is, encourages the minimization of the angular velocity. represents the weight adjustment matrix of the suspension rope direction loss function;

[0117] The control quantity is divided into two parts. Among them, the thrust minimization loss function is:

[0118] J f =q f (f-(m Q +m L ))g) 2 (20)

[0119] Among them, m Q and m L are the masses of the UAV and the load respectively, g is the acceleration due to gravity, f=(m Q +m L )g is the minimum lift required to maintain the stable hovering of the UAV-load suspension system. Therefore, Equation (20) encourages the minimization of the lift during the flight of the UAV, and q f is the weight adjustment amount of the thrust loss function. In addition, the UAV torque minimization loss function is shown in Equation (21).

[0120] J τ =(τ T -[0 0 0]) T Q τ (τ-[0 0 0] T ) (21)

[0121] Equation (21) encourages the UAV torque to approach the 0 vector, that is, encourages the minimization of the UAV torque. Q τ is the weight matrix of the UAV torque loss function;

[0122] The overall loss function is shown in Equation (22).

[0123]

[0124] Step 4) Construction of control quantity constraints

[0125] Considering the actual situation of the UAV-load suspension system, the upper limit of the thrust and the upper and lower limits of the torque of the control quantity are restricted to ensure the safe operation of the actuator. The restrictions on the control quantity are shown in Equations (23) and (24):

[0126] 0≤f≤f≤ u (23)

[0127] τ l ≤τ i ≤τ u ,i=x,y,z (24)

[0128] Among them, f u is the set upper limit of the thrust, and τ l and τ u are the set lower and upper limits of the torque;

[0129] According to Equation (2), the design of the loss function, discrete dynamic constraints, and the feasible region of the control quantity in the model predictive control algorithm has been completed so far.

[0130] Next, in combination with the accompanying drawings and specific examples, the present invention will be further described.

[0131] The technical solution of the present invention includes the following steps: First, a continuous dynamic model including the coupling relationship of the UAV, load, and suspension rope is constructed, and the continuous dynamic model is discretized by the fourth-order Runge-Kutta method to obtain a high-precision state transition equation under discrete time as the dynamic constraint of the nonlinear model predictive control, ensuring that the optimal control output of the algorithm conforms to the physical motion law of the UAV; design a composite loss function covering the UAV's desired position and speed tracking loss function, load position and speed tracking loss function, suspension rope swing direction and speed suppression loss function, UAV attitude stability and attitude angular velocity minimization loss function, thrust and torque minimization loss function, and set the weights occupied by each loss function through a weight matrix to form an optimal control function for the flight of the UAV-load suspension system, realizing the multi-objective optimal flight control of the UAV-load suspension system; add thrust amplitude constraints and torque boundary constraints as inequality constraint conditions for the nonlinear model predictive control to ensure that the obtained optimal control output conforms to the physical characteristics of the actuator. Finally, a multi-objective optimal control algorithm applicable to the UAV-load suspension system is realized, synchronously processing the optimal control effects of minimizing the trajectory tracking error, suppressing the swing energy, and improving the control smoothness.

[0132] The specific steps are as follows:

[0133] Step 1) System state variables and model predictive control problem definition

[0134] This invention focuses on the multi-objective flight control problem of the UAV-load suspension system. Define the system state vector to include the UAV position, velocity, attitude, angular velocity, load position, velocity, cable direction and its derivative, as shown in Equation (1):

[0135]

[0136] In Equation (1), each state variable is a 3D vector, and the overall system state is a 24D vector. Among them, p Q is the UAV position vector, v Q is the UAV velocity vector, R Q is the UAV attitude rotation matrix, ω Q is the UAV angular velocity vector, p L is the load position vector, v L is the load velocity vector, ρ is the cable direction vector, is the cable direction change velocity vector. The superscript T represents the transpose of a vector or matrix. In addition, define the system control quantity as u = [f τ T T , where f is the lift scalar generated by four rotors, τ is the three-dimensional torque vector generated by rotor differential, and the model predictive control problem is defined as shown in Equation (2):

[0137] subject to:

[0138] where J k is the loss function, subject to indicates the constraints that the variables need to satisfy, x k+1 = f(x k ,u k ) is the system discrete dynamics constraint, x0 = x m is the initial state constraint, and are the feasible region constraints of the system state and input quantity;

[0139] Equation (2) defines several abstract formulas, including the following categories:

[0140] a) J k , that is, the objective function, and the specific form of this objective function determines the purpose of the control method

[0141] b) X k+1 = f(x,u), that is, the state transition equation, and this equation makes the control output conform to the physical characteristics of the motion of the controlled system

[0142] ​c) X0 = Xm, Initial state constraint, which sets the initial state of the system and usually does not require specific design

[0143] d) U(k) ∈ U, Control constraint, which ensures that the control output of the system does not exceed the limit that the actuator can reach. For example, when the control variable is the motor speed, this constraint ensures that the motor speed in the optimal control output is not greater than the speed that the actual motor can reach.

[0144] e) X(k) belongs to X, State constraint, which ensures that the control output of the system does not cause the system state to exceed the set desired range. For example, when controlling a drone system, this constraint can ensure that the drone speed does not exceed x meters per second as set.

[0145] Step 2) Derivation of the dynamic model and construction of discrete dynamic constraints

[0146] To obtain the dynamic model of the drone-load suspension system, based on the Lagrange-D'Alembert principle, the continuous dynamic equation is derived, and the motion equations of the drone-load suspension system are obtained as shown in Equations (3) to (8).

[0147]

[0148]

[0149] In Equation (4), m Q represents the mass of the drone, m L represents the mass of the load, e3 represents the unit vector pointing in the positive direction of the z-axis, and l represents the rope length. In Equation (5), ω represents the angular velocity of the rope swing. In Equation (8), J Q represents the moment of inertia of the drone. To further obtain the differential dynamic equation of the state variables in Equation (1), it is first necessary to eliminate the angular velocity of the drone and derive the second-order differential component of the rope direction. After organizing the above equation, Equation (9) is obtained.

[0150]

[0151] By analyzing the forces on the system, the expression of the rope tension is obtained as shown in Equation (10).

[0152]

[0153] Finally, the complete dynamic equation of the drone for the state variables in Equation (1) is obtained, as shown in Equation (11).

[0154]

[0155] The continuous differential dynamics equation of the system state is shown in Equation (11). However, according to Equation (2), the discrete UAV dynamics equation x k+1 = f(x k , u k ) is required as a conditional constraint. First, Equation (11) is abbreviated as x = g(x, u), and the fourth-order Runge-Kutta method with high precision and high stability is used to discretize this differential equation;

[0156] Step 3) Construction of the multi-objective composite loss function

[0157] To meet the multi-objective requirements during the flight of the UAV-load suspension system, within the framework of Equation (2), multiple task objective functions for different flight process requirements are designed to solve the problems of simultaneous tracking and smooth flight of the UAV-load trajectory. Since all the following loss functions are evaluated at the same time step, the time subscript k will be omitted for a more concise expression;

[0158] The tracking flight of the UAV trajectory is one of the basic objectives of this control algorithm, mainly considering the tracking of the desired position and velocity of the UAV. The corresponding tracking loss functions are shown in Equations (12) and (13):

[0159]

[0160]

[0161] Equations (12) and (13) respectively encourage the actual position p Q of the UAV to be close to the desired position p Qd of the UAV, and the actual velocity v Q of the UAV to be close to the desired velocity v Qd of the UAV. Q pQ and Q vQ are the weight adjustment matrices for the UAV trajectory tracking loss function;

[0162] Design the load position and velocity tracking loss functions as shown in Equations (14) and (15)

[0163]

[0164] Loss functions (14) and (15) respectively encourage the actual position p L of the load to be close to the desired position p Ld of the load, and the actual velocity v L of the load to be close to the desired velocity v Ld of the load. Q pL and Q vL represent the weight adjustment matrices for the load trajectory tracking loss function;

[0165] First, design the suspension line direction loss function as shown in Equation (16)

[0166] J ρ = (ρ T - [00-1]) T Q ρ (ρ - [00-1] T ) (16)

[0167] The loss function (16) encourages the suspension line direction to approach the desired direction. The suspension line direction is defined as the relative position vector of the normalized load pointing to the UAV, and the desired direction [00-1] T indicates that the desired load direction is directly below the UAV with no relative displacement in the xy plane. Q ρ represents the weight adjustment matrix of the suspension line direction loss function;

[0168] In addition to the suspension line direction constraint, suppressing the suspension line swing speed can effectively eliminate the fast high-frequency swing of the suspension line during flight, increasing the flight stability of the UAV-load suspension system. Design the suspension line swing speed suppression loss function as shown in Equation (17)

[0169]

[0170] Equation (17) encourages the suspension line swing speed to approach the 0 vector, that is, to minimize the suspension line swing speed, represents the weight adjustment matrix of the suspension line swing speed loss function;

[0171] Design the UAV attitude stability loss function as shown in Equation (18)

[0172]

[0173] where the desired UAV attitude is set to the UAV's stable hovering attitude, and R Qd = I3 is the 3D identity matrix. Equation (18) encourages the UAV to maintain a stable attitude during flight, reduce the inclination angle of the UAV flight attitude, reduce the redundant acceleration in the xy plane, and improve the flight stability. Q RQ represents the weight adjustment matrix of the UAV attitude loss function;

[0174] The UAV attitude angular velocity minimization loss function is shown in Equation (19)

[0175]

[0176] Equation (19) encourages the UAV angular velocity to approach the 0 vector, that is, to encourage the minimization of the angular velocity, represents the weight adjustment matrix of the suspension line direction loss function;

[0177] The control quantity is divided into two parts. Among them, the thrust loss function is:

[0178] J f =q f (f - (m Q +m L ))g) 2 (20)

[0179] Among them, m Q and m L are the masses of the unmanned aerial vehicle and the load respectively, g is the acceleration due to gravity, f = (m Q +m L )g is the minimum lift required to maintain the stable hovering of the unmanned aerial vehicle-load suspension system. Therefore, equation (20) encourages the minimization of the lift during the flight of the unmanned aerial vehicle, and q f is the weight adjustment quantity of the thrust loss function. In addition, the loss function for minimizing the moment of the unmanned aerial vehicle is shown in equation (21)

[0180] J τ =(τ T -

[000] ) T Q τ (τ -

[000] T ) (21)

[0181] Equation (21) encourages the moment of the unmanned aerial vehicle to approach the 0 vector, that is, it encourages the minimization of the moment of the unmanned aerial vehicle, and Q τ is the weight matrix of the loss function of the moment of the unmanned aerial vehicle;

[0182] The overall loss function is shown in equation (22).

[0183]

[0184] Step 4) Construction of control quantity constraints

[0185] Considering the actual situation of the unmanned aerial vehicle-load suspension system, the upper limit of the thrust and the upper and lower limits of the moment of the control quantity are restricted to ensure the safe operation of the actuator. The restrictions on the control quantity are shown in equations (23) and (24):

[0186] 0 ≤ f ≤ f u (23)

[0187] τ l ≤ τ i ≤ τ u , i = x, y, z. (24)

[0188] Among them, f u is the set upper limit of the thrust, τ l and τ u are the set lower and upper limits of the moment;

[0189] According to Equation (2), the design of the loss function, discrete dynamic constraints, and control variable feasible region in the model predictive control algorithm has been completed so far. In addition, the feasible region constraint for the system state is not imposed, and the initial state constraint is calculated based on the real-time state during flight.

[0190] Among them, the nonlinear model predictive control framework of the UAV-load suspension system is given in Equation (2), and the continuous dynamic model is defined in Equation (11). The loss functions for UAV desired position and speed tracking are defined in Equations (12) and (13); the loss functions for load position and speed tracking are defined in Equations (14) and (15); the loss functions for suppressing the swing direction and speed of the suspension rope are defined in Equations (16) and (17); the loss functions for UAV attitude stability and minimizing attitude angular velocity are defined in Equations (18) and (19); the loss functions for minimizing thrust and torque are defined in Equations (20) and (21); finally, Equation (22) shows the composite loss function. The thrust amplitude constraint is defined in Equation (23), and the torque boundary constraint is defined in Equation (24).

[0191] In summary, the design of the complete model predictive control algorithm has been completed, and this algorithm can achieve the multi-objective flight control effect for the UAV-load suspension system.

[0192] To comprehensively verify the comprehensive performance of the nonlinear model predictive control method for the UAV-load suspension system proposed in the present invention, a number of simulations were carried out. First, to verify the trajectory tracking ability of this algorithm, two desired trajectories were set, namely the figure-eight trajectory and the complex spiral trajectory. These were used as the desired trajectories of the UAV and the load in sequence for tracking flight simulations. The trajectory tracking effect of this algorithm has been verified. Then, to verify the effectiveness of the swing suppression function of this algorithm, flight experiments were carried out using the algorithms with and without the swing suppression loss function respectively, and the swing conditions of the suspension rope were compared. Finally, to verify the effectiveness of the stable flight function of this algorithm, flight experiments were carried out using the algorithms with and without the stable flight loss function respectively, and the flight attitude and control input of the UAV were compared.

[0193] I. Simulation Verification of Multi-State Trajectory Tracking

[0194] To verify the effective trajectory tracking ability of the proposed algorithm, two complex trajectories were selected for tracking tests. The first trajectory is the figure-eight trajectory, which shows periodic motion in the x-y plane and the z-axis remains constant, as Figure 1 and Figure 5As shown, where the solid line represents the actual trajectory of the UAV, the dotted line represents the load trajectory, and the dashed line represents the desired trajectory; the second trajectory is a complex spiral trajectory, which presents a composite periodic motion in the x-y plane and moves uniformly along the z-axis, as Figure 3 and Figure 7 shown. The line pattern is the same as above. First, the UAV tracks the desired trajectory. The tracking effect of the UAV on the figure-eight trajectory is as Figure 1 and Figure 2 shown, where Figure 1 is a three-dimensional trajectory diagram, Figure 2 is a split trajectory diagram of the x, y, and z axes. It can be seen that the control algorithm enables the system to track the trajectory quickly and accurately, with only a slight height fluctuation in the initial acceleration stage, and the root mean square error of the overall trajectory tracking is 0.032 meters. The tracking result of the UAV on the complex spiral trajectory is as Figure 3 and Figure 4 shown, where Figure 3 is a three-dimensional trajectory diagram, Figure 4 is a split trajectory diagram of the x, y, and z axes. It can be seen that there is a slight oscillation phenomenon in the initial stage of the trajectory, but the controller quickly suppresses it, and the root mean square error of the trajectory tracking is 0.029 meters.

[0195] Compared with the UAV, the control quantity cannot act directly on the load, so the trajectory tracking of the load is more challenging. The same figure-eight trajectory and complex spiral trajectory are selected for the load trajectory tracking experiment. The tracking effect of the load on the figure-eight trajectory is as Figure 5 and Figure 6 shown. There is a slight oscillation in the load at the initial acceleration stage but it quickly stabilizes, and the root mean square error of the trajectory tracking is 0.09 meters. Figure 7 and Figure 8 show the tracking effect of the load on the complex spiral trajectory. It can be seen that the sudden acceleration motion in the initial stage makes it difficult for the load to track the desired trajectory, but the controller quickly adjusts to make the load motion converge quickly, and the root mean square error of the overall trajectory is 0.079 meters.

[0196] II. Performance Verification of the Multi-Objective Optimization Function

[0197] To verify the effectiveness of the load swing suppression function in this algorithm, the swing suppression function in this algorithm is removed and a comparative experiment is conducted with the complete proposed algorithm. The complex spiral trajectory that is prone to causing load swing is selected as the desired trajectory for the experiment. Figure 9It shows the changes in the direction of the suspension rope during the trajectory tracking process for both. The solid line represents the method without the anti-swing function, while the dashed line represents the complete algorithm with the anti-swing function. The results show that during the initial acceleration stage, the algorithm without the anti-swing function exhibits significant swings in the x-y axis and oscillations in the z axis, while the complete algorithm can effectively suppress the swings. In the middle and late stages of tracking, the algorithm without the anti-swing function still shows periodic oscillations, while the complete method can completely eliminate them.

[0198] In the proposed algorithm, the UAV angle penalty function, UAV angular velocity penalty function, UAV thrust penalty function, and UAV moment penalty function participate in the trajectory optimization as flight smoothness terms to suppress the aggressive flight postures and drastic control quantities of the UAV. By comparing the complete algorithm and the algorithm without the flight smoothness terms, this experiment aims to verify the effectiveness of the flight smoothness terms. A complex spiral trajectory with rich motion changes is selected as the desired trajectory to compare the UAV postures and input quantities during the tracking flight. Figure 10 It shows the changes in the UAV posture, represented by quaternions. When the aircraft hovers stably, its quaternion should be w = 1, x = 0, y = 0, z = 0. The dashed line in the figure is the flight result of the complete algorithm, while the solid line is the flight result without the flight smoothness terms. It can be seen that the complete algorithm can effectively control the flight posture to be stable near the stable posture and can effectively reduce the posture change rate, that is, the UAV angular velocity. Figure 11 It shows the changes in the UAV control quantities during the flight process. The dashed line is the control quantity corresponding to the complete algorithm, and the solid line is the control quantity without the flight smoothness terms. It can be seen from the figure that the complete algorithm has significantly smaller control quantities, which means that this algorithm can effectively reduce energy consumption and increase flight smoothness.

[0199] In summary, the model predictive control algorithm of the UAV-load suspension system proposed realizes the multi-state tracking control effect of the UAV and the load, improving the flexibility and application potential of the algorithm. By considering the flight requirements of the UAV-load suspension system, a composite multi-objective function including trajectory tracking, swing suppression, flight smoothness, and energy-saving optimization is designed, effectively achieving better tracking flights in multiple aspects.

[0200] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A multi-state multi-objective model predictive control method for an unmanned aerial vehicle (UAV)-payload suspension system, characterized in that, first, a non-linear model predictive control equation is constructed; a continuous dynamic model including the coupling relationship of the UAV, the payload and the suspension rope is constructed, and the fourth-order Runge-Kutta method is used to discretize the continuous dynamic model to obtain a high-precision state transition equation under discrete time as the dynamic constraint of the non-linear model predictive control equation, ensuring that the control output conforms to the physical motion law of the UAV; a composite loss function covering the UAV desired position and velocity tracking loss function, the payload position and velocity tracking loss function, the suspension rope swing direction and velocity suppression loss function, the UAV attitude stability and attitude angular velocity minimization loss function, and the thrust and torque minimization loss function is designed, and the weights occupied by each loss function are set through a weight matrix to form an optimal control function of the UAV-payload suspension system flight non-linear model predictive control equation, and the flight target of the UAV-payload suspension system is determined; thrust amplitude constraints and torque boundary constraints are added as inequality constraint conditions of the non-linear model predictive control equation to ensure that the obtained optimal control output conforms to the physical characteristics of the actuator; finally, the multi-objective optimal control of the UAV-payload suspension system is realized.

2. The multi-state and multi-objective model predictive control method for the unmanned aerial vehicle-load suspension system according to claim 1, characterized in that The specific steps are as follows: Step 1) System state variables and model predictive control problem definition Define the system state vector to include the UAV position, velocity, attitude, angular velocity, payload position, velocity, suspension rope direction and its derivative, as shown in Equation (1): Each state variable in Equation (1) is a 3D vector, and the overall system state is a 24D vector. Among them, p Q is the UAV position vector, v Q is the UAV velocity vector, R Q is the UAV attitude rotation matrix, ω Q is the UAV angular velocity vector, p L is the payload position vector, v L is the payload velocity vector, ρ is the suspension cable direction vector, is the suspension cable direction change velocity vector, and the superscript T represents the transpose of a vector or matrix; in addition, the system control quantity is defined as u = [f τ T T , where f is the lift scalar generated by the four rotors, τ is the three-dimensional moment vector generated by the rotor differential, and the model predictive control problem is defined as shown in Equation (2):​ Among which J k is the loss function, subject to indicates the constraints that the variables need to satisfy, and x k+1 = f(x k , u k ) is the discrete dynamic constraint of the system, x0 = x m is the initial state constraint, and are the feasible region constraints of the system state and input quantity; Step 2) Dynamics model derivation and discrete dynamics constraint construction In order to obtain the dynamics model of the UAV-payload suspension system, based on the Lagrange-D'Alembert principle, the continuous dynamics equation is derived, and the motion equations of the UAV-payload suspension system are obtained as Equations (3) to (8) m in Equation (4) Q represents the mass of the UAV, and m L represents the payload mass, e3 represents the unit vector pointing in the positive direction of the z-axis, l represents the rope length, ω in Equation (5) represents the angular velocity of the suspension rope swing, and J in Equation (8) Q represents the moment of inertia of the UAV. To further obtain the differential dynamics equation of the state variables in Equation (1), it is first necessary to eliminate the angular velocity of the UAV and derive the second-order differential component in the direction of the suspension rope Rearranging the above equation gives Equation (9) Analyze the forces acting on the system to obtain the suspension rope tension expression as shown in Equation (10) Finally, the complete UAV dynamics equation for the state variables in Equation (1) is obtained, as shown in Equation (11) The continuous differential dynamic equation of the system state is shown in Equation (11). However, according to Equation (2), the discrete UAV dynamic equation x k+1 = f(x k , u k ) is required as a conditional constraint. First, Equation (11) is abbreviated as and the fourth-order Runge-Kutta method with high precision and high stability is used to discretize this differential equation; Step 3) Multi-objective composite loss function construction In order to meet the multi-objective requirements during the flight of the UAV-payload suspension system, under the framework of Equation (2), multiple task objective functions for different flight process requirements are designed to solve the simultaneous tracking problem and stable flight problem of the UAV-payload trajectory. Since all the following loss functions are evaluated at the same time step, the time subscript k will be omitted for a more concise expression; The tracking flight of the UAV trajectory is one of the basic objectives of this control algorithm, mainly considering the tracking of the UAV desired position and velocity, and the corresponding tracking loss functions are shown in Equations (12) and (13): Equations (12) and (13) respectively encourage the actual position p of the UAV Q to approach the desired position p of the UAV Q d and the actual velocity v of the UAV Q to approach the desired velocity v of the UAV Qd , Q pQ and Q vQ are the weight adjustment matrices of the UAV trajectory tracking loss function; Design the payload position and velocity tracking loss functions as shown in Equations (14) and (15) The loss functions (14) and (15) respectively encourage the actual position p of the load L to approach the desired position p of the load Ld , and the actual velocity v of the load L to approach the desired velocity v of the load Ld , Q pL and Q vL represent the weight adjustment matrices of the load trajectory tracking loss function; First, design the sling swing direction loss function as shown in Equation (16) J ρ = (ρ T - [00-1]) T Q ρ (ρ - [00-1] T ) (16) The loss function (16) encourages the sling direction to be close to the desired direction, where the sling direction is defined as the relative position vector of the normalized load pointing to the drone, and the desired direction is [00-1] T Indicates that the desired load direction is directly below the drone with no relative displacement in the xy plane, Q ρ Represents the weight adjustment matrix of the sling direction loss function; In addition to the suspension rope direction constraint, suppressing the suspension rope swing speed can effectively eliminate the fast high-frequency swing of the suspension rope during flight and increase the flight stability of the UAV-payload suspension system. Design the suspension rope swing speed suppression loss function as shown in Equation (17) Equation (17) encourages the pendulum rope swing speed to approach the 0 vector, that is, to minimize the pendulum rope swing speed. It represents the weight adjustment matrix of the pendulum rope swing speed loss function. Design the UAV attitude stability loss function as shown in Equation (18) Among them, the expected attitude of the UAV is set as the stable hovering attitude of the UAV, R Qd = I3 is the three-dimensional identity matrix. Equation (18) encourages the UAV to maintain a stable attitude during flight, reduces the inclination angle of the UAV flight attitude, reduces the redundant acceleration in the xy plane, and improves the flight stability. Q RQ represents the weight adjustment matrix of the UAV attitude loss function; The UAV attitude angular velocity minimization loss function is shown in Equation (19) Equation (19) encourages the angular velocity of the UAV to approach the 0 vector, that is, it encourages the minimization of the angular velocity. It represents the weight adjustment matrix of the loss function in the suspension rope direction. The control quantity is divided into two parts. Among them, the thrust minimization loss function is: J f = q f (f - (m Q + m L ))g) 2 (20) where m Q and m L are the mass of the drone and the payload respectively, g is the acceleration due to gravity, and f = (m Q + m L )g is the minimum lift required to maintain the stable hovering of the drone-payload suspension system. Therefore, Equation (20) encourages the minimization of the lift during the flight of the drone. q f is the weight adjustment amount of the thrust loss function. In addition, the drone moment minimization loss function is shown in Equation (21). J τ = (τ T - [0 0 0]) T Q τ (τ - [0 0 0] T ) (21) Equation (21) encourages the UAV moment to approach the 0 vector, that is, it encourages the minimization of the UAV moment, and Q τ is the weight matrix of the UAV moment loss function; The overall loss function is shown in Equation (22): Step 4) Construction of control quantity constraints Considering the actual situation of the UAV-load suspension system, the upper limit of the thrust and the upper and lower limits of the torque of the control quantity are restricted to ensure the safe operation of the actuator. The restrictions on the control quantity are shown in Equations (23) and (24): 0 ≤ f ≤ f u (23) τ l ≤τ i ≤τ u , i = x, y, z (24) where f u is the set upper limit of the thrust, τ l and τ u are the set lower and upper limits of the torque; According to Equation (2), the design of the loss function, discrete dynamics constraints, and the feasible region of the control quantity in the model predictive control algorithm has been completed so far.

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