Four-rotor unmanned aerial vehicle elastic suspension model control method

Abstract

The invention designs a four-rotor unmanned aerial vehicle system controller based on an elastic rope hanging load, so that the technical scheme adopted by the invention is that an elastic hanging model of an unmanned aerial vehicle is analyzed, a concept of a load direction vector is introduced, an original model is corrected, and a control law is designed; the swing of the hanging load can be quickly inhibited while the quad-rotor unmanned aerial vehicle arrives at the designated position, and the swing angle of the load is gradually converged to zero while the quad-rotor unmanned aerial vehicle gradually converges to the target position. A Lyapunov equation is designed based on an energy function method, and then a controller is designed to control the suspended unmanned aerial vehicle. The method is mainly applied to hanging load flight transportation control of the rotor unmanned aerial vehicle.

Description

Technical Field

[0001] The present invention relates to a suspension model and control law design for a new four-rotor unmanned aerial vehicle (UAV) to fly with a suspended load, and particularly to a control method for a four-rotor UAV to fly and transport an object suspended by an elastic rope. Background Art

[0002] With the development of the times, more and more research has been carried out on four-rotor UAVs. Due to the special structure of the four-rotor compared with the fixed-wing, the fuselage can take off and land vertically without a runway. This enables the four-rotor UAV to easily complete some special tasks, such as disaster area search and rescue, pesticide spraying, mountain area express delivery work, etc. Now the four-rotor UAV has been applied in some places of people's lives. With the development of society and the maturity of technology, the popularity of the four-rotor UAV may become a standard to measure the advancement of a city.

[0003] In recent years, researchers have conducted extensive studies on the suspension of quadrotor UAVs. In (Journal: IEEE Transactions on Industrial Electronics, 2019, 67(3); Authors: Yang S, Xian B; Article Title: Energy-based nonlinear adaptive control design for the quadrotor UAV system with a suspended payload [J]; Pages: 2054 - 2064.), a nonlinear controller was designed using the energy analysis method to achieve the control of the coordinates of the quadrotor UAV and the swing angle of the suspended object. The stability of the quadrotor UAV rigging system was proven through Lyapunov stability analysis. In (Journal: IEEE / ASME Transactions on Mechatronics, 2020, 26(5); Authors: Xian B, Yang S; Article Title: Robust tracking control of a quadrotor unmanned aerial vehicle-suspended payload system [J]; Pages: 2653 - 2663.), a new type of robust nonlinear controller was designed to handle the errors generated by the feedback, reduce the swing of the load in the unknown airflow, complete the position trajectory tracking control, and finally verify the stability of the quadrotor UAV rigging system through the Lyapunov stability proof theory. The methods used in the first two articles are similar to the method used in this article, both adopting the nonlinear control method and using the Lyapunov theory to prove the stability. In the literature (Journal: 2018 37th Chinese control conference (CCC). IEEE; Authors: Sun B, Chaofang Hu, Cao L, et al.; Title: Trajectory planning of quadrotor uav with suspended payload based on predictive control [C] / / , 2018; Pages: 10049 - 10054.), a trajectory planning idea based on predictive control was designed, and the optimal trajectory was obtained by analyzing the angle of the target, the length of the UAV, and the size of the nearby obstacles. The difference is that this article focuses on the direction vector of the payload.In the literature (Journal: Asian Journal of Control, 2022, 24(5); Authors: Yang Y, Zhang D, Xi H, et al.; Title: Anti-swing control and trajectory planning of quadrotor suspended payload system with variable length cable [J]; Pages: 2424-2436.), a quadrotor variable rope length suspension model was proposed, a system coupling dynamics model was designed, the anti-swing control method for the entire model was completed, and some basic trajectory planning was carried out. A new type of quadrotor control system was designed. (Journal: Nonlinear Dynamics, 2021, 104(4); Authors: Alkomy H, Shan J; Title: Vibration reduction of a quadrotor with a cable-suspended payload using polynomial trajectories [J]; Pages: 3713-3735.) It considered the case of a payload suspended by a cable. The similarity between these two articles and this paper is that they both adopted a variable rope length model, but the difference is that the rope length adopted in this paper can be physically deformed and has an elastic coefficient.

[0004] In the literature (Journal: Nonlinear Dynamics, 2023, 111(20); Authors: Chang P, Yang S, Tong J, et al.; Title: A new adaptive control design for a quadrotor system with suspended load by an elastic rope [J]; Pages: 19073-19092.), a new quadrotor elastic suspension model was designed, a special control law was designed for the new model, and finally the convergence of the entire system was proved using Lyapunov theory and Lasalle's theorem.

[0005] In the literature (Author: Mofid O, Mobayen S. Title: Adaptive sliding mode control for finite-time stability of quad-rotor UAVs with parametric uncertainties [J]. Journal: ISA transactions, 2018, 72: Pages: 1 - 14 and Author: Esmail M S, Merzban M H, Khalaf A A M, et al. Title: Attitude and altitude nonlinear control regulation of a quadcopter using quaternion representation [J]. Journal: IEEE Access, 2022, 10: Pages: 5884 - 5894.), several sliding mode control methods were introduced and applied to the suspension model of quad-rotor UAVs, achieving good control effects; in the literature of Mofid O, a sliding mode control law for an unmanned aerial vehicle system with uncertainties and a tracking control problem were designed, and an adaptive tuning method based on the concept of Lyapunov stability was proposed to estimate the uncertain error of the quad-rotor UAV in real time, solving the stability problem and tracking control problem of the flight system with parametric uncertainties. Esmail M S designed a class of nonlinear control methods with feedback properties using the quaternion method and proved the stability of the control system based on Lyapunov theory. Due to the advantages of sliding mode control such as robustness and fast response, it has been more and more widely used in the control of quad-rotor UAVs.

[0006] To sum up, in recent years, there have been many research results on the UAV suspension system, which are of great significance and various forms. However, most of the research focuses on the swing angle and load of the UAV, and there is not much research on the attitude of the suspended load. Summary of the Invention

[0007] Aiming at the swing problem of the suspended load, the present invention analyzes the elastic suspension model of the UAV, introduces the concept of the load direction vector, modifies the original model, designs a control law, enables the system to quickly and stably reach the target position, and realizes rapid swing reduction.

[0008] The non - linear model of the elastic suspension of a quad - rotor UAV is re - improved and re - defined, and the concept of the load direction vector is introduced. The control algorithm designed in the present invention has been strictly mathematically proven and verified through data simulation, verifying the effectiveness and feasibility of the proposed control method. First, the forces on the quad - rotor UAV and the suspended object are analyzed to obtain the non - linear dynamic model of the quad - rotor UAV suspension system:

[0009]

[0010] The definitions of the variables and parameters in the formula are as follows: x, y, and z are the positions of the x, y, and z axes of the quad - rotor UAV in the ground coordinate system, M and m are the masses of the quad - rotor and the suspended object respectively, α and β are the longitudinal and lateral angles of the suspension ropes relative to the vertical direction of the quad - rotor UAV, F(t)=[F x F y F z T is the total lift force of the quad - rotor UAV, where F x , F y , F z are the decomposed forces of the total lift force in the longitudinal, lateral, and vertical directions of the quad - rotor UAV, g is the acceleration due to gravity, (x Q ,y Q ,z Q ) represents the position coordinates of the quad - rotor UAV. For the elastic suspension rope, L represents the real - time rope length, L0 is the initial rope length, k is the rope elastic coefficient, q = {q x q y q z} is the direction vector of the load, where q x , q y , q z respectively represent the decomposition of the direction vector of the suspended object relative to the quad - rotor UAV under the x, y, and z axes of the ground coordinate system.

[0011] Define the three - dimensional position of the suspended object as {x L ,y L ,z L}. According to the position relationship between the suspended object and the quad - rotor UAV, the following model can be obtained:

[0012]

[0013] Substituting the direction vector q of the suspended object, the non - linear dynamic model in formula (1) can be re - defined as

[0014]

[0015] where G = {0,0,g}, g is the acceleration due to gravity, k is the rope elastic coefficient, q = {q​x q y q z} is the direction vector of the suspended object, where q x , q y , q z respectively represent the decomposition of the direction vector of the load relative to the quadrotor UAV under the xyz coordinate axes of the ground coordinate system, p = {x, y, z}, p is the position of the quadrotor UAV in the ground coordinate system, where x, y, and z are the positions of the xyz coordinate axes of the quadrotor UAV in the ground coordinate system.

[0016] For the suspended quadrotor UAV model in equations (1) and (3), design the following controller:

[0017]

[0018] where e x , e y , e z respectively represent the deviations between the actual positions and the target positions of the quadrotor UAV in the xyz coordinate axes under the ground coordinate system, k x , k y , k z respectively represent the adjustment coefficients of the three position deviations, k dx , k dy , k dz respectively represent the adjustment coefficients of the quadrotor UAV's velocities in the x, y, and z directions, and n is a constant greater than 0.

[0019] The nonlinear dynamic model of the elastic suspension of the quadrotor UAV is re-improved and defined. The concept of the load direction vector is introduced, the original model is corrected, and a control algorithm is designed to enable the system to reach the target position quickly and stably, realizing rapid roll reduction. The direction vector of the suspended object can be expressed as:

[0020]

[0021] The steps to prove the asymptotic convergence characteristics of the controller for the re-defined control design method of the nonlinear model of the elastic suspension of the quadrotor UAV are as follows: The energy analysis of the quadrotor UAV model is carried out, and parameter weighting design is carried out for the roll reduction design.

[0022] The kinetic energy E Q of the quadrotor UAV and the kinetic energy E L of the suspended object are calculated as follows:

[0023]

[0024] The expression of the potential energy E Lp of the suspended object is as follows

[0025]

[0026] Define the total energy of the suspended object The formula is as follows

[0027]

[0028] For the elastic suspension system of a quadrotor UAV, the controller can make the quadrotor UAV gradually converge to the specified position, and the offset angle can gradually converge to 0.

[0029] The Lyapunov candidate function is constructed as follows:

[0030]

[0031] Taking the derivative gives

[0032]

[0033] Substitute Equation (4) into (10) and simplify to obtain:

[0034]

[0035] Using the LaSalle invariance principle to prove, first, define a set where is the system state variable, and then in Ω Substitute into the system and simplify to obtain the following formula: e = 0, so The stability of the controller of the elastic suspension system of the quadrotor UAV can be verified by LaSalle's theory.

[0036] The features and beneficial effects of the present invention are:

[0037] The present invention designs a controller for a quadrotor UAV system based on an elastic rope to suspend a load, realizing the flight control of the quadrotor suspended UAV. Analyze the elastic suspension model of the UAV, introduce the concept of the load direction vector, correct the original model, design the control law, and while ensuring that the quadrotor UAV reaches the specified position, it can quickly suppress the swing of the suspended load, realizing that while the quadrotor UAV asymptotically converges to the target position, the swing angle of the load also asymptotically converges to zero. Brief Description of the Drawings

[0038] Figure 1 is a schematic diagram of the structure of the quadrotor UAV suspension system;

[0039] Figure 2 is the control effect diagram for adjusting the simulation results;

[0040] Figure 3It is the control effect diagram of the load direction vector simulation;

[0041] Figure 4 It is the diagram of the rope length simulation result. Specific implementation manner

[0042] To more quickly suppress the swing of the suspended load, the present invention aims to propose a control method for the elastic suspension model of a quadrotor UAV, which can quickly suppress the swing of the suspended load while controlling the position of the quadrotor UAV. Refer to Figure 1 As shown, it is the structural schematic diagram of the quadrotor UAV suspension system. The technical solution adopted by the present invention is to analyze the elastic suspension model of the UAV, introduce the concept of the load direction vector, correct the original model, design the control law, and can quickly suppress the swing of the suspended load while ensuring that the quadrotor UAV reaches the specified position, realizing that while the quadrotor UAV asymptotically converges to the target position, the swing angle of the load also asymptotically converges to zero.

[0043] Based on the energy function method and designing the Lyapunov equation, and then designing a controller to realize the control of the suspended UAV.

[0044] First, conduct a force analysis on the quadrotor UAV and the suspended object to obtain the nonlinear dynamic model of the quadrotor UAV suspension system:

[0045]

[0046] The definitions of the variables and parameters in the formula are as follows: x, y, and z are the positions of the xyz coordinate axes of the quadrotor UAV in the ground coordinate system, M and m are the masses of the quadrotor and the suspended object respectively, α and β are the longitudinal and lateral angles of the suspension rope relative to the vertical direction of the quadrotor UAV, F(t)=[F x F y F z T is the total lift force of the quadrotor UAV, where F x , F y , F z are the decomposed forces of the total lift force in the longitudinal, lateral, and vertical directions of the quadrotor UAV, g is the acceleration due to gravity, (x Q , y Q , z Q ) represents the position coordinates of the quadrotor UAV. For the elastic suspension rope, L represents the real-time rope length, L0 is the initial rope length, k is the rope elastic coefficient, q={q x q y q z} is the direction vector of the load, where q x , q y , q z ​They respectively represent the decomposition of the direction vector of the suspended object relative to the quadrotor UAV along the xyz coordinate axes of the ground coordinate system.

[0047] Define the three-dimensional position of the suspended object as {x L , y L , z L}. According to the positional relationship between the suspended object and the quadrotor UAV, the following model can be obtained:

[0048]

[0049] Substitute the direction vector q of the suspended object into it, and the nonlinear dynamic model in formula (1) can be redefined as

[0050]

[0051] where G = {0, 0, g}, g is the acceleration due to gravity, k is the elastic coefficient of the rope, q = {q x q y q z} is the direction vector of the suspended object, where q x , q y , q z respectively represent the decomposition of the direction vector of the payload relative to the quadrotor UAV along the xyz coordinate axes of the ground coordinate system, p = {x, y, z}, p is the position of the quadrotor UAV in the ground coordinate system, where x, y, and z are the positions of the xyz coordinate axes of the quadrotor UAV in the ground coordinate system.

[0052] For the suspended quadrotor UAV model in formulas (1) and (3), design the following controller:

[0053]

[0054] where e x , e y , e z respectively represent the deviations between the actual positions and the target positions of the quadrotor UAV in the xyz coordinate axes in the ground coordinate system, k x , k y , k z respectively represent the adjustment coefficients of the three position deviations, k dx , k dy , k dz respectively represent the adjustment coefficients of the velocities of the quadrotor UAV in the x, y, and z directions, and n is a constant greater than 0.

[0055] The non - linear dynamic model of the elastic suspension of a quad - rotor UAV is re - improved and re - defined. The concept of the load direction vector is introduced to correct the original model, and a control algorithm is designed to enable the system to quickly and stably reach the target position and achieve rapid roll reduction. The direction vector of the suspended object can be expressed as:

[0056]

[0057] The design method of the control of the re - defined non - linear model of the elastic suspension of a quad - rotor UAV. The steps to prove the asymptotic convergence characteristics of the controller are as follows: The energy analysis of the quad - rotor UAV model is carried out, and parameter weighting design for the roll - reduction design is carried out.

[0058] The kinetic energy \(E\) of the quad - rotor UAV Q and the kinetic energy \(E\) of the suspended object L are calculated as follows:

[0059]

[0060] The potential energy \(E\) of the suspended object Lp is expressed as follows

[0061]

[0062] Define the total energy of the suspended object as follows

[0063]

[0064] For the elastic suspension system of a quad - rotor UAV, the controller can make the quad - rotor UAV gradually converge to the specified position, and the offset angle can gradually converge to 0.

[0065] The Lyapunov candidate function is constructed as follows:

[0066]

[0067] Taking the derivative gives

[0068]

[0069] Substitute Equation (4) into (10) and simplify to get:

[0070]

[0071] Using the LaSalle invariance principle to prove, first, define a set where is the system state variable, and then substitute it into the system in \(\Omega\) and simplify to obtain the following formula: \(e = 0\) Substitute it into the system and simplify to get the following formula: \(e = 0\)

[0072] Therefore

[0073] The stability of the controller of the elastic suspension system of a quadrotor UAV can be verified by the theory of Lasal le.

[0074] The technical problem to be solved by the present invention is to design a controller for a quadrotor UAV system based on an elastic rope to suspend a load, so as to realize that while the quadrotor UAV reaches the specified position, the swing of the suspended object can be suppressed quickly.

[0075] To verify the effectiveness of the control scheme in the present invention, numerical simulation steps of stable control and adjustment control are carried out. The control performance of the controller (4) for the quadrotor suspension flight system can meet the control requirements within a short time and effectively reduce the swing.

[0076] I. Introduction to Numerical Simulation

[0077] The relevant parameters of the quadrotor UAV suspension system are set as follows:

[0078] m = 0.5 kg, M = 2 kg, k = 100 N / m, L0 = 0.5 m, g = 10 m / s 2 .

[0079] Apply the controller (4) to the system (1) and select the following parameters:

[0080] k x = 6, k y = 6, k z = 10, k dx = 6, k dy = 6, k dz = 10, n = 3

[0081] II. Control Simulation

[0082] Combined with the above parameters, the initial state and target position of the system are set as follows:

[0083]

[0084] The model and controller designed in this paper are simulated in Matlab / Simulink, and the following results are obtained. Refer to Figure 2 As shown, for the control effect diagram of the adjustment simulation result, the coordinates of the quadrotor UAV can quickly converge to the target position, and x and y can reach the stable state within 5 seconds, and the jitter phenomenon is greatly suppressed. At the same time, z can also reach an obvious convergence trend at 2 seconds, with a very small jitter amplitude, and gradually converges to the target position stably. Refer to Figure 3As shown, it is the control effect diagram of the load direction vector simulation. On the load direction vector, α and β can reach a stable state within 5 seconds, while β has an obvious convergence trend within 2 seconds. Refer to Figure 4 As shown, it is the result diagram of the rope length simulation, which shows the change of the elastic rope deformation. Although k is slightly larger, L can also reach an obvious convergence trend within 2 seconds, proving the stability of the proposed quadrotor UAV suspension model and control law.

[0085] Through the above analysis, the effectiveness of the algorithm proposed in the present invention is verified.

[0086] It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or terminal device comprising a series of elements not only includes those elements, but also includes other elements not expressly listed, or elements inherent to such process, method, article or terminal device. Without further limitation, the elements defined by the statement "comprising..." or "including..." do not exclude the existence of additional elements in the process, method, article or terminal device comprising the said elements. In addition, in this article, "greater than", "less than", "more than" are understood not to include the present number; "above", "below", "within" are understood to include the present number.

[0087] Although the above embodiments have been described, those skilled in the art can make additional changes and modifications once they know the basic creative concept. Therefore, the above are only the embodiments of the present invention, and do not limit the patent protection scope of the present invention. Any equivalent structure or equivalent process transformation made by using the content of the specification and drawings of the present invention, or directly or indirectly applied in other related technical fields, are equally included in the patent protection scope of the present invention.

Claims

1. A quadrotor drone elastic suspension model control method, characterized in that: The following steps are involved: First, the force analysis of the quadrotor drone and the hanging object is carried out to obtain the nonlinear dynamic model of the quadrotor drone hanging system: The variables and parameters are defined as follows: x, y, z are the positions of the xyz coordinate axes of the quadrotor drone in the ground coordinate system, M and m are the masses of the quadrotor and the hanging object, α and β are the longitudinal and transverse angles of the hanging rope relative to the vertical direction of the quadrotor drone, F(t) = [F x F y F z ] T is the total lift of the quadrotor drone, where F z 、F y 、F z is the decomposition force of the total lift in the longitudinal, lateral and vertical directions of the quadrotor drone, g is the acceleration of gravity, (x Q ,y Q ,z Q ) represents the position coordinates of the quadrotor drone. For the elastic hanging rope, L represents the real-time rope length, L0 is the initial rope length, k is the rope elastic coefficient, q={q x q y q z } is the direction vector of the load, where q x ,q y ,q z They respectively represent the decomposition of the direction vector of the hanging object relative to the quadrotor drone under the xyz coordinate axis of the ground coordinate system; Define the three-dimensional position of the hanging object as {x L ,y L ,z L }, according to the positional relationship between the hanging object and the quadrotor drone, the following model can be obtained: Substituting the direction vector q of the hanging object, the nonlinear dynamic model in formula (1) can be redefined as: Where G = {0, 0, g}, g is the acceleration of gravity, k is the elastic coefficient of the rope, q = {q x q y q z } is the direction vector of the hanging object, where q x ,q y ,q z They represent the decomposition of the direction vector of the load relative to the quadrotor drone in the xyz coordinate system of the ground coordinate system, p = {x, y, z}, p is the position of the quadrotor drone in the ground coordinate system, where x, y, z are the positions of the xyz coordinate axes of the quadrotor drone in the ground coordinate system; For the suspended quad-rotor drone model in equations (1) and (3), the following controller is designed: where e x 、e y 、e z They represent the deviation between the actual position and the target position of the quadrotor drone in the xyz coordinate axis in the ground coordinate system, and k x , k y , k z Represent the adjustment coefficients of the three position deviations, k dx , k dy , k dz They represent the adjustment coefficients of the speed in the x, y, and z directions of the quadrotor drone, respectively, and n is a constant greater than 0.

2. The elastic suspension model control method of a quadrotor drone according to claim 1, characterized in that: It also includes the re-improvement and definition of the nonlinear dynamic model of the quadcopter UAV suspension system, the introduction of the concept of load direction vector, the correction of the original model, and the design of the control algorithm to enable the system to reach the target position quickly and stably and achieve rapid anti-shake. The direction vector of the suspended object can be expressed as:

3. The elastic suspension model control method of a quadrotor drone as claimed in claim 2, characterized in that: The steps to prove the asymptotic convergence characteristics of the controller are: energy analysis of the quadrotor drone model, The parameter weighting design of the anti-roll design was carried out. Quadcopter UAV kinetic energy E Q and the kinetic energy of the suspended object E L The calculation formula is as follows: The potential energy E of the suspended object Lp The expression is as follows Define the total energy of the suspended object The formula is as follows For the elastic suspension system of a quadrotor drone, the controller can make the quadrotor drone gradually converge to the specified position, and the offset angle can gradually converge to 0; The Lyapunov candidate function is constructed as follows: The derivative is Substituting equation (4) and into (10) to simplify, we obtain: Using the Lasalle invariance principle, first, define a set in is the system state variable, then in Ω Substituting into the system and simplifying it, we can get the following formula: e = 0, so The stability of the elastic suspension system controller of a quadrotor drone can be confirmed using Lasalle's theory.

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