Nonlinear Model Predictive Control Method for Amphibious Aerial and Aquatic UAV

Abstract

The present invention relates to the technical field of UAV control, and particularly to a non-linear model predictive control method for a water-air amphibious UAV, comprising the following steps: constructing a UAV motion mathematical model based on the quadcopter octocopter UAV; constructing a cost function for predictive control of the quadcopter octocopter UAV based on the UAV motion mathematical model; constructing a LESO extended observer according to the torque of the axes or the water resistance of the axes of the quadcopter octocopter UAV in the space coordinate system; obtaining the operating state through the sensors of the quadcopter octocopter UAV, and determining the power distribution mode for each rotor motor of the quadcopter octocopter UAV; solving the cost function according to the power distribution mode and the LESO extended observer to obtain the control results for each rotor motor of the quadcopter octocopter UAV. The present invention optimizes the operating attitude of the water-air amphibious UAV and makes the operating performance more efficient.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicle control, and particularly to a non-linear model predictive control method for an amphibious unmanned aerial vehicle. Background Art

[0002] In recent years, with the rapid development of information and manufacturing technologies, a wide variety of multi-rotor unmanned aerial vehicles with rich scenarios have emerged on the market. In water-air operations, people have gradually started to use equipment such as submersibles and unmanned aerial vehicles for work, which has greatly reduced labor, costs, and operational risks to a large extent. However, in the field of water-air unmanned aerial vehicles, most of the existing designs use the same control methods as those for aerial unmanned aerial vehicles, resulting in low movement efficiency of water-air unmanned aerial vehicles. There is also a design that uses two sets of motors for water-air movement switching in the market, but such a design increases the weight of the unmanned aerial vehicle and reduces the endurance time of the unmanned aerial vehicle.

[0003] In the field of unmanned aerial vehicle control, most control methods used are geometric control, PID control, etc. The control of underwater unmanned aerial vehicles does not consider the influence of water resistance on the movement of the airframe. In terms of the power distribution of unmanned aerial vehicles, the method of using a mixing control matrix is mostly used for distribution, but this method is not applicable to unmanned aerial vehicles with too many actuators that need to be optimized. Summary of the Invention

[0004] The present invention aims to solve the technical problem that the existing unmanned aerial vehicle control methods are not applicable to the water-air amphibious use scenario.

[0005] To solve the above technical problem, the present invention provides a non-linear model predictive control method for an amphibious unmanned aerial vehicle. The amphibious unmanned aerial vehicle is a four-axis and eight-rotor unmanned aerial vehicle. The non-linear model predictive control method includes the following steps:

[0006] Construct a mathematical model of the unmanned aerial vehicle movement based on the four-axis and eight-rotor unmanned aerial vehicle;

[0007] Construct a cost function for predictive control of the four-axis and eight-rotor unmanned aerial vehicle based on the mathematical model of the unmanned aerial vehicle movement;

[0008] Construct a LESO extended observer based on the torque or shaft water resistance of the axis of the four-axis and eight-rotor unmanned aerial vehicle in the space coordinate system;

[0009] Obtain the operating state through the sensors of the four-axis and eight-rotor unmanned aerial vehicle, and determine the power distribution mode of each rotor motor of the four-axis and eight-rotor unmanned aerial vehicle;

[0010] Solve the cost function according to the power distribution mode and the LESO extended observer to obtain the control results of each rotor motor of the four-axis and eight-rotor unmanned aerial vehicle.

[0011] Furthermore, the mathematical model of the UAV motion satisfies the following relational expressions:

[0012]

[0013] Wherein, represents the position of the quadrotor octocopter UAV in the space coordinate system, represents the velocity of the quadrotor octocopter UAV in the space coordinate system;

[0014] Φ 1 represents three Euler angles, and Φ 2 represents the angular velocity about the three body axes;

[0015] T represents the total thrust, ρ w / a represents the density of water or air, V represents the displacement, m represents the mass, g represents the acceleration due to gravity, and F D represents the water resistance or air resistance;

[0016] J represents the inertia matrix, Γ represents the torque generated by the rotor motors of the quadrotor octocopter UAV on the corresponding axes, and Γ D represents the torque generated by the water resistance.

[0017] Furthermore, the cost function satisfies the following relational expressions:

[0018]

[0019] st.x i+1 = f(x i , u i ) i = k, k + 1,..., k + N - 1;

[0020]

[0021] Wherein, k represents the current time step, N represents the number of sampling time steps within the prediction range, x k:k+N represents the predicted state trajectory, Q, Q N and R both represent positive definite weight matrices, u k:k+N represents the predicted system input, u represents the output lower bound, represents the output upper bound.

[0022] Furthermore, define the moment of inertia of the quadrotor octocopter UAV about the x-axis in the space coordinate system as I 11 , the system input as τ x , then the LESO extended observer of the quadrotor octocopter UAV about the x-axis in the space coordinate system satisfies the following relational expressions:

[0023]

[0024] Among them, z 1 , z 2 represents the estimated value of the state, and β 1 , β 2 represents the observation gain.

[0025] Furthermore, the LESO extended observer on the x-axis of the quadrotor octocopter in the space coordinate system has an observation error that satisfies the following relational expression:

[0026]

[0027] Among them, h = τ Dx , τ Dx represents the component of the drag force acting on the body on the x-axis.

[0028] Furthermore, the operating states include flight in the air and operation in water, and the power distribution modes include an air power distribution mode and a water power distribution mode. Among them, the air power distribution mode performs power distribution based on a mixing control matrix;

[0029] The water power distribution mode performs power distribution based on the following relational expression:

[0030]

[0031] Among them, f 1 …f 8 respectively represent the output thrusts of the eight rotor motors of the quadrotor octocopter, and T 1 , T 2 respectively represent the components of the total output thrust in the z-axis and x-axis of the space coordinate system, α and β respectively represent the tilting angles of the left and right steering gears when the forward direction of the quadrotor octocopter is the forward direction, l represents the wheelbase, and k represents the anti-twist coefficient.

[0032] Furthermore, in the power distribution of the water power distribution mode, the total output thrust f of the eight rotor motors of the quadrotor octocopter and the blade rotational angular velocity ω satisfy the following relational expression:

[0033] f = cω 2 ;

[0034] Among them, c represents the power coefficient.

[0035] Furthermore, the power distribution of the water power distribution mode has the following constraint:

[0036] α·β = 0;

[0037]

[0038] Further, according to the power distribution mode and the step of solving the cost function by the LESO extended observer, specifically:

[0039] Differentiate the power distribution expression of the underwater power distribution mode with respect to time t to obtain a system state equation satisfying the following relationship:

[0040]

[0041] Let the angle change law of the rotor motor be a constant value, that is The speed change law of the rotor motor is d. Based on the LESO extended observer, obtain the rotational speed of each rotor motor, and take the derivative of the rotational speed with respect to time to obtain the speed change law d;

[0042] Combine the speed change law d and the cost function to calculate the output rotational speed and rotation angle of each rotor motor of the quadrotor octocopter UAV as the control result.

[0043] The beneficial effects achieved by the present invention are as follows: A non - linear control method for an amphibious quadrotor octocopter UAV is proposed. This method models the configuration of the amphibious multi - axis and multi - motor UAV, designs a model predictive algorithm for position and attitude control, and takes into account the influence of water resistance and wind resistance during modeling and solving. Design an LESO extended state observer to observe the disturbance and perform feed - forward control; at the same time, design a corresponding power distribution method according to underwater operation, so that the operation attitude of the amphibious UAV controlled based on this method is optimized and the operation performance is more efficient. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 is a schematic flow chart of the steps of the non - linear model predictive control method for the amphibious UAV provided by the embodiment of the present invention;

[0045] Figure 2 is a schematic structural diagram of the amphibious UAV provided by the embodiment of the present invention;

[0046] Figure 3 is a schematic diagram of the operation state of the amphibious UAV provided by the embodiment of the present invention;

[0047] Figure 4 is a schematic diagram of the rotor motor control of the amphibious UAV provided by the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0048] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0049] Please refer to Figure 1 , Figure 1 which is a schematic flow chart of the steps of the non-linear model predictive control method for the water-air amphibious unmanned aerial vehicle provided by the embodiment of the present invention. As Figure 2 shown, the water-air amphibious unmanned aerial vehicle is a four-axis and eight-rotor unmanned aerial vehicle. Among them, the four axes mean that the unmanned aerial vehicle has four concentric and movable mechanical axes. At the outer end of each axis, there are two relatively arranged rotor motors, and the rotor motors can rotate along the axial direction of the mechanical axis to achieve attitude changes. Specifically, the non-linear model predictive control method includes the following steps:

[0050] S1. Construct a mathematical model of the unmanned aerial vehicle's motion based on the four-axis and eight-rotor unmanned aerial vehicle;

[0051] S2. Construct a cost function for predictive control of the four-axis and eight-rotor unmanned aerial vehicle based on the mathematical model of the unmanned aerial vehicle's motion;

[0052] S3. Construct a LESO extended observer based on the torque or axial water resistance of the axes of the four-axis and eight-rotor unmanned aerial vehicle in the space coordinate system;

[0053] S4. Obtain the operating state through the sensors of the four-axis and eight-rotor unmanned aerial vehicle and determine the power distribution mode of each rotor motor of the four-axis and eight-rotor unmanned aerial vehicle;

[0054] S5. Solve the cost function according to the power distribution mode and the LESO extended observer to obtain the control results of each rotor motor of the four-axis and eight-rotor unmanned aerial vehicle.

[0055] Furthermore, the mathematical model of the unmanned aerial vehicle's motion satisfies the following relationship:

[0056]

[0057] where represents the position of the four-axis and eight-rotor unmanned aerial vehicle in the space coordinate system, represents the velocity of the four-axis and eight-rotor unmanned aerial vehicle in the space coordinate system;

[0058] Φ 1 represents three Euler angles, and Φ 2 represents the angular velocity around the three body axes;

[0059] T represents the total thrust, and ρ w / aρ represents the density of water or air, V represents the displacement volume, m represents the mass, g represents the acceleration due to gravity, F D represents the water resistance or air resistance;

[0060] J represents the inertia matrix, Γ represents the torque generated by the rotor motors of the quadrotor octocopter on the corresponding axes, Γ D represents the torque generated by the water resistance.

[0061] In the above expressions, Φ 1 = [φ θ ψ] T and Φ 2 = [p q r] T and the body Euler angles φ = 0, θ = 0, ψ = ψ d where ψ d is the desired yaw angle.

[0062] Furthermore, the cost function satisfies the following relationship:

[0063]

[0064] st.x i+1 = f(x i , u i ) i = k, k + 1,..., k + N - 1;

[0065]

[0066] where k represents the current time step, N represents the number of sampling time steps within the prediction horizon, x k:k+N represents the predicted state trajectory, Q, Q N and R all represent positive definite weight matrices, u k:k+N represents the predicted system input, u represents the output lower bound, represents the output upper bound.

[0067] Furthermore, define the moment of inertia of the quadrotor octocopter about the x-axis in the space coordinate system as I 11 and the system input as τ x where:

[0068]

[0069] then the LESO extended observer of the quadrotor octocopter about the x-axis in the space coordinate system satisfies the following relationship:

[0070]

[0071] where z 1, z 2 represents the estimated value of the state, β 1 , β 2 represents the observation gain.

[0072] Furthermore, the LESO extended observer on the x-axis of the quadrotor octocopter in the space coordinate system has an observation error that satisfies the following relationship:

[0073]

[0074] Simplify it to:

[0075]

[0076] where h = τ Dx , τ Dx represents the component of the drag force acting on the body along the x-axis.

[0077] When calculating the LESO extended observer, it can be expressed as a characteristic polynomial:

[0078] f(λ) = λ 2 + β 1 λ + β 2 = (λ + ω o ) 2 ;

[0079] Then the observation gain can be expressed as:

[0080] β 1 = 2ω o , β 2 = ω o 2 .

[0081] It can be understood that the above process describes the observation calculation of the torque on the x-axis. The torque on the remaining y and z axes and the water resistance on the x, y, and z axes can be analogously used for the observer design.

[0082] Furthermore, the operating state includes flight in the air and operation in water. The power distribution mode includes the air power distribution mode and the water power distribution mode. Among them, the air power distribution mode performs power distribution based on the mixing control matrix;

[0083] Generally, the situation of the quadrotor octocopter operating in the air is consistent with the parameter control of the prior art. The embodiments of the present invention mainly discuss the situation of operating in water. As Figure 3 shown, when navigating in water, use the servo tilting structure to rotate the left and right arms to 0°, decoupling the hovering and forward movements; then, realize the hovering and diving of the drone through the front and rear four motors, and realize the forward and turning actions through the left and right four motors.

[0084] When there are lateral water waves in the environment, the drone needs to perform a roll motion to resist the lateral force. Assuming the drone will perform a clockwise roll motion around the x-axis, the right side of the drone maintains a 0° tilt unchanged, and the motors reverse to counteract the force generated by the left motors; the left motors will calculate the tilt angle by the power distribution system, the force along the z-axis will provide the force required for the roll motion, and the force along the x-axis will balance the reverse force on the right side. According to the above process, the drone will achieve a roll motion.

[0085] As Figure 4 shown, the underwater power distribution mode distributes power based on the following relationship:

[0086]

[0087] where f 1 …f 8 respectively represent the output thrusts of the eight rotor motors of the quadcopter octocopter drone, T 1 、T 2 respectively represent the components of the total output thrust in the z-axis and x-axis of the space coordinate system, α and β respectively represent the tilt angles of the left and right steering gears when the forward direction of the quadcopter octocopter drone is the forward direction, l represents the wheelbase, and k represents the anti-twist coefficient.

[0088] Furthermore, in the power distribution of the underwater power distribution mode, the total output thrust f of the eight rotor motors of the quadcopter octocopter drone and the blade rotational angular velocity ω satisfy the following relationship:

[0089] f = cω 2 ;

[0090] where c represents the power coefficient.

[0091] Furthermore, the power distribution of the underwater power distribution mode has the following constraints:

[0092] α·β = 0;

[0093]

[0094] Furthermore, according to the power distribution mode, the steps for the LESO extended observer to solve the cost function are specifically as follows:

[0095] According to the power distribution expression of the underwater power distribution mode, take the derivative with respect to time t to obtain the system state equation that satisfies the following relationship:

[0096]

[0097] Let the rotor motor angle change law be a constant value, that is The speed change law of the rotor motor is d. The rotation speed of each rotor motor is obtained based on the LESO extended observer, and the derivative of the rotation speed with respect to time is calculated to obtain the speed change law d.

[0098] Combining the speed change law d and the cost function, the output rotation speed and rotation angle of each rotor motor of the quadrotor octocopter drone are calculated as the control result.

[0099] The beneficial effects achieved by the present invention are as follows: A non-linear control method for a water-air amphibious quadrotor octocopter drone is proposed. This method models the configuration of the water-air amphibious multi-axis and multi-motor drone, designs a model predictive algorithm for position and attitude control, and takes into account the influence of water resistance and wind resistance during modeling and solution. An LESO extended state observer is designed to observe the disturbance and perform feedforward control. At the same time, a corresponding power distribution method is designed according to underwater operation, so that the operation attitude of the water-air amphibious drone controlled based on this method is optimized and the operation performance is more efficient.

[0100] Those of ordinary skill in the art can understand that all or part of the processes of implementing the methods in the above embodiments can be completed by instructing relevant hardware through a computer program. The program can be stored in a computer-readable storage medium. When the program is executed, it can include the processes of the above method embodiments. Among them, the storage medium can be a magnetic disk, an optical disk, a read-only memory (ROM), or a random access memory (RAM), etc.

[0101] It should be noted that in this article, the term "including", "comprising", or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article, or device including a series of elements not only includes those elements, but also includes other elements not explicitly listed, or further includes elements inherent to such process, method, article, or device. Without further limitations, an element defined by the statement "including a..." does not exclude the existence of additional identical elements in the process, method, article, or device including that element.

[0102] Through the description of the above embodiments, those skilled in the art can clearly understand that the above-described example methods can be implemented by means of software plus a necessary general hardware platform. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) and includes several instructions for causing a terminal (which can be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in various embodiments of the present invention.

[0103] The embodiments of the present invention have been described above in conjunction with the accompanying drawings. What is disclosed is only the preferred embodiments of the present invention. However, the present invention is not limited to the above specific embodiments. The above specific embodiments are merely illustrative and not restrictive. Under the inspiration of the present invention, those of ordinary skill in the art can also make many equivalent changes in form without departing from the spirit and scope protected by the claims of the present invention, and all of them belong to the protection scope of the present invention.

Claims

1. A nonlinear model predictive control method for an amphibious aerial drone, wherein the amphibious aerial drone is a quad-axis octarotor drone, characterized in that: The nonlinear model predictive control method comprises the following steps: Constructing a mathematical model of drone motion based on the four-axis eight-rotor drone; Constructing a cost function for predictive control of the quad-axis octarotor UAV based on the UAV motion mathematical model; A LESO expansion observer is constructed according to the torque or the axis water resistance of the axis of the quad-axis octarotor UAV in the spatial coordinate system; Acquiring the operating status through the sensor of the quad-axis octaro-rotor UAV and determining the power distribution mode for each rotor motor of the quad-axis octaro-rotor UAV; Solving the cost function according to the power distribution mode and the LESO extended observer to obtain control results for each rotor motor of the quad-axis octarotor drone; The mathematical model of UAV motion satisfies the following relationship: in, represents the position of the quadcopter octarotor drone in the spatial coordinate system, represents the speed of the quadcopter octarotor drone in the spatial coordinate system; Φ1 represents the three Euler angles, and Φ2 represents the angular velocity around the three axes of the body; T is the total thrust, ρ w / a represents the density of water or air, V represents the displacement, m represents the mass, g represents the acceleration due to gravity, and F D Indicates water resistance or wind resistance; J represents the inertia matrix, Γ represents the torque generated by the rotor motor of the quad-axis octarotor drone on the corresponding axis, and Γ D Indicates the torque generated by water resistance; The cost function satisfies the following relationship: Among them, k represents the current time step, N represents the number of sampling time steps in the prediction range, and x k:k+N represents the predicted state trajectory, Q, Q N and R both represent positive definite weight matrices, u k:k+N represents the predicted system input, u represents the output lower bound, Indicates the output upper bound; The moment of inertia of the x-axis of the quadcopter octarotor drone in the spatial coordinate system is defined as I 11 , the system input is τ x , then the LESO expansion observer on the x-axis of the quadcopter octarotor drone in the spatial coordinate system satisfies the following relationship: Among them, z1 and z2 represent the estimated values ​​of the state, and β1 and β2 represent the observation gains; The LESO expansion observer of the quad-axis octarotor drone on the x-axis in the spatial coordinate system has an observation error that satisfies the following relationship: in, h=τ Dx , τ Dx It represents the component of the drag acting on the body on the x-axis; The operating state includes flying in the air and operating in the water, and the power distribution mode includes an air power distribution mode and an underwater power distribution mode, wherein the air power distribution mode performs power distribution based on a mixing control matrix; The underwater power distribution mode distributes power based on the following relationship: Among them, f1...f8 respectively represent the output thrusts of the eight rotor motors of the four-axis eight-rotor drone, T1 and T2 respectively represent the components of the total output thrust in the z-axis and x-axis of the spatial coordinate system, α and β respectively represent the tilt angles of the left and right servos when the four-axis eight-rotor drone moves in the forward direction, l represents the wheelbase, and k represents the anti-torsion coefficient.

2. The nonlinear model predictive control method for an amphibious unmanned aerial vehicle according to claim 1 is characterized in that: In the power distribution of the underwater power distribution mode, the total output thrust f of the eight rotor motors of the four-axis eight-rotor drone and the blade rotation angular velocity ω satisfy the following relationship: f=cω 2 ; Where c represents the dynamic coefficient.

3. The nonlinear model predictive control method for an amphibious unmanned aerial vehicle according to claim 1 is characterized in that: The power distribution of the underwater power distribution mode has the following constraints: α·β＝0； 4. The nonlinear model predictive control method for an amphibious unmanned aerial vehicle according to claim 1, characterized in that: The steps of solving the cost function according to the power distribution mode and the LESO extended observer are specifically: According to the power distribution expression of the underwater power distribution mode, the system state equation satisfying the following relationship is obtained by differentiating the time t: Let the rotor motor angle change law be a constant, that is, The speed variation law of the rotor motor is d, the speed of each rotor motor is obtained based on the LESO expansion observer, and the speed variation law d is obtained by taking the derivative of the speed with respect to time; The output speed and rotation angle of each rotor motor of the quad-axis octaro-rotor UAV are calculated in combination with the speed variation law d and the cost function as the control result.

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