Nonlinear model predictive control method of water-air amphibious unmanned aerial vehicle

Abstract

The invention relates to the technical field of unmanned aerial vehicle control, in particular to a nonlinear model prediction control method for a water-air amphibious unmanned aerial vehicle, which comprises the following steps of: constructing an unmanned aerial vehicle motion mathematical model based on a four-axis eight-rotor unmanned aerial vehicle; constructing a cost function for predictive control of the four-axis eight-rotor unmanned aerial vehicle based on the unmanned aerial vehicle motion mathematical model; constructing an LESO extended observer according to the torque or shaft water resistance of the shafts of the four-shaft eight-rotor unmanned aerial vehicle in the space coordinate system; acquiring an operation state through a sensor of the four-axis eight-rotor unmanned aerial vehicle, and determining a power distribution mode for each rotor motor of the four-axis eight-rotor unmanned aerial vehicle; and according to the power distribution mode, the LESO extended observer solves the cost function to obtain a control result for each rotor motor of the four-axis eight-rotor unmanned aerial vehicle. According to the method, the operation attitude of the water-air amphibious unmanned aerial vehicle is optimized, and the operation performance is more efficient.

Description

Technical Field

[0001] The invention relates to the technical field of unmanned aerial vehicle control, and in particular to a nonlinear model predictive control method for an amphibious unmanned aerial vehicle. Background Art

[0002] In recent years, with the rapid development of information and manufacturing technology, a wide variety of multi-rotor drones with rich scenarios have emerged on the market. In water and air operations, people have gradually begun to use submersibles, drones and other equipment to work, which has greatly reduced labor, reduced costs, and reduced the risk of operations. However, in the field of water and air drones, most of the existing designs use the same control method as air drones, resulting in low efficiency of water and air drone movement. There are also solutions on the market that use two sets of motors to switch between water and air movements, but such a design increases the weight of the drone and reduces the drone's flight time.

[0003] In the field of drone control, most control methods are geometric control, PID control, etc. The control of underwater drones does not take into account the impact of water resistance on the body movement. In terms of drone power distribution, most of them use the mixed control matrix method for distribution, but this method is not suitable for drones with too many actuators and need to be optimized. Summary of the invention

[0004] The present invention aims to solve the technical problem that the existing UAV control method is not suitable for water and air amphibious use scenarios.

[0005] In order to solve the above technical problems, the present invention provides a nonlinear model predictive control method for an amphibious aerial drone, wherein the amphibious aerial drone is a four-axis eight-rotor drone, and the nonlinear model predictive control method comprises the following steps:

[0006] Constructing a mathematical model of drone motion based on the four-axis eight-rotor drone;

[0007] Constructing a cost function for predictive control of the quad-axis octarotor UAV based on the UAV motion mathematical model;

[0008] 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;

[0009] 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;

[0010] The cost function is solved according to the power distribution mode and the LESO extended observer to obtain control results for each rotor motor of the four-axis eight-rotor UAV.

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

[0012]

[0013] 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;

[0014] Φ1 represents the three Euler angles, and Φ2 represents the angular velocity around the three axes of the body;

[0015] 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;

[0016] 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.

[0017] Furthermore, the cost function satisfies the following relationship:

[0018]

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

[0020]

[0021] 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 upper bound of the output.

[0022] Furthermore, the moment of inertia of the x-axis of the quad-axis 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:

[0023]

[0024] Among them, z1 and z2 represent the estimated values ​​of the state, and β1 and β2 represent the observation gains.

[0025] Furthermore, the LESO expansion observer on the x-axis of the quad-axis octarotor drone in the spatial coordinate system has an observation error that satisfies the following relationship:

[0026]

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

[0028] Furthermore, 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;

[0029] The underwater power distribution mode distributes power based on the following relationship:

[0030]

[0031] 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.

[0032] Furthermore, 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:

[0033] f=cω 2 ;

[0034] Where c represents the dynamic coefficient.

[0035] Furthermore, the power distribution of the underwater power distribution mode has the following constraints:

[0036] α·β=0;

[0037]

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

[0039] 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:

[0040]

[0041] 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;

[0042] 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.

[0043] The beneficial effect achieved by the present invention is that a nonlinear control method for a four-axis eight-rotor UAV of water and air amphibians is proposed. The method models the configuration of the water and air amphibious multi-axis multi-motor UAV, designs a model prediction algorithm to control the position and attitude, takes the influence of water resistance and wind resistance into consideration when modeling and solving, and designs a LESO extended state observer 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 operating attitude of the water and air amphibious UAV controlled based on the method is optimized, and the operating performance is more efficient. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a schematic diagram of the steps of the nonlinear model predictive control method of the water-air amphibious UAV provided by an embodiment of the present invention;

[0045] Figure 2 Schematic diagram of the structure of the water-air amphibious UAV provided by an embodiment of the present invention;

[0046] Figure 3 Schematic diagram of the operating state of the water-air amphibious UAV provided by an embodiment of the present invention;

[0047] Figure 4 It is a schematic diagram of the rotor motor control of the water-air amphibious UAV provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0048] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with 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 intended to limit the present invention.

[0049] Please refer to Figure 1 , Figure 1FIG. 1 is a schematic diagram of the steps of the nonlinear model predictive control method for an amphibious unmanned aerial vehicle provided by an embodiment of the present invention. Figure 2 As shown, the water-air amphibious UAV is a four-axis eight-rotor UAV, wherein the four-axis means that the UAV has four concentric and movable mechanical axes, and the outer end of each axis is provided with two oppositely arranged rotor motors, and the rotor motor can rotate along the axial direction of the mechanical axis to achieve attitude changes. Specifically, the nonlinear model predictive control method includes the following steps:

[0050] S1. Constructing a mathematical model of drone motion based on the four-axis eight-rotor drone;

[0051] S2. constructing a cost function for predictive control of the quad-axis octarotor UAV based on the UAV motion mathematical model;

[0052] S3, constructing a LESO expansion observer according to the torque or axis water resistance of the axis of the quad-axis octarotor drone in the spatial coordinate system;

[0053] S4, obtaining the operating status through the sensor of the quad-axis octaro-rotor UAV, and determining the power distribution mode of each rotor motor of the quad-axis octaro-rotor UAV;

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

[0055] Furthermore, the mathematical model of the UAV motion satisfies the following relationship:

[0056]

[0057] 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;

[0058] Φ1 represents the three Euler angles, and Φ2 represents the angular velocity around the three axes of the body;

[0059] 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;

[0060] 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.

[0061] In the above expression, Φ1=[φθψ] T , Φ2=[pqr] T ,and Body Euler angle 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] 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 upper bound of the output.

[0067] Furthermore, the moment of inertia of the x-axis of the quad-axis octarotor drone in the spatial coordinate system is defined as I 11 , the system input is τ x ,in:

[0068]

[0069] Then the LESO expansion observer on the x-axis of the quad-axis octarotor drone in the spatial coordinate system satisfies the following relationship:

[0070]

[0071] Among them, z1 and z2 represent the estimated values ​​of the state, and β1 and β2 represent the observation gains.

[0072] Furthermore, the LESO expansion observer on the x-axis of the quad-axis octarotor drone in the spatial coordinate system has an observation error that satisfies the following relationship:

[0073]

[0074] Simplifying it to:

[0075]

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

[0077] The LESO extended observer can be expressed as a characteristic polynomial when calculated:

[0078] f(λ)=λ 2 +β1λ+β2=(λ+ω o ) 2 ;

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

[0080] β1=2ω o , β2=ω o 2 .

[0081] It can be understood that the above process describes the observation and calculation of the torque of the x-axis, and the observer design can be performed for the remaining y-axis and z-axis torques and the x-, y-, and z-axis water resistances by analogy.

[0082] Furthermore, 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;

[0083] In general, the operation of a quadcopter octarotor drone in the air is consistent with the parameter control of the prior art, and the embodiment of the present invention mainly discusses the operation in water. Figure 3 As shown, when sailing in water, the left and right arms are rotated to 0° using the servo tilt structure to decouple the hovering and forward motions; thereafter, the drone is hovered and submerged through the front and rear four motors, and forward and steering motions are achieved through the left and right four motors.

[0084] When there are lateral waves in the environment, the drone needs to achieve a roll to resist the lateral force. Assuming that the drone will roll clockwise around the x-axis, the right side of the drone will maintain a 0° tilt, and the motor will reverse to offset the force generated by the left motor; the left motor will be calculated 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] like Figure 4 As shown, the underwater power distribution mode distributes power based on the following relationship:

[0086]

[0087] 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.

[0088] Furthermore, 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:

[0089] f=cω 2 ;

[0090] Where c represents the dynamic coefficient.

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

[0092] α·β=0;

[0093]

[0094] Furthermore, the step of solving the cost function according to the power distribution mode and the LESO extended observer is specifically:

[0095] 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:

[0096]

[0097] 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;

[0098] 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.

[0099] The beneficial effect achieved by the present invention is that a nonlinear control method for a four-axis eight-rotor UAV of water and air amphibians is proposed. The method models the configuration of the water and air amphibious multi-axis multi-motor UAV, designs a model prediction algorithm to control the position and attitude, takes the influence of water resistance and wind resistance into consideration when modeling and solving, and designs a LESO extended state observer 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 operating attitude of the water and air amphibious UAV controlled based on the method is optimized, and the operating performance is more efficient.

[0100] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program, and the program can be stored in a computer-readable storage medium, and when the program is executed, it can include the processes of the embodiments of the above-mentioned methods. The storage medium can be a disk, an optical disk, a read-only memory (ROM) or a random access memory (RAM).

[0101] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the existence of other identical elements in the process, method, article or device including the element.

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

[0103] The embodiments of the present invention are described above in conjunction with the accompanying drawings. What is disclosed is only the preferred embodiment of the present invention. However, the present invention is not limited to the above-mentioned specific implementation manner. The above-mentioned specific implementation manner is only illustrative rather than restrictive. Under the enlightenment of the present invention, ordinary technicians in this field can also make many forms and equivalent changes without departing from the scope of protection of the purpose of the present invention and the claims, all of which are within the protection 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; The cost function is solved according to the power distribution mode and the LESO extended observer to obtain control results for each rotor motor of the four-axis eight-rotor UAV.

2. The nonlinear model predictive control method for an amphibious unmanned aerial vehicle according to claim 1 is characterized in that: 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.

3. The nonlinear model predictive control method for an amphibious unmanned aerial vehicle according to claim 2 is characterized in that: 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 upper bound of the output.

4. The nonlinear model predictive control method for an amphibious unmanned aerial vehicle according to claim 3 is characterized in that: 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.

5. The nonlinear model predictive control method for an amphibious unmanned aerial vehicle according to claim 4 is characterized in that: 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.

6. The nonlinear model predictive control method for an amphibious unmanned aerial vehicle according to claim 4 is characterized in that: 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.

7. The nonlinear model predictive control method for an amphibious unmanned aerial vehicle according to claim 6, 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.

8. The nonlinear model predictive control method for an amphibious unmanned aerial vehicle according to claim 6, characterized in that: The power distribution of the underwater power distribution mode has the following constraints: α·β＝0； 9. The nonlinear model predictive control method for an amphibious unmanned aerial vehicle according to claim 6, 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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