Vector six-rotor aircraft full state control method based on high-order dynamics model

Abstract

This invention relates to a full-state control method for vector hexacopter aircraft based on a high-order dynamics model, belonging to the field of vector hexacopter tracking control. The invention addresses the problems of poor accuracy and low precision in angular acceleration estimation found in existing vector hexacopter control methods based on jerk dynamics models. This invention designs an angular acceleration observer based on a high-order dynamics model and full-drive system theory, enabling effective estimation of angular acceleration signals without relying on external sensors. This allows for high-precision, high-speed tracking of the position and attitude of a six-DOF vector hexacopter aircraft. This invention is primarily applied to attitude tracking of six-DOF vector hexacopter aircraft.

Description

Technical Field

[0001] This invention belongs to the field of tracking and control of vector rotorcraft. Background Technology

[0002] Vector rotorcraft refers to an aerial flight system driven by a vector thrust unit consisting of a propeller powered by servo motors and an electric motor. Compared to traditional underactuated rotorcraft, this flight system has decoupled control capabilities for position and attitude: it can maintain a specific attitude during positional movements and can also change attitude while hovering. This characteristic makes vector rotorcraft superior in aerial operations such as pipeline structural strength inspection, high-voltage power grid insulator insulation inspection, and offshore wind turbine blade inspection.

[0003] However, the introduction of servo units significantly increases the complexity of vector rotorcraft models. The inertia of the servo drive unit is much greater than that of the propeller motor, making it difficult to track position commands directly. To address this, researchers have recently developed a control method for vector rotorcraft based on a jerk dynamics model. Compared to traditional acceleration-based control methods, which can only obtain acceleration commands, the jerk dynamics model-based method can obtain jerk control commands (the third derivative of position, i.e., jerk, also known as jerk). Since the servo speed command is related to the jerk signal of the vector rotorcraft, the jerk dynamics model-based control method can ensure continuous servo speed commands, thus achieving advantages such as smooth control and high control accuracy.

[0004] However, feedback controllers based on jerk models (full-state controllers) require acceleration feedback signals. While linear acceleration in vector aircraft can be directly acquired by accelerometers, and mature commercial accelerometer chips are readily available, angular acceleration acquisition is extremely difficult. This is because no mature commercial sensor chips are yet available, and commercially available triaxial angular accelerometers are far too large for the small flying robotic arm system studied in this paper, making their application impossible.

[0005] Existing angular acceleration estimation methods suffer from drawbacks such as poor estimation accuracy, low precision, sensitivity to noise and system parameter variations, and poor robustness. Furthermore, existing feedback controllers (full-state controllers) based on jerk signals generally exhibit slow response speed, poor control stability, and weak anti-interference capabilities. Therefore, these problems urgently need to be addressed. Summary of the Invention

[0006] To address the issues of poor accuracy and low precision in angular acceleration estimation in existing vector rotorcraft control methods based on jerk dynamics models, this invention provides a full-state control method for vector hexacopter aircraft based on a high-order dynamics model.

[0007] A full-state control method for a vector hexacopter aircraft based on a high-order dynamics model, comprising:

[0008] S1, the actual velocity of the entire state of the aircraft in the output state received by the angular acceleration observer at time t. angular velocity ω t and the rate of change of the control force screw output by the full-state controller at time t. Control torque change rate Process the data to estimate the angular acceleration at time t. t is an integer, and t≥1;

[0009] S2, the angular acceleration at time t The linear acceleration of the spacecraft at time t, as collected by the acceleration measurement unit By splicing the data, we obtain the reference value of the full-state acceleration at time t. T stands for transpose;

[0010] S3, The full-state controller determines the desired pose q of the full-state at time t. d,t All-state acceleration reference value The actual pose q of the entire state in the output state of the aircraft t Generate the rate of change of the control force spinor at time t+1. By using the control quantity allocation method The system distributes and generates control signals for the aircraft's servos and motors, controls the aircraft's servos and motors, changes the aircraft's output state at time t, and achieves full-state control of the aircraft.

[0011] Preferably, in step S1, the angular acceleration at time t is estimated. The implementation method is as follows:

[0012] S11, based on ω received by the angular acceleration observer t and The state equation of the angular acceleration observer at time t is obtained as follows:

[0013]

[0014] in,

[0015]

[0016]

[0017] x t-1，1 and x t-1，2 These are the first and second observations of the angular acceleration observer at time t-1, respectively, x t-1，1 and x t-1，2 The initial value is any given value. and x t-1，1 and x t-1，2 rate of change, x t，1 and x t，2 These are the first and second observations of the angular acceleration observer at time t, respectively, x t，1 and x t，2 The initial value is 0. and x t，1 and x t，2 The rate of change, Δt is the time interval, I3 is a 3×3 identity matrix, 03 is a 3×3 matrix with all elements being 0, and L0 and L1 are the first and second constant diagonal matrices, respectively.

[0018] B1(ω t ), Θ(ω) t ), Ω(J) are both intermediate variables, and Θ(ω0) is Θ(ω t The initial values ​​of ω and ω are: ω0 = ω0, ... i,k Let ω be the element in the i-th row and k-th position of J, where i = 1, 2, 3, k = 1, 2, 3. t1 ω t2 and ω t3 These are the angular velocity components of the aircraft in the X, Y, and Z axes, respectively;

[0019] S12. Based on the state equation of the angular acceleration observer at time t, x... t，1 and B1(ω) t Estimate the angular acceleration at time t.

[0020] Preferably, in step S12

[0021] Preferably,

[0022] Among them, l 01 ,l 02 ,l 03 ,l 11 ,l 12 ,l 13 These are the first to sixth adjustable parameters of the angular acceleration observer.

[0023] Preferably, in step S3, the rate of change of the control force spinor at time t+1 is generated. The implementation methods include:

[0024] S31. Based on the expected pose q of the full state at time t. d,t The actual pose q of the full state in the output state of the aircraft t Define the zeroth-order error in all states in,

[0025] q d,t =[p d,t Q d,t ] T p d,t Let Q be the desired position vector at time t. d,t Let be the expected attitude quaternion at time t;

[0026] q t =[p t Q t ] T p t Let Q be the actual position vector at time t. t Let t be the actual attitude quaternion at time t;

[0027] e t =p d,t -p t e t Let be the position error at time t;

[0028] Q e,t Let be the attitude error quaternion at time t. For Q t The conjugate quaternion, q e0,t and q ev,t The attitude error quaternion Q is respectively e,t The real and imaginary parts;

[0029] S32, e t Taking the derivative, we obtain the first-order position error. and second-order position error

[0030] S33, according to Q d,t The desired angular velocity ω in the ground coordinate system is obtained. d,t ;

[0031] S34, according to Q t , ω t and ω d,t Define angular velocity deviation ω e,t ;

[0032] S35, according to ω e,t Construct the attitude error quaternion Q e,t The real part q e0,t The second derivative and the imaginary part q ev,t The second derivative

[0033] S36, according to and Define intermediate variable q A ;

[0034] According to q e0,t and q ev,t Define intermediate variable q B ;

[0035] According to ω t , ω d,t and ω e,t Define intermediate variable Ω e / B ;

[0036]

[0037] in, For ω e,t The first derivative, and ω d,t The first and second derivatives, For q ev,t The first derivative of ; I3 is a 3×3 identity matrix, R EB This is the coordinate transformation matrix from the aircraft body coordinate system to the world coordinate system;

[0038] S37, according to q B Construct intermediate variables

[0039]

[0040] According to q A q B and Ω e / B Construct intermediate variable u t ;

[0041]

[0042]

[0043] Among them, v t and j t All are intermediate variables. For p t The second derivative, For p d,t The third derivative of , where m is the total mass of the spacecraft, J is the inertial tensor of the spacecraft, and p bc Let be the vector from the center of mass of the aircraft to the origin of the coordinate system containing the propeller. For gravity f g The first derivative of , where M is the inertia matrix of the aircraft. The first derivative of M;

[0044] according to and Construct the zero-order error e in all states 1,t first derivative and second derivative Thus, intermediate variables are obtained.

[0045] S38, according to u t and E t The rate of change of the control force spinor was obtained.

[0046] Preferably, in step S33,

[0047] It is Q d,t The conjugate quaternion, ω d / d,t Let t be the desired angular velocity in the desired attitude coordinate system at time t.

[0048] Preferably, in step S34,

[0049] Among them, R EB This is the coordinate transformation matrix from the aircraft's body coordinate system to the world coordinate system.

[0050] Preferably, in step S35,

[0051]

[0052] Where T is the transpose. For q ev,t The first derivative, and ω e,t The first and second derivatives, For q e0,t The first derivative.

[0053] Preferably, in step S37,

[0054] Preferably, in step S38,

[0055] Where A = [A0 A1 A2], A is the adjustment coefficient matrix of the full-state controller, and A0, A1 and A2 represent the first to third adjustment coefficients of the full-state controller, respectively.

[0056] The beneficial effects of this invention are:

[0057] This invention proposes a full-state control method for a vector hexacopter aircraft based on a high-order dynamics model. The main advantages of this invention include:

[0058] (1) An angular acceleration observer based on a high-order dynamic model and the theory of the full drive system is proposed, which can effectively estimate the angular acceleration signal without relying on external sensor devices and provide an accurate data basis for the subsequent control signal generation process;

[0059] (2) A full-state controller based on a high-order dynamic model is proposed, which can achieve high-precision and high-speed tracking of the position and attitude of a six-degree-of-freedom vector six-rotor aircraft. Based on the angular acceleration signal obtained by the angular acceleration observer and the linear acceleration signal measured by the angular acceleration measurement unit, the full-state controller further designs a high-level force and torque control, thereby achieving high-precision attitude control.

[0060] This invention uses an angular acceleration observer to effectively obtain an estimate of angular acceleration, and further uses the control force spinor change rate output by the full-state controller. By allocating control quantities and controlling the servos and motors of the aircraft, high-precision and high-speed tracking of the position and attitude of a six-degree-of-freedom vector six-rotor aircraft can be achieved. Attached Figure Description

[0061] Figure 1 This is a schematic diagram illustrating the principle of the vector hexacopter full-state control method based on a high-order dynamics model as described in this invention.

[0062] Figure 2 This is a physical image of a six-degree-of-freedom vector six-rotor aircraft. Detailed Implementation

[0063] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0064] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0065] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the invention.

[0066] Origin of the concept: This invention aims to address the shortcomings of traditional vector rotorcraft control methods based on jerk dynamics models, which suffer from poor accuracy and low precision in angular acceleration estimation, as well as the common drawbacks of jerk-based feedback controllers (full-state controllers) with slow response speed, poor control stability, and weak anti-interference capabilities. Therefore, this invention provides a full-state control method for vector hexacopter aircraft based on a high-order dynamics model. This invention mainly improves the technology in two aspects: first, an angular acceleration observer; and second, a full-state controller.

[0067] In existing technologies, there are already dynamic models for the acceleration stage of vector rotorcraft. By neglecting some disturbance terms such as the centrifugal force generated by the motion of the system's center of mass and the inertial force and Coriolis force caused by the tilting of the servo mechanism, a dynamic model of the acceleration stage of vector rotorcraft can be obtained.

[0068]

[0069] Where M is the inertia matrix of the vector rotorcraft, m is the total mass of the vector rotorcraft, and p bc R is the vector from the center of mass vector to the origin of the coordinate system where the propeller is located. EB Let J be the coordinate transformation matrix from the aircraft's body coordinate system to the world coordinate system, where J is the inertia tensor, p is the center of mass vector, and f is the coordinate transformation matrix from the aircraft's body coordinate system to the world coordinate system. g f represents gravity. dis and τ dis The total external disturbance force and torque, ω is the control force spinor at time t. t Let t be the angular velocity of the aircraft under the current system at time t.

[0070] Based on the acceleration-level dynamics model, differentiating this model with respect to time yields the jerk-level dynamics model (higher-order dynamics model) of the vector rotorcraft, as follows:

[0071]

[0072] In the formula, (*) (3) Represents the third derivative of the variable (*). For gravity in the body coordinate system C B rate of change in It is the derivative of the inertia matrix. and This represents the rate of change of total external disturbance force and torque. The output of the controller (rate of change of screw) is worth noting. Right now From the rate of change of control force and rate of change of control torque It consists of two parts, that is From It was obtained directly from the source.

[0073] The specific implementation method is as follows:

[0074] Specific Implementation Method 1: Combination Figure 1 As shown in this embodiment, the vector hexacopter full-state control method based on a high-order dynamics model includes:

[0075] S1, the actual velocity of the entire state of the aircraft in the output state received by the angular acceleration observer at time t. angular velocity ω t and the rate of change of the control force screw output by the full-state controller at time t. Control torque change rate Process the data to estimate the angular acceleration at time t. t is an integer, and t≥1;

[0076] S2, the angular acceleration at time t The linear acceleration of the spacecraft at time t, as collected by the acceleration measurement unit By splicing the data, we obtain the reference value of the full-state acceleration at time t. T stands for transpose;

[0077] S3, The full-state controller determines the desired pose q of the full-state at time t. d,t All-state acceleration reference value The actual pose q of the entire state in the output state of the aircraft t Generate the rate of change of the control force spinor at time t+1. By using the control quantity allocation method The system distributes and generates control signals for the aircraft's servos and motors, controls the aircraft's servos and motors, changes the aircraft's output state at time t, and achieves full-state control of the aircraft.

[0078] In practical applications, the control quantity allocation method is used to... When making the allocation, the control quantity allocation method can be implemented using existing technology, specifically algorithms such as pseudo-inverse method or null space projection method. and These are the rate of change of control force and the rate of change of control torque at time t+1, respectively.

[0079] See Figure 1The six-DOF vector hexacopter aircraft includes full-state actual pose q t =[p t Q t ] T and actual speed in all states The main function of the angular acceleration observer is to obtain the actual velocity of the rotor body in its entirety as it returns. angular velocity ω t and the rate of change of control torque output by the controller. These variables serve as inputs to the system, and the estimated angular acceleration values ​​are calculated based on them. It can accurately and robustly estimate the angular acceleration of an aircraft, while being insensitive to errors in nominal parameters such as the system's moment of inertia.

[0080] The theoretical derivation process for the angular acceleration observer design is as follows:

[0081] Here will be ω t The inertial tensor J of the aircraft is specifically expanded in component form as follows:

[0082]

[0083] According to Euler's law in classical mechanics, we can obtain:

[0084]

[0085] Differentiating both sides of the above equation, we get:

[0086]

[0087] This invention will ω t Substituting the specific components of J into the above equation From the expression, we can obtain the following second-order total measurement system:

[0088]

[0089] Among them and Let ω0 be the angular velocity at initial time 0, and Δt be the control time interval. The difference in angular velocity between the two control intervals (current time minus previous time) is Δω, which can be expressed as follows:

[0090]

[0091] Where, Θ(ω) t ) and Ω(J) are both intermediate variables in the calculation.

[0092] Then, based on the above formula, the present invention defines two observation variables as follows:

[0093]

[0094] It is worth noting that the two observed variables given here are only for defining two intermediate variables, based on x. t，1 and x t，2 The state-space equations of the angular acceleration observer were designed, thus constructing an angular acceleration observer.

[0095] Therefore, based on the above derivation process, the angular acceleration at time t estimated by the angular acceleration observer in step S1 is given. The implementation method is as follows:

[0096] S11, based on ω received by the angular acceleration observer t and The state equation of the angular acceleration observer at time t is obtained as follows:

[0097]

[0098] in,

[0099]

[0100]

[0101] x t-1，1 and x t-1，2 These are the first and second observations of the angular acceleration observer at time t-1, respectively, x t-1，1 and x t-1，2 The initial value is any given value, usually 0. and x t-1，1 and x t-1，2 rate of change, x t，1 and x t，2 These are the first and second observations of the angular acceleration observer at time t, respectively, x t，1 and x t，2 The initial value is 0. and x t，1 and x t，2 The rate of change, Δt is the time interval, I3 is a 3×3 identity matrix, 03 is a 3×3 matrix with all elements being 0, and L0 and L1 are the first and second constant diagonal matrices, respectively.

[0102] B1(ω t ), Θ(ω) t ), Ω(J) are both intermediate variables, and Θ(ω0) is Θ(ω tThe initial value of Θ(ω) is obtained by substituting the initial angular velocity ω0 into Θ(ω). t From the expression, Δω is the change in angular acceleration, ω0 is the initial value of angular velocity, and J is the inertial tensor of the aircraft; j i,k Let ω be the element in the i-th row and k-th position of J, where i = 1, 2, 3, k = 1, 2, 3. t1 ω t2 and ω t3 These represent the angular velocity components of the aircraft along the X, Y, and Z axes, respectively; [] × This represents the operation of taking the antisymmetric matrix from a vector;

[0103] l 01 ,l 02 ,l 03 ,l 11 ,l 12 ,l 13 These are the first to sixth adjustable parameters of the angular acceleration observer.

[0104] S12. Based on the state equation of the angular acceleration observer at time t, x... t，1 and B1(ω) t Estimate the angular acceleration at time t.

[0105] In this preferred embodiment, the angular acceleration at time t is estimated. In the specific process, the influence of the torque change rate on the angular acceleration of the aircraft is determined based on the accurate attitude dynamics model and the derivative equation of the model equation (referred to as the jerk dynamics model or higher-order dynamics model in this invention), and is taken into consideration in the observer algorithm. At the same time, the use of a higher-order system model, i.e., jerk dynamics modeling, makes the observer insensitive to constant disturbances such as nominal inertia matrix error and external constant torque disturbance.

[0106] In the design of the full-state controller, this invention is based on the expected pose q of the external full-state. d,t =[p d,t Q d,t ] T The first and second derivatives of the position error are obtained, and the actual pose q of the full state is output based on the system state. t =[p t Q t ] T Actual speed under all conditions And the values ​​estimated by the angular acceleration observer Measured by inertial measurement unit The combined full-state acceleration reference values The controller output is obtained through a series of calculations.

[0107] Furthermore, in step S3, the rate of change of the control force spinor at time t+1 is given. The implementation methods include:

[0108] S31. Based on the expected pose q of the full state at time t. d,t The actual pose q of the full state in the output state of the aircraft t Define the zeroth-order error in all states in,

[0109] q d,t =[p d,t Q d,t ] T p d,t Let Q be the desired position vector at time t. d,t Let be the expected attitude quaternion at time t;

[0110] q t =[p t Q t ] T p t Let Q be the actual position vector at time t. t Let t be the actual attitude quaternion at time t;

[0111] e t =p d,t -p t e t Let be the position error at time t;

[0112] Q e,t Let be the attitude error quaternion at time t. For Q t The conjugate quaternion, q e0,t and q ev,t The attitude error quaternion Q is respectively e,t The real and imaginary parts;

[0113] S32, e t Taking the derivative, we obtain the first-order position error. and second-order position error

[0114] S33, according to Q d,t The desired angular velocity ω in the ground coordinate system is obtained. d,t , specifically

[0115]

[0116] It is Q d,t The conjugate quaternion, ωd / d,t Let t be the desired angular velocity in the desired attitude coordinate system at time t;

[0117] S34, according to Q t , ω t and ω d,t Define angular velocity deviation ω e,t ;

[0118] Specifically,

[0119] R EB This is the coordinate transformation matrix from the aircraft body coordinate system to the world coordinate system;

[0120] S35, according to ω e,t Construct the attitude error quaternion Q e,t The real part q e0,t The second derivative and the imaginary part q ev,t The second derivative

[0121] Specifically,

[0122]

[0123] Where T is the transpose. For q ev,t The first derivative, and ω e,t The first and second derivatives, For q e0,t The first derivative;

[0124] S36, according to and Define intermediate variable q A ;

[0125] According to q e0,t and q ev,t Define intermediate variable q B ;

[0126] According to ω t , ω d,t and ω e,t Define intermediate variable Ω e / B ;

[0127]

[0128] in, For ω e,t The first derivative, and ω d,t The first and second derivatives, For q ev,t The first derivative of ; I3 is a 3×3 identity matrix, R EB This is the coordinate transformation matrix from the aircraft body coordinate system to the world coordinate system;

[0129] S37, according to q B Construct intermediate variables

[0130]

[0131] According to q A q B and Ω e / B Construct intermediate variable u t ;

[0132]

[0133]

[0134] Among them, v t and j t All are intermediate variables. For p t The second derivative, For p d,t The third derivative of , where m is the total mass of the spacecraft, J is the inertial tensor of the spacecraft, and p bc Let be the vector from the center of mass of the aircraft to the origin of the coordinate system containing the propeller. For gravity f g The first derivative of , where M is the inertia matrix of the aircraft. The first derivative of M;

[0135] according to and Construct the zero-order error e in all states 1,t first derivative and second derivative Thus, intermediate variables are obtained. in,

[0136] S38, according to u t and E t The rate of change of the control force spinor was obtained.

[0137] Where A = [A0 A1 A2], A is the adjustment coefficient matrix of the full-state controller, and A0, A1 and A2 represent the first to third adjustment coefficients of the full-state controller, respectively.

[0138] In this preferred embodiment, the rate of change of the control force spinor is obtained. The process considered position and attitude errors, as well as their first and second derivatives, especially the dynamics of position and attitude. In particular, it accurately modeled the position and attitude dynamics and solved the derivatives on both sides of the dynamic equation (referred to as the jerk dynamics model in this invention). Through a quaternion-based attitude representation method, it achieved an accurate and singular-free representation of the attitude error, resulting in... It is superior, with the implemented control method having a fast response speed, high control accuracy, and good robustness.

[0139] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A full-state control method for a vector hexacopter aircraft based on a high-order dynamic model, characterized in that, The method includes: S1, the angular acceleration observer receives its data. Real speed in all states of the spacecraft's output state at any given time angular velocity in ,as well as Rate of change of control force spinor output by the all-state controller at all times Control torque change rate Process and estimate angular acceleration at time t , It is an integer, and ; estimate angular acceleration at time t The implementation method is as follows: S11, based on the data received by the angular acceleration observer and ,get The state equation of the angular acceleration observer at time t is: ； ； in, ； ； ； ； and They are respectively At time t, the first and second observations of the angular acceleration observer, and The initial value is any given value. and They are respectively and rate of change, and They are respectively At time t, the first and second observations of the angular acceleration observer, and The initial value is 0. and They are respectively and rate of change, For time intervals, It is a 3×3 identity matrix. It is a 3×3 matrix where all elements are 0. and These are the first and second constant diagonal matrices, respectively; , , , All are intermediate variables. for initial value, The change in angular acceleration. The initial value of the angular velocity. For the inertial tensor of the aircraft; for The Middle Line number One element, , , , and These are the angular velocity components of the aircraft in the X, Y, and Z axes, respectively; S12, according to The state equation of the time angular acceleration observer and Estimate angular acceleration at time t ; S2, will angular acceleration at time t Compared with the data collected by the acceleration measurement unit linear acceleration of the spacecraft By splicing them together, we get All-state acceleration reference value at all times , For transpose; S3, Full-State Controller According to Full-state expected pose at time 1 All-state acceleration reference value The actual pose of the aircraft in all states in the output state ,generate Rate of change of control force spinor at time By using the control quantity allocation method The system distributes and generates control signals for the aircraft's servos and motors, thereby controlling and changing these signals. It monitors the output status of the aircraft at all times, enabling full-state control of the aircraft.

2. The full-state control method for a vector hexacopter aircraft based on a high-order dynamic model according to claim 1, characterized in that, In step S12 .

3. The full-state control method for a vector hexacopter aircraft based on a high-order dynamic model according to claim 1, characterized in that, ； in, These are the first to sixth adjustable parameters of the angular acceleration observer.

4. The full-state control method for a vector hexacopter aircraft based on a high-order dynamic model according to claim 1, characterized in that, In step S3, generate Rate of change of control force spinor at time The implementation methods include: S31, according to Full-state expected pose at time 1 and the actual pose of the full state in the output state of the aircraft Define the zeroth-order error in all states ;in, , for The expected position vector at time t. for The expected attitude quaternion at the given time; , for The actual position vector at time t. for The actual attitude quaternion at the given moment; , for Position error at time; , for At this moment, the attitude error quaternion, for The conjugate quaternion, and These are the attitude error quaternions. The real and imaginary parts; S32, to Taking the derivative, we obtain the first-order position error. and second-order position error ; S33, according to The desired angular velocity in the ground coordinate system is obtained. ; S34, according to , , and Define angular velocity deviation ; S35, according to Construct attitude error quaternions real part The second derivative and the imaginary part The second derivative ; S36, according to , , and Define intermediate variables ; according to and Define intermediate variables ; according to , , and Define intermediate variables ; ； in, for The first derivative, and They are respectively The first and second derivatives, for The first derivative; It is a 3×3 identity matrix. This is the coordinate transformation matrix from the aircraft body coordinate system to the world coordinate system; S37, according to Construct intermediate variables ; ； according to Construct intermediate variables ; ； ； ； in, and All are intermediate variables. for The second derivative, for The third derivative, The total mass of the aircraft For the inertial tensor of the aircraft, Let be the vector from the center of mass of the aircraft to the origin of the coordinate system containing the propeller. gravity The first derivative, The inertia matrix of the aircraft. for The first derivative; according to , , and Construct the zero-order error in all states first derivative and second derivative Thus, intermediate variables are obtained. ; S38, according to , and The rate of change of the control force spinor was obtained. .

5. The full-state control method for a vector hexacopter aircraft based on a high-order dynamic model according to claim 4, characterized in that, In step S33, ; yes The conjugate quaternion, for The desired angular velocity in the desired attitude coordinate system at the given time.

6. The full-state control method for a vector hexacopter aircraft based on a high-order dynamic model according to claim 4, characterized in that, In step S34, ; in, This is the coordinate transformation matrix from the aircraft's body coordinate system to the world coordinate system.

7. The full-state control method for a vector hexacopter aircraft based on a high-order dynamic model according to claim 4, characterized in that, In step S35, ； in, For transpose, for The first derivative, and They are respectively The first and second derivatives, for The first derivative.

8. The full-state control method for a vector hexacopter aircraft based on a high-order dynamic model according to claim 4, characterized in that, In step S37, .

9. The full-state control method for a vector hexacopter aircraft based on a high-order dynamic model according to claim 4, characterized in that, In step S38, ; in, , This is the adjustment coefficient matrix of the full-state controller. , and These represent the first to third adjustment coefficients of the full-state controller, respectively.

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