Robust geometric control method for event-driven microminiature unmanned helicopter

Abstract

The present application relates to the robust geometric control of the ultra-micro unmanned helicopter with the mass less than 100 grams, for reducing the dependence of the ultra-micro unmanned helicopter with the mass less than 100 grams on the system model, improving the stability and robustness in the actual flight process, and reducing the consumption of the on-board computing resources. For this purpose, the technical scheme adopted by the present application is as follows: 1) establishing the dynamic model of the ultra-micro unmanned helicopter; 2) designing the position controller of the ultra-micro unmanned helicopter, using the event-driven position controller design; 3) designing the attitude controller of the ultra-micro unmanned helicopter based on the robust integral sign error (RISE). The present application is mainly applied to the design and manufacture of the ultra-micro unmanned helicopter.

Description

Technical Field

[0001] This invention relates to robust geometric control of ultra-miniature unmanned helicopters with a mass of less than 100 grams, and more specifically to an event-driven robust geometric control method for ultra-miniature unmanned helicopters. Background Technology

[0002] With the rapid development of microelectromechanical systems (MEMS), small unmanned aerial vehicles (UAVs) have attracted considerable attention and are widely used in military and civilian applications such as terrain exploration, aerial photography, and military strikes (Journal: International Journal of Adaptive Control and Signal Processing; Authors: Xun Gu, Bin Xian, and Jieqi Li; Publication Date: January 2022; Article Title: Model Free Adaptive Control Design for a TiltTrirotor Unmanned Aerial Vehicle with Quaternion Feedback: Theory and Implementation; Pages: 122–137). Compared to quadcopter UAVs, single-rotor unmanned helicopters have advantages in terms of compact structure, high payload capacity, and high maneuverability, making them more advantageous in the aforementioned application scenarios. However, its complex mechanical structure and the strong nonlinear characteristics of the system model pose a significant challenge to the design of the control system (Conference: 40th Chinese Control Conference (CCC) in 2021; Authors: Xun Gu and Bin Xian; Publication date: October 2021; Article title: Geometry Control on SE(3) for a Small Size Unmanned Helicopter; Pages: 285–290).

[0003] To address the agile flight control of single-rotor unmanned aerial vehicles (UAVs), scholars have proposed various nonlinear control algorithms. For example, some scholars, considering the uncertainties in the single-rotor UAV system model, designed a robust controller based on geometric control theory and verified its effectiveness through flight experiments (Conference: IEEE 56th Annual Conference on Decision and Control (CDC); Authors: Nidhish Raj, Ravi N. Banavar, Abhishek; Publication Date: December 2017; Article Title: Attitude Tracking Control for Aerobatic Helicopters: A Geometric Approach; Pages: 1951–1956). Some scholars have also designed backstepping controllers based on geometric control theory for the position and attitude models of unmanned helicopters, and demonstrated the feasibility of the proposed control algorithms through numerical simulations (Journal: IEEE Transactions on Control Systems Technology; Authors: Ioannis A. Raptis, Kimon P. Valavanis, and Wilfrido A. Moreno; Publication Date: March 2011; Article Title: A Novel Nonlinear Backstepping Controller Design for Helicopters Using the Rotation Matrix; Pages: 465–473).

[0004] On the other hand, limited by the onboard size of its ultra-miniature unmanned helicopter, it is necessary to conserve computational resources as much as possible under existing control strategies. A better solution is to introduce event-triggered conditions, which can significantly save communication and computational resources. For example, some researchers have proposed an event-driven nonlinear controller for quadcopter UAVs and verified through numerical simulations that the proposed control algorithm can significantly reduce communication pressure (Journal: IEEE Transactions on Industrial).

[0005] Electronics; Authors: Wang C, Guo L, Wen C; Publication Date: March 2020; Title: Event-triggered adaptive attitude tracking control for spacecraft with unknown actuator faults; Pages: 2241–2250. However, compared to quadcopter UAVs, single-rotor unmanned helicopters have higher system nonlinearity and stronger state coupling in their attitude loop. This can lead to a significant reduction in flight performance or even loss of control during agile flight. Therefore, inspired by Mustafa A et al. (Journal: IEEE / CAA Journal of Automatica Sinica; Authors: Mustafa A, Dhar NK, Verma NK; Publication Date: July 2020; Title: Event-triggered sliding mode control for trajectorytracking of nonlinear systems; Pages: 307–314), an event-driven position robust controller is proposed for single-rotor unmanned helicopters, which can save computational resources while maintaining agile flight performance.

[0006] In summary, while researchers have made some progress in the control of micro-unmanned helicopters, some limitations remain: 1) The dynamic models of micro-unmanned helicopters are complex and highly sensitive to external disturbances. To demonstrate agile flight, robust nonlinear control algorithms need to be designed. 2) Existing controllers rarely consider the limited onboard computing power of micro-unmanned helicopters, which restricts the practical application of some complex nonlinear control algorithms. Summary of the Invention

[0007] To overcome the shortcomings of existing technologies, this invention aims to reduce the dependence of ultra-miniature unmanned helicopters weighing less than 100 grams on system models, improve stability and robustness during actual flight, and simultaneously reduce the consumption of onboard computing resources. To this end, the technical solution adopted by this invention is an event-driven robust geometric control method for ultra-miniature unmanned helicopters, the steps of which are as follows:

[0008] 1) Establish a dynamic model for an ultra-miniature unmanned helicopter;

[0009] 2) Design of a position controller for an ultra-miniature unmanned helicopter, utilizing an event-driven position controller design;

[0010] 3) Attitude control of ultra-miniature unmanned helicopters based on robust integral sign error (RISE).

[0011] The specific steps are as follows:

[0012] 1) Establish a dynamic model of an ultra-miniature unmanned helicopter

[0013] The position loop dynamics model of the ultra-miniature unmanned helicopter is as follows:

[0014]

[0015] Where vector and The matrix represents the three-dimensional position and linear velocity of a single-rotor unmanned helicopter. Let represent the transition matrix from the body coordinate system to the inertial coordinate system, and scalars m and g represent the transition matrices from the body coordinate system to the inertial coordinate system. e3 =

[001] T scalar Represents total thrust, vector This represents an unknown external disturbance, with the external unknown disturbance vector Δ. p There is a supremum δ p That is, ||Δ p ||≤δ p , where δ p It is a normal function;

[0016] The attitude loop dynamics equation of the ultra-miniature unmanned helicopter is:

[0017]

[0018] Where vector Represents the angular velocity in the body coordinate system, a diagonal matrix. The inertia matrix represents that of a single-rotor unmanned helicopter. This represents the control input in the body coordinate system, Δ. a and Let G(t) represent the external unknown disturbance and the modeling uncertainty in the body coordinate system, respectively. The operator skw(·) represents the anti-diagonal matrix spanned by three-dimensional vectors. The unmodeled uncertainty G(t) and the external unknown disturbance Δ are respectively represented by G(t) and G(t). a Continuously differentiable, and G(t), is first-order continuously differentiable with bounded derivatives, with an unknown external perturbation Δ. a There exists a positive upper bound δ a ;

[0019] The actual control input to the attitude loop of the ultra-miniature unmanned helicopter is the flapping angle α. s ,b s and the total thrust T of the tail rotor t Vector χ = [a s b sT t The conversion relationship between ] and τ is:

[0020] χ=X(T N )τ+Y(T N (3)

[0021] Among them, matrix and Let be the transition matrix from the virtual control input τ(t) to the actual control input χ(t);

[0022] 2) Design of a position controller for an ultra-miniature unmanned helicopter

[0023] Define position tracking error Linear velocity tracking error And the auxiliary filter error s is

[0024]

[0025] Where ξ d (t) and Let α represent the desired position and desired linear velocity, respectively. p To represent a positive control gain, the last term in equation (4) is differentiated with respect to time, and combined with equation (1), we get:

[0026]

[0027] Auxiliary control input Choose f = T N Ψe3, the auxiliary control input is designed as follows:

[0028]

[0029] Where β is a positive gain coefficient, and sgn(·) denotes the sign function, combining (6) and (5), the closed-loop dynamic equation of s is:

[0030]

[0031] Furthermore, an event-driven position controller design method is adopted: the auxiliary state variable λ(t) is defined as λ=[ξ(t)v(t], and defined... for And the event triggering error is defined as:

[0032] e = r(t) i )-r(t) (8)

[0033] in r(t i ) indicates the time t during the switching process. iThe state value is based on the position controller designed in equation (6), and the event-driven position tracking controller is selected as follows:

[0034]

[0035] Substituting (9) into (5), we obtain the closed-loop dynamic equation of the system as follows:

[0036]

[0037] Expected trajectory ξ d (t), v d (t) and For a sequence that is continuous and satisfies the Lipschitz condition in a compact set, the following inequality holds:

[0038]

[0039] Where ρ ξ It is a positive number;

[0040] 3) Attitude control of ultra-miniature unmanned helicopters based on robust integral sign error (RISE)

[0041] Define attitude error e Ψ and attitude angular velocity error e ω for:

[0042]

[0043] in Indicates the desired attitude angle. Represents the desired angular velocity, symbol (·). ∨ This represents the inverse operation of skw(·);

[0044] Define attitude filtering error and for:

[0045]

[0046] Where α a1 and For a positive control gain, the derivative of r1(t) with respect to time is taken, and substituting (13) into the result, we get:

[0047]

[0048] Where the auxiliary function H(Ψ,Ψ) d )for:

[0049]

[0050] The operator tr(·) represents the trace of the matrix. The second equation in equation (13) is differentiated with respect to time, and substituting (14) into the result, we get:

[0051]

[0052] Where the auxiliary function Π(Ψ,Ψ) d ,ω,ω d ) is defined as

[0053]

[0054] Furthermore, the auxiliary function N(t) is defined as:

[0055]

[0056] Therefore, (16) can be further simplified to:

[0057]

[0058] The attitude controller for the ultra-miniature unmanned helicopter is designed as follows:

[0059]

[0060] in The control gain is positive. Taking the time derivative of equation (20) and substituting (19) into the differentiated equation, we can obtain the closed-loop dynamic equation of the single-rotor unmanned helicopter as follows:

[0061]

[0062] The features and beneficial effects of this invention are:

[0063] A robust nonlinear controller based on event-driven principles was designed for ultra-miniature unmanned helicopters weighing less than 100 grams, and agile indoor flight of the ultra-miniature UAV was achieved using an indoor motion capture system. The designed controller provides compensation for model uncertainties and unknown external disturbances. Furthermore, it is easier to implement in engineering compared to existing geometric control methods. On the other hand, due to the limitations of the ultra-miniature helicopter's fuselage mass and onboard computing power, an event-driven nonlinear robust control strategy was designed in the position loop. Indoor flight test results show that the control algorithm proposed in this invention effectively reduces the resource consumption of the control algorithm while ensuring the tracking accuracy of the ultra-miniature unmanned helicopter during agile flight. Attached image description:

[0064] Figure 1 This is a schematic diagram of the fully free-degree-of-freedom ultra-miniature unmanned helicopter flight platform used in this invention;

[0065] Figure 2This is a 3D image of UAV rectangular tracking using the robust controller (without event-driven part) proposed in this invention;

[0066] Figure 3 This is a diagram showing the rectangular tracking effect of a UAV using the robust controller (without event-driven components) proposed in this invention.

[0067] Figure 4 This is a rectangular tracking error diagram of a UAV using the robust controller (without event-driven part) proposed in this invention;

[0068] Figure 5 This is a 3D image of a UAV rectangular tracking system using the event-driven robust controller proposed in this invention.

[0069] Figure 6 This is a diagram showing the rectangular tracking effect of a UAV using the event-driven robust controller proposed in this invention;

[0070] Figure 7 This is a rectangular tracking error diagram of a UAV using the event-driven robust controller proposed in this invention;

[0071] Figure 8 It is a curve showing the control of resource conservation ratio;

[0072] Figure 9 It is a 3D image of UAV rectangular tracking using cascaded PID;

[0073] Figure 10 This is a diagram showing the rectangular tracking effect of a drone using cascaded PID control.

[0074] Figure 11 This is a rectangular tracking error diagram of a UAV using cascaded PID control. Detailed Implementation

[0075] This invention relates to robust geometric control for ultra-miniature unmanned helicopters weighing less than 100 grams. Addressing the limitations of airframe size and payload capacity, which make it difficult to deploy complex nonlinear control algorithms in existing flight control boards, this invention proposes a control algorithm that is easy to implement in engineering and possesses strong robustness. This method employs Robust Integral Signed Error (RISE) control to compensate for modeling uncertainties and unknown external disturbances in the system. Considering the limited control resources, an event-driven control strategy is introduced into the position loop control strategy. This achieves accurate tracking flight control for the ultra-miniature unmanned helicopter and demonstrates robustness to external disturbances. Specifically, it relates to an event-driven nonlinear control method for the position and attitude of the ultra-miniature unmanned helicopter.

[0076] The purpose of this invention is to overcome the shortcomings of existing technologies, reduce the dependence of ultra-micro unmanned helicopters (UHHH) with a mass of less than 100 grams on system models, improve stability and robustness during actual flight, and reduce the consumption of onboard computing resources. Specifically: 1) Considering the complexity of the dynamic model of the ultra-micro UHHH and its sensitivity to external disturbances, a RISE-based nonlinear control algorithm is adopted to compensate for system modeling uncertainties and external disturbances. 2) Considering the limited onboard computing power of the ultra-micro UHHH, an event-driven control strategy is introduced in the position loop to save control and communication resources. By reasonably setting the event-driven triggering conditions, the designed event-driven nonlinear position control algorithm can better guarantee tracking accuracy while effectively reducing control resources. 3) The effectiveness of the control algorithm designed in this invention is verified through an indoor full-degree-of-freedom flight experiment based on a motion capture system. The implementation steps of the technical solution adopted in this invention are as follows:

[0077] 1) Establish a dynamic model of an ultra-miniature unmanned helicopter

[0078] The position loop dynamics model of the ultra-miniature unmanned helicopter can be written as:

[0079]

[0080] Where vector and The matrix represents the three-dimensional position and linear velocity of a single-rotor unmanned helicopter. This represents the transition matrix from the body coordinate system to the inertial coordinate system. Scalars m and g represent the transition matrices from the body coordinate system to the inertial coordinate system. e3 =

[001] T scalar Represents total thrust, vector This represents an unknown external disturbance. The external unknown disturbance vector Δ p (t) has a supremum δ p That is, ||Δ p (t)||≤δ p Where δ p It is a normal function.

[0081] The attitude loop dynamics equation of the ultra-miniature unmanned helicopter can be written as:

[0082]

[0083] Where vector Represents the angular velocity in the body coordinate system, a diagonal matrix. The inertia matrix represents that of a single-rotor unmanned helicopter. This represents the control input in the body coordinate system, Δ. a (t) and Let G(t) represent the external unknown disturbance and the modeling uncertainty in the body coordinate system, respectively. The operator skw(·) represents the anti-diagonal matrix spanned by three-dimensional vectors. The unmodeled uncertainty G(t) and the external unknown disturbance Δt are also represented. a (t) is continuously differentiable, and G(t),Δ a (t) is first-order continuously differentiable and its derivative is bounded. External unknown disturbance Δ a (t) There exists a positive supremum δ a .

[0084] Furthermore, the actual control input to the attitude loop of the ultra-miniature unmanned helicopter is the flailing angle α. s (t),b s (t) and total thrust T of the tail rotor t (t). Vector χ=[a s b s T t The transformation relationship between ] and τ(t) can be summarized as follows (Journal: IEEE Transactions on Control Systems Technology; Authors: Raptis IA, Valavanis KP, Moreno WA; Publication Date: February 2011; Article Title: A novel nonlinear backstepping controller design for helicopters using the rotation matrix; Pages: 465–473):

[0085] χ=X(T N )τ+Y(T N (3)

[0086] Among them, matrix and The transition matrix from the virtual control input τ(t) to the actual control input χ(t) (Conference: In 2021 40th Chinese Control Conference (CCC); Authors: Xun Gu and Bin Xian; Publication date: October 2021; Article title: Geometry Control on SE(3) for a SmallSize Unmanned Helicopter; Pages: 285–290).

[0087] 2) Design of a position controller for an ultra-miniature unmanned helicopter

[0088] Define position tracking error Linear velocity tracking error The auxiliary filtering error s(t) is

[0089]

[0090] Where ξ d (t) and Let α represent the desired position and desired linear velocity, respectively. p This represents a positive control gain. Taking the time derivative of the last term in equation (4) and combining it with (1), we get:

[0091]

[0092] Auxiliary control input Choose f = T N Ψe3. The auxiliary control input can be designed as follows (Conference: In 2019 American Control Conference (ACC); Authors: Gamagedara K, Bisheban M, Kaufman E; Publication Date: July 2019; Article Title: Geometric controls of a quadrotor UAV with decoupled yaw control)

[0093]

[0094] Where β is a positive gain coefficient, and sgn(·) denotes the sign function. Therefore, combining (6) and (5), the closed-loop dynamic equation of s(t) can be written as:

[0095]

[0096] Furthermore, to conserve onboard computing resources, an event-driven position controller design method is proposed. The auxiliary state variable λ(t) is defined as λ=[ξ(t) v(t)], and defined... for And the event triggering error is defined as

[0097] e = r(t) i )-r(t) (8)

[0098] in r(t i ) indicates the time t during the switching process. iThe state value. Based on the position controller designed in equation (6), the event-driven position tracking controller can be selected as (Journal: IEEE / CAA Journal of Automatica Sinica; Authors: Mustafa A, Dhar NK, Verma NK; Publication date: July 2020; Article title: Event-triggered sliding mode control for trajectory tracking of nonlinear systems; Pages: 307–314):

[0099]

[0100] Substituting (9) into (5), we obtain the closed-loop dynamic equation of the system as follows:

[0101]

[0102] Expected trajectory ξ d (t), v d (t) and Continuous and satisfying the Lipschitz condition in a compact set, in particular, the following inequality holds.

[0103]

[0104] Where ρ ξ It is a positive number.

[0105] 3) Attitude control of ultra-miniature unmanned helicopters based on robust integral sign error (RISE)

[0106] Define attitude error e Ψ (t) and attitude angular velocity error e ω (t) is:

[0107]

[0108] in Indicates the desired attitude angle. Represents the desired angular velocity, symbol (·). ∨ This represents the inverse operation of skw(·).

[0109] Define attitude filtering error and for:

[0110]

[0111] Where α a1 and The control gain is positive. Taking the derivative of r1(t) with respect to time and substituting (13) into the result, we get:

[0112]

[0113] Where the auxiliary function H(Ψ,Ψ) d )for

[0114]

[0115] The operator tr(·) represents the trace of the matrix. Similarly, differentiating the second equation in equation (13) with respect to time and substituting (14) into the result, we get:

[0116]

[0117] Where the auxiliary function Π(Ψ,Ψ) d ,ω,ω d ) is defined as

[0118]

[0119] Furthermore, the auxiliary function N(t) is defined as follows:

[0120]

[0121] Therefore, (16) can be further simplified to:

[0122]

[0123] The attitude controller for the ultra-miniature unmanned helicopter is designed as follows:

[0124]

[0125] in The control gain is positive. Taking the time derivative of equation (20) and substituting (19) into the differentiated equation, we can obtain the closed-loop dynamic equation of the single-rotor unmanned helicopter as follows:

[0126]

[0127] The following is a specific implementation example:

[0128] I. Introduction to the Experimental Platform

[0129] This invention utilizes Figure 1The experimental platform shown verifies the effectiveness of the designed event-driven robust geometry control method for the ultra-miniature unmanned helicopter. The ultra-miniature unmanned helicopter has a fuselage length of 260mm, a height of 83mm, a main rotor diameter of 275mm, and a fuselage weight of 68.9g. The flight control board uses Holybro's open-source flight controller KakuteF7 mini V2, measuring 33x26x6mm. It is equipped with a high-performance STM32F745VGH6 microcontroller with a main frequency of 216MHz, and onboard sensor components, including MPU6000 and BMP280, providing real-time attitude angular velocity, angular acceleration, and barometer data, respectively.

[0130] On the other hand, the flight control software system is based on ArduPilot, a relatively mature and stable open-source flight control system. ArduPilot is developed using the lightweight real-time system framework ChibiOS and supports control of various aircraft types, including unmanned vehicles, unmanned ships, rotorcraft, and fixed-wing aircraft. Furthermore, to meet the control requirements of different unmanned systems, it features multiple control modes such as stability augmentation, position control, aerobatic control, and guidance, and automatically configures safety degradation strategies, providing the necessary software framework and safety guarantees for the secondary development of the ultra-miniature unmanned helicopter described in this paper.

[0131] Furthermore, a fully free-degree-of-freedom high-precision flight platform was built by combining the Optitrack indoor motion capture system. At the same time, considering the limited carrying capacity of the ultra-miniature unmanned helicopter, real-time data interaction with the ground station was achieved through the Wi-Fi module. The data content includes: (1) pose data obtained from Motive, 50Hz; (2) drone unlock status, remote controller data, fused pose, etc., obtained through the Mavlink drone general communication protocol, 5Hz; (3) sending commands such as unlock, lock, and mode switching to the drone.

[0132] II. Flight Test Results

[0133] To better verify the effectiveness of the event-driven nonlinear control algorithm proposed in this invention, this section implements a rectangular trajectory tracking experiment of a UAV based on a self-built indoor test platform for micro-helicopters. During the experiment, the micro-helicopter is first hovered at the starting point, and then a 1m × 1m rectangle is set as the reference trajectory in the x and y directions. The trajectory running time for each side of the rectangle is given as 10 seconds, and the maximum flight speed is 0.2 m / s. This section completes three sets of experiments: Experiment 1: Flight experiment based on robust geometric control; Experiment 2: Flight experiment based on event-driven robust geometric control; Experiment 3: Flight experiment based on cascade flight control law.

[0134] Experiment 1: Flight Experiment Based on Robust Geometric Control

[0135] First, based on the control algorithm proposed in this invention, a rectangular tracking experiment was completed without considering event-driven operation. The control gain was selected as K = diag{(0.15, 0.15, 0.44)}, α a1 =30,α a2 =10,∈=0.1,β=0.1,α p =4. Experimental results are as follows Figure 2-4 As shown.

[0136] from Figure 2 and Figure 3 As can be seen, the nonlinear control algorithm proposed in this invention enables the ultra-miniature unmanned helicopter to track rectangular trajectories well, with relatively small errors in the x, y, and z directions during flight. From Figure 4 It can be seen that the steady-state error in the x-direction is kept within 0.2m, the steady-state error in the y-direction is within ±0.1m, and the steady-state error in the height direction is within 0.04m.

[0137] Experiment 2: Event-Driven Robust Geometric Control Flight Experiment

[0138] Under the same conditions, an event-driven condition is added to further reduce the control frequency of the position loop and decrease the computational resource consumption of the control algorithm. During the experiment, the reference trajectory remains unchanged, the control gain is the same as in Experiment 1, and the event triggering condition parameter r is... p =0.3,ρ ξ =0.1, Ω=0.1. Experimental results are as follows: Figure 5-8 As shown.

[0139] from Figure 5 and Figure 6 It can be seen that even after adding event triggering conditions, the ultra-miniature unmanned helicopter can still track a given rectangular trajectory quite well. From Figure 7 It can be seen that the steady-state error in the x-direction remains between 0 and 0.2 m, the steady-state error in the y-direction remains between -0.2 m and 0.1 m, and the steady-state error in the height direction remains between ±0.02 m. Furthermore, Figure 8 The figure shows the resource saving rate for the position loop computation of the ultra-miniature unmanned helicopter after the addition of event-driven triggering conditions. As can be seen from the figure, the computational resource saving rate is approximately 50%, with a maximum of 56%, while maintaining the existing control accuracy.

[0140] Experiment 3: Flight Experiment Based on Cascade Flight Control Law

[0141] Finally, a cascaded PID control strategy was selected for comparison to verify the superiority of the control algorithm proposed in this invention. Cascaded controllers are widely used in various commercial and open-source flight controllers (such as APM, PIXHAWK, etc.). These controllers have advantages such as clearly defined parameters and ease of adjustment. In this experiment, the position loop adopted a P-PID control structure for position and linear velocity, and the attitude loop adopted a P-PID control structure for angle and angular velocity. The experimental parameters are shown below.

[0142] Position ring: k p =1.5; Linear velocity loop: k vp =1.5,k vi =0.1,k vd =0.5;

[0143] Angle ring: k q =4.5; Angular velocity loop:

[0144] The experimental results are as follows Figure 9-11 As shown.

[0145] from Figure 9 and Figure 10 As can be seen, the ultra-miniature single-rotor UAV based on the cascade control algorithm can track a given rectangular trajectory. During its steady-state flight, the aircraft's position fluctuates to some extent, and there is a certain tracking phase lag problem. From... Figure 11 As can be seen, the steady-state error in the x-direction fluctuates between -0.2m and 0.1m, the steady-state error in the y-direction fluctuates between -0.2m and 0.2m, and the convergence in the height direction is slower, with the steady-state error fluctuating between -0.2m and 0.1m.

[0146] Experiments 1 and 3 demonstrate that, compared to traditional cascaded PID controllers, the nonlinear robust control algorithm proposed in this invention offers advantages such as fast trajectory tracking speed, no phase lag, and high tracking accuracy. Furthermore, referring to Experiments 1 and 2, it can be seen that by introducing event-driven conditions and selecting appropriate event trigger parameters, the computational resources of the position loop can be significantly reduced while maintaining position tracking accuracy, thereby saving microcontroller computational resources. A comparison of Experiments 2 and 3 shows that the control performance is still significantly improved compared to cascaded PID controllers after introducing event-driven control conditions.

[0147] In summary, the event-driven robust geometric control method for ultra-miniature unmanned helicopters proposed in this invention saves computational resources while possessing high control accuracy and good feasibility.

[0148] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A robust geometric control method for ultra-miniature unmanned helicopters based on event-driven principles, characterized by the following steps: as follows: 1) Establish a dynamic model for an ultra-miniature unmanned helicopter; 2) Design of a position controller for an ultra-miniature unmanned helicopter, utilizing an event-driven position controller design; 3) Attitude control of ultra-miniature unmanned helicopters based on robust integral sign error (RISE); The specific steps are as follows: 1) Establish a dynamic model for ultra-miniature unmanned helicopters The position loop dynamics model of the ultra-miniature unmanned helicopter is as follows: （1） Where vector and The matrix represents the three-dimensional position and linear velocity of a single-rotor unmanned helicopter. The scalar represents the transition matrix from the body coordinate system to the inertial coordinate system. and This represents the transition matrix from the body coordinate system to the inertial coordinate system. scalar Represents total thrust, vector Represents an unknown external disturbance; the external unknown disturbance vector. There is a supremacy , that is || ,in It is a normal function; The attitude loop dynamics equation of the ultra-miniature unmanned helicopter is: （2） Where vector Represents the angular velocity in the body coordinate system, a diagonal matrix. The inertia matrix represents that of a single-rotor unmanned helicopter. This represents the control input in the body coordinate system. and The operators represent the external unknown disturbance and the modeling uncertainty in the body coordinate system, respectively. This represents the anti-diagonal matrix spanned by three-dimensional vectors, with unmodeled uncertainties. and unknown external disturbances Continuously differentiable, and First-order continuous differentiable with bounded derivative, external unknown perturbation There exists a positive upper bound. ; The actual control input to the attitude loop of the ultra-miniature unmanned helicopter is the flapping angle. and total thrust of tail rotor Vector and The conversion relationship is as follows: （3） Among them, matrix and For virtual control input To actual control input The transition matrix; 2) Design of a position controller for an ultra-miniature unmanned helicopter Define position tracking error Linear velocity tracking error and auxiliary filtering error for （4） in and Represent the desired position and desired linear velocity, respectively, scalars To represent a positive control gain, the last term in equation (4) is differentiated with respect to time, and combined with equation (1), we get: （5） Auxiliary control input Selected as The auxiliary control input is designed as follows: （6） in A positive gain coefficient. The function is represented by the symbol, which combines (6) and (5). The closed-loop dynamic equation is: （7） Furthermore, an event-driven position controller design method is adopted: auxiliary state variables are defined. ,definition And the event triggering error is defined as: （8） in , Indicates the time of switching The state value is based on the position controller designed in equation (6), and the event-driven position tracking controller is selected as follows: （9） Substituting (9) into (5), we obtain the closed-loop dynamic equation of the system as follows: （10） Expected trajectory , and For a sequence that is continuous and satisfies the Lipschitz condition in a compact set, the following inequality holds: （11） in It is a positive number; 3) Attitude control of ultra-miniature unmanned helicopters based on robust integral sign error (RISE) Define attitude error and attitude angular velocity error for: （12） in Indicates the desired attitude angle. Represents the desired angular velocity, symbol express The inverse operation; Define attitude filtering error for: （13） in and A positive control gain Taking the derivative with respect to time and substituting (13) into the result, we get: （14） Where auxiliary function for: （15） Operator Representing the trace of the matrix, the second equation in equation (13) is differentiated with respect to time, and substituting (14) into the result, we get: （16） Where auxiliary function Defined as （17） Furthermore, define auxiliary functions. for: （18） Therefore, (16) can be further simplified to: （19） The attitude controller for the ultra-miniature unmanned helicopter is designed as follows: （20） in , Assuming a positive control gain, the time derivative of equation (20) is taken, and equation (19) is substituted into the differentiated equation to obtain the closed-loop dynamic equation of the single-rotor unmanned helicopter: （21）。

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