A Quadrotor UAV Attitude Decoupling Control Method Based on Improved Active Disturbance Rejection Technology

Abstract

This invention discloses a decoupling-free attitude control method for quadrotor unmanned aerial vehicles (UAVs) based on an improved active disturbance rejection (ADR) technology. The method includes defining the quadrotor UAV's coordinate system and attitude angles; dynamic modeling of the quadrotor UAV; design of the ADR control strategy; design of a high-order extended state observer; introduction of a Levante differentiator; and design of a parameter estimator. This invention utilizes an extended state observer to estimate system dynamics and environmental disturbances, combined with parameter estimation to compensate for unknown disturbances in real time, enhancing anti-interference capability and dynamic response performance. Simultaneously, a Levante differentiator is introduced to replace the traditional tracking differentiator (TD) stage, and the parameter estimator estimates the unknown disturbances. The decoupling-free control strategy avoids the complex decoupling process in traditional methods, improving control efficiency. Finally, simulation experiments demonstrate the effectiveness of the proposed improved ADR control scheme in maintaining good tracking accuracy under high-frequency disturbances.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) control technology, and in particular to an attitude control method and system for a quadcopter UAV. Background Technology

[0002] With the rapid development of drone technology, quadcopter drones, with their flexible maneuverability and ease of operation, have demonstrated enormous application potential in multiple fields. For example, in the power industry, quadcopter drones can be used for high-voltage transmission line inspection, quickly detecting line faults; in agriculture, they can be used for farmland irrigation and pesticide spraying, improving operational efficiency; and in logistics and delivery, quadcopter drones can achieve rapid last-mile delivery. Furthermore, they have been widely used in environmental monitoring, emergency rescue, and aerial filming. However, the flight attitude control of quadcopter drones faces numerous challenges. Their flight system is a highly complex nonlinear system. The uncertainty of their own parameters (such as changes in motor performance, battery power fluctuations, and changes in fuselage mass distribution) and strong coupling characteristics make the drone highly susceptible to external interference during flight. In the modeling process, the coupling problem mainly manifests in: the aerodynamic coupling between the rotors affects lift and thrust output; the coupling relationship between attitude and position causes attitude changes to affect the flight trajectory, while position adjustments, in turn, affect attitude stability. These coupling characteristics increase the complexity of the control system, making it more difficult to achieve precise control and stable flight. Furthermore, UAVs are subject to various external disturbances during flight, such as wind speed changes, airflow turbulence, electromagnetic interference, and terrain undulations. These disturbances interact with the coupling characteristics of the UAV, further exacerbating the complexity of flight attitude control. Currently, existing control methods are mainly designed based on small-disturbance linearized models or nonlinear models. While small-disturbance linearized methods are relatively simple in theoretical analysis, they are difficult to adapt to the control requirements of UAVs in large-scale motion and complex environments. Nonlinear control methods, while better describing the dynamic characteristics of UAVs, require high model accuracy and have high computational complexity, making them difficult to implement in real-time control systems. In addition, some studies have used neural networks to compensate for the uncertainties caused by unknown disturbances, but the training process of neural networks requires a large amount of data support, and their generalization ability may be insufficient when facing unseen disturbance patterns. Although these existing control methods can control the attitude of UAVs to a certain extent, they still have significant limitations when facing complex coupling relationships and multi-source disturbances, making it difficult to meet the high requirements for stable flight of UAVs in complex environments. Especially when the random airflow is too large or too complex, the tracking accuracy and attitude control stability of UAVs are often difficult to guarantee, resulting in problems such as inaccurate tracking and poor attitude control stability. These issues not only affect the operational efficiency and safety of UAVs, but also limit their application in a wider range of fields. Therefore, developing an attitude control method for quadrotor UAVs that can effectively cope with complex coupling relationships and multi-source interference is of great practical significance for improving the performance and application range of UAVs. Summary of the Invention

[0003] The purpose of this invention is to address the shortcomings of existing technologies by providing a decoupling-free attitude control method for quadrotor UAVs based on improved active disturbance rejection (ADRC) technology, aiming to achieve high-precision control of the UAV's flight attitude. This invention uses ADRC as the core main controller, responsible for the main attitude adjustment tasks. An adaptive estimator serves as an auxiliary module, estimating unknown disturbances in real time and inputting the results into the ADRC to aid in precise control. The attitude controller, based on improved ADRC technology, minimizes the deviation between the actual attitude and the target attitude through an optimized algorithm, achieving efficient and precise adjustment. To improve system robustness, an adaptive estimator is introduced to preprocess sensor data, reducing sensitivity to external disturbances and enhancing anti-interference capabilities. Simultaneously, a decoupling-free mechanism is introduced to reduce system complexity and computational load, simplifying the system structure and ensuring the stability of the control effect.

[0004] To achieve the above objectives, the technical solution provided by this invention is as follows:

[0005] Step 1: Establish a dynamic model of the quadcopter UAV, the model including the body coordinate system. and inertial coordinate system Define the pitch angle, roll angle, and yaw angle of the quadcopter UAV; determine the dynamic model of the quadcopter UAV as follows:

[0006]

[0007] in, These represent the pitch, roll, and yaw angles of a quadcopter drone, respectively. The moment of inertia about the fuselage axis and the external disturbance torque are respectively about the fuselage axis. , and Moment of inertia, , and To bypass , , The rotational torque of the shaft, The air drag coefficient, For total disturbance;

[0008] definition Differential, and denoted as :

[0009]

[0010] Step 2: Introduce a Levante differentiator to optimize the command rate of change response speed; the expression of the Levante differentiator is as follows:

[0011]

[0012] in, For the signal that needs to be differentiated, yes The tracking signal To track The first-order differential signal, To track The second-order differential signal, To track The third-order differential signal, , , , These are the parameters to be adjusted in the differentiator. , , As an intermediate variable, For symbolic functions

[0013] Step 3: Design a higher-order extended state observer, the expression of which is as follows:

[0014]

[0015] in, , and These are the state variables of a higher-order extended state observer, used to estimate the system output. Output derivative Total Interference ; , and It is an adjustable observer gain, and , , , It is an adjustable observer bandwidth. It is a control input. It is about controlling the gain. Represents the parameters of the observer. It is the differential of the total interference;

[0016] Step 4: Design the core main controller. Analyze the dynamic model from Step 1 and combine the data output from Steps 2 and 3 to calculate the system input.

[0017] Step 5: Design an estimator using least squares with exponential forgetting to estimate unknown disturbances in real time;

[0018] Step 6: Design a decoupling-free controller based on the dynamic model to achieve three-channel decoupling-free control; the decoupling-free controller design is as follows:

[0019]

[0020] in, ;

[0021] Step 7: Combine parameter estimation to compensate for unknown disturbances in real time, enhance anti-interference capability and dynamic response performance, and construct an active disturbance rejection controller that integrates error change rate estimation to achieve precise control of the attitude of the quadcopter UAV.

[0022] Establish the active disturbance rejection control law for the higher-order extended state observer described in step 3, and use the transfer function of this active disturbance rejection control law as the control signal. The transfer function is expressed as:

[0023]

[0024]

[0025] in, It is an adjustable controller bandwidth. This indicates that it is a parameter of the controller; It is a complex variable representing the frequency in the Laplace transform domain, and since all poles of the transfer function are located in the left half of the complex plane (with negative real parts), the system is guaranteed to be stable.

[0026] The control bandwidth The calculation formula is as follows:

[0027]

[0028] in, Let the order be the system order. The time required for the system response curve to first reach and remain at 98% of its final value.

[0029] Furthermore, the core main controller described in step 4 adopts a linear state error feedback control law based on disturbance estimation, and the specific expression of the control input is as follows:

[0030]

[0031] in, This is the output of the Levante differentiator, which estimates the desired attitude angle and its derivative. , and They are respectively for , and The first output of the designed state observer, i.e., the response to the system input... The estimated value; , and It is the second output of the state observer, that is, the response to the system input. The derivative estimate; , and These are the third output of the state observer, namely the estimate of the total disturbance. It controls the gain.

[0032] Furthermore, the method described in step 5 also includes estimating the unknown parameters in the system based on online parameter estimation and combining the attitude angle change rate tracking error, and then estimating the unknown parameters. The estimation method is as follows:

[0033]

[0034] in, It is a signal matrix. For unknown parameters The estimate, describing the relationship between the system and unknown parameters, can be obtained from measurements of the system signal, including the gain. The update pattern is as follows:

[0035]

[0036] in, and These are positive constants, representing the maximum forgetting rate and the gain matrix, respectively. The preset boundaries.

[0037] Furthermore, the method described in step 7 also includes solving for the actual control quantity, i.e., the rotor speed, under the condition of force balance in the height direction, as follows:

[0038]

[0039] in, For along Total lift of the shaft, , and To bypass , , The rotational torque of the shaft, The lift coefficient, The inverse torque coefficient, The distance from the rotor center to the drone's center of mass. The rotational speeds of the four rotors.

[0040] The proposed composite improved active disturbance rejection method for quadrotor UAV attitude control significantly improves the performance of the quadrotor UAV attitude control system, mainly in the following aspects:

[0041] 1. Improved System Stability: The designed high-order extended state observer can accurately estimate and compensate for disturbances in the system in real time, ensuring that the UAV maintains attitude stability when facing external disturbances and internal changes. Meanwhile, the optimized control law design and stable system transfer function further enhance the system's stability and anti-interference capability in complex environments, effectively avoiding attitude fluctuations and system instability caused by disturbances.

[0042] 2. Reduced decoupling complexity: The three-channel decoupling-free control based on active disturbance rejection technology eliminates the need for complex and difficult-to-precise decoupling operations on the coupled parts, allowing direct control of the coupled system. This significantly reduces the design difficulty of the controller and the complexity of the system, improves the reliability and feasibility of the control system, and simplifies the overall control process.

[0043] 3. Optimized Control Accuracy: The introduced Levante differentiator optimizes the response speed of the command rate of change, enabling the system to respond quickly and accurately to attitude command changes and reducing control latency. Furthermore, real-time compensation for unknown parameter changes through online parameter estimation, along with accurate system state estimation provided by a high-order extended state observer, jointly assist the controller in accurately calculating control inputs, thereby achieving high-precision control of the UAV's attitude and significantly improving control accuracy and the system's dynamic response performance. Attached Figure Description

[0044] Figure 1 This is a flowchart of an attitude decoupling control method for a quadrotor UAV based on improved active disturbance rejection technology proposed in this invention.

[0045] Figure 2 This is a schematic diagram of the attitude decoupling control method for a quadrotor UAV based on improved active disturbance rejection technology proposed in this invention.

[0046] Figure 3 This is the target tracking curve in Experiment Example 1.

[0047] Figure 4 This is the random airflow disturbance curve in Experiment Example 1.

[0048] Figure 5 The pitch angle trajectory tracking curve is shown in Experiment Example 1.

[0049] Figure 6 The image shows the roll angle trajectory tracking curve in Experiment Example 1.

[0050] Figure 7 The yaw angle trajectory tracking curve is shown in Experiment Example 1.

[0051] Figure 8 The pitch angle trajectory tracking error curve is shown in Experiment Example 1.

[0052] Figure 9 The image shows the roll angle trajectory tracking error curve in Experiment Example 1.

[0053] Figure 10 The curve showing the yaw angle trajectory tracking error in Experiment Example 1.

[0054] Figure 11 This is the estimation curve for the unknown parameter in the pitch angle in Experiment Example 1.

[0055] Figure 12 This is the estimated curve for the unknown parameters in the roll angle in Experiment Example 1.

[0056] Figure 13 The curves represent the estimation curves of the unknown parameters in the yaw angle in Experiment Example 1.

[0057] Figure 14 The pitch angle tracking error curve under noise conditions is shown in Experiment Example 1.

[0058] Figure 15 The rolling angle tracking error curve under noise conditions is shown in Experiment Example 1.

[0059] Figure 16 The pitch angle tracking error curve under noise conditions is shown in Experiment Example 1.

[0060] Figure 17 The rotor speed response curve is shown in Experiment Example 1. Detailed Implementation

[0061] The present application will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present application, but do not limit the present application in any way. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of the present application. These fall within the scope of protection of the present application.

[0062] Example 1

[0063] To achieve the above objectives, the technical solution provided by this invention is as follows:

[0064] Step 1: Establish a dynamic model of the quadcopter UAV, the model including the body coordinate system. and inertial coordinate system Define the pitch angle, roll angle, and yaw angle of the quadcopter UAV; determine the dynamic model of the quadcopter UAV as follows:

[0065]

[0066] in, These represent the pitch, roll, and yaw angles of a quadcopter drone, respectively. The moment of inertia about the fuselage axis and the external disturbance torque are respectively about the fuselage axis. , and Moment of inertia, , and To bypass , , The rotational torque of the shaft, The air drag coefficient, For total disturbance;

[0067] definition Differential, and denoted as :

[0068]

[0069] Step 2: Introduce a Levante differentiator to optimize the command rate of change response speed; the expression of the Levante differentiator is as follows:

[0070]

[0071] in, For the signal that needs to be differentiated, yes The tracking signal To track The first-order differential signal, To track The second-order differential signal, To track The third-order differential signal, , , , These are the parameters to be adjusted in the differentiator. , , As an intermediate variable, For symbolic functions

[0072] Step 3: Design a higher-order extended state observer, the expression of which is as follows:

[0073]

[0074] in, , and These are the state variables of LESO, used to estimate the system output. Output derivative Total Interference ; , and It is an adjustable observer gain, and , , , It is an adjustable observer bandwidth. It is a control input. It is about controlling the gain. Represents the parameters of the observer. It is the differential of the total interference;

[0075] Step 4: Design the core main controller. Analyze the dynamic model from Step 1 and combine the data output from Steps 2 and 3 to calculate the system input.

[0076] Step 5: Design an estimator using least squares with exponential forgetting to estimate unknown disturbances in real time;

[0077] Step 6: Design a decoupling-free controller based on the dynamic model to achieve three-channel decoupling-free control; the decoupling-free controller design is as follows:

[0078]

[0079] in, ;

[0080] Step 7: Combine parameter estimation to compensate for unknown disturbances in real time, enhance anti-interference capability and dynamic response performance, and construct an active disturbance rejection controller that integrates error change rate estimation to achieve precise control of the attitude of the quadcopter UAV.

[0081] Establish the active disturbance rejection control law for the higher-order extended state observer described in step 3, and use the transfer function of this active disturbance rejection control law as the control signal. The transfer function is expressed as:

[0082]

[0083]

[0084] in, It is an adjustable controller bandwidth. This indicates that it is a parameter of the controller; It is a complex variable representing the frequency in the Laplace transform domain, and since all poles of the transfer function are located in the left half of the complex plane (with negative real parts), the system is guaranteed to be stable.

[0085] The control bandwidth The calculation formula is as follows:

[0086]

[0087] in, Let the order be the system order. The time required for the system response curve to first reach and remain at 98% of its final value.

[0088] Furthermore, the core main controller described in step 4 adopts a linear state error feedback control law based on disturbance estimation, and the specific expression of the control input is as follows:

[0089]

[0090] in, This is the output of the Levante differentiator, which estimates the desired attitude angle and its derivative. , and They are respectively for , and The first output of the designed state observer, i.e., the response to the system input... The estimated value; , and It is the second output of the state observer, that is, the response to the system input. The derivative estimate; , and These are the third output of the state observer, namely the estimate of the total disturbance. It controls the gain.

[0091] Furthermore, the method described in step 5 also includes estimating the unknown parameters in the system based on online parameter estimation and combining the attitude angle change rate tracking error, and then estimating the unknown parameters. The estimation method is as follows:

[0092]

[0093] in, It is a signal matrix. For unknown parameters The estimate, describing the relationship between the system and unknown parameters, can be obtained from measurements of the system signal, including the gain. The update pattern is as follows:

[0094]

[0095] in, and These are positive constants, representing the maximum forgetting rate and the gain matrix, respectively. The preset boundaries.

[0096] Furthermore, the method described in step 7 also includes solving for the actual control quantity, i.e., the rotor speed, under the condition of force balance in the height direction, as follows:

[0097]

[0098] in, For along Total lift of the shaft, , and To bypass , , The rotational torque of the shaft, The lift coefficient, The inverse torque coefficient, The distance from the rotor center to the drone's center of mass. The rotational speeds of the four rotors.

[0099] The following simulation demonstrates the effectiveness and feasibility of the attitude decoupling control method for a quadrotor UAV based on improved active disturbance rejection technology disclosed in this application. The specific parameters are as follows: UAV mass is 0.8 kg, x-axis moment of inertia is 5.445 × 10⁻³ kg·m², y-axis moment of inertia is 5.445 × 10⁻³ kg·m², z-axis moment of inertia is 1.089 × 10⁻² kg·m², rotor-to-center of mass distance is 0.165 m, and control gain is 2 × 10⁻³ kg·m². 6 The lift coefficient is 2.98 × 10⁻ 5 The air drag coefficient is 9×10⁻².

[0100] Simulation results are as follows Figures 3 to 17 And the corresponding performance table shows the target. The tracking curve is as follows. Figure 3 As shown. For comparison, the target tracking curve, the proportional-integral-derivative (PID) controller, and the traditional ADRC are the control experimental curves, while LPADRC and HPADRC are the attitude control algorithms designed in this invention. Figures 3-16 It can be concluded that after the disturbance occurs, the UAV experiences small disturbances around 2s, 6s, 12s, and 25s. However, through comparison, under strong interference environments, the HPADRC and LPADRC methods can achieve high-precision tracking of attitude commands. The traditional ADRC method can guarantee high-precision tracking of attitude commands under interference-free or low-interference conditions, but the attitude angle tracking accuracy decreases significantly under high-frequency disturbances. The PID control method exhibits steady-state errors when unknown disturbances are present.

[0101] Figure 8 , 9Figures 1 and 10 show the trajectory tracking error curves for pitch, roll, and yaw angles. As can be seen from the figures, the design using the improved controller in the attitude loop is significantly superior to ADRC and PID, exhibiting better robustness than traditional ADRC and PID control algorithms. The pitch-time curves clearly show that the LPADRC controller has fewer amplitude fluctuations and jitter frequencies, smaller jitter amplitudes, and shorter convergence times. HPADRC, on the other hand, has stronger suppression capabilities against high-frequency interference. Overall, different control methods exhibit different response speeds when adjusting the target angle. It can be observed that LPADRC always has the fastest response speed when disturbances occur, and in terms of stability, HPADRC always approaches the target curve most of the time, demonstrating better stability. PID, however, shows larger fluctuations when disturbances occur, exhibiting relatively poor stability.

[0102] Figure 11 , 12 Figures 1 and 13 show the estimation curves for unknown parameters in pitch, roll, and yaw angles. As can be seen in the figures, the curves exhibit error fluctuations at 2, 6, and 12 seconds. This is because a disturbance is added to the UAV before and after these time points to simulate random airflow disturbances. However, through offline parameter estimation, the instrument is able to quickly adapt to this change within approximately 1.4 seconds, achieving accurate estimation of the unknown disturbance.

[0103] Figure 14 , 15 Figure 16 shows the attitude angle tracking error curve under noise, illustrating the attitude angle tracking performance in a noisy environment. Gaussian white noise with a mean of 0 and a covariance of 0.001 was introduced into the attitude angle measurement. It can be clearly observed from the figure that despite the influence of measurement noise, the attitude tracking error decreases rapidly after system startup and eventually converges to a small range close to zero. This result demonstrates that the developed control strategy can not only effectively handle uncertainties and external disturbances in the system but also maintain high control accuracy under noise interference. Figure 17 The rotor speed response curves of the UAV under the condition that lift cancels out gravity are presented.

[0104] The technical means disclosed in this invention are not limited to those disclosed in the above embodiments, but also include technical solutions that are any combination of the above technical features. It should be noted that for those skilled in the art, various improvements and modifications can be made without departing from the principle of this invention, and these modifications are also considered within the scope of protection of this invention.

Claims

1. A quadrotor unmanned aerial vehicle attitude decoupling control method based on improved active disturbance rejection technology, the method can include the following steps: Step 1: Establishing a dynamic model of the quadcopter, the model including a body coordinate system and an inertial coordinate system , defining a pitch angle, a roll angle and a yaw angle of the quadcopter; determining a dynamic model of the quadcopter as follows: (1) wherein, denote the pitch angle, roll angle and yaw angle of the quadrotor respectively, are the moments of inertia about the body axes and the external disturbance moments about the body axes respectively are the moments of inertia about the body axes , and the moments of inertia about the body axes, , and the moments of inertia about the body axes, , , the moments of inertia about the body axes, is the air resistance coefficient, is the total disturbance; Definitions differentiable, and denoted by : (2) Step 2: Introducing the Lyapunov differentiator, optimizing the command rate of change response speed; The expression of the Lyapunov differentiator is as follows: (3) in, For the signal that needs to be differentiated, yes The tracking signal To track The first-order differential signal, To track The second-order differential signal, To track The third-order differential signal, , , , These are the parameters to be adjusted in the differentiator. , , As an intermediate variable, It is a symbolic function; Step 3: Design a high-order extended state observer, the expression of the high-order extended state observer is as follows: (4) wherein , and are state variables of the high-order extended state observer, which estimate the system's output , output derivative and total disturbance , respectively; , and are adjustable observer gains, and , , , is an adjustable observer bandwidth, is a control input, is a control gain, denotes parameters of the observer, is a differential of the total disturbance; Step 4: Design the core main controller, analyze the dynamic model in step 1, and combine the data output by steps 2 and 3 to calculate the system input; Step 5: Use the least square method with exponential forgetting to design the estimator to estimate the unknown disturbance in real time; Step 6: According to the dynamic model, design the decoupling controller to realize three-channel decoupling control; The decoupling controller is designed as follows: (5) wherein ; Step 7: Combine the parameter estimation to compensate for the unknown disturbance in real time, enhance the anti-interference ability and dynamic response performance, and build an active disturbance rejection controller that integrates error rate estimation to realize accurate control of the quadrotor unmanned aerial vehicle attitude; Establish the active disturbance rejection control law of the high-order extended state observer in step 3, and take the transfer function of this active disturbance rejection control law as the control signal, which is expressed as: (6) (7) wherein is an adjustable controller bandwidth, denotes that it is a parameter of the controller; is a complex variable representing the frequency in the Laplace transform domain and ensures that the system is stable since all poles of the transfer function are located in the left half of the complex plane (negative real part). The controller bandwidth The formula is as follows: (8) wherein, is the order of the system, is the time required for the system response curve to first enter and remain at a level of 98% of its final value.

2. The attitude decoupling-free control method for a quad-rotor UAV based on improved active disturbance rejection technology according to claim 1, characterized in that, The core main controller in step 4 adopts a linear state error feedback control law based on disturbance estimation, and the specific expression of the control input is as follows: (9) wherein are the estimates of the desired attitude angles and their derivatives output by the levant filter; , and are the first outputs of the state observer designed for , and are the estimates of the system inputs ; , and are the second outputs of the state observer, i.e. the derivative estimates of the system inputs ; , and are the third outputs of the state observer, i.e. the estimates of the total disturbance, is the control gain.

3. The attitude decoupling-free control method for a quad-rotor UAV based on improved active disturbance rejection technology according to claim 1, characterized in that, The method described in step 5 further comprises estimating unknown parameters present in the system based on the online parameter estimation, incorporating the tracking error of the attitude angular rate, and estimating the unknown parameters The method of estimating is as follows: (10) wherein is a signal matrix, is an estimate of the unknown parameter , describing the relationship of the system to the unknown parameter, is obtainable from measurements of the system signal, the update law for the gain is as follows: (11) wherein, and are normal numbers, respectively representing the preset boundary of the maximum forgetting rate and the gain matrix .

4. The improved active disturbance rejection control based attitude decoupled control method for quadrotor unmanned aerial vehicle according to claim 1, wherein, The method in step 7 also includes solving the real control quantity, i.e. the rotor speed, under the condition of force balance in the height direction, and the method is as follows: (12) wherein, is the total lift along the axis, , and is the moment of rotation about the , , axis, is the lift coefficient, is the anti-torque coefficient, is the distance from the center of the rotor to the center of mass of the drone, is the rotational speed of the four rotors.

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