A method for coupled dynamics compensation and vibration suppression for an aerial work platform

Abstract

The present application relates to the technical field of robot and unmanned aerial vehicle control, solve the technical problem that the system total centroid is caused by the movement of the mechanical arm to offset violently, and then produce the interference torque of dynamic change, cause the unmanned aerial vehicle attitude to be unstable and even lose control when the existing technology unmanned aerial vehicle platform carries out the work with the mechanical arm, especially relate to a kind of coupling dynamics compensation and vibration suppression method for air operation platform, including obtaining the feedforward compensation torque for offsetting the interference torque generated by the total centroid position change, and by mixed control matrix decoupling into control unmanned aerial vehicle platform multiple rotor thrust control instruction, realize the accurate control of unmanned aerial vehicle platform.The present application can perceive and predict the centroid change caused by the movement of the mechanical arm in real time by introducing adaptive feedforward compensation mechanism, and generate feedforward compensation torque accordingly, actively offset the interference torque generated thereby, so as to significantly improve the attitude stability and operation accuracy of unmanned aerial vehicle platform.

Description

Technical Field

[0001] This invention relates to the field of robot and drone control technology, and in particular to a method for coupled dynamics compensation and vibration suppression for aerial work platforms. Background Technology

[0002] Drones equipped with robotic arms (i.e., aerial work platforms) have shown great potential in fields such as power line inspection, high-altitude operations, and logistics grasping. However, existing technologies typically decouple the drone platform control from the robotic arm joint control when controlling such integrated systems, ignoring the strong dynamic coupling effect between the two. This traditional decoupling control strategy faces intractable core control challenges in actual aerial operations.

[0003] Specifically, existing technologies heavily rely on a precise and fixed system dynamics model. However, in real-world applications, the total mass, center of mass, and moment of inertia of an aerial work platform change significantly with the movement of the robotic arm and the load (e.g., grasping objects of varying weights). When the robotic arm moves in the air, the change in its mass distribution causes a drastic and rapid shift in the total center of mass of the entire system. This generates a powerful, dynamically changing disturbance torque in the gravitational field. Traditional UAV-based PID feedback controllers, due to their inherent response delay, cannot effectively compensate for such disturbances, leading to severe fluctuations in flight attitude, and in severe cases, even loss of control. Simultaneously, environmental disturbances (such as sudden gusts of wind), the nonlinearity of motor performance, and unmodeled high-frequency vibrations all pose significant challenges to the stability and accuracy of the control system.

[0004] Therefore, relying solely on a fixed feedforward compensation model and a simple disturbance observer is far from sufficient. Existing technologies generally lack online adaptive capabilities and mechanisms for learning from experience, and cannot adjust their control strategies in real time to adapt to changes in system parameters and complex nonlinear disturbances. This results in unsatisfactory robustness and performance under variable tasks and complex environments. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a coupled dynamics compensation and vibration suppression method for aerial work platforms. This method solves the technical problem in existing technologies where, when a drone platform is equipped with a robotic arm for operation, the movement of the robotic arm causes a severe shift in the system's total center of mass, resulting in dynamically changing disturbance torques that lead to drone instability or even loss of control.

[0006] To address the aforementioned technical problems, the present invention provides the following technical solution: a method for coupled dynamics compensation and vibration suppression for an aerial work platform, wherein the aerial work platform includes a drone platform and a robotic arm mounted on the drone platform, and the method includes the following steps:

[0007] S1. Real-time acquisition of the joint angles of the robotic arm and the system parameters of the aerial work platform, the system parameters including the total mass of the aerial work platform;

[0008] S2. Calculate the overall center of gravity position of the aerial work platform based on the joint angle and system parameters, and obtain the feedforward compensation torque to counteract the interference torque caused by the change in the overall center of gravity position.

[0009] S3. The feedforward compensation torque is combined with the feedback torque output by the PID feedback controller to obtain the total control torque, and then decoupled into control commands for controlling the thrust of multiple rotors of the UAV platform through the hybrid control matrix, so as to achieve precise control of the UAV platform.

[0010] S4. Responding to the instructions from the host computer, and converting them into instructions to drive the robotic arm. Joint torques of each joint This ensures that the robotic arm follows a preset target trajectory and suppresses vibrations during movement.

[0011] Furthermore, a recursive least squares algorithm is employed to update system parameters online in real time by comparing the differences between the external forces and torques measured by the sensors and those predicted by the system model.

[0012] Furthermore, by using the forward kinematics model of the robotic arm, the center of mass position of each link of the robotic arm is calculated in combination with the mass and joint angle of each link. Then, by combining the center of mass position of the UAV platform and the total mass of the aerial work platform, the total center of mass position of the entire aerial work platform is calculated.

[0013] Furthermore, the disturbance torque is obtained by calculating the cross product of the vector of the total centroid position and the gravity vector, and a feedforward compensation torque with the same magnitude but opposite direction to the disturbance torque is generated.

[0014] Furthermore, suppressing vibrations during the movement of the robotic arm includes:

[0015] The input shaping module preprocesses the target trajectory to generate a shaped trajectory that avoids exciting the inherent vibration modes of the robotic arm;

[0016] In addition, a model feedforward module for real-time monitoring of the motion state of the robotic arm and compensating for the gravity compensation torque and nonlinear friction compensation torque of the robotic arm based on feedback information; and a model reference adaptive control module for adjusting the control gain online based on the trajectory error between the actual trajectory and the reference model.

[0017] In addition, a disturbance observer for estimating and compensating for base vibration transmitted by the UAV platform; and a learning residual compensator for compensating for nonlinear residual disturbances that the disturbance observer fails to compensate for.

[0018] Furthermore, the final feedforward torque is obtained based on the sum of the gravity compensation torque and the nonlinear friction compensation torque. .

[0019] By employing the above technical solution, the present invention provides a method for coupled dynamics compensation and vibration suppression for aerial work platforms, which has at least the following beneficial effects:

[0020] 1. By introducing an adaptive feedforward compensation mechanism, this invention can sense and predict the change in the center of mass caused by the movement of the robotic arm in real time, and generate a feedforward compensation torque accordingly to actively counteract the interference torque generated therefrom, thereby significantly improving the attitude stability and operational accuracy of the UAV platform.

[0021] 2. This invention introduces a learning-based composite jitter suppression control mechanism, which can calculate the required joint torque based on a preset target trajectory and drive the robotic arm to move precisely along that trajectory. Simultaneously, it can monitor the robotic arm's motion status in real time and adjust the joint torque based on feedback information, thereby effectively suppressing vibrations that may occur during movement.

[0022] 3. While maintaining the stability of the UAV platform, this invention significantly improves the operational accuracy and stability of the robotic arm, enabling it to effectively suppress vibrations caused by its own movement or external interference when performing complex tasks, thereby avoiding the adverse effects of vibration on the operation quality and the flight of the UAV platform. Attached Figure Description

[0023] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0024] Figure 1 This is a schematic diagram of the aerial work platform in Embodiment 1 of the present invention;

[0025] Figure 2 This is a schematic diagram of the system model of the aerial work platform in Embodiment 1 of the present invention;

[0026] Figure 3 This is a comparison of the attitude stability of the UAV with robotic arm in Embodiment 2 of the present invention;

[0027] Figure 4 This is a comparison chart of the attitude control torque of the UAV, taking the Roll axis torque as an example, in Embodiment 2 of the present invention;

[0028] Figure 5 This is a comparison of the tracking errors of the robotic arm's end effector in the X and Y directions in Embodiment 2 of the present invention.

[0029] Figure 6 This is a diagram showing the vibration suppression effect of comparing the joint torque spectrum in Embodiment 2 of the present invention. Detailed Implementation

[0030] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. This will allow for a full understanding of how the present application uses technical means to solve technical problems and achieve technical effects, and to facilitate its implementation.

[0031] The integrated control system of aerial work platforms heavily relies on a precise and fixed system dynamics model. However, in real-world applications, the following problems still exist:

[0032] Platform stability issues: When the robotic arm moves in the air, changes in its mass distribution cause a drastic and rapid shift in the overall center of mass of the system. This generates a powerful, dynamically changing disturbance torque in the gravitational field. Traditional PID feedback controllers used by drones, due to their inherent response delay, cannot effectively compensate for such disturbances, leading to violent fluctuations in flight attitude, and in severe cases, even loss of control.

[0033] Precision issues in robotic arms: Joint elasticity, frictional nonlinearity, sensor noise, and high-frequency vibrations from the drone frame can all cause unnecessary shaking at the end effector of the robotic arm. This shaking reduces operational accuracy and may damage the target object.

[0034] Existing technologies typically decouple drone platform control from robotic arm joint control, ignoring the strong dynamic coupling effect between the two and lacking an active suppression mechanism for the robotic arm's own vibration.

[0035] Example 1:

[0036] This embodiment proposes a coupled dynamics compensation and vibration suppression method for aerial work platforms. By introducing an adaptive feedforward compensation mechanism, it can sense and predict the change in the center of mass caused by the movement of the robotic arm in real time, and generate a feedforward compensation torque accordingly to actively counteract the resulting disturbance torque, thereby significantly improving the attitude stability and operational accuracy of the UAV platform. Figure 1As shown, the aerial work platform includes a drone platform and a robotic arm mounted on the drone platform. Specifically, the drone platform can be a hexacopter drone platform, which controls its flight attitude and position through the thrust of its six rotors. The robotic arm can be a three-degree-of-freedom planar robotic arm with three rotatable joints, capable of performing grasping and manipulation tasks in a plane.

[0037] like Figure 2 The diagram shown is a schematic of the system model of the aerial work platform. The aerial work platform mainly consists of a hexacopter UAV platform and a three-degree-of-freedom (3-DOF) robotic arm. Figure 2 Two coordinate systems are defined: the inertial coordinate system and the tactical coordinate system. and the body coordinate system fixed at the geometric center of the UAV The drone generates thrust through its six rotors. and rotational speed To control its movement and posture. The robotic arm consists of three links. Composition. The entire aerial work platform is in a gravitational field. In motion. Based on this, the coupled dynamics compensation and vibration suppression method proposed in this embodiment includes the following steps:

[0038] S1. Real-time acquisition of the joint angles of the robotic arm and the system parameters of the aerial work platform, including the total mass of the aerial work platform. In this embodiment, these real-time joint angles are acquired through encoders or angle sensors installed at each joint of the robotic arm.

[0039] In some operating conditions, relying solely on traditional parameter estimation methods may not be able to quickly and accurately track changes in system parameters, especially when subjected to external disturbances or rapid changes in the robotic arm's motion state. To address this, this embodiment proposes using a recursive least squares algorithm to update real-time system parameters online. This is achieved by comparing the differences between external forces and torques measured by sensors and those predicted by the system model, thus updating the system parameters in real time. This online estimation method ensures the system's good adaptability to load changes and environmental disturbances. Specifically, it includes online identification of time-varying system parameters and adaptive estimation of the centroid offset vector, i.e.:

[0040] To address system parameter variations caused by the robotic arm grasping unknown loads, this embodiment introduces an online parameter identification mechanism. Let the system parameter vector to be identified be:

[0041] ;

[0042] in, Represents the estimated values ​​of system parameters; Indicates time The estimated total mass of the system (including the drone platform, robotic arm, and grasping payload). Indicates time An estimate of the product of the total mass of the system and the component of the total center of mass along the X-axis in the body coordinate system; Indicates time An estimate of the product of the total mass of the system and the component of the total center of mass along the Y-axis in the body coordinate system; This represents the components of the vector along the X and Y axes of the body coordinate system.

[0043] The online identification results are obtained by updating the data using the recursive least squares method with a forgetting factor (RLS-FF). ,Right now:

[0044] ;

[0045] in, For the updated system parameters; for Estimated values ​​of system parameters at time points; These are the actual external forces and torques acting on the UAV platform, measured by the IMU. It is based on the real-time status of the robotic arm The observation matrix constructed using the forward kinematics model; It is a gain matrix calculated by the RLS algorithm and dynamically adjusted based on historical data and current prediction error.

[0046] The core of this formula lies in continuously comparing the differences between "actual sensor measurements" and "predictions based on the old model" to iteratively correct the estimated values ​​of the total mass and system parameters of the aerial work platform. This enables it to converge quickly and track real changes.

[0047] As a preferred implementation, consider an aerial work platform consisting of a six-rotor unmanned aerial vehicle (UAV) platform equipped with a three-DOF planar manipulator. During aerial operations, the manipulator's movement causes changes in the system's total mass and center of mass position. Force or torque sensors mounted on the UAV platform can measure external forces and torques in real time. Using a recursive least squares algorithm, the differences between the sensor-measured external forces and torques and those predicted by the system model are compared, and the estimated total system mass is updated online. This estimate is then used to calculate the total center of mass position and feedforward compensation torque, thereby improving the attitude control accuracy and stability of the UAV platform.

[0048] This embodiment employs a recursive least squares algorithm to more accurately estimate the real-time system parameters of the aerial work platform, thus providing a more reliable data foundation for subsequent calculation of the overall center of mass position and generation of feedforward compensation torque. This effectively counteracts the disturbance torque caused by changes in the overall center of mass position, improving the stability and control accuracy of the aerial work platform.

[0049] S2. Calculate the overall center of mass position of the aerial work platform based on joint angles and system parameters, and obtain a feedforward compensation torque to counteract the disturbance torque caused by changes in the overall center of mass position. In this embodiment, the center of mass position of each link of the robotic arm is calculated using the forward kinematics model of the robotic arm, combined with the mass and joint angle of each link. Then, the overall center of mass position of the entire aerial work platform is calculated by combining the center of mass position of the UAV platform and the total mass of the aerial work platform. Specifically, this includes establishing a forward kinematics model, namely:

[0050] Establish a body coordinate system fixed to the geometric center of the UAV In the body coordinate system Below, let's define the joint angles of the robotic arm. for:

[0051] ;

[0052] in, These are the real-time rotation angles of the first, second, and third joints of the robotic arm, respectively; superscript For transpose;

[0053] The first parameter of the robotic arm is derived using the standard Denavit-Hartenberg (DH) parameter method or rotation matrix method. Root connecting rod (mass) ,length The position of the center of mass of ) For a planar RRR-type robotic arm, its center of mass position can be represented as:

[0054] ;

[0055] in, For the first The rotation matrix of each joint; For the first The length of the connecting rod; This is the fixed position vector of the robotic arm base relative to the geometric center of the drone; For the first The rotation angle of each joint; For the first The length of the connecting rod; For the first The rotation angle of each joint; For the first The rotation matrix of each joint;

[0056] System parameters based on online identification results The adaptive offset vector of the overall centroid position of the entire aerial work platform relative to the geometric center of the UAV is derived as follows:

[0057] ;

[0058] in, The location of the total centroid obtained through online identification; Indicates time The total system mass estimate, including the drone platform, robotic arm, and grasping payload, comes directly from the online identification results, ensuring real-time adaptability to load changes; For the first The mass of the connecting rod; These represent the real-time offsets of the system's (i.e., the aerial work platform's) total centroid relative to the UAV's geometric center in the X, Y, and Z axis directions, respectively.

[0059] When calculating the feedforward compensation torque, accurately and quickly obtaining the required feedforward compensation torque from the total centroid position is a crucial consideration. This embodiment provides a specific calculation method: by calculating the cross product of the vector of the total centroid position and the gravity vector, the disturbance torque is obtained, and a feedforward compensation torque of equal magnitude but opposite direction to the disturbance torque is generated. This feedforward compensation mechanism can proactively and predictively cancel the coupling interference caused by the robot arm's movement, avoiding attitude response lag.

[0060] Here, the vector representing the total center of mass refers to the vector pointing from the origin of the UAV platform to the total center of mass, and this vector contains the coordinate information of the total center of mass in three-dimensional space. The gravity vector is the direction of gravitational acceleration in the UAV platform coordinate system, and its magnitude is equal to the value of gravitational acceleration. By calculating the cross product of these two vectors, a torque vector perpendicular to both vectors can be obtained, and this torque vector is the disturbance torque.

[0061] As a preferred implementation, adaptive feedforward compensation torque The derivation is as follows:

[0062] The disturbance torque caused by the displacement of the total centroid position is:

[0063] ;

[0064] in, It represents the constant of gravitational acceleration (its direction is usually along the negative Z-axis of the inertial coordinate system);

[0065] To counteract this disturbance, the required feedforward compensation torque for:

[0066] ;

[0067] in, This represents the total real-time mass of the system as identified online.

[0068] This formula shows the feedforward compensation torque. No longer just joint angles It is not a static function, but rather depends on time. The dynamic function. This embodiment utilizes an online identification mechanism to obtain the system's real-time total mass. Location of the total center of mass It can predict and accurately counteract coupling interference caused by the real, time-varying total mass of the system.

[0069] Specifically, changes in the position of the overall center of mass cause changes in the attitude of the aerial work platform, generating an additional torque acting on the UAV platform; this additional torque is the disturbance torque. This disturbance torque affects the stability and control accuracy of the UAV platform, thus requiring compensation. This embodiment calculates the cross product of the vector of the overall center of mass position and the gravity vector to quickly and accurately obtain the magnitude and direction of the disturbance torque. Then, by generating a feedforward compensation torque that is equal in magnitude but opposite in direction to the disturbance torque, the influence of the disturbance torque can be effectively counteracted, thereby improving the stability and control accuracy of the UAV platform.

[0070] This embodiment can directly obtain the disturbance torque through vector cross product operation. The calculation process is simple and efficient, and it is easy to implement in actual engineering. This ensures that the aerial work platform can quickly respond to the disturbance caused by the change of the center of mass position and maintain the stable flight attitude of the platform.

[0071] S3. The feedforward compensation torque is combined with the feedback torque output by the PID feedback controller to obtain the total control torque, and then decoupled into control commands for controlling the thrust of multiple rotors of the UAV platform through the hybrid control matrix, thereby achieving precise control of the UAV platform.

[0072] As a preferred implementation, this embodiment will use adaptive feedforward compensation torque. Feedback torque of the PID feedback controller output The torque is superimposed to form the total control torque of the fused control vector. ,Right now:

[0073] ;

[0074] in, This represents the expected total vertical thrust required for UAV flight control. , , These represent the three-axis control torques output by the UAV's PID attitude feedback controller; , These represent the components of the feedforward compensation torque used to counteract coupling interference, calculated based on the state of the robotic arm, in the X and Y axes, respectively.

[0075] For a hexacopter UAV, the relationship between its thrust F and the generated force or total control torque U is as follows: ,in It is a 6×4 mixing matrix. Its pseudo-inverse is solved. This means obtaining the real-time state of the robotic arm and the thrust of the six rotors. The final adaptive mapping formula is:

[0076] ;

[0077] in, This represents the total mass of the system (the identified value). , This represents the offset of the system's total centroid relative to the UAV's geometric center along the X and Y axes.

[0078] In this embodiment, the feedback controller provides feedback torque, which is calculated based on the error between the actual and desired states of the system, aiming to improve system stability and response speed. The total control torque is formed by adding the feedforward compensation torque to the feedback torque, comprehensively considering the system's feedforward compensation and feedback control requirements. The hybrid control matrix is ​​a mathematical transformation used to distribute the total control torque to each rotor of the UAV platform, thereby obtaining the thrust command for each rotor.

[0079] Specifically, the feedforward compensation torque is generated based on the prediction of the system's dynamic characteristics, aiming to proactively offset the disturbance torque caused by changes in the position of the total centroid, thereby improving the system's dynamic performance. The feedback controller, on the other hand, generates a feedback torque based on the error between the actual and desired states of the system, further enhancing the system's stability and robustness. By adding the feedforward compensation torque and the feedback torque, the advantages of both feedforward and feedback control can be fully utilized, enabling precise control of the UAV platform.

[0080] Furthermore, the design of the hybrid control matrix needs to consider the structural and dynamic characteristics of the UAV platform. For example, for a six-rotor UAV platform, the hybrid control matrix needs to decompose the total control torque into thrust commands for the six rotors and ensure that the UAV platform can achieve the desired attitude and position control. As a preferred implementation method, the hybrid control matrix can be designed using methods such as pseudo-inverse methods and optimization algorithms.

[0081] This embodiment achieves precise control of the UAV platform by combining feedforward compensation torque and feedback torque, and decoupling them into thrust commands for multiple rotors of the UAV platform through a hybrid control matrix. Compared with using feedforward control or feedback control alone, it can better improve the dynamic performance, stability, and robustness of the system. In addition, through the decoupling of the hybrid control matrix, the total control torque can be easily distributed to each rotor, thereby achieving precise control of the attitude and position of the UAV platform.

[0082] This embodiment ensures real-time adaptability to load changes by updating system parameters such as the total mass of the aerial work platform online. Then, it accurately calculates the position of the total center of mass using real-time joint angles and system parameters, and generates a feedforward compensation torque that is equal in magnitude but opposite in direction to the disturbance torque. This feedforward compensation mechanism fundamentally solves the problem of attitude response lag in traditional methods, significantly improving the attitude stability and control accuracy of the UAV platform during the robotic arm's movement.

[0083] The aerial work platform of this embodiment demonstrates superior performance in addressing the platform stability issues mentioned in the background art. When the robotic arm moves in the air, changes in its mass distribution cause a drastic and rapid shift in the overall center of mass of the system, generating a powerful and dynamically changing disturbance torque in the gravitational field. This embodiment utilizes an active, predictive cancellation strategy based on coupled dynamics effects, enabling the UAV platform to maintain a highly stable flight attitude with maximum fluctuations limited to a small range. This significantly improves the attitude stiffness and stability of the aerial work platform, allowing it to better adapt to complex and ever-changing high-altitude working environments.

[0084] However, during actual operation, the robotic arm may vibrate during movement, especially under high-speed or high-load operation. This vibration can affect the accuracy and stability of the operation, and may even have an adverse effect on the drone platform. Based on the aforementioned steps S1-S3, this embodiment also proposes step S4.

[0085] S4. Responding to the instructions from the host computer, and converting them into instructions to drive the robotic arm. Joint torques of each joint This ensures that the robotic arm follows a preset target trajectory and suppresses vibrations during movement.

[0086] When the robotic arm performs a task, it can calculate the required joint torque based on a preset target trajectory and drive the robotic arm to move precisely along that trajectory. Simultaneously, it can monitor the robotic arm's motion status in real time and adjust the joint torque based on feedback information, thereby effectively suppressing vibrations that may occur during movement. Therefore, suppressing vibrations during the robotic arm's movement includes:

[0087] In practice, if the design of the target trajectory fails to fully consider the dynamic characteristics of the robotic arm itself, especially its inherent vibration modes, the robotic arm may still be excited to generate undesirable vibrations during movement. This not only affects the accuracy of the operation but may also accelerate the wear and tear of the robotic arm. Therefore, this embodiment proposes an input shaping module to preprocess the target trajectory and generate a shaped trajectory to avoid exciting the inherent vibration modes of the robotic arm.

[0088] The purpose is to generate a new, "shaped" trajectory by performing specific mathematical transformations or filtering on the original target trajectory. This shaped trajectory is designed in the frequency domain to avoid or suppress the robot arm's inherent vibration frequencies, thus effectively preventing the excitation of internal resonance when the robot arm executes the trajectory. Specifically, the input shaping module can employ a zero-vibration (ZV) shaper, which superimposes a series of pulses with specific delays and amplitude adjustments onto the input signal. This allows the vibrations generated by the robot arm in response to these pulses to cancel each other out, ultimately achieving a vibration-free or low-vibration response.

[0089] As a preferred embodiment, this example aims to prevent the excitation of flexible vibrations in the robotic arm from the source. Firstly, the dominant natural vibration frequency of the robotic arm is identified experimentally. Damping ratio Subsequently, a convolution kernel for a zero-vibration (ZV) shaper consisting of two pulses was designed, with pulse amplitude A and time delay... Derived from the following formula:

[0090] ;

[0091] ;

[0092] in, This represents the amplitude of two pulses in a zero-vibration (ZV) shaper; This indicates the time delay of the second pulse relative to the first pulse; Indicated based on damping ratio Calculated intermediate coefficients;

[0093] Any original target trajectory Before being fed into the controller, the trajectory is first shaped to generate a vibration-free shaped trajectory, i.e.:

[0094] ;

[0095] in, This represents the generated integer trajectory.

[0096] In practical applications, the gravitational torque and frictional torque of the robotic arm can affect the control accuracy. Simple control algorithms are difficult to overcome the interference caused by these factors. To address this, this embodiment proposes a model feedforward module that monitors the motion state of the robotic arm in real time and compensates for the gravitational compensation torque and nonlinear frictional compensation torque of the robotic arm based on feedback information; and a model reference adaptive control module that adjusts the control gain online based on the trajectory error between the actual trajectory and the reference model.

[0097] As a preferred implementation, this embodiment employs model feedforward to counteract the dominant, predictable nonlinear torques at the joints. The final feedforward torque... This is the sum of the gravity compensation torque and the nonlinear friction compensation torque, i.e.:

[0098] ;

[0099] in, This is the gravity compensation torque for the robotic arm; Nonlinear friction compensation torque for the robotic arm; gravity compensation torque Derived from an accurate Lagrangian dynamics model; nonlinear frictional compensation torque The Stribeck model, which can describe the viscosity-slip effect, was used for calculations.

[0100] To address issues such as time-varying friction coefficients and uncertain connecting rod inertia, Model Reference Adaptive Control (MRAC) is used instead of traditional fixed-gain PID control. The controller forces the actual joint dynamics to track an ideal reference model through an adaptive law. Its core control law is:

[0101] ;

[0102] In the formula, The output of the Model Reference Adaptive Controller (MRAC) represents the first... Control torque of each joint;

[0103] The adaptive gain and Online updates are performed based on Lyapunov stability theory, namely:

[0104] ;

[0105] in, The error between the actual trajectory and the reference model trajectory; This is the sliding mode error term; This is the derivative of the error between the actual trajectory and the reference model trajectory (i.e., the velocity error). For proportional gain Adaptive update rate; Differential gain Adaptive update rate; It is a time variable.

[0106] This mechanism enables the controller to fine-tune its parameters in real time to optimally compensate for model uncertainties within the system.

[0107] It should be further explained that the model feedforward module is used to compensate for the gravitational torque and frictional torque of the robotic arm, while the model reference adaptive control module is used to adjust the control gain online based on the trajectory error between the actual trajectory and the reference model. Specifically, the model feedforward module uses the robotic arm's dynamic model to pre-calculate the gravitational torque and frictional torque and compensates for them during the control process. The model reference adaptive control module compares the actual trajectory with the trajectory of the reference model and adaptively adjusts the control gain according to the magnitude of the error to ensure that the robotic arm can accurately track the target trajectory.

[0108] The proposed solution compensates for gravitational and frictional torques using a model feedforward module, effectively reducing their impact on control accuracy. Simultaneously, the model reference adaptive control module adjusts the control gain online based on actual conditions, further enhancing the robustness and adaptability of the control system. This combination enables precise control of the robotic arm's motion, improving the operational efficiency and accuracy of aerial work platforms.

[0109] This embodiment also proposes a disturbance observer for estimating and compensating for base vibration transmitted by the UAV platform; and a learning residual compensator for compensating for nonlinear residual disturbances that the disturbance observer fails to compensate for.

[0110] Although the joint torques driving the robotic arm enable it to follow the target trajectory and suppress vibrations during movement, the base vibrations transmitted from the UAV platform and the nonlinear residual disturbances that the disturbance observer fails to compensate for still adversely affect the control accuracy of the robotic arm. To address this, this embodiment further introduces a disturbance observer and a learning-type residual compensator to effectively suppress and compensate for the aforementioned disturbances.

[0111] As a preferred implementation, this embodiment designs a disturbance observer (DOB) to suppress unmodeled disturbances such as base vibration. By comparing the difference between the actual dynamics and the ideal model dynamics, the total disturbance is estimated in reverse. ,Right now:

[0112] ;

[0113] in, This represents the actual output torque of the motor. This is the actual angular velocity; Nominal inertia; The filter time constant; This represents the Laplace operator (a variable in the complex frequency domain).

[0114] To address highly complex residuals, such as the cogging effect, that cannot be perfectly compensated by the Disturbance Observer (DOB) and Model Reference Adaptive Controller (MRAC), this embodiment innovatively introduces a reinforcement learning (RL) agent. The agent's policy network... Output a compensation torque To actively counteract residual disturbances, i.e.:

[0115] ;

[0116] Among them, state for:

[0117] ;

[0118] In the formula, This represents the generated integer trajectory.

[0119] reward function Designed to minimize tracking error and control costs, this mechanism empowers the controller to learn from experience, autonomously learning an optimal nonlinear compensation function through online trial and error. Reward function. The expression is:

[0120] ;

[0121] in, These are the weighting coefficients for the position tracking error term and the velocity tracking error term, respectively. The weighting coefficient for the penalty term of the control action (output torque).

[0122] By fusing all the above control components, the joint torque of the final multi-level composite joint control law of this invention is formed. ,Right now:

[0123] ;

[0124] in, The first output of the Model Reference Adaptive Controller (MRAC) Control torque of each joint; The feedforward torque output by the model feedforward module; The total disturbance estimated by the disturbance observer; For policy networks Output compensating torque.

[0125] The composite joint control law proposed in this embodiment integrates the robustness of adaptive control, the accuracy of model feedforward, the speed of disturbance observation, and the intelligence of reinforcement learning, tracking the shaped trajectory after input shaping. At that time, it can achieve extreme and systematic suppression of jitter.

[0126] It should be further explained that the disturbance observer is used to estimate and compensate for the base vibration transmitted by the UAV platform, while the learning residual compensator is used to compensate for nonlinear residual disturbances that the disturbance observer fails to compensate for. Specifically, the disturbance observer can estimate the impact of base vibration on the robotic arm based on the system's dynamic model and actual measurement data, and counteract this vibration by adding a corresponding compensation term to the control torque. The learning residual compensator can establish a compensation model by learning residual disturbance patterns from historical data, and predict and compensate for these residual disturbances based on the current system state during subsequent control processes.

[0127] As a preferred implementation, the disturbance observer can be designed using methods such as Kalman filtering to improve its estimation accuracy and robustness for base vibration. Simultaneously, learning-based residual compensators can be designed using machine learning methods such as neural networks and support vector machines to enhance their compensation capability for nonlinear residual disturbances.

[0128] This embodiment of the aerial work platform, while maintaining the stability of the UAV platform, significantly improves the operational accuracy and stability of the robotic arm. This allows the robotic arm to effectively suppress vibrations caused by its own movement or external interference when performing complex tasks, thereby avoiding the adverse effects of vibration on work quality and the flight of the UAV platform. This precise control over the robotic arm's movement and vibration suppression capability enables the aerial work platform to handle higher precision, more complex, and more delicate aerial work tasks, such as high-altitude inspection, precision grasping, and spraying, greatly expanding the application range and operational efficiency of the aerial work platform.

[0129] Example 2:

[0130] The integrated control system described in this embodiment is a specific application of the coupled dynamics compensation and vibration suppression method proposed in Embodiment 1. This embodiment is based on a hexacopter UAV platform with a wheelbase of 550mm, equipped with a three-degree-of-freedom (3-DOF) planar RRR-type robotic arm with a total length of 40cm, and uses CUAV V5+NANO flight controller as the main controller.

[0131] 1) Hardware system configuration:

[0132] Unmanned aerial vehicle platform: a hexacopter drone with a wheelbase of 550mm.

[0133] Motor: 700KV brushless motor.

[0134] ESC: 40A ESC.

[0135] Base controller: CUAV V5+NANO flight controller (based on STM32F765 processor, running open source firmware such as PX4 / ArduPilot).

[0136] Robotic arm: A three-degree-of-freedom (3-DOF) planar RRR type robotic arm with a total length of approximately 40cm.

[0137] Robotic arm control system: The robotic arm uses an independent DSP or ARM Cortex-M7 / H7 microcontroller to perform high-frequency, complex second-inventive-point compound joint control.

[0138] Communication: The flight control system (CUAV V5+NANO) communicates with the robotic arm controller via a high-speed CAN bus to ensure the required joint angles at the first invention point. It can transmit with high real-time performance.

[0139] Control frequencies: Flight controller (attitude control and dynamic compensation) operates at 200Hz-400Hz. Robotic arm joint controller operates at 1kHz-5kHz.

[0140] System parameter acquisition:

[0141] Precisely measure the mass of the drone body .

[0142] Precisely measure the mass of each link of the 40cm long robotic arm. and length .

[0143] Hybrid control matrix of a six-rotor drone .

[0144] 2) First invention point: Dynamic feedforward compensation control.

[0145] This control module should run at high frequency in the attitude control loop of the CUAV V5+NANO flight control firmware (e.g., PX4 or ArduPilot).

[0146] Data input: Receives the current joint angle from the robotic arm controller in real time via the CAN bus. .

[0147] Model Implementation: Incorporating the robot arm's DH parameters and centroid offset model Compile it into the flight controller firmware.

[0148] Compensation calculation: In the attitude control main loop, the feedforward compensation torque is calculated in real time. .

[0149] Integration and Output:

[0150] feedforward compensation torque Feedback torque output from the attitude PID / LQR controller inside the flight controller Superimposed on top of each other. A customized 550mm hexacopter mixing matrix is ​​used. pseudo-reversal The total control torque Decoupling to target throttle or thrust for 6 motors Finally, the thrust Send to 40A ESC for execution.

[0151] 3) Second invention point: High-performance jitter suppression control.

[0152] This control module should operate at high frequency in the robotic arm's independent controller.

[0153] Parameter identification: Due to the robotic arm's total length of only 40cm, its connecting rods have relatively high stiffness, resulting in its dominant natural vibration frequency. Relatively high.

[0154] Modal parameters: These must be accurately identified to ensure that the Input Shaping filter can accurately counteract the inherent vibrations of this small-scale robotic arm.

[0155] Friction parameters: The frictional nonlinearity of the 700KV motor and transmission mechanism may significantly affect the accuracy of the 40cm robotic arm. Friction model parameters... Precise identification is required.

[0156] Input Shaping: At the trajectory planning or command generation end (which can be a host computer or a robotic arm controller), the target trajectory is shaped. Perform convolution to generate a shaped trajectory. .

[0157] Feedforward torque of the model feedforward for:

[0158] Gravity compensation torque Calculated based on the Lagrange dynamics model of the robotic arm at frequencies above 1kHz.

[0159] Nonlinear friction compensation torque Real-time based on speed Calculate nonlinear friction compensation.

[0160] Disturbance Observer (DOB):

[0161] Filter: The time constant needs to be adjusted. The setting is small enough (e.g., 5ms-10ms) to ensure effective tracking and counter-suppression of high-frequency disturbances at the drone base.

[0162] Data input: Accurately obtain the actual output torque of the motor. (For example, through current feedback from the motor) and angular velocity .

[0163] Final control law synthesis: The final composite control law, i.e., the joint torque, is executed at a frequency of 1kHz-5kHz. .

[0164] This embodiment illustrates the feasibility of the present invention and the technical effects achieved based on actual experimental results. As follows:

[0165] like Figure 3 As shown, this paper compares the temporal response of the present invention (DG) with that of the traditional decoupled control method (LMC) in terms of flight attitude angles (roll, pitch, yaw) when the robotic arm performs a continuous dynamic motion task.

[0166] Traditional technology (LMC - dotted line): Because traditional pure feedback controllers cannot effectively compensate for the strong coupling interference torque generated by the robotic arm's motion, the drone's attitude angle is... A large and sustained fluctuation occurred a few seconds later, with the maximum overshoot reaching ±35°, seriously threatening flight stability and mission execution.

[0167] This invention (DG-solid line): Through dynamic feedforward compensation control (first inventive point), this invention achieves active cancellation of coupling torque. The attitude angle curve remains highly stable, with the maximum fluctuation limited to within ±5°, demonstrating the attitude stiffness and stability of this invention under strongly dynamic coupling conditions.

[0168] like Figure 4 As shown, this illustrates the coupling disturbance torque generated in the robotic arm. (Yellow dashed line) indicates the total control torque output by both control methods.

[0169] Disturbance torque of robotic arm coupling (Yellow dashed line): The periodic change over time represents the external disturbances generated by the robotic arm's movement on the platform.

[0170] Total control torque of traditional technology (Red dotted line): Due to the lack of a feedforward mechanism, LMC relies on hysteretic feedback to correct attitude deviations. Therefore, its output control torque... It exhibits characteristics of phase lag, amplitude overshoot, and irregular fluctuations with the disturbance torque. This violent torque output is the main cause of attitude instability.

[0171] The feedforward compensation torque of this invention (Thin black solid line): This torque and the disturbance torque With the same amplitude and opposite phase, it achieves proactive and early cancellation of interference.

[0172] Total control torque of the present invention (Thick blue solid line): Due to feedforward compensation torque With most of the interference already neutralized, the total output torque required by the DG controller remains close to zero, containing only a very small residual feedback component, resulting in a relatively smooth curve.

[0173] like Figure 5 As shown, the time-domain comparison of the position error (in millimeters) of the present invention (DG) and the conventional control method (LMC) in the trajectory tracking task of the robotic arm end effector is presented.

[0174] Traditional technology (LMC - dashed line): The error curve shows obvious high-frequency vibration. There are a large number of high-frequency burrs on the curve surface, with an amplitude close to ±3mm. This is due to the failure to suppress the vibration of the base and the flexible vibration of the joint.

[0175] Large steady-state / dynamic errors. The error baseline fluctuates greatly (exceeding ±4 mm), and there is a non-zero steady-state error in the X direction, which is a result of uncompensated friction and nonlinearity.

[0176] This invention (DG - solid line): The error curve shows a significant improvement through the composite joint control system at the second inventive point. See below:

[0177] High-frequency vibration suppression: The curve is highly smooth, indicating that the Disturbance Observer (DOB) effectively suppresses high-frequency vibrations of the base and the unmodeled area.

[0178] Reduced steady-state / dynamic errors: The error amplitude is limited to within ±0.5mm, and the input shaping and friction model feedforward significantly reduce the overshoot and steady-state errors in trajectory tracking.

[0179] like Figure 6 As shown, a spectrum analysis comparison of the joint driving torque of the robotic arm during its movement is presented to illustrate the effect of the second inventive point of this invention (high-performance jitter suppression joint control).

[0180] Traditional technique (LMC - red dotted line): Two significant energy peaks can be clearly observed in its torque spectrum, namely:

[0181] There is a peak at a low frequency (about 2Hz), which corresponds to the inherent flexible mode vibration of the robotic arm itself.

[0182] There is another peak at a high frequency (about 30Hz), which corresponds to the high-frequency vibration of the base generated by the drone motor and frame being transmitted to the robotic arm.

[0183] This invention (DG - solid blue line): After adopting the composite control strategy of this invention, the joint torque spectrum changed significantly, namely:

[0184] The modal vibration peaks at low frequencies are significantly suppressed, thanks to the input shaping technique which avoids the excitation of this mode at the source.

[0185] The high-frequency base vibration peaks were also significantly suppressed, thanks to the perturbation observer (DOB) which effectively estimated and compensated for unmodeled high-frequency perturbations.

[0186] Example 3:

[0187] This embodiment illustrates the architecture and data flow of an integrated two-layer control algorithm for an aerial work platform with a robotic arm. The core idea of ​​this algorithm is to decompose the complex control task into two parallel subsystems that are tightly coupled through key information, aiming to simultaneously address the two core challenges of platform attitude stability and robotic arm operation accuracy.

[0188] 1. Core architecture: Two-layer parallel control.

[0189] The entire control system is divided into two logically independent but functionally complementary layers:

[0190] Platform Layer: Its sole purpose is to maintain the absolute stability of the drone platform's attitude. It is responsible for handling all calculations related to the drone's flight attitude and ultimately outputting commands to the drone's rotor motors.

[0191] Manipulation Layer: Its sole purpose is to ensure that the robotic arm's end effector can accurately and smoothly complete the specified task. It is responsible for handling all calculations related to the robotic arm's joint movements and ultimately outputting torque commands to the robotic arm's joint motors.

[0192] 2. Key technologies at the platform layer: dynamic feedforward compensation.

[0193] The innovation of the platform layer lies in its proactive, feedforward-type interference compensation mechanism.

[0194] It not only relies on traditional PID attitude feedback control (passive correction based on IMU data), but more importantly, it acquires the joint angles of the robotic arm in real time. The total centroid shift of the system caused by the movement of the robotic arm was accurately calculated.

[0195] Based on this offset, it will calculate a feedforward compensation torque in advance. This torque is precisely enough to counteract the coupling interference that will be generated by the robotic arm's movement. This "predict and cancel" strategy fundamentally solves the problem of attitude response lag in traditional methods.

[0196] 3. Key technologies for the operation layer: suppression of complex disturbances.

[0197] The innovation of the operation layer lies in its systematic and multi-dimensional composite disturbance suppression strategy, which ensures the motion accuracy of the robotic arm from three levels:

[0198] Instruction source (input shaping): The target trajectory is preprocessed from the beginning to generate a smooth trajectory without vibration excitation, thus avoiding the excitation of the robot arm's own flexible vibration.

[0199] Predictable disturbances (model feedforward): Actively compensate for deterministic torques generated by gravity and friction using known dynamic models.

[0200] Unpredictable disturbances (Disturbance Observer (DOB)): Real-time estimation and compensation for unknown disturbances caused by unmodeled factors such as high-frequency vibrations of the UAV base.

[0201] 4. The core of system integration: information coupling.

[0202] The key information bridge connecting these two parallel control layers is the "joint angle". The operation layer transmits this crucial data to the platform layer in real time, enabling the platform layer to perform precise feedforward compensation. It is this information coupling that "integrates" the two independent controllers into a highly efficient and collaborative whole.

[0203] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0204] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. Since the above embodiments are substantially similar to the method embodiments, their descriptions are relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0205] The above embodiments provide a detailed description of the present invention. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for coupled dynamics compensation and vibration suppression for an aerial work platform, comprising: The aerial work platform comprises a UAV platform and a mechanical arm arranged on the UAV platform, and the method comprises the following steps: S1, real-time acquisition of joint angles of the mechanical arm and system parameters of the aerial work platform, the system parameters comprising total mass of the aerial work platform; S2, calculation of total center of mass position of the aerial work platform according to the joint angles and the system parameters, and obtaining of a feedforward compensation torque for offsetting an interference torque generated due to change of the total center of mass position; S3, combination of the feedforward compensation torque and a feedback torque output by a PID feedback controller to obtain a total control torque, decoupling of the total control torque into control instructions for controlling thrust of multiple rotors of the UAV platform through a hybrid control matrix, and realization of accurate control of the UAV platform; S4. Responding to the instructions from the host computer, and converting them into instructions to drive the robotic arm. Joint torques of each joint This ensures that the robotic arm follows a preset target trajectory and suppresses vibrations during movement; The vibration suppression during the movement of the mechanical arm comprises: An input shaping module is arranged to pre-process the target trajectory to generate a shaped trajectory for avoiding excitation of inherent vibration modes of the mechanical arm, namely: ； wherein, represents the generated reshaped trajectory; is a preset target trajectory; , represents the amplitude of the two pulses in the zero-vibration reshaper; is a time delay; represents the time delay of the second pulse relative to the first pulse; A model feedforward module is arranged to monitor the movement state of the mechanical arm in real time and compensate for a model of a gravity compensation torque and a nonlinear friction compensation torque of the mechanical arm according to feedback information; and a model reference adaptive control module is arranged to adjust control gain on line according to a trajectory error between an actual trajectory and a reference model trajectory; A disturbance observer is arranged to estimate and compensate for base vibration transmitted by the UAV platform; and a learning residual compensator is arranged to compensate for nonlinear residual disturbance that cannot be compensated for by the disturbance observer. The disturbance observer estimates the total disturbance in reverse by comparing the difference between the actual dynamics and the ideal model dynamics That is: ； wherein is the actual output torque of the electric machine; is the actual angular velocity; is the nominal inertia; is the filter time constant; denotes the Laplace operator; An reinforcement learning agent is introduced as a learning residual compensator, the policy network of the reinforcement learning agent An output compensation torque to actively cancel the residual disturbance, i.e.: ； wherein the state is: ； wherein represents the generated shaping trajectory; is the error of the actual trajectory from the reference model trajectory; is the derivative of the error of the actual trajectory from the reference model trajectory; Joint torque formed by fusing multiple control components to form a multi-level composite joint control law i.e.: ； wherein, Mj represents the control torque of the jth joint output by the model reference adaptive controller; Mj represents the control torque of the jth joint output by the model reference adaptive controller; Mj represents the control torque of the jth joint output by the model reference adaptive controller; Mj represents the control torque of the jth joint output by the model reference adaptive controller; Mj represents the control torque of the jth joint output by the model reference adaptive controller; Mj represents the control torque of the jth joint output by the model reference adaptive controller; 2. The coupling dynamics compensation and vibration mitigation method of claim 1, wherein, In step S1, a recursive least square algorithm is adopted to update system parameters on line in real time by comparing differences between external force and torque measured by a sensor and external force and torque predicted by a system model, namely: ； wherein, is the updated system parameter; is is the estimated value of the system parameter at the moment; is the actual external force and torque acting on the UAV platform measured by the IMU; is the observation matrix constructed according to the real-time state of the manipulator and the forward kinematics model; is the gain matrix dynamically adjusted according to the historical data and the current prediction error calculated by the RLS algorithm.

3. The coupling dynamics compensation and vibration mitigation method of claim 1, wherein, In step S2, a forward kinematics model of the mechanical arm is used to calculate center of mass positions of each link of the mechanical arm in combination with mass of each link and joint angles, and then the center of mass positions of each link of the mechanical arm are used to calculate total center of mass position of the entire aerial work platform in combination with center of mass position of the UAV platform and total mass of the aerial work platform.

4. The coupling dynamics compensation and vibration mitigation method of claim 3, wherein, The method comprises the following steps: Establish a body coordinate system fixed to the geometric center of the UAV In the body coordinate system Next, let the joint angle of the robot arm Be: ； wherein, are real-time rotation angles of the first, second, and third joints of the robot arm, respectively; superscript is the transpose. The center of mass position of the root link is derived by the standard Denavit-Hartenberg parameter method or the rotation matrix method, and is expressed as: The center of mass position of the root link is derived by the standard Denavit-Hartenberg parameter method or the rotation matrix method, and is expressed as: The center of mass position of the root link is derived by the standard Denavit-Hartenberg parameter method or the rotation matrix method ； wherein, is a rotation matrix of the jth joint; is a length of the ith link; is a fixed position vector of the robot base relative to the geometric center of the UAV; is a rotation angle of the jth joint; is a length of the ith link; is a length of the ith link; is a rotation angle of the jth joint; is a rotation matrix of the jth joint;​​​​​ Based on system parameters The adaptive offset vector of the overall aerial work platform's total center of mass position relative to the UAV geometric center is derived as follows: ； wherein, is the total mass position obtained from online identification; denotes the system total mass estimate at time including the UAV platform, the robotic arm and the grasped payload; is the mass of the th link; are the real-time offsets of the system total mass center relative to the UAV geometric center in the X, Y and Z axes directions, respectively.

5. The coupling dynamics compensation and vibration mitigation method of claim 4, wherein, The interference torque is obtained by calculating a cross product of a vector of the total center of mass position and a gravity vector, and a feedforward compensation torque equal in size and opposite in direction to the interference torque is generated, namely: Disturbance moments resulting from total center of mass position offsets is: ； wherein g represents the gravitational acceleration constant; to counteract the disturbing torque the required feedforward compensation torque is ； wherein, represents the system real-time total mass identified online.

6. The coupling dynamics compensation and vibration mitigation method of claim 1, wherein, In step S3, the method comprises the following steps: Adaptive feedforward compensation torque feedback torque output by the PID feedback controller superimposed to form a total control torque of the fusion control vector i.e.: ； wherein, represents the vertical total thrust expectation value required for the UAV flight control; , , respectively represent three-axis control moments output by the UAV PID attitude feedback controller; , respectively represent components of the feedforward compensation moment for offsetting the coupling disturbance calculated based on the state of the mechanical arm in the X-axis and the Y-axis. Based on the relationship between the thrust F of the multi-rotor drone and the resulting force or total control moment U is wherein is a 6x4 mixing matrix; By solving the pseudo-inverse of the mixing matrix , i.e. , the final adaptive mapping formula from the real-time state of the robotic arm to the multiple rotor thrusts is obtained, i.e. ； wherein, represents the total mass of the system; , represents the offset of the total center of mass of the system relative to the geometric center of the drone in the X and Y axes.

7. The coupling dynamics compensation and vibration mitigation method of claim 1, wherein, The model feedforward module comprises the following steps: The final feedforward torque is obtained based on the sum of the gravity compensation torque and the nonlinear friction compensation torque That is: ； wherein, is a gravity compensation moment of the robot arm; is a nonlinear friction compensation moment of the robot arm; The on-line adjustment of the control gain comprises the following steps: The model reference adaptive control is adopted to replace a traditional fixed gain PID, and a controller forces actual joint dynamics to track an ideal reference model through an adaptive law, and a core control law of the controller is as follows: ； In the formula, Jm represents the control torque of the m-th joint of the model reference adaptive controller; and Jm represents the control torque of the m-th joint of the model reference adaptive controller; and The adaptive gain in which and The online update is according to Lyapunov stability theory, that is: ； wherein, is a sliding mode error term; is a proportional gain adaptive update rate of the proportional gain; is a differential gain adaptive update rate of the differential gain; is a time variable.

8. The coupling dynamics compensation and vibration mitigation method of claim 1, wherein, Establishing a reward function of learning type residual compensator aiming at minimizing tracking error and control cost , learning an optimal nonlinear compensation function autonomously through online trial and error, the expression of the reward function is ； wherein, are weight coefficients corresponding to the position tracking error term and the velocity tracking error term, respectively; is a weight coefficient of the control action penalty term.

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