A flexible robot joint harmonic reducer high-frequency resonance suppression method

Abstract

The application discloses a flexible robot joint harmonic reducer high-frequency resonance suppression method, relates to the technical field of servo system control, and can solve the problem of low mechanical arm position tracking precision and torque output precision caused by the influence of high-frequency resonance and nonlinear transmission torque caused by the physical structure and assembly error of the harmonic reducer itself in the control of the robot flexible joint driven by the harmonic reducer. The application comprises the following steps: in the first step, a corresponding mathematical model is constructed according to the dynamics relationship of the flexible joint of the mechanical arm. In the second step, appropriate parameters are selected, and a harmonic disturbance observer is designed to online and real-time estimate the high-order harmonic vibration caused by the flexibility of the harmonic reducer. In the third step, the harmonic disturbance estimation value obtained in the second step is combined with the PD feedback controller of the flexible joint of the mechanical arm to compensate and suppress the second harmonic disturbance of the system, thereby forming the harmonic reducer high-frequency resonance suppression method of the flexible joint of the mechanical arm.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of servo system control, and particularly relates to a flexible robot joint harmonic reducer high-frequency resonance suppression method. BACKGROUND

[0002] On the robot platform, the key factor to realize dynamic decoupling (Dynamic Coupling), high-precision position and force control is accurate torque transmission. The traditional pure position control cannot meet the hardware requirements of the current robot dynamic motion performance control, so the joint design with accurate force feedback (force sensor) becomes the mainstream. In the field of humanoid robots, the requirements of output (torque / mass) density and flexibility determine that the driving joint needs to be equipped with a harmonic reducer (Harmonic Drive) and a flexible body.

[0003] A general flexible joint is composed of five parts from left to right. They are: output flange, torque sensor, harmonic reducer, motor and motor driver. The working principle is that the motor outputs torque, which is amplified by the harmonic reducer according to the corresponding reduction ratio, and then transmitted to the output side of the joint. The actual torque borne by the joint is fed back to the motor driver through the force sensor, so as to realize closed-loop control of the joint torque.

[0004] However, in the harmonic transmission system, the transmission flexibility will cause output oscillation, among which the second harmonic generated at twice the joint rotation frequency is the most obvious, which will directly affect the joint performance, especially in the flexible joint using the joint output side torque sensor and position sensor:

[0005] (1) The disturbance is directly observed by the torque sensor, which is an unexpected torque entering the torque control loop as the torque control, causing the control loop to oscillate. To avoid oscillation, the loop gain is reduced, which will lose the force control performance and reduce the torque control accuracy.

[0006] (2) In position control, the disturbance is directly observed by the position sensor. To avoid oscillation, the loop gain (stiffness) is reduced, which will lose the position control accuracy and reduce the mechanical arm performance under heavy load.

[0007] (3) During the movement of the mechanical arm, high-frequency harmonic vibration causes corresponding fluctuations in speed, acceleration and other state feedbacks. The control loop related to these state feedbacks and the zero force drag based on force control performance will be directly affected.

[0008] In summary, the accuracy of the torque and position output at the end of the robot depends on the accuracy of the joint torque control, and the high-frequency resonance of the harmonic reducer is an important bottleneck for achieving high-precision joint force control. Therefore, it is necessary to study how to suppress the high-frequency resonance of the harmonic reducer, especially the double-frequency resonance.

[0009] At present, the anti-disturbance control method for the flexible joint driven by the harmonic reducer is less researched by domestic and foreign experts and scholars, and most of the researches are concentrated on the modeling research on the torque transmission model of the harmonic reducer, the paper "Joint-Level Control of the DLR Lightweight Robot SARA" is based on a passive system, a impedance controller is designed, a virtual damping is added in the feedback controller of the torque, so as to suppress the influence of the torque fluctuation, but the suppression effect on the high-frequency resonance is limited. The paper "Modeling and compensation for angular transmission error of harmonic drive gearings in high precision positioning" obtains the dynamic model of the high-frequency resonance in the harmonic reducer through the accurate modeling of the transmission model of the harmonic reducer, and suppresses the high-frequency resonance caused by the harmonic reducer in the form of feedforward compensation. From the experimental results, the suppression effect is not obvious, and the modeling process is complex, and it does not have the characteristics of strong engineering practicability. SUMMARY

[0010] Therefore, the present application provides a flexible robot joint harmonic reducer high-frequency resonance suppression method, which can solve the problem of low mechanical arm position tracking accuracy and torque output accuracy caused by the influence of high-frequency resonance and nonlinear transmission torque caused by the physical structure and assembly error of the harmonic reducer in the control of the robot flexible joint driven by the harmonic reducer.

[0011] To achieve the above purpose, the technical scheme of the present application comprises the following steps:

[0012] First, according to the dynamic relationship of the flexible joint of the mechanical arm, a corresponding mathematical model is constructed.

[0013] Second, select appropriate parameters, design a harmonic disturbance observer to estimate the high-order harmonic vibration caused by the flexibility of the harmonic reducer online and in real time.

[0014] Third, the harmonic disturbance estimation value obtained in the second step is combined with the PD feedback controller of the flexible joint of the mechanical arm, and the second harmonic disturbance of the system is compensated and suppressed, forming the harmonic reducer high-frequency resonance suppression method of the flexible joint of the mechanical arm.

[0015] Further, in the first step, a mathematical model is established according to the dynamic relationship of the flexible joint of the mechanical arm, and the constructed mathematical model is specifically:

[0016]

[0017]

[0018] Where M(q) and C(q) are the inertia parameter matrix and Coriolis force parameter matrix of the flexible joint link, respectively, and g(q) is the gravity parameter matrix; q is the absolute position of the joint link. and These are its second and first derivatives, respectively, which correspond to the acceleration and velocity on the joint link side; τ am For the output torque of the harmonic reducer, J m Let θ be the moment of inertia on the motor side. m This refers to the absolute position on the motor side. The second derivative of the position is the acceleration on the motor side; u m This provides the output torque for the motor.

[0019] Based on the influence of the disturbance on the dynamic model, a harmonic disturbance torque τ is added. am In the dynamic model, and in the single-degree-of-freedom manipulator dynamic model, ignoring the influence of Coriolis force, the overall dynamic relationship is rewritten as follows:

[0020]

[0021]

[0022] Where τ d This is the second harmonic disturbance torque;

[0023] This leads to a conventional linear perturbation observer:

[0024]

[0025] in This is an estimate of the second harmonic disturbance torque. For the estimated observer state variables, These are adjustment parameters related to the observer's state variables.

[0026] Furthermore, in the second step, appropriate parameters are selected to design a harmonic interference observer to perform online real-time estimation of high-order harmonic vibrations caused by the flexibility of the harmonic reducer. Specifically:

[0027] The observer is rewritten as a second harmonic disturbance nonlinear observer based on the system feedback.

[0028] Define an auxiliary variable z:

[0029]

[0030] Let the parameters in the above formula be the state variables to be defined. satisfy:

[0031]

[0032] Therefore, the differential of the auxiliary variable z is:

[0033]

[0034] The final adjusted nonlinear observer is as follows:

[0035]

[0036]

[0037] Choose the appropriate get:

[0038]

[0039]

[0040] c is an adjustable constant, and c > 0; substituting it into the robotic arm's dynamics equations, we get:

[0041]

[0042]

[0043]

[0044] in

[0045] Furthermore, the third step is as follows:

[0046] The estimated disturbance signal is combined with the feedback controller. Specifically, the disturbance signal is fed forward to the control signal input and subtracted from the system input obtained from the feedback controller to obtain the final desired motor input. u fb This is the output of the feedback controller.

[0047] Beneficial effects:

[0048] Compared to traditional disturbance observers and offline identification methods such as harmonic modeling, this invention fully utilizes the changes in velocity and torque signals caused by harmonic vibrations in the harmonic reducer to design a nonlinear disturbance observer to estimate the interference of high-frequency harmonic vibrations on the link side. This effectively reduces the impact of vibrations on the robotic arm's performance and improves its dynamic performance. Compared to other solutions, it has the following main advantages:

[0049] 1. Compared with traditional transmission models for harmonic reducers, this method reduces the tedious measurement and modeling process and suppresses vibration interference caused by the physical structure of the harmonic reducer itself through online identification.

[0050] 2. This harmonic vibration suppression method has the advantages of simple structure, few parameters, low data processing difficulty, no need for multiple parameters in the robot dynamics model, only the link side inertia parameter is needed to achieve the effect, and strong engineering applicability. Attached Figure Description

[0051] Figure 1 This is a diagram of the overall system.

[0052] Figure 2 This is a flowchart illustrating the implementation steps of the present invention. Detailed Implementation

[0053] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0054] This invention provides a method for suppressing high-frequency resonance of the harmonic reducer in a flexible joint of a robotic arm driven by a harmonic reducer, specifically addressing issues such as... Figure 1 The robotic arm flexible joint system structure shown is used for high-frequency resonance suppression of the harmonic reducer. The specific process is as follows: Figure 2 As shown, the specific steps include:

[0055] The first step is to construct a corresponding mathematical model based on the dynamic relationship of the flexible joints of the robotic arm;

[0056] The second step is to select appropriate parameters and design a harmonic interference observer to perform online real-time estimation of high-order harmonic vibrations caused by the flexibility of the harmonic reducer.

[0057] The third step involves combining the harmonic disturbance estimate obtained in the second step with the PD feedback controller of the robotic arm's flexible joint to compensate for and suppress the second harmonic interference of the system, thus forming the high-frequency resonance suppression method for the harmonic reducer of the robotic arm's flexible joint.

[0058] The implementation steps are as follows:

[0059] The first step is to establish a mathematical model based on the dynamic relationship of the flexible joints of the robotic arm:

[0060]

[0061]

[0062] Where M(q) and C(q) are the inertia parameter matrix and Coriolis force parameter matrix of the flexible joint link, respectively, and g(q) is the gravity parameter matrix; q is the absolute position of the joint link. and These are its second and first derivatives, respectively, which correspond to the acceleration and velocity on the joint link side. τ am For the output torque of the harmonic reducer, J m Let θ be the moment of inertia on the motor side. m This refers to the absolute position on the motor side. The second derivative of the position is the acceleration on the motor side. u m This is the output torque of the motor.

[0063] Based on the influence of the disturbance on the dynamic model, a harmonic disturbance torque τ is added. am In the dynamic model, and in the single-degree-of-freedom manipulator dynamic model, ignoring the influence of Coriolis force, the overall dynamic relationship is rewritten as follows:

[0064]

[0065]

[0066] Where τ d This is the second harmonic disturbance torque.

[0067] This leads to a conventional linear perturbation observer:

[0068]

[0069] in For the estimated second harmonic disturbance torque, For the estimated observer state variables, These are adjustment parameters related to the observer's state variables.

[0070] The second step is to rewrite the observer as a second harmonic disturbance nonlinear observer based on the system feedback.

[0071] This scheme is based on a torque sensor-based joint impedance control method for robotic arms. However, on typical robotic platforms, joint angular acceleration is not a common and observable measurement. Furthermore, the angular acceleration obtained by repeatedly differentiating the joint angle is often accompanied by significant noise. Therefore, to obtain an observable state variable for the observer, the aforementioned traditional linear observer needs to be adjusted. First, an auxiliary variable z is defined:

[0072]

[0073] Let the parameters in the above formula be the state variables to be defined. satisfy:

[0074]

[0075] Therefore, the differential of the auxiliary variable z can be obtained as follows:

[0076]

[0077] The final adjusted nonlinear observer is as follows:

[0078]

[0079]

[0080] Choose the appropriate get:

[0081]

[0082]

[0083] Where c is an adjustable constant, and c > 0.

[0084] Substituting the equations of motion of the robotic arm, we can obtain

[0085]

[0086]

[0087]

[0088] in

[0089]

[0090]

[0091] The third step is to combine the estimated disturbance signal with the feedback controller. Specifically, the disturbance signal is fed forward to the control signal input and subtracted from the system input obtained from the feedback controller to obtain the final desired motor input. u fb This is the output of the feedback controller.

[0092] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A flexible robot joint harmonic reducer high-frequency resonance suppression method, characterized in that, Comprising the following steps: In the first step, a corresponding mathematical model is constructed according to the dynamics of the flexible joint of the mechanical arm; the constructed mathematical model is specifically: where M(q), C(q) are the flexible joint link side inertia parameter matrix and Coriolis force parameter matrix, respectively, and g(q) is the gravity term parameter matrix; q is the absolute position of the joint link side, and are its second and first derivatives, respectively, and the corresponding physical meanings are the joint link side acceleration and velocity; τ am is the harmonic reducer output torque, J m is the motor side rotational inertia, θ m is the motor side absolute position, is the second derivative of the position, i.e., the motor side acceleration; τ m is the motor output torque; According to the influence of the disturbance on the dynamics model, the quadratic harmonic disturbance torque τ d is added to the dynamics model, and in the single degree of freedom robot arm dynamics model, the influence of the Coriolis force is ignored, and the overall dynamics relationship is rewritten as follows: where τ d is the second harmonic disturbance torque; From which a traditional linear disturbance observer can be obtained: wherein is an estimated value of the second harmonic disturbance torque, is an estimated observer state quantity, is a tuning parameter related to the observer state quantity; In the second step, appropriate parameters are selected, and a harmonic disturbance observer is designed to estimate the high-order harmonic vibration caused by the flexibility of the harmonic reducer in real time, specifically: According to the system feedback, the observer is rewritten as a second harmonic disturbance nonlinear observer; An auxiliary variable z is defined: For the state variable to be defined, let the parameter in the above equation satisfy: The differential of the auxiliary variable z is obtained as: Finally, the adjusted nonlinear observer is obtained as: Selecting the appropriate Obtained: C is an adjustable constant, and c>0; bringing it into the dynamics equation of the mechanical arm obtains: wherein In the third step, the harmonic disturbance estimation value obtained in the second step is combined with the PD feedback controller of the flexible joint of the mechanical arm to compensate and suppress the second harmonic disturbance of the system, forming the harmonic reducer high-frequency resonance suppression method of the flexible joint of the mechanical arm.

2. The method of claim 1, wherein the harmonic wave reducer is a harmonic wave reducer of a flexible robot joint. The third step is specifically: The estimated disturbance signal is combined with the feedback controller by feeding the estimated disturbance signal forward to the input of the control signal and subtracting the result from the system input obtained from the feedback controller to obtain the final desired torque input: u fb is the output of the feedback controller.

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