Auto-disturbance rejection control method for linear electrically-driven joint of humanoid robot

Abstract

The invention discloses an active-disturbance-rejection control method for a linear electrically-driven joint of a humanoid robot. The active-disturbance-rejection control method comprises the steps that a dynamic model is established for a linear electrically-driven joint system of the humanoid robot; determining an extended state observer according to the kinetic model, estimating the state variable and unknown disturbance of the system in real time, and dynamically compensating the disturbance through the extended state observer; determining a nonlinear feedback control law based on the state observed by the extended state observer and the estimated disturbance information; and analyzing the stability of the extended state observer and the nonlinear feedback control law, and performing parameter adjustment on the extended state observer and the nonlinear feedback control law based on an analysis result. According to the active-disturbance-rejection control method for the linear electrically-driven joint of the humanoid robot, the active-disturbance-rejection control technology is applied, the limitation of traditional PID control in a nonlinear and uncertain system is overcome, efficient control over the linear electrically-driven joint is achieved, and therefore the dynamic performance and robustness of the humanoid robot are enhanced.

Description

Technical Field

[0001] The present invention belongs to the technical field of linear electric drive joint control for humanoid robots, and particularly relates to an active disturbance rejection control method for linear electric drive joints of humanoid robots. Background Art

[0002] With the continuous development of robot technology, humanoid robots are increasingly widely used in the fields of intelligent manufacturing, home service, intelligent medicine, etc. In order to achieve high-precision and high-stability motion control of humanoid robots, it is particularly important to study efficient joint control methods. Traditional PID control methods often fail to achieve ideal effects when facing complex nonlinear systems and external disturbances. As a new type of control method, active disturbance rejection control (ADRC) has strong robustness and good dynamic performance, and can effectively suppress the uncertainties and external disturbances in the system. Summary of the Invention

[0003] The present invention provides an active disturbance rejection control method for linear electric drive joints of humanoid robots to solve the above-mentioned technical problems, and specifically adopts the following technical solutions: An active disturbance rejection control method for linear electric drive joints of humanoid robots, comprising: S1: Establish a dynamic model for the linear electric drive joint system of a humanoid robot; S2: Determine an extended state observer according to the dynamic model, and estimate the state variables and unknown disturbances of the system in real time, and dynamically compensate for the disturbances through the extended state observer; S3: Determine a nonlinear feedback control law based on the state observed by the extended state observer and the estimated disturbance information; S4: Analyze the stability of the extended state observer and the nonlinear feedback control law, and adjust the parameters of the extended state observer and the nonlinear feedback control law based on the analysis results.

[0004] Further, in the step S1, the dynamic model of the linear electric drive joint system of a humanoid robot is:

[0005] where M is the equivalent mass of the actuator, B is the damping coefficient, K is the stiffness coefficient, q is the joint position, and F is the control input.

[0006] Further, in the step S1, the dynamic model is also transformed to obtain the state space model of the system.

[0007] Further, in the step S1, the specific method for transforming the dynamic model to obtain the state space model of the system is: Define state variables:

[0008] The state vector is , and the dynamic model is converted into the state - space form: ,

[0009] Finally, the state - space model of the dynamic model of the system is obtained, and its state equation is: .

[0010] Furthermore, in the step S2, the system is affected by an unknown disturbance d(t) . The unknown disturbance d(t) is regarded as the total disturbance and estimated by the extended state observer. The total disturbance d(t) is:

[0011] The total disturbance d(t) and the system state are jointly estimated by expanding a new state variable z. The extended state observer is: , , ,

[0012] where: is the estimated system state, is the estimated total disturbance, y = x 1 is the system output, β 1 ,β 2 ,β 3 is the gain parameter of the extended state observer.

[0013] Furthermore, in the step S3, the non - linear error feedback control law is used to generate the control input F to make the system reach the desired output. The non - linear error feedback control law is:

[0014] where, v is the virtual control quantity, which is used to generate the desired dynamic behavior:

[0015] where: q ref is the desired joint position, k 1 and k2 is the control gain parameter.

[0016] Furthermore, in step S4, construct the Lyapunov function V(e) Conduct a stability analysis on the extended state observer:

[0017] For the Lyapunov function V(e) Take the derivative to obtain:

[0018] Based on the formula of the extended state observer in step S2, obtain the error equation, and substitute the error dynamic equation into the above formula to get:

[0019] Select the parameter β 1 ,β 2 ,β 3 such that to ensure the asymptotic stability of the system.

[0020] Furthermore, in step S4, analyze the non - linear error feedback control law, and substitute the non - linear error feedback control law into the system equation to obtain the closed - loop system:

[0021] Consider the closed - loop system without disturbance as:

[0022] The characteristic equation is: λ 2 +k 2 λ + k 1 =0 Select k 1 and k 2 to ensure that the eigenvalues have negative real parts, thus ensuring the stability of the system.

[0023] Furthermore, k 1 and k 2 The value ranges of k 1 are: k 2 > 0, .

[0024] The beneficial effect of the present invention lies in the provided active disturbance rejection control method for the linear electric drive joint of a humanoid robot. By applying the active disturbance rejection control technology, it overcomes the limitations of traditional PID control in nonlinear and uncertain systems, realizes efficient control of the linear electric drive joint, and thus enhances the dynamic performance and robustness of the humanoid robot.

[0025] The beneficial effect of the present invention lies in the provided active disturbance rejection control method for the linear electric drive joint of a humanoid robot. Through verification, it has superiority in suppressing external disturbances and uncertainties, ensuring that the robot joint can maintain stable motion performance under various working conditions. Description of the Drawings

[0026] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0027] Figure 1 It is a flowchart of the active disturbance rejection control method for the linear electric drive joint of the humanoid robot of the present invention; Figure 2 It is a drawing of the step response control result of the active disturbance rejection control method for the linear electric drive joint of the humanoid robot of the present invention; Figure 3 It is a drawing of the step response control input of the active disturbance rejection control method for the linear electric drive joint of the humanoid robot of the present invention; Figure 4 It is a drawing of the constant disturbance applied to the step response control of the active disturbance rejection control method for the linear electric drive joint of the humanoid robot of the present invention; Figure 5 It is a drawing of the sine response control result of the active disturbance rejection control method for the linear electric drive joint of the humanoid robot of the present invention; Figure 6 It is a drawing of the sine response control input of the active disturbance rejection control method for the linear electric drive joint of the humanoid robot of the present invention; Figure 7 It is a drawing of the constant disturbance applied to the sine response control of the active disturbance rejection control method for the linear electric drive joint of the humanoid robot of the present invention. Detailed Embodiments

[0028] Embodiments of the present invention will be described in detail below. Examples of the embodiments are shown in the accompanying drawings, where like or similar reference numerals denote like or similar elements or elements having like or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to explain the present invention, and should not be construed as limiting the present invention.

[0029] As Figure 1 shown, a linear electro - drive joint active disturbance rejection control method for a humanoid robot in this application includes: Step S1: Establish a dynamic model for the linear electro - drive joint system of the humanoid robot.

[0030] In the embodiment of this application, the dynamic model of the linear electro - drive joint system of the humanoid robot is:

[0031] where M is the equivalent mass of the actuator, B is the damping coefficient, K is the stiffness coefficient, q is the joint position, and F is the applied force or control input.

[0032] In the embodiment of this application, for the convenience of designing the controller, the dynamic model is transformed to obtain the state - space model of the system.

[0033] The specific method for transforming the dynamic model to obtain the state - space model of the system is as follows: Define the state variables:

[0034] Then the state vector is , and the dynamic model is transformed into the state - space form: ,

[0035] Finally, the state - space model of the dynamic model of the system is obtained, and its state equation is: .

[0036] Step S2: Determine an extended state observer according to the dynamic model to estimate the state variables and unknown disturbances of the system in real - time, and dynamically compensate for the disturbances through the extended state observer.

[0037] The purpose of the extended state observer is to estimate the state and total disturbance of the system. In active disturbance rejection control, it is assumed that the system is affected by an unknown disturbance d(t) , and the unknown disturbance is regarded as the total disturbance and estimated by the extended state observer. Assume that the total disturbance d(t) is:

[0038] The total disturbance d(t) and the system state are jointly estimated by expanding a new state variable z. The extended state observer is as follows: , , ,

[0039] where: is the estimated system state, is the estimated total disturbance, y = x 1 is the system output, β 1 ,β 2 ,β 3 are the gain parameters of the extended state observer, and by adjusting them, the response speed and accuracy of the observer can be controlled.

[0040] Step S3: Based on the state observed by the extended state observer and the estimated disturbance information, determine the nonlinear feedback control law.

[0041] In the embodiments of the present application, the nonlinear error feedback control law is used to generate the control input F to make the system reach the desired output. In the active disturbance rejection control, the nonlinear error feedback control law is:

[0042] where, v is the virtual control quantity, which is used to generate the desired dynamic behavior:

[0043] where: q ref is the desired joint position, k 1 and k 2 are the control gain parameters.

[0044] v The design of ensures that the response of the system meets the expectations, and the speed and stability of the response can be controlled by k 1 and k 2 The control input F includes the feedback of the disturbance estimate , and can dynamically compensate for the disturbance and improve the control effect.

[0045] Step S4: Analyze the stability of the extended state observer and the nonlinear feedback control law, and based on the analysis results, adjust the parameters of the extended state observer and the nonlinear feedback control law to obtain the final controller.

[0046] In an embodiment of the present application, a Lyapunov function is constructed V(e) Perform stability analysis on the extended state observer:

[0047] For the Lyapunov function V(e) Take the derivative to obtain:

[0048] Based on the formula of the extended state observer in step S2, obtain the error equation, and substitute the error dynamic equation into the above formula to obtain:

[0049] Select parameters β 1 ,β 2 ,β 3 Such that To ensure the asymptotic stability of the system.

[0050] Specifically, β 1 >0. Preferably, select a larger one to increase β 1 , which can ensure that The negative contribution of the term to the overall derivative is greater, making it easier to satisfy .

[0051] , to offset the influence brought by the cross term. Preferably, .

[0052] β 3 >0, preferably, select a larger β 3 : Increase β 3 , which can ensure that The negative contribution of the term to the overall derivative is greater, making it easier to satisfy .

[0053] By combining the above conditions and reasonably selecting these parameters, it can be ensured that the derivative of the Lyapunov function is always negative, thereby ensuring that the error dynamics of the system is asymptotically stable. When conducting actual design, in addition to the theoretical parameter selection, it is also necessary to verify the effectiveness of the parameters and the robustness of the system through simulation and experiments.

[0054] In an embodiment of the present application, analyze the non - linear error feedback control law, and substitute the non - linear error feedback control law into the system equation to obtain the closed - loop system: , ,

[0055] Consider the closed-loop system without disturbances as follows:

[0056] The characteristic equation is: λ 2 +k 2 λ + k 1 =0 Select k 1 and k 2 to ensure that the eigenvalues have negative real parts, thus guaranteeing the stability of the system.

[0057] Specifically, by selecting appropriate k 1 and k 2 to ensure that the eigenvalues have negative real parts, thus guaranteeing the stability of the system. To ensure the stability of the system, the roots of the characteristic equation (i.e., the eigenvalues) must have negative real parts. This can be achieved through the following conditions: k 1 > 0, ensuring that the constant term of the characteristic equation is positive. This is one of the necessary conditions to ensure that the natural frequency of the system is positive.

[0058] k 2 > 0, ensuring that the coefficient of the linear term is positive. This helps to provide sufficient damping so that the system converges quickly.

[0059] The discriminant is less than 0. To ensure that the eigenvalues are complex and have negative real parts, the discriminant needs to satisfy:

[0060] This means that the eigenvalues are a complex conjugate pair, and since k 2 > 0, their real parts are negative. k 1 > 0 and k 2 > 0: These conditions ensure that the system has a positive natural frequency and sufficient damping. Ensure that the eigenvalues are in complex form, and due to k 2 being positive, the real parts of the eigenvalues are negative, which means that the response of the system is stable and has oscillatory characteristics.

[0061] By meeting these conditions, the closed-loop dynamic behavior of the system will remain stable under perturbations and uncertainties. Selecting the appropriate k 1 and k 2 usually requires debugging and verification through examples according to the specific requirements and performance indicators of the system.

[0062] The following verifies the active disturbance rejection control method for the linear electric drive joint of a humanoid robot proposed by the present invention through a design example. During the implementation process of the present invention, the following three performances of the system are analyzed through experiments: Tracking performance: Check whether the system can track the set point quickly and without overshoot q ref .

[0063] Disturbance rejection performance: By applying different perturbations d(t) , test the ability of the controller to suppress perturbations.

[0064] Steady-state error: Verify whether there is a deviation in the system at steady state to ensure the accuracy of the controller.

[0065] The system parameters and parameter design of the controller of the present invention are shown in Table 1 below: Table 1 Controller parameters Parameter Name β1 β2 β3 k1 k2 Parameter Gain 30 300 1000 500 50 To verify the performance of the controller, a step response and a sine response are designed to achieve position control, and disturbances are applied to verify the tracking and anti-disturbance performance of the active disturbance rejection control algorithm. To verify the performance of the active disturbance rejection controller, test methods of step response and sine response are adopted, and the tracking and anti-disturbance performance of the control algorithm are evaluated by applying external disturbances. The following are the specific designs and processes.

[0066] 1. Step response test The step response test is an important method to verify the response speed and stability of a control system. Test objective: Verify the fast response ability of the controller when facing a sudden input signal, and examine the rise time, overshoot, and steady-state error of the system. Implementation method: Suddenly change the target value of the joint position (step change), for example, change from the initial position 0 to a fixed target position (such as 0.1 m), and observe whether the system can track the target quickly and smoothly. Apply disturbance: During the step response process, apply a disturbance (such as a constant disturbance force or a pulse disturbance force) at the control input or output of the system to simulate the environmental disturbances that the system may be subjected to. By observing the response of the system, evaluate the recovery ability of the controller under the disturbance.

[0067] 2. Sine response test The sine response test is used to evaluate the dynamic tracking performance and phase response ability of the control system. Test objectives: Verify the accuracy and phase delay of the controller when tracking a periodic input signal (sine signal), and examine its response characteristics under a continuously changing reference signal. Implementation method: Given a sine position input signal, such as a sine signal with an amplitude of 0.1 m and a frequency of 0.5 Hz, observe the tracking effect of the system throughout the cycle.

[0068] Applying interference: During the sine tracking process, apply different types of interference (such as random noise, periodic perturbations, etc.), and observe the error change and recovery time of the control system after being interfered. This step can test the anti-interference ability of the controller under continuous dynamic inputs.

[0069] The experimental results are as Figures 2 - 7 shown. The experimental results show that the controller performs excellently in both the step response and sine response tests, and the specific performance is as follows: 3. Analysis of step response test results The step response results are as Figures 2 - 4 shown, where Figure 2 is the step response result, Figure 3 is the corresponding control input, and Figure 4 is the applied constant external interference.

[0070] Rise time: During the process where the system's target position suddenly changes from 0 to 0.1 m, it shows a short rise time and quickly reaches 90% of the target value. This indicates that the controller has a fast response ability and can promptly follow the changes in the input signal.

[0071] Overshoot: It can be Figure 2 observed that the overshoot of the system during the rising process is small, and there is basically no obvious overshoot phenomenon. This means that the controller parameter design is reasonable, which can effectively suppress the unstable oscillation of the system, so that there is no significant fluctuation when reaching the target position.

[0072] Steady-state error: As Figure 2 shown, the error of the system after reaching the steady state is extremely small, and it can accurately maintain near the target value of 0.1 m, with the steady-state error being about 0.01 mm. This shows that the controller has good steady-state performance and can ensure that the system is consistent with the target position in the final state.

[0073] Anti-interference ability: After applying a constant interference force during the step response process (as Figure 4 shown), the system shows strong anti-interference ability. Although there is a short deviation under the interference, the system quickly returns to the target position. This indicates that the controller has strong recovery ability and robustness when facing sudden interference.

[0074] Overall, the step response test results show that the controller has fast and stable response characteristics and can effectively resist external disturbances.

[0075] 4. Analysis of Sine Response Test Results The sinusoidal response results are as follows Figures 5 - 7 As shown, Figure 5 is the sinusoidal response result, Figure 6 is the corresponding control input, Figure 7 is the constant external disturbance applied.

[0076] Tracking accuracy: Figure 5 As shown in the figure, when following a sinusoidal signal with a frequency of 0.5Hz and an amplitude of 0.1m, the system output is highly consistent with the input signal, showing excellent tracking accuracy with an error of about 0.01mm. The amplitude error of the system within the sinusoidal period is extremely small, indicating that the controller can accurately track the periodic input signal.

[0077] Phase delay: Figure 5 As shown in the figure, the experimental results show that the phase difference between the system output signal and the input sinusoidal signal is very small, indicating that the controller has good phase response capability and can keep pace with the input signal. This feature is particularly important for dynamic tracking tasks, indicating that the controller is suitable for application scenarios that require frequent adjustments and fast responses.

[0078] Anti-interference performance: Figure 5 As shown in the figure, in the sinusoidal tracking test, after adding random noise and periodic disturbances, the system quickly returns to normal after a short deviation, showing strong anti-interference performance. The error change under the influence of interference is small and the recovery time is short, indicating that the controller has the ability to effectively suppress interference under dynamic input.

[0079] In summary, the sinusoidal response test results show that the controller can not only accurately track the periodic input signal, but also maintain a high degree of stability and tracking accuracy when subjected to disturbances.

[0080] Overall, the experimental results show that the controller of the invention performs as expected in both step response and sinusoidal response tests, verifying the good dynamic response characteristics and anti-interference ability of the invention. Through the analysis of the results of the examples of the invention, the controller has the robustness and response characteristics that meet the needs of practical applications, and can provide reliable guarantees for the stability and accuracy requirements in practical engineering.

[0081] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the above embodiments do not limit the present invention in any form, and any technical solution obtained by equivalent replacement or equivalent transformation falls within the protection scope of the present invention.

Claims

1. A humanoid robot linear electric drive joint self-disturbance rejection control method, characterized in that: include: S1: Establish a dynamic model for the linear electric drive joint system of a humanoid robot; S2: Determine the extended state observer according to the dynamic model, estimate the state variables and unknown disturbances of the system in real time, and dynamically compensate for the disturbances through the extended state observer; S3: Determine a nonlinear feedback control law based on the state observed by the extended state observer and the estimated disturbance information; S4: Analyze the stability of the extended state observer and the nonlinear feedback control law, and adjust the parameters of the extended state observer and the nonlinear feedback control law based on the analysis results.

2. The humanoid robot linear electric drive joint auto-disturbance rejection control method according to claim 1, characterized in that: In step S1, the dynamic model of the linear electric drive joint system of the humanoid robot is: ， Where M is the equivalent mass of the actuator, B is the damping coefficient, K is the stiffness coefficient, q is the joint position, and F is the control input.

3. The humanoid robot linear electric drive joint auto-disturbance rejection control method according to claim 2, characterized in that: In the step S1, the dynamic model is also transformed to obtain a state space model of the system.

4. The method for controlling linear electric drive joints of a humanoid robot according to claim 3, characterized in that: In step S1, the specific method of converting the dynamic model to obtain the state space model of the system is: Define the state variables: ， Then the state vector is , convert the dynamic model into state space form: ， ， Finally, the state space model of the system's dynamic model is obtained, and its state equation is: 。 5. The method for controlling linear electric drive joints of a humanoid robot according to claim 4, characterized in that: In step S2, the system is subjected to an unknown disturbance d(t) The impact of unknown disturbances d(t) Considered as a total disturbance and estimated by the extended state observer, the total disturbance d(t) is: ， The total disturbance d(t) and the system state are estimated jointly by expanding a new state variable z, and the extended state observer is: ， ， ， in: is the estimated system state, is the estimated total disturbance, y=x1 is the system output, β 1 ,β 2 ,β 3 is the gain parameter of the extended state observer.

6. The humanoid robot linear electric drive joint auto-disturbance rejection control method according to claim 5, characterized in that: In step S3, the nonlinear error feedback control law is used to generate the control input F so that the system reaches the desired output. The nonlinear error feedback control law is: ， in, v is a virtual control variable used to generate the desired dynamic behavior: ， in: q ref is the desired joint position, k 1 and k 2 is the control gain parameter.

7. The humanoid robot linear electric drive joint auto-disturbance rejection control method according to claim 6, characterized in that: In step S4, a Lyapunov function is constructed. V(e) Perform stability analysis on the extended state observer: ， Taking the derivative of the Lyapunov function, we get: ， Based on the formula of the extended state observer in step S2, the error equation is obtained. Substituting the error dynamic equation into the above equation, we get: ， Select Parameters β 1 ,β 2 ,β 3 Make To ensure the asymptotic stability of the system.

8. The method for controlling linear electric drive joints of a humanoid robot according to claim 6, characterized in that: In step S4, the nonlinear error feedback control law is analyzed, and the nonlinear error feedback control law is substituted into the system equation to obtain a closed-loop system: ， ， The closed-loop system without disturbance is: ， The characteristic equation is: λ 2 +k 2 λ+k 1 =0， choose k 1 and k 2 , ensuring that the eigenvalue has a negative real part, thus ensuring the stability of the system.

9. The humanoid robot linear electric drive joint auto-disturbance rejection control method according to claim 8, characterized in that: k 1 and k 2 The value range of is: k 1 >0, k 2 >0, .

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