Active disturbance rejection control method for linear electric drive joints of humanoid robots
Through the self-immune disturbance control method, a dynamic model is established and the system state and perturbation is estimated in real time, the nonlinearity and uncertainty problems of traditional PID control in the linear electric driving joints of humanoid robots are solved, efficient joint control is achieved, and the dynamic performance and robustness of the robot are enhanced.
Patent Information
- Application Number
- CN202510536110.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-27
- Publication Date
- 2025-08-19
- Estimated Expiration
- 2045-04-27
AI Technical Summary
Traditional PID control methods are difficult to achieve high-precision and high-stability motion control in nonlinear and uncertain systems of linearly driven joints of humanoid robots, especially in the face of complex external interference.
By establishing a dynamic model, the expansion state observer is determined, the system state and unknown disturbance are estimated in real time, and parameter adjustment is performed based on the expansion state observer and nonlinear feedback control law, so as to achieve efficient control of linear electrically driven joints.
It enhances the dynamic performance and robustness of humanoid robots, can effectively suppress external disturbances and uncertainties, and ensures that the robot joints maintain stable motion performance under various operating conditions.
Smart Images
Figure CN120056136B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of linear electric drive joint control of humanoid robots, and in particular relates to an auto-disturbance rejection control method for linear electric drive joints of humanoid robots. Background Art
[0002] With the continuous development of robotics technology, humanoid robots are increasingly being used in intelligent manufacturing, home services, smart healthcare, and other fields. To achieve high-precision and high-stability motion control for humanoid robots, it is particularly important to research efficient joint control methods. Traditional PID control methods often struggle to achieve ideal results when faced with complex nonlinear systems and external disturbances. Active disturbance rejection control (ADRC), as a new control method, offers strong robustness and excellent dynamic performance, effectively suppressing system uncertainties and external disturbances. Summary of the Invention
[0003] The present invention provides an auto-disturbance rejection control method for linear electric drive joints of a humanoid robot to solve the above-mentioned technical problems, specifically adopting the following technical solutions:
[0004] A method for controlling linear electric drive joints of a humanoid robot with anti-disturbance control, comprising:
[0005] S1: Establish a dynamic model for the linear electric drive joint system of a humanoid robot;
[0006] S2: Determine the extended state observer based on the dynamic model, estimate the state variables and unknown disturbances of the system in real time, and dynamically compensate for the disturbance through the extended state observer;
[0007] S3: Determine the nonlinear feedback control law based on the state observed by the extended state observer and the estimated disturbance information;
[0008] 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.
[0009] Furthermore, in step S1, the dynamic model of the linear electric drive joint system of the humanoid robot is:
[0010]
[0011] 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.
[0012] Furthermore, in step S1, the dynamic model is converted to obtain a state space model of the system.
[0013] Furthermore, in step S1, the specific method of converting the dynamic model to obtain the state space model of the system is:
[0014] Define state variables:
[0015]
[0016] Then the state vector is , convert the dynamic model into state space form:
[0017] ,
[0018]
[0019] Finally, the state space model of the system's dynamic model is obtained, and its state equation is:
[0020] .
[0021] Furthermore, in step S2, the system is subjected to an unknown disturbance d(t) The impact of unknown disturbances d(t) is regarded as a total disturbance and estimated by the extended state observer. d(t) for:
[0022]
[0023] The total disturbance d(t) and the system state are estimated jointly by extending a new state variable z, and the extended state observer is:
[0024] ,
[0025] ,
[0026] ,
[0027] 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.
[0028] Furthermore, in step S3, a nonlinear error feedback control law is used to generate a control input F so that the system achieves a desired output. The nonlinear error feedback control law is:
[0029]
[0030] in, v is a virtual control variable used to generate the desired dynamic behavior:
[0031]
[0032] in: q ref is the desired joint position, k 1 and k 2 is the control gain parameter.
[0033] Furthermore, in step S4, the Lyapunov function is constructed V(e) Perform stability analysis on the extended state observer:
[0034]
[0035] For Lyapunov function V(e) Taking the derivative, we get:
[0036]
[0037] The error equation is obtained based on the formula of the extended state observer in step S2. Substituting the error dynamic equation into the above equation, we get:
[0038]
[0039] Select Parameters β 1 ,β 2 ,β 3 Make To ensure the asymptotic stability of the system.
[0040] Furthermore, 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:
[0041]
[0042] The closed-loop system under the condition of no disturbance is:
[0043]
[0044] The characteristic equation is:
[0045] λ 2 +k 2 λ+k1 =0
[0046] choose k 1 and k 2 , ensuring that the eigenvalue has a negative real part, thus ensuring the stability of the system.
[0047] Further, k 1 and k 2 The value range of is: k 1 >0, k 2 >0, .
[0048] The benefit of the present invention lies in the self-disturbance rejection control method for the linear electric drive joints of a humanoid robot provided. By applying the self-disturbance rejection control technology, the limitations of traditional PID control in nonlinear and uncertain systems are overcome, and efficient control of the linear electric drive joints is achieved, thereby enhancing the dynamic performance and robustness of the humanoid robot.
[0049] The benefit of the present invention lies in the self-disturbance rejection control method for the linear electric drive joints of a humanoid robot provided. It has been verified that it has superiority in suppressing external disturbances and uncertainties, ensuring that the robot joints can maintain stable motion performance under various working conditions. BRIEF DESCRIPTION OF THE DRAWINGS
[0050] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.
[0051] Figure 1 This is a flow chart of the humanoid robot linear electric drive joint auto-disturbance rejection control method of the present invention;
[0052] Figure 2 A plot of the step response control results of the active disturbance rejection control method for the linear electric drive joints of a humanoid robot according to the present invention;
[0053] Figure 3 A step response control input diagram of the active disturbance rejection control method for the linear electric drive joint of a humanoid robot according to the present invention;
[0054] Figure 4A constant disturbance plot is provided for the step response control of the auto-disturbance rejection control method for the linear electric drive joint of a humanoid robot according to the present invention;
[0055] Figure 5 A plot showing the sinusoidal response control results of the active disturbance rejection control method for linear electric drive joints of a humanoid robot according to the present invention;
[0056] Figure 6 A plot of the sinusoidal response control input of the active disturbance rejection control method for linear electric drive joints of a humanoid robot according to the present invention;
[0057] Figure 7 The figure shows the constant disturbance applied by the sinusoidal response control of the humanoid robot linear electric drive joint auto-disturbance rejection control method of the present invention. DETAILED DESCRIPTION
[0058] The following describes embodiments of the present invention in detail. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to explain the present invention, but are not to be construed as limiting the present invention.
[0059] like Figure 1 The present invention shows a method for controlling linear electric drive joints of a humanoid robot, comprising:
[0060] Step S1: Establish a dynamic model for a humanoid robot using a linear electric drive joint system.
[0061] In the embodiment of the present application, the dynamic model of the linear electric drive joint system of the humanoid robot is:
[0062]
[0063] 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.
[0064] In the embodiment of the present application, in order to facilitate the design of the controller, the dynamic model is transformed to obtain a state space model of the system.
[0065] The specific method of converting the dynamic model to obtain the state space model of the system is:
[0066] Define state variables:
[0067]
[0068] Then the state vector is , convert the dynamic model into state space form:
[0069] ,
[0070]
[0071] Finally, the state space model of the system's dynamic model is obtained, and its state equation is:
[0072] .
[0073] Step 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.
[0074] The purpose of the extended state observer is to estimate the state and total disturbance of the system. In the active disturbance rejection control, it is assumed that the system is subject to an unknown disturbance d(t) The unknown disturbance is considered as the total disturbance and estimated by the extended state observer. Assuming the total disturbance d(t) for:
[0075]
[0076] The total disturbance d(t) and the system state are jointly estimated by expanding a new state variable z. The extended state observer is:
[0077] ,
[0078] ,
[0079] ,
[0080] in: is the estimated system state, is the estimated total disturbance, y=x1 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.
[0081] Step S3: Determine a nonlinear feedback control law based on the state observed by the extended state observer and the estimated disturbance information.
[0082] In the embodiment of the present application, the nonlinear error feedback control law is used to generate the control input F so that the system achieves the desired output. In the active disturbance rejection control, the nonlinear error feedback control law is:
[0083]
[0084] in, v is a virtual control variable used to generate the desired dynamic behavior:
[0085]
[0086] in: q ref is the desired joint position, k 1 and k 2 is the control gain parameter.
[0087] v The design ensures that the system responds as expected and can be k 1 and k 2 The speed and stability of the control response. The control input F includes the disturbance estimate Feedback can dynamically compensate for disturbances and improve control effects.
[0088] Step 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 to obtain the final controller.
[0089] In the embodiment of the present application, the Lyapunov function is constructed V(e) Perform stability analysis on the extended state observer:
[0090]
[0091] For Lyapunov function V(e) Taking the derivative, we get:
[0092]
[0093] The error equation is obtained based on the formula of the extended state observer in step S2. Substituting the error dynamic equation into the above equation, we get:
[0094]
[0095] Select Parameters β 1 ,β 2 ,β 3 Make To ensure the asymptotic stability of the system.
[0096] Specifically, β 1 >0. Preferably, choose a larger one, increaseβ 1 , which ensures The negative contribution of the term to the overall derivative is greater, making it easier to satisfy .
[0097] , to offset the impact of the cross terms. Preferably, .
[0098] β 3 >0, preferably, choose a larger β 3 : Increase β 3 , which ensures The negative contribution of the term to the overall derivative is greater, making it easier to satisfy .
[0099] By combining the above conditions and selecting these parameters appropriately, we can ensure that the derivative of the Lyapunov function is always negative, thus ensuring that the system's error dynamics are asymptotically stable. In practical designs, in addition to theoretical parameter selection, simulations and experiments are also necessary to verify the validity of the parameters and the robustness of the system.
[0100] In the embodiment of the present application, the nonlinear error feedback control law is analyzed and substituted into the system equation to obtain a closed-loop system:
[0101] ,
[0102] ,
[0103] The closed-loop system under the condition of no disturbance is:
[0104]
[0105] The characteristic equation is:
[0106] λ 2 +k 2 λ+k 1 =0
[0107] choose k 1 and k 2 , ensuring that the eigenvalue has a negative real part, thus ensuring the stability of the system.
[0108] Specifically, by choosing the appropriate k 1 andk 2 , ensuring that the eigenvalue has a negative real part, thus ensuring the stability of the system. In order to ensure the stability of the system, the roots of the characteristic equation (i.e., the eigenvalue) must have a negative real part. This can be achieved by the following conditions:
[0109] 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.
[0110] k 2 >0, ensuring that the linear term coefficient is positive. This helps provide sufficient damping and allows the system to converge quickly.
[0111] The discriminant is less than 0. To ensure that the eigenvalue is complex and has a negative real part, the discriminant needs to satisfy:
[0112]
[0113] This means that the eigenvalues are complex conjugate pairs, and since k 2 >0, its actual part is negative. k 1 >0 and k 2 >0: These conditions ensure that the system has positive natural frequencies and adequate damping. Ensure that the eigenvalues are complex and that k 2 The positive value of , and the real part of the eigenvalue is negative, which means that the response of the system is stable and has oscillatory characteristics.
[0114] By satisfying these conditions, the closed-loop dynamic behavior of the system will remain stable under disturbances and uncertainties. k 1 and k 2 It is usually necessary to debug and verify through examples based on the specific requirements and performance indicators of the system.
[0115] The following design example verifies the proposed humanoid robot linear electric drive joint auto-disturbance rejection control method. During the implementation of the present invention, the following three performances of the system are experimentally analyzed:
[0116] Tracking performance: Checks whether the system can track the set point quickly and without overshoot q ref .
[0117] Anti-disturbance performance: by applying different disturbances d(t) , to test the controller's ability to suppress disturbances.
[0118] Steady-state error: Verify whether the system has deviation in steady state to ensure the accuracy of the controller.
[0119] The system parameters and parameter design of the controller of the present invention are shown in Table 1 below:
[0120] Table 1 Controller parameters
[0121] Parameter name β1 β2 β3 k1 k2 Parameter gain 30 300 1000 500 50
[0122] To verify the controller's performance, a step response and a sinusoidal response were designed to implement position control. Disturbance was then applied to verify the tracking and disturbance rejection performance of the active disturbance rejection control algorithm. To verify the performance of the active disturbance rejection controller, a step response and a sinusoidal response test were used to evaluate the control algorithm's tracking and disturbance rejection performance by applying external disturbances. The following is the detailed design and process.
[0123] 1. Step response test
[0124] Step response test is an important method to verify the response speed and stability of the control system. Test objective: To verify the controller's ability to respond quickly to sudden changes in input signals, and to examine the system's rise time, overshoot, and steady-state error. Implementation method: The target value of a given joint position changes suddenly (step change), for example, from the initial position 0 to a fixed target position (such as 0.1m), and observe whether the system can track the target quickly and smoothly. Apply interference: During the step response process, interference (such as a constant interference force or a pulse interference force) is applied to the control input or output of the system to simulate the environmental interference that the system may be subject to. By observing the response of the system, the controller's ability to recover under interference is evaluated.
[0125] 2. Sine response test
[0126] The sinusoidal response test evaluates a control system's dynamic tracking performance and phase response capabilities. The test objective is to verify the controller's accuracy and phase delay when tracking a periodic input signal (sinusoidal signal), and examine its response characteristics under a continuously varying reference signal. Implementation: Given a sinusoidal position input signal, such as one with an amplitude of 0.1m and a frequency of 0.5Hz, observe the system's tracking performance over the entire period.
[0127] Applying disturbances: During sinusoidal tracking, apply different types of disturbances (such as random noise and periodic disturbances) and observe the change in control system error and recovery time after the disturbance. This step tests the controller's ability to resist disturbances under continuous dynamic inputs.
[0128] The experimental results are as follows Figure 2-7 As shown in the figure, the experimental results show that the controller performs well in both step response and sinusoidal response tests, as shown below:
[0129] 3. Analysis of step response test results
[0130] The step response results are as follows: Figure 2-4 As shown, Figure 2 is the step response result, Figure 3 is the corresponding control input, Figure 4 is the constant external disturbance applied.
[0131] Rise Time: When the target position changes from 0 to 0.1 m, the system exhibits a short rise time, quickly reaching 90% of the target value. This demonstrates the controller's fast response and ability to keep up with changes in the input signal.
[0132] Overshoot: From Figure 2 We observed that the system had minimal overshoot during the ascent, with virtually no significant overshoot. This suggests that the controller parameters are well-designed and can effectively suppress the system's unstable oscillations, resulting in no significant fluctuations when reaching the target position.
[0133] Steady-state error: Figure 2 As shown in the figure, the system has minimal error after reaching steady state, and can accurately maintain the target value of 0.1m, with a steady-state error of about 0.01mm. 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.
[0134] Anti-interference ability: After applying a constant interference force during the step response (such as Figure 4 (as shown in Figure 3), the system demonstrates strong anti-interference capabilities. Although the disturbance briefly deviates, the system quickly recovers to the target position. This demonstrates the controller's strong resilience and robustness in the face of sudden disturbances.
[0135] Overall, the step response test results show that the controller has fast and stable response characteristics and can effectively resist external disturbances.
[0136] 4. Analysis of sinusoidal response test results
[0137] The sinusoidal response results are as follows Figure 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.
[0138] Tracking accuracy: Figure 5As shown in the figure, when following a sinusoidal signal with a frequency of 0.5 Hz and an amplitude of 0.1 μm, the system's output remains highly consistent with the input signal, demonstrating excellent tracking accuracy with an error of approximately 0.01 mm. The system's amplitude error within the sinusoidal cycle is extremely small, demonstrating that the controller can accurately track periodic input signals.
[0139] Phase delay: such as 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 maintain synchronization with the input signal. This characteristic is particularly important for dynamic tracking tasks and shows that the controller is suitable for applications that require frequent adjustments and fast response.
[0140] Anti-interference performance: Figure 5 As shown in the figure, in the sinusoidal tracking test, after the addition of random noise and periodic disturbances, the system quickly recovered after a brief deviation, demonstrating strong anti-interference performance. The error change under the influence of the disturbance was small, and the recovery time was short, indicating that the controller has the ability to effectively suppress disturbances under dynamic input.
[0141] 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.
[0142] Overall, the experimental results demonstrate that the controller performs as expected in both step and sinusoidal response tests, validating the invention's excellent dynamic response characteristics and anti-interference capabilities. Analysis of the results from the present invention's practical examples demonstrates that the controller possesses the robustness and response characteristics required for practical applications, providing reliable assurance for the stability and accuracy required in real-world projects.
[0143] 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 solutions obtained by equivalent replacement or equivalent transformation fall within the scope of protection of the present invention.
Claims
1. A method for controlling linear electric drive joints of a humanoid robot, 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 based on the dynamic model, estimate the state variables and unknown disturbances of the system in real time, and dynamically compensate for the disturbance through the extended state observer; S3: Determine the 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; 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; In step S1, the dynamic model is also transformed to obtain a state space model of the system; In step S1, the specific method of converting the dynamic model to obtain the state space model of the system is: Define 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: 。 2. The method for controlling linear electric drive joints of a humanoid robot according to claim 1, characterized in that: In step S2, the system is subjected to an unknown disturbance d(t) The impact of unknown disturbances d(t) is regarded as a total disturbance and estimated by the extended state observer. d(t) for: ， The total disturbance d(t) and the system state are estimated jointly by extending 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.
3. The method for controlling linear electric drive joints of a humanoid robot according to claim 2, characterized in that: In step S3, the nonlinear error feedback control law is used to generate the control input F so that the system achieves 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.
4. The method for controlling linear electric drive joints of a humanoid robot according to claim 3, characterized in that: In step S4, the Lyapunov function is constructed V(e) Perform stability analysis on the extended state observer: ， Taking the derivative of the Lyapunov function, we get: ， The error equation is obtained based on the formula of the extended state observer in step S2. Substituting the error dynamic equation into the above equation, we get: ， Select Parameters β 1, β 2, β 3 makes To ensure the asymptotic stability of the system.
5. The method for controlling linear electric drive joints of a humanoid robot according to claim 3, characterized in that: In step S4, the nonlinear error feedback control law is analyzed and substituted into the system equation to obtain a closed-loop system: ， ， The closed-loop system under the condition of no 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.
6. The method for controlling linear electric drive joints of a humanoid robot according to claim 5, characterized in that: k 1 and k 2 The value range of is: k 1 >0, k 2 >0, .