Robotic arm disturbance rejection tracking control method and system based on variable gain compound observer
Patent Information
- Application Number
- CN202611467448.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-09-21
- Publication Date
- 2026-10-27
AI Technical Summary
本发明将机械臂扰动划分为结构化扰动与集总扰动两类，并分别采用专用扰动观测器和变增益扩张状态观测器进行分层估计。相较于传统方法将全部扰动统一作为单一集总扰动处理的方案，本发明能够充分利用周期性负载、谐波扰动等具有先验结构信息的扰动特征，由专用扰动观测器对其进行精准估计；而无法精确建模的参数失配、摩擦变化、外部突加负载等不确定性，则由变增益扩张状态观测器进行宽范围覆盖。二者分工明确、互补协同，既降低了单一扩张状态观测器的估计负担，又避免了先验信息被淹没在集总扰动中无法利用的问题，从而在机理层面提升了多源扰动并存条件下的整体扰动估计精度。
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Figure CN122975699A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of robot control and electromechanical servo control technology, and in particular to a disturbance rejection tracking control method and system for robotic arms based on a variable gain composite observer. Background Technology
[0002] Robotic arms inherently possess significant nonlinear, strongly coupled, and time-varying characteristics. Their dynamics are influenced by factors such as the inertia matrix, Coriolis term, centrifugal term, gravity term, and joint friction. When the system is subjected to multi-source disturbances, traditional control methods are prone to problems such as increased tracking error, decreased response speed, control input fluctuations, and insufficient robustness.
[0003] Existing robotic arm trajectory tracking control methods mainly include PID control, robust control, adaptive control, sliding mode control, backstepping control, and active disturbance rejection control. Among them, PID control has a simple structure and is easy to implement in engineering, but its adaptability to model nonlinearity and external disturbances is limited; robust control and sliding mode control have strong disturbance rejection capabilities, but may require high control gain and are prone to introducing control chattering; adaptive control can adjust parameters online, but parameter convergence and control performance may be affected under conditions of multi-source disturbances and rapid load changes; active disturbance rejection control estimates the total disturbance by extending the state observer and has good engineering application value, but if all disturbances are treated as lumped disturbances, it is difficult to fully utilize the disturbance information with structural priors.
[0004] In practical robotic arm systems, disturbances are not entirely homogeneous. Some disturbances have usable structural information, such as periodic load disturbances, harmonic disturbances, and regular disturbances caused by repetitive operations; others are difficult to model accurately, such as inertial parameter mismatch, frictional changes, sudden external loads, gravity compensation errors, and unmodeled dynamics. If all of these disturbances are uniformly incorporated into a single lumped disturbance for estimation, it will increase the observer's workload and affect the accuracy of disturbance estimation and the effectiveness of compensation. Summary of the Invention
[0005] To address the shortcomings of existing technologies, this invention provides a disturbance rejection tracking control method and system for robotic arms based on a variable gain composite observer; On the one hand, a disturbance rejection tracking control method for robotic arms based on a variable gain composite observer is provided, including: Based on the dynamic model of the n-degree-of-freedom robotic arm, construct its state-space model; The disturbances of the robotic arm are classified and modeled. Disturbances with available prior structural information are classified as structured disturbances, while disturbances that are difficult to model accurately or have uncertain online changes are classified as lumped disturbances. Based on the state-space model and structured perturbation, a structured perturbation observer is constructed. The sum of the lumped disturbance and the structured disturbance estimation error is defined as the extended state. Based on the state space model, an error-driven variable gain extended state observer is constructed. Based on the state variable information of the state space model, a trajectory tracking error is constructed, and a virtual control quantity is designed based on the backstepping method. Based on the state-space model, the actual controller is constructed according to the disturbance estimate of the structured disturbance observer, the extended state estimate of the error-driven variable gain extended state observer, the trajectory tracking error and the virtual control quantity, and outputs the joint control input of the robotic arm. The joint control input of the robotic arm is applied to the joint drive device of the robotic arm.
[0006] On the other hand, a disturbance rejection tracking control system for a robotic arm based on a variable gain composite observer is provided, including: The model building module is used to construct the state space model of the n-DOF robotic arm based on its dynamics model. The disturbance classification module is used to classify and model the disturbances of the robotic arm. Disturbances with available prior structural information are classified as structured disturbances, while disturbances that are difficult to model accurately or have uncertainties in online changes are classified as lumped disturbances. The disturbance observation module is used to construct a structured disturbance observer based on the state-space model and the structured disturbance, and output the structured disturbance estimate. The variable gain extended state observation module is used to define the sum of the estimation errors of the lumped disturbance and the structured disturbance as the extended state, and construct an error-driven variable gain extended state observer based on the state space model to output the extended state estimate. The tracking error construction and virtual control quantity calculation module is used to construct the trajectory tracking error and design the virtual control quantity based on the backstepping method. The actual controller module is connected to the disturbance observation module, the variable gain extended state observation module, and the tracking error construction and virtual control quantity calculation module, respectively. It is used to construct the actual controller based on the structured disturbance estimate, the extended state estimate, the trajectory tracking error, and the virtual control quantity, and output the joint control input of the robotic arm. The drive execution module, connected to the actual controller module, is used to apply the control input of the robotic arm joint to the robotic arm joint drive device.
[0007] Furthermore, an electronic device is also provided, including: Memory, used for non-transitory storage of computer-readable instructions; and Processor, for executing the computer-readable instructions, When the computer-readable instructions are executed by the processor, they perform the method described in the first aspect above.
[0008] In another aspect, a computer-readable storage medium is also provided for non-transitory storage of computer-readable instructions, wherein when the non-transitory computer-readable instructions are executed by a computer, the method described in the first aspect is performed.
[0009] In another aspect, a computer program product is also provided, including software code, wherein the program in the software code performs the steps of the method described in the first aspect of the present invention.
[0010] The above technical solution has the following advantages or beneficial effects: This invention classifies robotic arm disturbances into two categories: structured disturbances and lumped disturbances, and employs a dedicated disturbance observer and a variable-gain extended state observer for hierarchical estimation, respectively. Compared to traditional methods that treat all disturbances as a single lumped disturbance, this invention fully utilizes disturbance characteristics with prior structural information, such as periodic loads and harmonic disturbances, which are accurately estimated by the dedicated disturbance observer. Uncertainties such as parameter mismatch, frictional changes, and sudden external loads, which cannot be accurately modeled, are covered by the variable-gain extended state observer with a wide range of coverage. The two have clear division of labor and complement each other, reducing the estimation burden of a single extended state observer and avoiding the problem of prior information being submerged in lumped disturbances and becoming unusable. Thus, at the mechanistic level, the overall disturbance estimation accuracy under conditions of multiple source disturbances coexisting is improved.
[0011] Meanwhile, this invention constructs an error-driven variable-gain extended state observer, dynamically adjusting the observer gain according to the magnitude of the observation error. When the error is large, the observer automatically increases the gain to accelerate the estimation of sudden loads, frictional abrupt changes, and model mismatches; when the error is small, the observer automatically decreases the gain to reduce measurement noise amplification and control input fluctuations. Attached Figure Description
[0012] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.
[0013] Figure 1 This is a flowchart of the method in Example 1; Figure 2 Comparison of joint position tracking curves with no observation compensation, variable gain composite observation compensation, and reference trajectory; where (a) is a comparison of joint 1 position tracking curves; (b) is a comparison of joint 2 position tracking curves. Figure 3The following are the joint tracking error curves with no observation compensation and variable gain composite observation compensation; where (a) is the tracking error curve of joint 1; and (b) is the tracking error curve of joint 2. Figure 4 The control input curves are for no observation compensation and variable gain composite observation compensation; where (a) is the control input curve for joint 1; and (b) is the control input curve for joint 2. Figure 5 The images show a local comparison of the joint tracking error between the fixed-gain composite observation method and the variable-gain composite observation method under sudden disturbance; where (a) is a local comparison of the tracking error of joint 1 after a sudden disturbance of 5s; and (b) is a local comparison of the tracking error of joint 2 after a sudden disturbance of 7s. Detailed Implementation
[0014] All data acquisition in this embodiment is carried out in accordance with laws and regulations and with user consent, and the data is used legally.
[0015] Example 1 This embodiment provides a disturbance rejection tracking control method for a robotic arm based on a variable gain composite observer, such as... Figure 1 As shown, it includes: S1. Based on the dynamic model of the n-degree-of-freedom robotic arm, construct its state-space model.
[0016] Specifically, the dynamic model of the n-degree-of-freedom robotic arm is expressed as follows:
[0017] In the formula, For the joint position vector of the robotic arm; This is the joint velocity vector; This is the joint acceleration vector; For the robotic arm's inertia matrix, For Coriolis terms and centrifugal terms; This is the term related to gravity. For joint friction; For joint control input of the robotic arm; and These represent the structured perturbation and lumped perturbation equivalent to the joint acceleration channel, respectively. This represents the torque path representation of the equivalent disturbance in the robotic arm's dynamics equations. Furthermore, state variables are introduced.
[0018] Then there is
[0019] Choose an invertible nominal input gain matrix Define the nominal nonlinear dynamics term of the robotic arm. The state-space model is then expressed as:
[0020] In the formula, This is a nominal nonlinear dynamic term constructed based on the nominal model of the robotic arm, used to characterize the known or nominally known dynamic effects formed by inertial coupling, Coriolis terms, centrifugal terms, gravity terms, and friction terms. Parameter mismatch, friction variations, external load variations, and unmodeled dynamics between the nominal and real models are uniformly classified into lumped disturbances. .
[0021] S2. Classify and model the disturbances of the robotic arm. Disturbances with available prior structural information are classified as structured disturbances, while disturbances that are difficult to model accurately or have uncertainties in online changes are classified as lumped disturbances.
[0022] Among them, the structured disturbance With available prior structural information, such as periodic load disturbances, harmonic disturbances, repetitive operation disturbances, or disturbances that can be described by an external system, it can be represented as:
[0023] In the formula, The external system state vector is the disturbance. , , Given a matrix; For modeling errors or bounded input terms of the external system; The lumped disturbance Used to characterize uncertainties that are difficult to model accurately or change online, including but not limited to inertial parameter mismatch, gravity parameter deviation, joint friction variation, sudden external load, and unmodeled coupled dynamics.
[0024] By using the above classification method, perturbations with prior structural information and perturbations that cannot be accurately modeled can be treated separately, making full use of known perturbation structures and reducing the estimation burden of a single observer.
[0025] S3. Construct a disturbance observer for estimating structured disturbances.
[0026] For structured disturbances Design the following disturbance observer:
[0027] In the formula, This is an estimate of the external system state. This is an estimate of the structured disturbance; The internal state of the observer; The observer gain matrix; The disturbance observation error is defined as:
[0028] In the formula, Let be the state vector of the disturbed external system. This is the estimated state of the external system. This represents the external system state estimation error. For structured perturbations, This is an estimate of the structured perturbation. This represents the error in the structured perturbation estimation.
[0029] Then we have:
[0030] In the formula, This represents the error in estimating structured perturbations. Under the conditions of lumped disturbances and bounded external system modeling errors, and matrix Under detectable conditions, select a symmetric positive definite matrix. and matrix To satisfy And let the perturbation observer gain matrix be At this time, the matrix This is the Hurwitz matrix. Under lumped perturbation... and external system modeling errors or bounded input terms Under bounded conditions, the external system state estimation error and structured perturbation estimation error Maintaining boundedness; under ideal modeling conditions, i.e. and When the estimation error asymptotically converges to zero, the estimation error will eventually converge to zero.
[0031] S4. Combine the lumped disturbance and the structured disturbance estimation error into an extended state, and construct an error-driven variable gain extended state observer.
[0032] Specifically, the expansion state is represented as
[0033] The state equation of the robotic arm can be written as:
[0034] In the formula, The extended state derivative is assumed to be bounded; The design error-driven variable gain extended state observer is as follows:
[0035] In the formula, For state The estimated value; This indicates that the extended state observer is on the state. The observation error; This is an estimate of the expansion state; and It is an error-driven variable gain function; , For design parameters; It is a nonlinear function, defined by its components as follows: ,in, express The One variable; Furthermore, the constant gain in the traditional fixed-gain extended state observer is replaced with an error-driven variable gain, specifically in the following form:
[0036] in, , It is a scalar gain function that acts on the observation error components in each dimension; , Basic observation gain; , This is the gain adjustment coefficient; To prevent small constants with a denominator of zero; From the above variable gain function, it can be seen that when the observation error... When it is large, and Automatically increasing the size enables the extended state observer to estimate disturbances faster; when observation errors occur... When smaller, and Automatic reduction lowers the observer's noise sensitivity during the steady-state phase, thus minimizing control input fluctuations. Simultaneously, due to... as well as Therefore, the gain of the variable gain extended state observer always remains positively bounded, and there will be no gain divergence problem.
[0037] The error-driven variable gain extended state observer can be used to uniformly estimate the residuals of lumped disturbances and structured disturbances, and the estimation results can be used for control input compensation.
[0038] S5. Construct trajectory tracking error, and design virtual control quantity based on backstepping method.
[0039] Specifically, let the reference joint trajectory of the robotic arm be:
[0040] Define the first-layer trajectory tracking error of the backstepping method:
[0041] Depend on achievable
[0042] In the formula, for The first derivative; in the backstepping method, This is considered a virtual control input in the first step of the design; To make the first layer error Convergence, constructing virtual control variables:
[0043] In the formula, It is a positive definite gain matrix; Define the second-level error variables:
[0044] achievable
[0045] Substituting this into the first-level error derivative of the backstepping method, we get:
[0046] Selecting the first step, the Lyapunov function:
[0047] Taking its derivative, we get:
[0048] From the above formula, we can see that For negative definite terms, These are the coupling terms that need to be addressed in the next step of controller design.
[0049] S6. Construct the actual controller based on the disturbance estimate of the structured disturbance observer, the extended state estimate of the error-driven variable gain extended state observer, the trajectory tracking error and the virtual control quantity. The output of the actual controller is applied to the robotic arm joint drive device to achieve disturbance-resistant tracking control of the robotic arm joint trajectory to the reference joint trajectory.
[0050] Based on the design results of the composite observer, the observation-compensated robotic arm system can be written as:
[0051] in For the estimation error of the extended state; Substituting the system dynamics into the derivative of the second-level error, we get:
[0052] Constructing the second Lyapunov function:
[0053] Differentiating it, we have:
[0054] Will and Substitute and get
[0055] To offset the nominal nonlinearity of the robotic arm, the disturbance observation compensation term, and the error coupling term, the actual control input is selected as follows:
[0056] in, It is a positive definite gain matrix. The virtual control quantity is designed for the first step of the backstepping method. This is the second-level error variable.
[0057] The virtual control quantity and the second-level error variable are respectively:
[0058]
[0059] It can also be known that Therefore, the actual control input can be directly based on and control gain matrix Calculated.
[0060] Substitute the actual control input available: Furthermore, stability is proven, and the specific steps are as follows: Consider the second step, the Lyapunov function. ,in, Furthermore, as can be seen from the aforementioned derivation, under the action of the designed control law, there is .
[0061] When the observer estimates are ideal, i.e. At that time, there were:
[0062] because and Given a positive definite matrix, and with the reference trajectory and related closed-loop signals bounded, according to Lyapunov stability theory and Barbalat's lemma, the first-level error in the closed-loop system can be determined. Second layer error Gradually convergent.
[0063] In general, composite observers suffer from estimation errors. Therefore, using Young's inequality, we have:
[0064] therefore:
[0065] Furthermore, we can obtain:
[0066] When the control gain matrix satisfy At that time, in the closed-loop system and Bounded. If the expansion state estimation error If the signal is bounded, then all signals in the closed-loop system are bounded, and the trajectory tracking error is consistent and eventually bounded.
[0067] If as the observer converges, we have Given that the reference trajectory and its derivative are bounded, the observation error converges, and the correlated signals of the closed-loop system are bounded, we can further obtain... Furthermore, due to the speed tracking error of the robotic arm... ,Depend on achievable Right now Therefore, when Sometimes, .
[0068] Therefore, it can be concluded that when the observer residual approaches zero, the robotic arm's position tracking error... and speed tracking error All converge asymptotically to zero.
[0069] In summary, based on the reference trajectory When the system is bounded, the observer estimation error is bounded, and the control gain meets the design conditions, the robotic arm disturbance rejection trajectory tracking control method based on variable gain composite observer and backstepping method proposed in this invention can guarantee that: all signals in the closed-loop system are bounded; under general bounded disturbance conditions, the system error is consistent and eventually bounded; and when the observer residual approaches zero, the position tracking error and velocity tracking error asymptotically converge to zero.
[0070] To verify the effect of composite observation compensation, a comparison was made between no observation compensation and variable gain composite observation compensation. To further verify the role of the variable gain mechanism, a fixed gain composite observation method was added as a supplementary comparison in the local interval of sudden disturbance. Figure 2 Joint position tracking curves under two different methods are presented. After applying the method of this invention, the actual trajectories of both joints can better approximate the reference trajectory, and the tracking deviation of joint 2 is significantly reduced. Figure 3 Joint tracking error curves for two different methods are presented. In comparison, after using variable gain composite observation compensation, the tracking errors of both joints decrease rapidly and remain near zero, while the steady-state error and error fluctuation amplitude are significantly reduced. Figure 4 The control input curves for two different methods are presented. As can be seen from the figures, after using composite observation compensation, the overall trend of the control input is similar to that of the method without observation compensation, with no divergence or abnormal spikes. This indicates that the method of this invention improves trajectory tracking accuracy without introducing significant drastic fluctuations in the control input. To further demonstrate the effect of the variable gain mechanism compared to the fixed gain mechanism, Figure 5 The error local amplification curves of the fixed-gain composite observation method and the variable-gain composite observation method after a sudden disturbance are presented. It can be seen that after sudden disturbances at 5s and 7s, the error fluctuation amplitude of the fixed-gain composite observation method is relatively large, and there is some oscillation during the recovery process. The variable-gain composite observation method can automatically increase the observation gain during the sudden disturbance phase, reducing the error peak and making the recovery process smoother. These results demonstrate that the variable-gain extended state observer can improve the disturbance estimation and error recovery performance under sudden loads.
[0071] In summary, simulation results show that under complex working conditions such as parameter uncertainty, joint friction, structured periodic disturbances, and sudden external loads, the variable gain composite observer anti-disturbance trajectory tracking control method proposed in this invention can effectively improve the tracking accuracy of the robotic arm joint trajectory, reduce tracking errors and error fluctuations caused by disturbances, and enhance the system's ability to suppress sudden disturbances while maintaining stable control input.
[0072] Example 2 This embodiment provides a disturbance rejection tracking control system for a robotic arm based on a variable gain composite observer, including: The model building module is used to construct the state space model of the n-DOF robotic arm based on its dynamics model. The disturbance classification module is used to classify and model the disturbances of the robotic arm. Disturbances with available prior structural information are classified as structured disturbances, while disturbances that are difficult to model accurately or have uncertainties in online changes are classified as lumped disturbances. The disturbance observation module is used to construct a structured disturbance observer based on the state-space model and the structured disturbance, and output the structured disturbance estimate. The variable gain extended state observation module is used to define the sum of the estimation errors of the lumped disturbance and the structured disturbance as the extended state, and construct an error-driven variable gain extended state observer based on the state space model to output the extended state estimate. The tracking error construction and virtual control quantity calculation module is used to construct the trajectory tracking error and design the virtual control quantity based on the backstepping method. The actual controller module is connected to the disturbance observation module, the variable gain extended state observation module, and the tracking error construction and virtual control quantity calculation module, respectively. It is used to construct the actual controller based on the structured disturbance estimate, the extended state estimate, the trajectory tracking error, and the virtual control quantity, and output the joint control input of the robotic arm. The drive execution module, connected to the actual controller module, is used to apply the control input of the robotic arm joint to the robotic arm joint drive device.
[0073] The descriptions of each embodiment in the above embodiments have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.
[0074] The proposed system can be implemented in other ways. For example, the system embodiments described above are merely illustrative, and the division of modules described above is only a logical functional division. In actual implementation, there may be other division methods. For example, multiple modules may be combined or integrated into another system, or some features may be ignored or not executed.
[0075] Example 3 This embodiment also provides an electronic device, including: one or more processors, one or more memories, and one or more computer programs; wherein, the processor is connected to the memory, and the one or more computer programs are stored in the memory. When the electronic device is running, the processor executes the one or more computer programs stored in the memory to cause the electronic device to perform the method described in Embodiment 1.
[0076] It should be understood that in this embodiment, the processor can be a central processing unit (CPU), or it can be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor, etc.
[0077] Memory may include read-only memory and random access memory, and provides instructions and data to the processor. A portion of memory may also include non-volatile random access memory. For example, memory may also store information about the device type.
[0078] In the implementation process, each step of the above method can be completed by the integrated logic circuits in the processor hardware or by software instructions.
[0079] The method in Embodiment 1 can be directly implemented by a hardware processor, or implemented by a combination of hardware and software modules within the processor. The software modules can reside in readily available storage media in the art, such as random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, or registers. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method. To avoid repetition, a detailed description is not provided here.
[0080] Those skilled in the art will recognize that the units and algorithm steps described in connection with the various examples of this embodiment can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this invention.
[0081] Example 4 This embodiment also provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, complete the method described in Embodiment 1.
[0082] Example 5 Embodiment 5 of the present invention provides a computer program product.
[0083] A computer program product includes software code, wherein the program in the software code performs the steps described in Embodiment 1 of the present invention.
[0084] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. 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 disturbance rejection tracking control method for a robotic arm based on a variable gain composite observer, characterized in that, include: Based on the dynamic model of the n-degree-of-freedom robotic arm, construct its state-space model; The disturbances of the robotic arm are classified and modeled. Disturbances with available prior structural information are classified as structured disturbances, while disturbances that are difficult to model accurately or have uncertain online changes are classified as lumped disturbances. Based on the state-space model and structured perturbation, a structured perturbation observer is constructed. The sum of the lumped disturbance and the structured disturbance estimation error is defined as the extended state. Based on the state space model, an error-driven variable gain extended state observer is constructed. Based on the state variable information of the state space model, a trajectory tracking error is constructed, and a virtual control quantity is designed based on the backstepping method. Based on the state-space model, the actual controller is constructed according to the disturbance estimate of the structured disturbance observer, the extended state estimate of the error-driven variable gain extended state observer, the trajectory tracking error and the virtual control quantity, and outputs the joint control input of the robotic arm. The joint control input of the robotic arm is applied to the joint drive device of the robotic arm.
2. The disturbance rejection tracking control method for a robotic arm based on a variable gain composite observer according to claim 1, characterized in that, The state-space model is represented as follows: In the formula, The nominal nonlinear dynamic term is constructed based on the nominal model of the robotic arm. The nominal input gain matrix is invertible. For robotic arm joint control input, and These represent the structured perturbation and lumped perturbation equivalent to the joint acceleration channel, respectively.
3. The disturbance rejection tracking control method for a robotic arm based on a variable gain composite observer according to claim 1, characterized in that, The disturbance observer is represented as: In the formula, This is an estimate of the external system state. This is an estimate of the structured disturbance; , Given a matrix; The internal state of the observer; The observer gain matrix is... For state variables, The nominal input gain matrix is invertible. The nominal nonlinear dynamic term is constructed based on the nominal model of the robotic arm. This is the input for controlling the robotic arm joints.
4. The disturbance rejection tracking control method for a robotic arm based on a variable gain composite observer according to claim 1, characterized in that, The error-driven variable gain extended state observer is: In the formula, State variables The estimated value; This indicates that the extended state observer is on the state. The observation error; This is an estimate of the expansion state; and It is an error-driven variable gain function; , For design parameters; It is a nonlinear function. The nominal input gain matrix is invertible. The nominal nonlinear dynamic term is constructed based on the nominal model of the robotic arm. This is the input for controlling the robotic arm joints.
5. The disturbance rejection tracking control method for a robotic arm based on a variable gain composite observer according to claim 1, characterized in that, The virtual control quantity is represented as: In the formula, It is a positive definite gain matrix. for The first derivative, For the reference joint trajectory of the robotic arm, This represents the tracking error of the first layer of trajectory.
6. The disturbance rejection tracking control method for a robotic arm based on a variable gain composite observer according to claim 1, characterized in that, The actual control input is: In the formula, The nominal input gain matrix is invertible. It is a positive definite gain matrix. The nominal nonlinear dynamic term is constructed based on the nominal model of the robotic arm. For the second layer of error variables in the backstepping method, This is an estimate of the structured perturbation. For the expansion state estimate, The first derivative of the virtual control quantity. This represents the tracking error of the first layer of trajectory.
7. A disturbance rejection tracking control system for a robotic arm based on a variable gain composite observer, characterized in that, include: The model building module is used to construct the state space model of the n-DOF robotic arm based on its dynamics model. The disturbance classification module is used to classify and model the disturbances of the robotic arm. Disturbances with available prior structural information are classified as structured disturbances, while disturbances that are difficult to model accurately or have uncertain online changes are classified as lumped disturbances. The disturbance observation module is used to construct a structured disturbance observer based on the state-space model and the structured disturbance, and output the structured disturbance estimate. The variable gain extended state observation module is used to define the sum of the estimation errors of the lumped disturbance and the structured disturbance as the extended state, and construct an error-driven variable gain extended state observer based on the state space model to output the extended state estimate. The tracking error construction and virtual control quantity calculation module is used to construct the trajectory tracking error and design the virtual control quantity based on the backstepping method. The actual controller module is connected to the disturbance observation module, the variable gain extended state observation module, and the tracking error construction and virtual control quantity calculation module, respectively. It is used to construct the actual controller based on the structured disturbance estimate, the extended state estimate, the trajectory tracking error, and the virtual control quantity, and output the joint control input of the robotic arm. The drive execution module, connected to the actual controller module, is used to apply the control input to the robotic arm joint drive device.
8. An electronic device, characterized in that, It includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the robotic arm disturbance rejection tracking control method based on a variable gain composite observer as described in any one of claims 1-6.
9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps in the disturbance rejection tracking control method for a robotic arm based on a variable gain composite observer as described in any one of claims 1-6.
10. A computer program product, comprising software code, characterized in that, The program in the software code executes the steps in the disturbance rejection tracking control method for a robotic arm based on a variable gain composite observer as described in any one of claims 1-6.