A method for variable impedance control of spherical joints based on force field sensing and biomimetic strategy learning

Abstract

This invention discloses a spherical joint variable impedance control method based on force field perception and biomimetic strategy learning, belonging to the field of robot control technology. The method includes: establishing a spherical joint dynamic model; constructing an adaptive control module based on Lyapunov stability in a Jacobi-free inverse Cartesian space; designing a perturbation observer based on angular momentum conservation and a recursive least squares force field parameter identification module with an adaptive forgetting factor; designing a retention rate regulator based on the difference between estimated and adaptive impedance to achieve intelligent impedance modulation; designing a biomimetic strategy learning mechanism to use historically optimal parameters for repetitive task initialization; and conducting simulation verification. This invention improves computational efficiency and singularity robustness through inverse-matrix Cartesian space impedance adaptation, solves overfitting problems through intelligent retention rate regulation, and achieves human-like learning-saving characteristics through an explicit memory mechanism, significantly enhancing the robot's adaptability to dynamic and unknown environments.

Description

Technical Field

[0001] This invention belongs to the field of robot control technology, and more specifically relates to a method for variable impedance control of spherical joints with configuration of force field perception and biomimetic strategy learning. Background Technology

[0002] In recent years, as the application boundaries of high-end equipment such as humanoid robots and surgical robots have expanded from structured environments to unstructured, human-robot collaborative scenarios, their ability to proactively adapt to dynamic and unknown environments has become a core challenge. Against this backdrop, variable impedance control, as a key paradigm for achieving compliance and safety in physical interactions, is widely regarded as a crucial technology for enabling robots to cope with environmental uncertainties by simulating the behavior of the human nervous system in regulating the mechanical impedance of limbs. Humans exhibit remarkable adaptability in their interactions with the environment, the core of which lies in their ability to dynamically adjust their limb impedance (especially stiffness) and learn and optimize the impedance behavior required for specific tasks through repeated practice. More importantly, human motor learning mechanisms transcend simple stability, exhibiting advanced characteristics such as conservation, maintenance, and generalization. Among these features, "saving" refers to the ability to relearn faster when encountering familiar perturbations than during the initial learning; "retention" reflects the persistence of learning outcomes, meaning that after a period of undisturbed interval, the error level remains low when re-performing the task, rather than being completely forgotten; and "generalization" allows individuals to flexibly apply acquired task experience to new and similar task situations, achieving knowledge transfer. These advanced learning characteristics are of great significance for robots to achieve rapid reconstruction, stable maintenance, and broad adaptation to interactive tasks in changing environments. However, existing robotic systems have not yet fully replicated these biomimetic learning capabilities.

[0003] Currently, mainstream variable impedance control methods can be divided into two categories: model-based nonlinear adaptive control and data-driven learning. Nonlinear adaptive methods (such as those based on Lyapunov stability theory) provide the theoretical basis for ensuring interaction stability, but their performance heavily depends on the accuracy of the robot model. Data-driven methods (such as reinforcement learning) can reduce dependence on the model, but their exploration process is often limited by safety constraints, making them prone to getting trapped in local optima and difficult to guarantee stability. Further analysis reveals that current variable impedance controllers generally face some common challenges: First, the impedance update law based on tracking error is susceptible to noise and disturbances, often causing the impedance parameter to continuously increase to unnecessarily high levels, resulting in additional energy consumption and safety risks, i.e., the overfitting problem. Secondly, there is an inherent contradiction in the selection of the control space—impedance fitting in joint space is inefficient in Cartesian space due to its reliance on joint errors, and the configuration dependency of the Jacobian matrix easily leads to excessively high operation space impedance near singularities; while fitting directly in Cartesian space cannot avoid frequent Jacobian inverse matrix calculations, resulting in a sharp deterioration in performance near singularities. Furthermore, existing methods generally lack mechanistic embedding of advanced learning characteristics such as "saving," "preservation," and "generalization," making it difficult to achieve long-term retention, rapid retrieval, and flexible transfer of experience like humans. Summary of the Invention

[0004] To address the above technical problems, this invention proposes a method for controlling the variable impedance of a spherical joint by configuring force field sensing and biomimetic strategy learning. The specific technical solution is as follows:

[0005] A method for controlling the variable impedance of a spherical joint by configuring force field sensing and biomimetic strategy learning includes the following steps:

[0006] Step 1, establish the dynamic model of the spherical joint: Consider a three-degree-of-freedom spherical joint, establish the dynamic equations including the inertia matrix, Coriolis force and centripetal force terms, gravity terms, input torque and environmental interaction torque, and introduce constant force, divergent stiffness field and divergent damping field that are independent of error into the interaction torque;

[0007] Step 2, construct the adaptive control module: calculate the Cartesian space adaptive impedance control law without Jacobi inverse matrix, construct the positive definite Lyapunov candidate function by defining the joint space tracking error vector and the impedance parameter adaptive error, and derive the control law and the impedance parameter adaptive law that include dynamic feedforward, adaptive impedance term and error vector.

[0008] Step 3: Design a real-time force field parameter identification module for the perturbation observer: Use a perturbation observer based on angular momentum conservation to estimate the perturbation torque on the end effector of the spherical joint online to avoid dependence on joint acceleration. Map the estimated torque to the end effector using the Tikhonov regularization method. Use a recursive least squares method with an adaptive forgetting factor to identify the stiffness, damping and constant force parameters of the environmental force field in real time. The adaptive forgetting factor is dynamically adjusted based on the statistical characteristics of the estimated residuals and the confidence level constructed by the convergence state of the angular momentum observer.

[0009] Step 4, design the retention rate regulator: By comparing the difference between the norm of the real environmental impedance parameter estimated in Step 3 and the norm of the impedance parameter obtained by adaptation in Step 2, the retention rate parameter is dynamically adjusted. This is achieved using a smooth switching function: when the adaptation is excessive, the retention rate is reduced to allow impedance defitting; when the adaptation is insufficient, the retention rate is increased to enhance the adaptation.

[0010] Step 5, design the biomimetic strategy learning mechanism module: In repetitive tasks, the final impedance parameter learned at the end of the previous task and the historical maximum impedance parameter are used as the initial conditions for the next task. Through explicit recall and reuse mechanism, the controller can directly call the historical optimal parameters for initialization when it encounters the same disturbance field again.

[0011] Step 6: Perform simulation verification on the designed variable impedance controller.

[0012] The beneficial effects of this invention are as follows:

[0013] 1. This invention proposes an online impedance adaptation law in Cartesian space without the Jacobian inverse. By constructing a unified adaptive framework that integrates joint space and workspace errors, this invention directly adjusts impedance parameters online in Cartesian space without calculating the inverse of the Jacobian matrix. This not only improves computational efficiency but also fundamentally overcomes the bottleneck of performance degradation near kinematic singularities in traditional Cartesian space control methods, significantly expanding the stable operation capability of ball joints within the complete workspace.

[0014] 2. This invention proposes an intelligent impedance modulation mechanism based on interference observation. Addressing the common impedance overfitting problem in variable impedance impedance, this invention designs an intelligent modulation strategy based on a variable hold rate. This strategy dynamically adjusts the hold rate by comparing the estimated impedance with the environmental impedance in real time, thereby achieving precise impedance "fitting" and "unfitting," effectively avoiding the ineffective accumulation of impedance parameters. While ensuring tracking performance, it greatly improves energy efficiency and safety during human-computer interaction.

[0015] 3. This invention proposes a biomimetic learning strategy incorporating human-like characteristics. Inspired by the "saving" phenomenon in human motor learning, this invention designs an explicit recall and reuse mechanism. This mechanism enables the controller to actively recall and initialize historically optimal impedance parameters when repeatedly executing tasks, thereby significantly improving the robot's ability to quickly adapt to periodic tasks when faced with previously learned perturbation fields. Attached Figure Description

[0016] Figure 1 A variable impedance control process for a spherical joint with force field sensing and biomimetic strategy learning;

[0017] Figure 2 The graph shows the error components and adaptive parameters of a ball joint under different independent force fields.

[0018] Figure 3 This represents the variation of the Cartesian space trajectory of the end of a spherical joint under different independent force fields. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other. To achieve the above objectives, this invention adopts the following technical solution.

[0020] Please refer to Figure 1 This invention provides a method for controlling the variable impedance of a spherical joint by configuring force field sensing and biomimetic strategy learning. The specific implementation steps are as follows:

[0021] Step 1: Establish a dynamic model of the ball joint;

[0022] Step 2, construct the adaptive control module;

[0023] Step 3: Design the real-time force field parameter identification module for the perturbation observer;

[0024] Step 4: Design the retention rate regulator;

[0025] Step 5: Design the biomimetic strategy learning mechanism module;

[0026] Step 6: Simulate the designed variable impedance controller and obtain the simulation results.

[0027] As described in step 1 of this invention, in order to better observe and verify the motion of the ball joint and the controller, a dynamic model is established based on the ball joint:

[0028] (1)

[0029] in, It is a joint angle vector. It is the joint angular velocity vector. It is time. It is the inertia matrix. It is a matrix representing the Coriolis force and centripetal force terms. It is the gravity term (including terms related to potential energy). It is the torque vector input to the ball joint. This represents the interaction torque generated between the environment and the ball joint end effector. Stiffness and damping disturbances are incorporated into the consideration of external disturbances, while inertial disturbances are intentionally excluded. This approach aims to maintain the consistency of the system's relative order and prevent non-causality. To illustrate the proposed controller, the interaction torque between the environment and the ball joint end effector is considered to be generated by a combination of divergent and error-independent force fields, as shown below:

[0030] (2)

[0031] in, It is the Jacobian matrix of the robotic arm. It belongs to the category of external disturbance constant force (force that is independent of error). It is the Cartesian space stiffness of the divergent force field. It is the Cartesian spatial position error, defined as , and These are the position and desired position vectors of the ball joint end effector, respectively. It is the Cartesian space damping of the divergent force field. The interaction torque can be expressed by a simpler formula:

[0032] (3)

[0033] in, It is the product of the Jacobian matrix and the Cartesian spatial position error matrix, defined as:

[0034] (4)

[0035] in, It represents the error in the X, Y, and Z directions of Cartesian space. It is an identity matrix. In formula (3) It is a vector containing external force field parameters, represented as:

[0036] (5)

[0037] in, It is a column vectorization operator.

[0038] As described in step 2 of this invention, an adaptive impedance control module in Cartesian space is designed. Its core is a control law and parameter update law based on Lyapunov stability. The key innovation of this step lies in achieving Cartesian space impedance adaptation without calculating the inverse Jacobian matrix. The core objective of the controller is to directly adjust the impedance parameters in Cartesian space while avoiding the calculation of the inverse Jacobian matrix, thereby enhancing robustness near singular points. To achieve this objective, firstly, a... This is the tracking error vector in joint space. This vector combines error information related to joint angular position and angular velocity, and its expression is as follows:

[0039] (6)

[0040] in, This represents the joint angle position error. Represents the joint angular velocity error. It is a positive definite gain matrix. (Vector) The introduction of this facilitation facilitates the derivation of subsequent stability analysis. The adaptive error of the impedance parameter is defined as:

[0041] (7)

[0042] in, It is an adaptive Cartesian space impedance parameter. Let be the impedance parameters of the real external force field. To prove the stability of the closed-loop system, a positive definite Lyapunov candidate function is chosen:

[0043] (8)

[0044] in, It is a positive definite matrix (note) (Also positive definite). If If the condition is continuous and negative semi-definite, then the stability of the system can be guaranteed. Therefore, for Differentiation yields a And a control law is derived such that Continuous and From formulas (6) and (8), we can derive:

[0045] (9)

[0046] in, It is the reference acceleration. Applying formulas (1) and (9), we can obtain:

[0047] (10)

[0048] To ensure The following adaptive control law is designed:

[0049] (11)

[0050] This control law includes dynamic feedforward and adaptive impedance terms. ) and error vector ( Substituting the control law into formula (10), and considering the assumed environmental field... This quasi-static property is a safety measure employed in the widespread use of collaborative robots to regulate the speed of the end effector. When the end effector speed exceeds a predetermined threshold, this measure stops the robot's operation. To maintain safety, the reference trajectory of these robots is designed with a low Cartesian velocity, ensuring that the impedance parameters of the end effector change slowly, and their impact on these changes remains negligible. Therefore, it can be considered... This means We can obtain:

[0051] (12)

[0052] To eliminate the parameter error term, the following adaptive law for impedance parameters is designed:

[0053] (13)

[0054] Substituting this adaptive law, the derivative of the Lyapunov function simplifies to:

[0055] (14)

[0056] From formula (14) we can know It is continuous and negative semi-positive definite, therefore, using Barbara's theorem, we arrive at the conclusion. This makes (because (Since it is positive definite), the control law with impedance adaptation ensures the convergence and asymptotic stability of the error. It is noteworthy that the controller adjusts the impedance parameters in Cartesian space without requiring the Jacobian inverse matrix. As previously stated, the control law formula (11) and the impedance adaptation law formula (13) can be used independently for Cartesian impedance adaptation. However, the derived controller accumulates impedance over time and cannot adapt in the absence of an external force field or a low-intensity force field. This impedance accumulation poses a risk to human-machine interaction and requires costly control efforts. Therefore, the focus shifts to techniques for effectively adapting impedance using an adaptively varying hold rate. The hold rate, derived from the difference between the estimated impedance parameters and the adaptive impedance parameters, helps to effectively regulate the impedance adaptation process and provides separation between error-dependent and undependent force fields.

[0057] According to step 3 of this invention, a real-time force field parameter identification module for the perturbation observer is designed (including a perturbation observer, a perturbation force field estimation module, and an adaptive forgetting factor module). First, the perturbation torque experienced by the spherical joint end effector is estimated online using a perturbation observer based on angular momentum conservation, avoiding dependence on joint acceleration. Then, this estimated torque is mapped to the spherical joint end effector using a regularization method, and a recursive least squares method with a forgetting factor is employed to identify the specific parameters of the environmental force field—stiffness, damping, and a constant force independent of error—in real time through the perturbation force field estimation module. Simultaneously, an adaptive forgetting factor module is added to ensure a suitable forgetting rate. Based on the angular momentum of the spherical joint end effector... yes Substituting into formula (1) Differentiation yields:

[0058] (15)

[0059] in, and The relationship between them can be represented as:

[0060] (16)

[0061] Substituting formula (16) into formula (15) yields:

[0062] (17)

[0063] However, because I don't know Therefore, the angular momentum is estimated as:

[0064] (18)

[0065] in, It is the estimated angular momentum. As an estimate of the disturbance torque, where This is the proportional gain of the angular momentum estimation error. Next, the external force field can be estimated based on the estimated disturbance torque and kinematic error.

[0066] The relationship between the Cartesian space kinematics error and the estimated perturbation force can be seen from the perturbation force estimation module as follows:

[0067] (19)

[0068] in, It is the estimated stiffness. It is the estimated damping. It is an estimate of external force that is independent of Cartesian space errors. The estimated interaction force is obtained using the estimated perturbation torque and Tikhonov regularization on the Jacobian matrix, as shown below:

[0069] (20)

[0070] in, is a parameter used to achieve robust inverse near singularities. Although updating the adaptation parameter does not require inverting the Jacobian matrix, equation (20) uses the Jacobian inverse matrix. However, the need for this equation can be eliminated by integrating a torque sensor. The external force field is now estimated using recursive least squares:

[0071] (twenty one)

[0072] in, , It is the estimated stiffness. It is the estimated damping. The estimated interaction force is obtained using the estimated perturbation torque and Tikhonov regularization on the Jacobian matrix, and ,in , It is a Cartesian spatial position error. It is to estimate the gain matrix. It is an adaptive forgetting factor based on confidence assessment:

[0073] (twenty two)

[0074] in, It is the smallest forgetting factor. It is the largest forgetting factor. The confidence level is constructed by estimating the statistical properties of the residuals and the convergence state of the angular momentum observer.

[0075] (twenty three)

[0076] in, It is the residual confidence level. This is the convergence confidence score, based on the error of the angular momentum observer, reflecting the transient performance of the perturbation estimation. The formula is as follows:

[0077] (twenty four)

[0078] in, It is to estimate the residuals. It is the historical mean of the residual variance. It is a sensitivity parameter.

[0079] The retention rate regulator is designed according to step 4 of this invention. A parameter called the "retention rate" is dynamically adjusted by comparing the "currently adaptive impedance" with the "true impedance estimated in the previous step." When the adaptation becomes excessive, the retention rate is decreased to de-adapt (reduce impedance); conversely, it is increased to enhance adaptation, thereby achieving intelligent adjustment of the impedance level. To avoid impedance parameter accumulation, the retention rate is adjusted using the difference between the estimated impedance parameter norm and the adaptive impedance parameter norm, as shown below:

[0080] (25)

[0081] (26)

[0082] (27)

[0083] in, It is the estimated stiffness. It is the estimated damping. The estimated interaction force is obtained using the estimated perturbation torque and Tikhonov regularization on the Jacobian matrix. It is an adaptive stiffness parameter. It is an adaptive damping parameter. It is an adaptive constant force parameter. It is a safety margin, and Therefore, the intuitive form of the retention rate is:

[0084] (28)

[0085] in, It is a smooth switching function that returns 1 when the difference is positive and less than 1 when the difference is negative. It is a 9th-order identity matrix. It is a 3x3 identity matrix. A candidate switching function is:

[0086] (29)

[0087] in, For the set constant, It is the hyperbolic tangent function.

[0088] The biomimetic strategy learning module is designed according to step 5 of this invention. In repetitive tasks, the impedance parameters learned at the end of the previous task are used as the initial values ​​for the next task. This mechanism mimics the motor learning characteristics of humans, enabling the robot to readjust much faster when encountering the same perturbation again. Research shows that humans can relearn faster by using explicit recall strategies, and this result can be used to design a cost-saving strategy. Consider a situation where the task is periodic, or a single task is repeated (multiple trials). To save costs, the controller adjusts the impedance and force during the trial and passes the learned impedance and force values ​​to the beginning of the subsequent trial. That is, the last learned impedance and force value becomes the initial condition of the controller in the subsequent trial, while recording the largest impedance and force parameters that appeared in the previous trial, such as:

[0089] (30)

[0090] (31)

[0091] (32)

[0092] in, , and yes proportional gain, , , These are the values ​​of the adaptive stiffness, damping, and force parameters of the controller at the end of the previous test. , , It represents the maximum values ​​of the adaptive stiffness, damping, and force parameters experienced by the controller at the end of the test. , , This represents the adaptive stiffness, damping, and force parameters of the controller at the start of the next test. This adjustment of initial conditions can save resources. Analogous to human motor learning behavior, when errors exceed a certain threshold, people tend to explicitly recall the best course of action from previous experience to maximize cost savings. This cost-saving strategy is best suited for force-field-aware adaptive impedance regulation because it reduces excessive adaptive impedance and avoids the risk of impedance accumulation caused by over-adaptation.

[0093] As described in step 6 of this invention, a simulation platform for the variable impedance controller is built based on the MATLAB platform. To demonstrate the performance of the proposed controller in different scenarios, different disturbances are provided at each stage of the spherical joint. Note that the experimental environment is set to be subject to noise. After 50 baseline tests, 50 tests are conducted with only a constant force field, followed by 50 tests with only a divergent stiffness field, and then 50 tests with only a divergent damping field. Figure 2 The results demonstrate the ability of the ball joint controller to independently estimate and adapt to different components of the force field. It can also be observed that after the decay phase (experiments 200-250), the controller adapts faster in the re-perturbation phase (experiments 250-400) compared to the initial perturbation phase (experiments 50-200).

[0094] Figure 2 Simulations of a spherical joint using the proposed controller revealed both a force field based on divergent error and an error-independent force field. Three perturbation stages were applied independently: first, a constant force perturbation, highlighted in cyan; second, a stiffness perturbation, highlighted in magenta; and third, a damping perturbation, highlighted in green. The error curves are represented by the blue dashed line, indicating the average error norm of each stage. In the adaptive parameters, the red line represents the norm of the parameter evolution during the experiment, and the blue dashed line represents the norm of the parameter under applied perturbation. Results show that the controller can selectively identify and adapt to different components of the force field in different parts of the experiment.

[0095] Figure 3 Showing Figure 2 Task space analysis at different adaptation stages visually demonstrates faster relearning. The terminal trajectories of the 5th, 10th, 30th, and 50th trials of the ball joint at each stage were selected (black solid line represents the desired trajectory, red solid line represents the 5th trial, green dashed line represents the 10th trial, purple dashed line represents the 30th trial, and pink dashed line represents the last trial). (A) and (B) indicate only applying... Cartesian space trajectory variation diagrams of the end effector of a ball joint under constant force perturbation and constant force re-perturbation; (C) and (D) represent only applying Cartesian space trajectory variation diagrams of the ball joint end effector under stiffness perturbation and stiffness re-perturbation; (E) and (F) indicate only the application of stiffness perturbation. The diagram shows the Cartesian space trajectory changes of the ball joint end effector under damped perturbation and damped re-perturbation. It can be observed that the re-perturbation stage learns faster than the initial perturbation stage in all initial perturbation stages.

[0096] Table 1 will Figure 2 Faster relearning is quantized as a reduction in the error trapezoidal numerical integral, defined as... This provides a more intuitive demonstration of the controller's energy-saving effects.

[0097] Table 1. Savings Results

[0098]

Claims

1. A method for controlling the variable impedance of a spherical joint by configuring force field sensing and biomimetic strategy learning, characterized in that, Includes the following steps: Step 1, establish the dynamic model of the spherical joint: Consider a three-degree-of-freedom spherical joint, establish the dynamic equations including the inertia matrix, Coriolis force and centripetal force terms, gravity terms, input torque and environmental interaction torque, and introduce constant force, divergent stiffness field and divergent damping field that are independent of error into the interaction torque; Step 2, construct the adaptive control module: calculate the Cartesian space adaptive impedance control law without Jacobi inverse matrix, construct the positive definite Lyapunov candidate function by defining the joint space tracking error vector and the impedance parameter adaptive error, and derive the control law and the impedance parameter adaptive law that include dynamic feedforward, adaptive impedance term and error vector. Step 3: Design a real-time force field parameter identification module for the perturbation observer: Use a perturbation observer based on angular momentum conservation to estimate the perturbation torque on the end effector of the spherical joint online to avoid dependence on joint acceleration. Map the estimated torque to the end effector using the Tikhonov regularization method. Use a recursive least squares method with an adaptive forgetting factor to identify the stiffness, damping and constant force parameters of the environmental force field in real time. The adaptive forgetting factor is dynamically adjusted based on the statistical characteristics of the estimated residuals and the confidence level constructed by the convergence state of the angular momentum observer. Step 4, design the retention rate regulator: By comparing the difference between the norm of the real environmental impedance parameter estimated in Step 3 and the norm of the impedance parameter obtained by adaptation in Step 2, the retention rate parameter is dynamically adjusted. This is achieved using a smooth switching function: when the adaptation is excessive, the retention rate is reduced to allow impedance defitting; when the adaptation is insufficient, the retention rate is increased to enhance the adaptation. Step 5, design the biomimetic strategy learning mechanism module: In repetitive tasks, the final impedance parameter learned at the end of the previous task and the historical maximum impedance parameter are used as the initial conditions for the next task. Through explicit recall and reuse mechanism, the controller can directly call the historical optimal parameters for initialization when it encounters the same disturbance field again. Step 6: Perform simulation verification on the designed variable impedance controller.

2. The spherical joint variable impedance control method based on force field sensing and biomimetic strategy learning according to claim 1, characterized in that, The dynamic model described in step 1 is as follows: (1) in, It is a joint angle vector. It is the joint angular velocity vector. It is time. It is the inertia matrix. It is a matrix representing the Coriolis force and centripetal force terms. It is the gravity term. It is the torque vector input to the ball joint. This represents the interaction torque generated between the environment and the ball joint end effector. The interaction torque is produced by a combination of divergent and error-independent force fields, as shown below: (2) in, It is the Jacobian matrix of the robotic arm. It belongs to the external disturbance constant force. It is the Cartesian space stiffness of the divergent force field. It is the Cartesian spatial position error, defined as , and These are the position and desired position vectors of the ball joint end effector, respectively. It is the Cartesian space damping of the divergent force field; the interaction torque is expressed by a simpler formula as: (3) in, It is the product of the Jacobian matrix and the Cartesian spatial position error matrix, defined as: (4) in, It represents the error in the X, Y, and Z directions of Cartesian space. It is an identity matrix; in formula (3) It is a vector containing external force field parameters, represented as: (5) in, It is a column vectorization operator.

3. The spherical joint variable impedance control method based on force field sensing and biomimetic strategy learning according to claim 1, characterized in that, In step 2: definition This is the tracking error vector in joint space, and its expression is as follows: (6) in, This represents the joint angle position error. Represents the joint angular velocity error. It is a positive definite gain matrix, and the adaptive error of the impedance parameter is defined as: (7) in, It is an adaptive Cartesian space impedance parameter. The impedance parameters are those of the real external force field; a positive definite Lyapunov candidate function is selected: (8) in, It is a positive definite matrix, if If the condition is continuous and negative semi-definite, then the system is stable. Therefore, for Differentiation yields a And a control law is derived such that Continuous and From formulas (6) and (8), we can derive: (9) in, The reference acceleration is given by substituting formula (1) into formula (9): (10) To ensure The following adaptive control law is designed: (11) Substituting the control law into formula (10), we assume that... ,but ,get: (12) Design an adaptive law for the following impedance parameters: (13) Substituting this adaptive law, the derivative of the Lyapunov function simplifies to: (14)。 4. The spherical joint variable impedance control method based on force field sensing and biomimetic strategy learning according to claim 1, characterized in that, In step 3: Based on the angular momentum of the ball joint end effector yes Substituting into formula (1) Differentiation yields: (15) in, and The relationship between them is represented as follows: (16) Substituting formula (16) into formula (15) yields: (17) However, because I don't know Therefore, the angular momentum is estimated as: (18) in, It is the estimated angular momentum. As an estimate of the disturbance torque, where It is the proportional gain of the angular momentum estimation error.

5. The spherical joint variable impedance control method based on force field sensing and biomimetic strategy learning according to claim 4, characterized in that, Step 3 further includes: From the perturbation field estimation module, the relationship between the Cartesian space kinematic error and the estimated perturbation force is as follows: (19) in, It is the estimated stiffness. It is the estimated damping. It is an estimate of external force that is independent of Cartesian space errors. The estimated interaction force is obtained using the estimated perturbation torque and Tikhonov regularization on the Jacobian matrix, as shown below: (20) in, It is a parameter used to implement robust inverses near singularities.

6. The spherical joint variable impedance control method based on force field sensing and biomimetic strategy learning according to claim 5, characterized in that, Step 3 further includes: The external force field is estimated using the recursive least squares method as follows: (21) in, , It is the estimated stiffness. It is the estimated damping. The estimated interaction force is obtained using the estimated perturbation torque and Tikhonov regularization on the Jacobian matrix, and ,in , It is a Cartesian spatial position error. It is to estimate the gain matrix. It is an adaptive forgetting factor based on confidence assessment: (22) in, It is the smallest forgetting factor. It is the largest forgetting factor. The confidence level is constructed by estimating the statistical properties of the residuals and the convergence state of the angular momentum observer. (23) in, It is the residual confidence level. It is the convergence confidence score, and the formula is as follows: (24) in, It is to estimate the residuals. It is the historical mean of the residual variance. It is a sensitivity parameter.

7. The spherical joint variable impedance control method based on force field sensing and biomimetic strategy learning according to claim 6, characterized in that, In step 4, The retention rate is adjusted by utilizing the difference between the estimated impedance parameter norm and the adaptive impedance parameter norm, as shown below: (25) (26) (27) in, It is the estimated stiffness. It is the estimated damping. The estimated interaction force is obtained using the estimated perturbation torque and Tikhonov regularization on the Jacobian matrix. It is an adaptive stiffness parameter. It is an adaptive damping parameter. It is an adaptive constant force parameter. It is a safety margin, and Therefore, the intuitive form of the retention rate is: (28) in, It is a smooth switching function that returns 1 when the difference is positive and less than 1 when the difference is negative. It is a 9th-order identity matrix. Given a 3x3 identity matrix, a candidate switching function is: (29) in For the set constant, It is the hyperbolic tangent function.

8. The method for controlling the variable impedance of a spherical joint by configuring force field sensing and biomimetic strategy learning according to claim 7, characterized in that, In step 5, the specific design of the retention rate regulator is as follows: record the maximum impedance and force parameters that occurred in previous tests, such as: (30) (31) (32) in , and yes proportional gain, , , These are the values ​​of the adaptive stiffness, damping, and force parameters of the controller at the end of the previous test. , , It represents the maximum values ​​of the adaptive stiffness, damping, and force parameters experienced by the controller at the end of the test. , , This represents the values ​​of the adaptive stiffness, damping, and force parameters of the controller at the start of the next test.

9. The method for controlling the variable impedance of a spherical joint by configuring force field sensing and biomimetic strategy learning according to claim 1, characterized in that, The simulation verification in step 6 specifically includes: A simulation environment incorporating noise effects was built on the MATLAB platform. After setting 50 baseline tests, 50 tests were conducted in sequence for a constant force field only, a divergent stiffness field only, and a divergent damping field only. After 50 decay phases, the re-perturbation phase tests for each force field were conducted again.

10. An electronic device, characterized in that, include: One or more processors; A memory for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method of any one of claims 1 to 9.

Images