Joint robot singular system control method based on interval type-2 fuzzy sliding mode

Abstract

The invention provides a joint robot singular system control method based on an interval type-2 fuzzy sliding mode, and the method comprises the steps: sensing and quantifying the dynamic drift of a singular region caused by the change of a tail end load in real time, and constructing a dynamic singular interval; inputting the dynamic singular interval into an interval type-2 fuzzy system, and outputting a disturbance prediction interval and a nominal disturbance prediction quantity; generating a dynamically adjusted sliding mode surface according to the uncertainty reflected by the disturbance prediction interval; fusing nominal dynamics feed-forward compensation, correction feedback based on a sliding mode surface and feed-forward disturbance compensation based on nominal disturbance predictive quantity to synthesize a final joint control moment; the final joint control torque is executed, the actual response is collected, closed-loop evaluation is formed, and online correction is conducted on the dynamic singular interval according to the closed-loop performance. The method can sense and actively adapt to dynamic drifting of the singular area in real time so that it can be guaranteed that when the robot passes through the time-varying singular area under the complex working condition, the dynamic drifting of the time-varying singular area can be accurately detected. And high-precision and high-stability trajectory tracking can still be realized.

Description

Technical Field

[0001] This disclosure relates to the field of industrial robot control, and in particular to a control method for singular articulated robot systems based on interval type II fuzzy sliding mode. Background Technology

[0002] Multi-joint industrial robots need to maintain continuous and stable motion control performance within their workspace when performing trajectory tracking tasks. However, singular configurations in robot kinematics have long been a technical challenge. When a robot approaches a singular pose, its motion control matrix becomes ill-conditioned, leading to abnormal joint velocity calculations, increased tracking errors, and decreased system stability.

[0003] To address this issue, existing technologies typically trigger avoidance strategies by monitoring the singular values ​​of the Jacobian matrix and setting a fixed threshold. This approach is applicable when robot dynamics parameters remain constant. However, in many real-world industrial scenarios, robot end effectors are often equipped with eccentric tools such as welding torches or grippers. The eccentricity of the load changes in real-time with variations in the robotic arm's posture, altering the overall inertia distribution and dynamic characteristics of the system. This makes static discrimination methods based on fixed singular thresholds unable to accurately match the system's real-time state. In this case, static discrimination methods based on fixed thresholds reveal their inherent limitations: they cannot accurately follow real-time changes in singular regions, causing the controller to either intervene prematurely, resulting in lost motion performance, or exhibit a delayed response, failing to provide sufficient robustness in truly hazardous areas. Ultimately, this affects the robot's control accuracy and reliability in variable load, highly dynamic tasks.

[0004] Therefore, there is an urgent need for a control method that can sense and actively adapt to the dynamic drift of singular regions in real time, so as to ensure that the robot can still achieve high-precision and high-stability trajectory tracking when traversing time-varying singular regions under complex working conditions. Summary of the Invention

[0005] In view of this, in order to solve the problems caused by the prior art, this application provides a control method for singular articulated robot systems based on interval type II fuzzy sliding mode.

[0006] In a first aspect, this disclosure provides a control method for a singular articulated robot system based on interval type II fuzzy sliding mode, the method comprising: S1. Real-time sensing and quantification of the dynamic drift of singular regions caused by changes in end-load, and construction of dynamic singular intervals; S2. Input the dynamic singular interval into the interval type II fuzzy system and output the disturbance prediction interval and the nominal disturbance prediction quantity; S3. Based on the uncertainty reflected by the disturbance prediction interval, a dynamically adjustable sliding surface is generated; S4. The nominal dynamic feedforward compensation, the correction feedback based on the sliding surface, and the feedforward disturbance compensation based on the nominal disturbance prediction are integrated to synthesize the final joint control torque. S5. Execute the final joint control torque and collect the actual response to form a closed-loop evaluation, and make online corrections to the dynamic singular interval based on the closed-loop performance.

[0007] Optionally, S1 includes: Simultaneously collect joint motion state and end-effector load parameters, calculate the increase in equivalent rotational inertia of the joint caused by the end-effector load, and calculate the singular values ​​of the Jacobian matrix based on the current robot configuration; The singular values ​​are smoothed to obtain the singularity measure; Based on the singularity metric, a numerical interval with dynamically updated upper and lower boundaries is generated, which serves as the dynamic singular interval.

[0008] Optionally, S2 includes: Extract scalar features representing the degree of singularity risk and their corresponding uncertainty widths from the dynamic singular intervals; Using the scalar features and the uncertainty width as input, the upper and lower bounds of the equivalent perturbation are estimated through interval type II fuzzy inference; The upper bound estimate and the lower bound estimate constitute the disturbance prediction interval, and the midpoint value is calculated as the nominal disturbance prediction amount.

[0009] Optionally, S3 includes: Based on the aforementioned disturbance prediction interval, calculate the normalized disturbance ratio, which reflects the global uncertainty level; The global dynamic contraction factor is determined based on the normalized perturbation ratio, and the local safety factor is determined based on the equivalent rotational inertia increment of each joint. By integrating the global dynamic contraction factor, the local safety factor, and the preset basic sliding mode gain, a time-varying sliding mode gain is generated for each joint; A dynamically adjustable sliding surface is constructed using the time-varying sliding mode gain and joint trajectory tracking error.

[0010] Optionally, the global dynamic contraction factor is determined based on the normalized perturbation ratio, satisfying the following relationship: ,in, The global dynamic contraction factor, The normalized perturbation ratio is given. and These are the preset minimum and maximum shrinkage coefficients, respectively; The determination of the local safety factor based on the equivalent rotational inertia increment of each joint satisfies the following relationship: ,in, Let be the local safety factor of the i-th joint. Let be the equivalent rotational inertia increment of the i-th joint. This is the preset inertia sensitivity coefficient.

[0011] Optionally, S4 includes: Based on the desired trajectory and the current value of the sliding surface, the nominal compensation torque is calculated; The sliding mode gain amplification factor is dynamically adjusted based on the disturbance prediction range and the nominal disturbance prediction amount, and the sliding mode correction torque is constructed using a saturation function; The nominal compensation torque, the sliding mode correction torque, and the feedforward disturbance compensation torque based on the nominal disturbance prediction are superimposed to obtain the final control torque of each joint.

[0012] Optionally, the sliding mode gain amplification factor is dynamically adjusted based on the disturbance prediction interval and the nominal disturbance prediction amount, satisfying the following relationship: ,in, Let be the sliding mode gain amplification factor for the i-th joint; This is the preset base value; The nominal disturbance prediction value; The width of the disturbance prediction interval; and This is the preset gain adjustment coefficient.

[0013] Optionally, S5 includes: The final joint control torque is applied to the physical joint, and the actual joint angle and angular velocity are measured simultaneously. Based on the measured data, the closed-loop tracking error, the closed-loop sliding mode surface value, and the singularity metric based on the actual pose are recalculated, and a stability index is constructed accordingly. Based on the deviation between the stability index and a preset reference value, the upper and lower boundaries of the dynamic singular interval are adjusted, and the adjusted interval is used for the next control cycle. Secondly, this disclosure provides an electronic device including a memory and at least one processor. The memory stores a computer program, and the processor executes the computer program to implement the method described in the first aspect.

[0014] Thirdly, this disclosure provides a computer storage medium storing a computer program that, when executed, implements the method described in the first aspect.

[0015] The beneficial effects of this disclosure are that, compared with the prior art, this disclosure has the following advantages: 1) By real-time acquisition of joint motion states and end-effector load parameters, the equivalent inertia increment of the joint caused by the load is calculated, and singular value analysis of the updated Jacobian matrix is ​​integrated to construct a dynamically changing singular region, replacing the traditional fixed threshold discrimination method. This disclosure effectively solves the problem that static thresholds cannot accurately follow the real-time drift of the robot's singular region caused by end-effector eccentric load, enabling the control system to perceive and quantify the dynamic changes of singular risks in real time, providing an accurate and adaptive singular state description for subsequent control decisions.

[0016] 2) By mapping the dynamic singular interval to the input of an interval type II fuzzy system and utilizing the system's ability to handle uncertainty, the predicted interval and nominal predicted value of the equivalent disturbance are output. This disclosure overcomes the shortcomings of traditional methods in inaccurate disturbance estimation when facing uncertainties caused by singular drift, and provides the controller with a forward-looking disturbance estimate that includes the range of variation. This enables the control system to generate targeted compensation strategies in advance, significantly enhancing the system's adaptability and robustness to unmodeled dynamics and load changes.

[0017] 3) Based on the uncertainty reflected in the disturbance prediction interval, the sliding surface parameters and sliding feedback gain are dynamically adjusted in layers. The sliding surface parameters are dynamically constructed and the final control law is synthesized, realizing real-time adaptive adjustment of sliding mode convergence strength and control torque. This disclosure solves the problem that traditional sliding mode control is difficult to balance control performance and chattering suppression near singular regions. By rationally allocating control resources while ensuring trajectory tracking convergence speed, a balance between high-precision tracking and system stability is achieved, effectively suppressing control input chattering caused by model uncertainty and drastic changes.

[0018] 4) By driving physical joints to execute control laws and collecting actual responses, a closed-loop stability assessment and parameter update mechanism is formed. This disclosure solves the limitation that open-loop or static parameter control strategies cannot self-optimize in long-term operation, enabling the judgment of singular risks, the confidence level of disturbance prediction, and the key parameters of the controller to be calibrated online based on actual operating performance. This ensures the continuous stability and control accuracy of the entire control system under actual complex operating conditions, realizing robust control throughout the entire lifecycle from theoretical design to actual service. Attached Figure Description

[0019] The accompanying drawings, which are incorporated in and form a part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure.

[0020] Figure 1 A flowchart of the singular system control method for articulated robots based on interval type II fuzzy sliding mode provided in this disclosure is shown. Figure 2A flowchart of dynamic singularity sensing and perturbation interval prediction provided in an embodiment of this disclosure is shown; Figure 3 A flowchart illustrating the adaptive sliding mode control torque synthesis process provided in an embodiment of this disclosure is shown.

[0021] The accompanying drawings have illustrated specific embodiments of this disclosure, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concepts of this disclosure to those skilled in the art through reference to particular embodiments. Detailed Implementation

[0022] The present disclosure will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present disclosure and should not be used to limit the scope of protection of the present disclosure.

[0023] The components of the embodiments of the invention described and illustrated herein can typically be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0024] In the following, the terms “comprising,” “having,” and their cognates, which may be used in various embodiments of the invention, are intended only to indicate a particular feature, number, step, operation, element, component, or combination thereof, and should not be construed as excluding, firstly, the presence of one or more other features, numbers, steps, operations, elements, components, or combinations thereof, or adding the possibility of one or more features, numbers, steps, operations, elements, components, or combinations thereof.

[0025] Unless otherwise specified, all terms used herein (including technical and scientific terms) shall have the same meaning as commonly understood by one of ordinary skill in the art to which the various embodiments of the invention pertain. Terms (such as those defined in commonly used dictionaries) shall be interpreted as having the same meaning as in their contextual meaning in the relevant technical field and shall not be interpreted as having an idealized or overly formal meaning, unless clearly defined in the various embodiments of the invention.

[0026] Before proceeding to the formal steps, the following terms in this invention need to be explained: Singularity: In robot kinematics, singularity refers to the state in which the rank of the Jacobian matrix of a robotic arm decreases when it is in certain specific configurations, resulting in the loss of motion capability of the end effector in certain directions or the need for joint velocities to approach infinity in order to achieve small displacements.

[0027] The Jacobian matrix is ​​a mathematical tool used to describe the linear mapping between robot joint velocities and the linear and angular velocities of the end effector. Its elements are determined by the robot's configuration parameters, and the singularity of the matrix directly reflects the kinematic performance of the robot in its current posture. By using singular value decomposition to decompose the Jacobian matrix, the robot's motion flexibility and singular proximity can be quantitatively evaluated.

[0028] Interval Type-2 Fuzzy System: This is an extension of fuzzy logic systems. Its membership function is an interval value rather than a definite value, which can more effectively handle system uncertainty, measurement noise and linguistic ambiguity.

[0029] Sliding Mode Control (SMC) is a nonlinear control strategy based on variable structure systems. Its core idea is to design a sliding surface and use a control law to drive the system state to reach and maintain motion on the sliding surface within a finite time.

[0030] Dynamic Interval: refers to the range of values ​​whose upper and lower bounds are updated in real time as the system state changes over time. It is used to characterize the feasible region of system uncertainty, risk level, or control variables.

[0031] Disturbance: In a control system, disturbance refers to external or internal factors that affect the output of the controlled object but are unrelated to the control input. These include unmodeled dynamics, parameter uncertainties, external load variations, and measurement noise. In this invention, disturbance mainly refers to the equivalent torque or motion error caused by changes in the robot's singular configuration, end-effector load dynamic coupling, and environmental interaction. Specifically, when the robot approaches a singular configuration, its Jacobian matrix tends to be ill-conditioned, leading to significant errors or even inaccuracies in velocity planning based on kinematic models or torque calculations based on dynamic models. This control difficulty caused by model failure or a sharp decline in performance is characterized as a significant equivalent disturbance in the control system. Therefore, a measure of the degree of singular approach can be used to indirectly predict the magnitude of such disturbances.

[0032] Figure 1 The flowchart of the singular system control method for articulated robots based on interval type II fuzzy sliding mode provided in the embodiments of this disclosure is as follows: Figure 1 As shown, the process may include the following steps: S1: Real-time sensing and quantification of the dynamic drift of singular regions caused by changes in end-load, and construction of dynamic singular intervals.

[0033] The system senses and quantifies the dynamic changes in singular regions caused by eccentric loading at the robot's end effector in real time, transforming these changes into a dynamic numerical range with upper and lower bounds. This provides an accurate, time-varying description of singular risks for subsequent intelligent control decisions. Detailed procedures for constructing this dynamic singular range and predicting subsequent disturbances can be found in [link to relevant documentation]. Figure 2 The flowchart shown illustrates the dynamic singularity sensing and perturbation interval prediction process. It is implemented through the following sub-steps.

[0034] S1.1: Synchronously collect joint angle, angular velocity, and end-load mass and eccentricity parameters.

[0035] First, real-time kinematic data of each joint of the robot and known physical parameters of the end effector load are collected synchronously. For the i-th joint, the raw angle measurement value at the current time t is directly read through its built-in high-precision encoder, and this value is directly defined as the real-time angle of that joint. Where i is the joint number, and for a typical 6-8 degree-of-freedom industrial robotic arm, the value of i ranges from 1 to n. The vector formed by the angles of all joints is defined as follows: .

[0036] Meanwhile, in order to obtain velocity information of joint movement, a fixed control sampling period is used. The angle values ​​at consecutive time points are calculated using differential methods. Specifically, the joint angular velocity at the current time t... Through formula Calculated. Sampling period. The typical value range is 1-10 milliseconds, in order to balance the requirements of real-time performance and data smoothness.

[0037] Besides the joint's own motion, the dynamic parameters of the tool carried by the end effector are crucial. The mass of the end effector load is read from a preset process database or calibration file. and the eccentricity of its center of mass relative to the robot's end flange coordinate system In applications such as welding and handling, The typical value range is 2-4 kg. The typical range of values ​​is 0.05-0.25 meters. These fundamental variables form the starting point for describing the complete physical scenario of the actual robotic arm posture plus the actual eccentric load.

[0038] When the control system starts, the initial value of the preset dynamic singular interval is... .

[0039] This step models the robot body and the working tool as a unified dynamic system, providing real and synchronous input data for subsequent accurate analysis of the impact of load changes on the singular characteristics of the overall system, and ensuring the consistency between singular drift analysis and real working conditions.

[0040] S1.2: Calculate the equivalent rotational inertia increments of each joint caused by the end-effector load under the current robot configuration.

[0041] Based on the joint angle sequence obtained in the previous sub-step And end-effector load parameters. This step quantitatively calculates the specific impact of eccentric load on the dynamic characteristics of each joint of the robot, specifically manifested as the equivalent rotational inertia increment of each joint.

[0042] First, calculate the equivalent moment of inertia of the end load itself relative to a specific axis of its center of mass. In terms of load quality and eccentricity In cases where the inertia is typically constant during a single task, this inertia can be simplified to... Although its value may be constant, it is still based on... This is to emphasize its effectiveness in terms of temporal correlation.

[0043] The effect of this end effector inertia on each joint is not equal, but rather varies depending on the robot's current geometry (as determined by the angle vector). (Description) Coupling and allocation are performed. Therefore, an attitude-related coupling coefficient needs to be calculated for each joint i. The coefficient ranges from 0 to 1 and is determined by the robot's kinematic model and geometric parameters. It accurately reflects the proportion of the end effector's rotational inertia transmitted to the i-th joint via the kinetic chain.

[0044] Finally, the equivalent inertia increment introduced by the i-th joint at time t due to the end-effector load is... From the formula This calculation explicitly and quantitatively maps the dynamic effects of the remote load to each joint, thereby transforming the abstract load influence into a concrete physical quantity that can be used in subsequent singular value analysis of the Jacobian matrix, laying the dynamic foundation for singular drift analysis.

[0045] S1.3: Update the Jacobian matrix, calculate and smooth its minimum singular value to obtain a stable singular metric.

[0046] The obtained joint inertia increments are fed back into the robot's kinematic model, thereby updating the key indicator for evaluating the singularity of the system, namely the minimum singular value of the Jacobian matrix.

[0047] Based on the joint angle vector acquired at the current moment Calculate the Jacobian matrix of the robot in this pose. Joint inertia increment It reflects the changes in dynamic state caused by end-load. Although the Jacobian matrix is ​​essentially a kinematic quantity, its calculation depends only on the joint angle vector. However, changes in the dynamic state are an important background for predicting the evolution of singular risks. In subsequent singular value analysis and controller parameter adjustments, information on the kinematic configuration (Jacobi matrix) and dynamic load (increment of inertia) will be integrated. Therefore, the current dynamic background will be comprehensively analyzed during the subsequent singular value decomposition process.

[0048] For the updated Jacobian matrix Perform singular value decomposition and extract the minimum value among all singular values, denoted as . This value is a scalar that directly reflects how close the current pose is to the singular configuration: The smaller the value, the worse the robot's mobility and the closer it is to a singular state.

[0049] Because it is calculated directly from sensor data and models The singular values ​​may contain high-frequency noise or minute jitter. To obtain a feature quantity that can stably reflect the singular drift trend, the original singular values ​​need to be smoothed. Here, a first-order exponential smoothing method is used to obtain the smoothed singular metric. Its calculation formula is .in, This is the smoothed value from the previous sampling period, and β is the smoothing coefficient, selected based on the robotic arm's structural stiffness, motion speed, and system noise level. A typical value range is between 0.7 and 0.95, and this coefficient is determined through system identification or offline experiments. The physical meaning of this smoothing process is to perform low-pass filtering on the original singular value signal. Its technical effect is to filter out high-frequency fluctuations caused by measurement noise or minor joint jitter, while retaining the low-frequency trend of the true drift of the singular region due to load changes or configuration alterations. The resulting smoothed singularity metric... This becomes a continuous and traceable singular trend feature, providing a stable and reliable input for subsequent construction of the dynamic range and avoiding misjudgments by the controller due to noise. This processing effectively suppresses instantaneous fluctuations, making... It becomes a continuous and traceable singular trend feature, providing a stable input for constructing dynamic intervals.

[0050] S1.4: Based on the smoothed singularity metric, the upper and lower boundaries of the dynamic singular interval are generated through the singularity proximity index.

[0051] Based on smoothed singularity metric Construct a dynamic range that can intuitively and quantitatively represent the current singular risks and their range of uncertainty. .

[0052] First, define a term called the singular proximity index. A dimensionless index. This index is obtained by using a preset reference singular threshold. With smooth singularity measure The ratio is used to construct the fraction. To prevent the denominator from being zero, a very small bias ε is added, i.e. , where reference threshold Based on engineering experience, the typical value range is 0.05-0.2. The physical meaning of this formula lies in transforming dimensional singular values ​​into a dimensionless singularity risk index. Its technical effect is to achieve a nonlinear amplification indication of approaching singular states: when the robot's motion flexibility is high and the singular value is large, the index is close to zero, indicating low singular risk; when the robot approaches a singularity and the singular value decreases, the index increases rapidly, thus generating a highly sensitive warning for high-risk areas. This nonlinear amplification characteristic allows the control system to detect singular threats in advance, buying time for subsequent adjustments to the control strategy. When smoothing the singularity measure... When it approaches 0, It will increase significantly. The larger the value of ε, the closer the current state of the system is to the singular region; ε is a very small positive number to prevent the denominator from being zero. This value is set to a fixed small constant in advance according to the numerical accuracy requirements of the system, such as 0.001. The synonymous parameters below are all represented by ε.

[0053] Then, using This generates the upper and lower boundaries of the dynamic interval. Define the lower bound of the interval. upper bound of the interval .in, and The range scaling factor satisfies 0 < < The typical value ranges for these two coefficients are 0.8-1.2 and 1.5-2.5, respectively. These coefficients are preset based on engineering experience and the required system safety margin. By appropriately setting these two coefficients, the width of the interval can be adjusted to adapt to different safety margin requirements in different application scenarios. When the singular risk increases, i.e. Increase, the entire interval This will shift upwards and may widen, thus dynamically defining the possible range of exotic risks.

[0054] In the technical solution of this disclosure, by synchronously collecting joint motion states and end-effector load parameters, the equivalent inertia increment of the joints caused by the eccentric load at the end of the robotic arm is calculated in real time, thereby integrating the load dynamics influence into the singular value analysis of the Jacobian matrix. By smoothing the minimum singular value and constructing a singular interval with dynamically updated upper and lower bounds, a real-time, quantitative characterization of singular risks and their uncertainties is achieved. This method overcomes the shortcomings of traditional fixed threshold discrimination methods that cannot adapt to singular region drift caused by load changes, providing an accurate and time-varying description of singular states for subsequent control decisions, thus laying an accurate perception foundation for the robot to stably traverse singular regions under varying load conditions.

[0055] S2: Input the dynamic singular interval into the interval type II fuzzy system and output the disturbance prediction interval and the nominal disturbance prediction quantity.

[0056] The dynamic singular interval output in step S1 This is transformed into a disturbance prediction range that can be used for feedforward compensation. The singular risk information in interval form is processed into input features suitable for fuzzy inference. Then, an interval-type II fuzzy system is used to handle the uncertainty in the input, and the upper and lower bound estimates of the equivalent dynamic disturbance are mapped through fuzzy inference rules. Finally, a disturbance prediction interval containing the nominal value is output, providing a forward-looking and quantitative compensation basis for the robust design of the controller. This is achieved through the following sub-steps.

[0057] S2.1: Extract scalar singular input quantities and their interval widths from the dynamic singular intervals, and use them as inputs to the fuzzy system.

[0058] Based on the upper and lower bounds of the dynamic singular interval obtained in step S1 and Feature extraction is performed to generate two key quantities: an interval width representing the magnitude of uncertainty, and a comprehensive scalar input for driving fuzzy inference. First, the width of the current singular interval is calculated. Its value is the difference between the upper and lower bounds, i.e. This width directly reflects the confidence level or uncertainty of the system's judgment on its singular proximity. The larger the value, the more severe the singular drift caused by dynamic changes in the end load, or the more significant the uncertainty in the system modeling. This information is crucial for subsequent design to adapt to control strategies that address uncertainties.

[0059] To transform bounded interval information into a single numerical input that a fuzzy inference system can process, a scalar singular input quantity needs to be constructed. The design goal of this quantity is to simultaneously reflect the central tendency and range information of singular risks. This is achieved here by taking the midpoint of the range, i.e. Through this calculation, the original interval information is synthesized into a single scalar feature. And an auxiliary quantity describing the range of uncertainty of this feature. Scalar The numerical synthesis reflects the degree to which the system approaches a singular state and the range of uncertainty in the assessment. A larger value generally means a higher singular risk and a more uncertain assessment. This transformation converts the dynamic and uncertain description of singular risk into a standardized input form that the fuzzy logic system can directly receive and process.

[0060] S2.2: Construct an interval type II fuzzy membership function for a scalar input whose uncertainty is adjusted by the interval width.

[0061] Obtain scalar singular input and its corresponding interval width Then, it is input into a pre-defined interval type II fuzzy inference system, and the corresponding upper and lower membership functions are constructed. The core advantage of interval type II fuzzy logic is that its membership function itself is a region on a plane rather than a single line. This region is characterized by upper and lower boundaries, thus naturally and directly describing the uncertainty in the input signal.

[0062] First, input the scalar. By performing linear normalization, the input is transformed to the 0-1 interval, resulting in a dimensionless input. The normalization process relies on global parameters pre-defined based on the robot's workspace and singularity threshold analysis, namely the minimum singularity index. With the maximum singularity index The calculation formula is: This ensures that inputs under different operating conditions can be measured on a uniform scale.

[0063] The fuzzy system predefines multiple semantic levels, such as low singularity, medium singularity, and high singularity. For each level k, a membership function is defined. above membership function Membership function The traditional membership function form of a triangle can be used, based on its left boundary. Peak point and right boundary Confirm, when input When located in different intervals, their membership degree is calculated through linear relationships.

[0064] In order to incorporate the uncertainty information carried by the input... Embedded into the fuzzy reasoning process, upper membership function The support interval needs to be dynamically expanded based on the membership function. Expansion amount With interval width Proportional, that is ,in, The interval expansion coefficient is preset using fuzzy system design experience to adjust the degree of influence of uncertainty on the membership function. Therefore, the effective boundary of the upper membership function becomes... and This design allows for changes in interval width. When the upper membership function is larger, indicating higher input uncertainty, its coverage is broader. The fuzzy system automatically considers a wider range of possibilities during inference, thus making its output more robust to uncertainty. The upper and lower membership functions together constitute a fuzzy set, the size of which is directly determined by the input uncertainty. adjust.

[0065] S2.3: Calculate the activation intensity of the fuzzy rule and obtain the upper and lower bound estimates of the equivalent disturbance amplitude by defuzzification.

[0066] After the fuzzy membership degree calculation is completed, fuzzy inference is performed. Fuzzy inference is the core computational process of the interval-type II fuzzy system. Based on a pre-set fuzzy rule base, it maps the fuzzy sets of input variables to the fuzzy sets of output variables through logical operations. Specifically, this step transforms expert knowledge based on linguistic rules into numerical estimates of the upper and lower bounds of equivalent perturbations.

[0067] K fuzzy rules are predefined, which establish the correlation between the degree of singular risk and the equivalent disturbance based on robot dynamics and control experience. Each rule consists of a premise and a conclusion. The premise corresponds to a specific input fuzziness level, and the conclusion corresponds to a numerical base value representing a typical disturbance amplitude. These rules specifically embody empirical knowledge in robot control: when the robot approaches a low degree of singularity, the expected equivalent disturbance torque is small; when approaching a moderate degree of singularity, the expected disturbance torque increases accordingly; and when approaching a high degree of singularity, the expected disturbance torque increases significantly. In practical systems, these rules and their corresponding baseline values ​​can be determined through offline experiments or online learning to adapt to the needs of specific robot models and control tasks.

[0068] For the current input, the premise of each rule will be activated to varying degrees. The activation strength of the lower-level rules for the k-th rule is... The degree of membership of the antecedent of the rule is directly taken as the lower membership degree of the corresponding fuzzy level. Similarly, its upper-layer activation intensity Then take the upper membership degree. .

[0069] Subsequently, a weighted average method was used to defuzzify all activated rules, and the perturbation estimates were calculated for each rule. Compared with the above perturbation estimate The specific calculations are as follows: ; Here, ε is a very small positive number used to prevent the denominator from being zero, ensuring numerical stability. The physical meaning of this defuzzification calculation lies in the weighted fusion of rule conclusions based on the current activation level of each fuzzy rule, thereby transforming the verbalized fuzzy reasoning result into a deterministic numerical output. Its technical effect in control systems is the realization of the fusion and quantification of uncertain information: by integrating all partially activated expert experience, an interval estimate containing both the most probable disturbance value and its possible range of variation is output. This provides the controller with representative and robust disturbance prediction information, enabling the controller to perform accurate feedforward compensation and adjust the feedback gain according to the uncertainty range, thus comprehensively improving the system's adaptability near singular regions. Through this process, the fuzzy system integrates all activated rule information, transforming reasoning based on the verbalized description of singular risks into a numerical disturbance estimate with clear upper and lower boundaries.

[0070] S2.4: Integrate upper and lower bound estimates to output the disturbance prediction interval and the nominal disturbance prediction amount.

[0071] The upper and lower bound estimates of the fuzzy inference output are finally integrated and formatted to form an output quantity that can directly serve the design of the control law.

[0072] The lower perturbation estimate Directly defined as the lower bound of the perturbation prediction interval The upper disturbance estimate Defined as the upper bound of the disturbance prediction interval Thus, the complete disturbance prediction range is obtained. This interval quantitatively describes the possible range of variation of the expected equivalent perturbation under the current singular drift characteristics.

[0073] Meanwhile, in order to provide a clear compensation benchmark in subsequent control law design, a scalar disturbance prediction quantity is defined. The value at the midpoint of the disturbance interval, i.e. This nominal forecast amount This represents the optimal point estimate of the disturbance amplitude given the available information and will serve as the core input for the feedforward compensation term in subsequent steps.

[0074] In the technical solution of this disclosure, the risk description of a dynamic singular interval, which contains uncertainty, is transformed into an input form suitable for fuzzy inference through feature extraction. Leveraging the inherent advantages of type-2 fuzzy systems in handling uncertainty, the singular risk is mapped to an equivalent disturbance prediction interval with upper and lower bounds through the aforementioned rule-based fuzzy inference and defuzzification calculation process. This process not only outputs a nominal disturbance prediction quantity for feedforward compensation but, more importantly, retains information on the potential range of disturbance changes. This provides the controller with a forward-looking, quantitative disturbance estimate, enabling the control system to anticipate and prepare for dynamic disturbances caused by singular drift, thus enhancing the initiative and adaptability of the control strategy.

[0075] S3: Generate a dynamically adjustable sliding surface based on the uncertainty reflected by the disturbance prediction interval.

[0076] Based on the uncertainty reflected in the obtained disturbance prediction interval, a sliding surface capable of adapting to the model uncertainty caused by singular drift is designed. Traditional sliding mode control uses a sliding surface with fixed parameters, which struggles to balance control performance and robustness when the system faces drastic changes or increased uncertainty. By introducing a dynamic adjustment mechanism, the shape of the sliding surface can be adjusted according to the disturbance prediction interval. The reflected uncertainty level contracts or relaxes in real time, thereby effectively suppressing chattering of the control input while ensuring rapid convergence of the system trajectory, achieving an optimal balance between stability and dynamic performance. The process for generating the dynamic sliding surface and synthesizing the final control torque can be found in [reference needed]. Figure 3 The flowchart shown is for the adaptive sliding mode control torque synthesis. It is implemented through the following sub-steps.

[0077] S3.1: Calculate the normalized perturbation ratio from the perturbation prediction interval.

[0078] To predict the disturbance range The upper and lower bound information needs to be transformed into scalar parameters that can be used to adjust the sliding surface. This requires calculating a key indicator that directly reflects the uncertainty of the model, namely the normalized perturbation ratio. For calculation First, we define an intermediate variable, namely the disturbance amplitude index. .

[0079] Disturbance amplitude index It is obtained by averaging the absolute values ​​of the upper and lower bounds of the disturbance interval, i.e. This indicator reflects the average strength of the disturbance and is the basis for calculating the proportion of uncertainty.

[0080] Next, the normalized perturbation ratio of the core is calculated. This ratio will be the nominal disturbance prediction amount. Absolute value and disturbance amplitude index Related, the calculation formula is as follows Where ε is a very small positive number used to prevent numerical calculations where the denominator is zero. Normalized perturbation ratio. It is a dimensionless quantity ranging from 0 to 1. Its numerical value has a definite physical meaning: when... When it approaches 0, it indicates the nominal disturbance prediction amount. It is very close to the center of the disturbance interval, which indicates that the point estimate based on the current information is relatively reliable and the uncertainty is relatively low; when When it approaches 1, it means Approaching the boundary of the perturbation interval indicates high model uncertainty and decreased reliability of point estimates. Therefore, The magnitude of directly quantifies the level of uncertainty faced by the control system. In adaptive sliding mode control design, It is used as a key indicator for adjusting the convergence strength of the controller: the larger its value, the higher the uncertainty of the system, and the controller will use more conservative and more convergent parameters (such as a larger sliding mode gain) to ensure robustness; the smaller its value, the smoother and more energy-efficient control parameters can be used.

[0081] S3.2: Determine the global dynamic contraction factor based on the normalized perturbation ratio, and determine the local safety factor based on the inertia increment of each joint.

[0082] Based on the normalized perturbation ratio that reflects uncertainty Two types of adjustment parameters need to be generated: a global dynamic factor to control the overall shrinkage strength of the sliding surface, and a set of local safety factors to differentiate between each joint, so as to achieve synergistic optimization of global robustness and local accuracy.

[0083] First, construct the dynamic contraction factor. This factor is designed to allow the shrinkage rate of the sliding surface to adapt to the level of uncertainty. Its design follows a simple linear interpolation principle: within a preset minimum shrinkage coefficient... With the maximum shrinkage coefficient Between, according to A linear mapping is performed on the size of the elements. The specific relationship is as follows: .in, and These are constants set based on engineering experience, with typical values ​​ranging from 0.5 to 0.8 and from 1.0 to 1.5. These two boundary values ​​were obtained through offline calibration by analyzing the stability requirements of the system under typical singular operating conditions. When An increase in uncertainty, meaning a rise in system uncertainty, with the nominal disturbance prediction approaching the boundary of the disturbance interval, leads to a decrease in model reliability. As this increases, the sliding surface of the subsequent construction will have a steeper slope, thereby driving the system state to converge toward the equilibrium point with greater force to counteract the increased uncertainty.

[0084] Meanwhile, considering that the effect of the end-effector eccentric load on the dynamics of each joint in the robot's kinematic chain is uneven, a local safety amplification factor must be introduced for each joint. This coefficient, along with the inertia increment calculated in step S1.2 that reflects the effect of load on each joint, is related to this coefficient. Proportional, the calculation formula is: .in It is the inertia sensitivity coefficient, with a typical value range of 0.1-0.5. This coefficient is determined by fitting experimental data to analyze the impact of changes in the equivalent inertia of the joint on the control performance. The value of is greater than or equal to 1. A larger value indicates a heavier additional inertial burden on the i-th joint due to end-effector load in the current configuration, making it more vulnerable to singular drift. Therefore, a higher weight or stronger constraint needs to be assigned to this joint in the sliding mode control. These are the key parameters for achieving this differentiated local enhancement.

[0085] S3.3: Combine the global dynamic contraction factor, local safety factor and basic gain to synthesize the time-varying sliding mode gain of each joint.

[0086] Integrating the above global contraction factors Local safety factor of each joint Calculate a real-time updated sliding mode gain for each joint. This gain is the core parameter for constructing the sliding surface expression, and it directly determines the weight of the position error term in the sliding surface.

[0087] Each joint i has a pre-calibrated base sliding gain based on its physical characteristics (such as rated torque and transmission stiffness). Its typical value ranges from 5 to 15, and this value is determined through dynamic model identification and closed-loop debugging of each joint. Dynamic sliding mode gain. It is composed of the product of the base gain, the dynamic shrinkage factor, and the safety amplification factor of the joint, i.e. The physical significance of this synthesis formula lies in constructing an adaptive sliding mode gain that integrates three factors: baseline performance, global uncertainty adjustment, and local load differences. Its technical effect is to achieve fine-grained real-time control of the sliding mode convergence strength: the base gain... It ensures the basic tracking performance of each joint under nominal operating conditions; global dynamic contraction factor The convergence strength is scaled uniformly based on the overall uncertainty level of the system to counteract common risks; local safety factor. Differentiated gain compensation is then applied to joints affected by varying end-load conditions to provide targeted protection for vulnerable components. This calculation contains a clear control logic: First, It provides a baseline control strength based on hardware characteristics; secondly, This benchmark is scaled overall based on the level of global uncertainty, with an overall enhancement when the risk is high; finally... Based on this, fine-tuning is performed at the joint level to apply stronger control to joints that are more affected by load.

[0088] To ensure the numerical stability and physical realizability of the control system, it is necessary to perform calculations on the calculated values. Perform amplitude limiting to confine it to a reasonable physical range. The specific steps are as follows: .in, and These are preset boundary values, typically ranging from 5-10 and 15-30, respectively. These boundary values ​​are set based on the physical torque output limit and safe operating range of each joint actuator. After this step, each joint obtains a sliding mode gain that is optimized and adjusted according to real-time operating conditions (singular risks, load distribution) and is within a safe range.

[0089] S3.4: Using time-varying sliding mode gain and joint trajectory tracking error, construct the sliding surface function of each joint and the system as a whole.

[0090] By combining the real-time trajectory tracking error with the dynamic sliding mode gain obtained in the previous step, a specific sliding mode surface function is constructed for each joint, and these functions are combined to form a vector sliding mode surface that describes the tracking state of the entire multi-joint robot system.

[0091] First, calculate the tracking error for each joint. Define the position error of the i-th joint at time t. Its actual joint angle With the desired joint angle The difference, that is Correspondingly, its speed error Actual joint angular velocity With the desired joint angular velocity The difference, that is .

[0092] Subsequently, the dynamic sliding mode gain calculated in real time for this joint was utilized. Construct its sliding surface function The function takes the form of a linear combination, that is... The sliding surface defined by this formula has core physical significance in robot trajectory tracking control: it represents a time-varying constraint relationship between position error and velocity error. Its technical effect is that once the system state is driven onto this sliding surface and maintains sliding, the tracking error will follow a preset time-varying trajectory, i.e., in accordance with... The relevant exponential rate converges to zero. From a control theory perspective, =0 defines a time-varying hyperplane in the error state space, called the sliding surface. The goal of the control system is to design a control law that drives the system state trajectory to reach this sliding surface and then slides along it to the origin, i.e., the error is zero. As a parameter of the sliding surface slope, its dynamic change means that the direction of the sliding hyperplane is constantly being adjusted: when As the value increases, the penalty weight for positional errors in the sliding mode increases, and the system will more actively correct the pose deviation, thereby achieving faster convergence when facing high uncertainty.

[0093] Scalar of the sliding surfaces of all n joints Combining these elements, we obtain a vector characterizing the tracking performance of the entire robot system, namely the global sliding surface. .

[0094] It should be noted that during the above-mentioned sliding surface construction process, the sliding gain... By normalizing the perturbation ratio Indirectly dependent on the nominal disturbance prediction With disturbance amplitude index The purpose is to dynamically adjust the convergence strength of the sliding surface based on the overall uncertainty level of the disturbance prediction, which is a feedforward disturbance rejection strategy. The subsequent sliding surface correction torque... In the calculation, the sliding mode gain amplification factor Then directly depends on With the width of the disturbance interval Its function is to adjust the gain strength of the sliding mode feedback in real time according to the magnitude and uncertainty range of the disturbance, which is a feedback-based disturbance rejection strategy. Although both originate from the same set of disturbance prediction parameters ( , , However, their control objectives and levels of action differ: the former is used to construct the desired dynamic convergence trajectory, while the latter is used to enhance closed-loop robustness. This hierarchical dependency design enables full utilization and coordinated control of predicted disturbance information, ensuring both the adaptive convergence characteristics of the sliding surface and enhancing the real-time disturbance rejection capability of the sliding feedback, thereby improving the overall control accuracy and stability of the system under singular drift conditions.

[0095] In the technical solution of this disclosure, the key parameters of the sliding surface are dynamically adjusted based on the uncertainty reflected in the disturbance prediction interval. By constructing a dynamic contraction factor that varies with the proportion of global disturbance uncertainty, and combining it with a local safety factor that reflects the differences in the load influence on each joint, a time-varying sliding gain is generated for each joint. The sliding surface constructed using this gain and the trajectory tracking error has convergence characteristics that automatically increase with the increase of uncertainty, while also taking into account the overall coordination of the system through joint-differential adjustments. This design enables the sliding controller to allocate control resources more rationally while ensuring trajectory tracking convergence speed, effectively suppressing control input chattering, and achieving a balance between robustness and dynamic performance.

[0096] S4: Integrate nominal dynamic feedforward compensation, sliding surface-based correction feedback, and feedforward disturbance compensation based on nominal disturbance prediction to synthesize the final joint control torque.

[0097] By comprehensively utilizing the dynamic sliding surface, nominal dynamic model, and disturbance prediction information constructed in the preceding steps, the torque command finally sent to each joint actuator is synthesized. The design goal of this control law is to achieve the organic integration of three functions: first, model-based feedforward compensation to track the desired trajectory; second, using sliding mode feedback to ensure that the system state converges to the sliding surface under uncertainty; and third, introducing feedforward disturbance compensation to actively counteract the equivalent disturbance predicted by singular drift. Through the synergistic effect of these three parts, the final control output can respond in real time to the dynamic changes in the singular region, thereby maintaining high-precision and highly robust trajectory tracking performance under complex load and attitude changes. This is specifically achieved through the following sub-steps.

[0098] S4.1: Based on the desired trajectory and the current value of the sliding surface, calculate the corrected desired acceleration, and then calculate the nominal dynamic compensation torque.

[0099] The nominal dynamic compensation term forms the basic framework of the control law, and its role is to provide the robot with a theoretical torque reference required to achieve the desired motion. Based on the desired trajectory and the current value of the sliding surface, a corrected desired acceleration is calculated, and then the corresponding compensation torque is generated using the robot's dynamic model.

[0100] First, the desired joint angular acceleration is corrected. The nominal control acceleration of the i-th joint is defined. It depends not only on the predetermined desired joint angular acceleration. It also introduces the current sliding surface function value. The negative feedback is calculated using the following formula: .in, It is a sliding surface feedback gain constant with dimensions of [1 / time], typically ranging from 5 to 20 seconds. -1Between these parameters, the gain is tuned based on the desired system error convergence rate requirement. The significance of this correction lies in adjusting the sliding surface function value... This translates into an immediate adjustment of the desired acceleration, thereby injecting a corrective tendency into the control loop in advance and accelerating the process of the system state converging towards the sliding surface.

[0101] Subsequently, the nominal compensation torque was calculated based on the equivalent dynamic model of a single joint. This model typically includes inertial terms, Coriolis and centrifugal force terms, and gravity terms. The calculation formula is as follows: .in, It is the equivalent inertia estimation parameter of the i-th joint, and its value is obtained through offline calibration or online identification; It is the equivalent Coriolis force and centrifugal force coefficient, as well as the viscous damping coefficient; This refers to the actual joint angular velocity; It depends on the current joint angle. The gravity compensation term is calculated based on the actual joint angles. These parameters together constitute the feedforward model of robot dynamics. The physical meaning of this nominal dynamic compensation formula is to perform feedforward calculations based on the known dynamic model of the robot. Its technical effect is to partially linearize and decouple the dynamics of the controlled robot by compensating in advance for the main, modelable dynamic components such as inertial force, Coriolis force, centrifugal force, and gravity. This allows the subsequent sliding mode feedback controller to focus on handling the remaining unmodeled dynamics, parameter uncertainties, and external disturbances, thereby reducing the burden of feedback control, reducing control chattering, and improving the overall control efficiency of the system while ensuring trajectory tracking accuracy. Through this calculation, the nominal compensation torque... It provides the basic dynamic driving force for the robot to perform the desired motion, while embedding preliminary correction based on sliding mode deviation.

[0102] S4.2: Dynamically adjust the sliding mode gain amplification factor based on the disturbance prediction range and the nominal disturbance prediction amount, and construct a robust sliding mode feedback correction torque in combination with the saturation function.

[0103] The nominal compensation torque mainly relies on the model's feedforward, which may be insufficient when facing model uncertainties and external disturbances. Therefore, it is necessary to design a torque based on the sliding surface. Its own robust feedback term, namely the sliding mode correction torque. Its core function is to strongly suppress the tendency of the system state to deviate from the sliding surface, thus ensuring the stability of the closed-loop system.

[0104] First, the gain of the sliding mode term is dynamically adjusted based on the nominal disturbance prediction information. The disturbance interval width is defined. The difference between the absolute values ​​of the upper and lower bounds of the perturbation is, i.e. Based on this width and nominal perturbation prediction amount Construct the sliding mode gain amplification factor for the i-th joint. The calculation formula is as follows: .in, This is the basic sliding mode gain of the joint; and These are adjustment coefficients related to the nominal disturbance amplitude and the disturbance range width, respectively, and their typical values ​​range from 0.5 to 2.0. Stability was determined through stability testing under undisturbed operating conditions. and The tuning is then performed through control experiments under different disturbance levels. The design of this formula embodies the composite adaptive mechanism of sliding mode feedback gain: The term makes the gain increase linearly with the magnitude of the predicted disturbance, so as to provide a matching suppression force; This term increases the gain as the uncertainty of the disturbance prediction increases, enhancing feedback robustness to cover possible worst-case scenarios. Together, these two factors ensure that the sliding mode control force matches the amplitude and uncertainty level of the disturbance in real time and accurately when traversing time-varying singular regions.

[0105] To suppress the severe chattering caused by sign function switching in traditional sliding mode control, a boundary layer saturation function is used instead of the sign function. The saturation function input for the i-th joint is defined as the normalized sliding surface value, i.e. ,in The boundary layer thickness constant preset for this joint typically ranges from 0.1 to 0.5. This constant is selected based on the acceptable level of chattering from the controller output. Saturation function. In implementation, a piecewise linear approximation is used: when When, the output equals ;when When, the output equals .

[0106] Based on the above parameters, the sliding mode correction torque of the i-th joint is constructed. Sliding mode correction torque Calculated by the following formula: The negative sign indicates that the direction of the torque is always opposite to the direction of the sliding surface deviation, thus generating a force that pulls the system state back to the sliding surface. By combining dynamic gain and boundary layer saturation, this corrective torque can effectively smooth the control signal and suppress high-frequency chattering while ensuring strong robustness.

[0107] S4.3: The nominal compensation torque, sliding mode correction torque and feedforward disturbance compensation torque are superimposed to synthesize the final joint control torque.

[0108] Building upon the first two steps that provide the feedforward benchmark and robust feedback, a third step is introduced: based on the perturbation prediction interval. Feedforward disturbance compensation is used to actively counteract the expected equivalent disturbance. Thus, disturbance prediction information is used at three levels: sliding mode surface construction, sliding mode feedback gain adjustment, and feedforward disturbance compensation, forming a multi-layered, collaborative disturbance rejection control architecture. These three parts are then superimposed to form a final control torque that combines feedforward accuracy, feedback robustness, and look-ahead compensation capability.

[0109] First, an average disturbance baseline is generated for compensation. The midpoint value of the disturbance interval, i.e., the nominal disturbance prediction, is then used. Multiplied by a feedforward disturbance compensation weighting factor The average compensation scalar for feedforward disturbance is obtained. Weighting coefficients Used to adjust the compensation intensity and avoid overcompensation that could lead to excessive system rigidity or oscillations, its typical value range is 0.5-1.5. This coefficient is optimized and determined through experimental evaluation of the feedforward compensation effect.

[0110] Considering that each joint is located at a different position in the powertrain and thus experiences varying degrees of load distribution at the end of the chain, a global compensation is required. According to the preset joint allocation coefficient Distribute the allocation. The allocation coefficients satisfy the conditions of all joints. The sum of these is one, and its value is usually determined based on the degree to which the joint approaches the end point or the proportion of the inertia increment calculated in step S1.2. These coefficients are pre-allocated based on the structural characteristics of the robot's kinematics and dynamics. The feedforward disturbance compensation torque component obtained by the i-th joint is... .

[0111] Finally, the total control torque of the i-th joint at time t It consists of three superimposed parts: This synthesis formula represents the final embodiment of the control law of this method. Its core physical significance lies in achieving multi-level integrated control combining feedforward and feedback, model-based and data-based approaches, and active compensation and robust suppression. The resulting comprehensive technical effect is: nominal compensation term... Utilizing a dynamic model to provide precise feedforward driving force lays the foundation for efficient tracking; sliding mode correction term Through dynamic gain and boundary layer design, robust and smooth feedback convergence is provided to ensure stability; perturbation compensation term Based on look-forward prediction using a type-II fuzzy system, targeted feedforward cancellation force is provided to proactively reduce the feedback burden. The synergy of these three elements enables the robot to simultaneously achieve high-precision trajectory tracking, strong robust stability, and smooth control output when traversing dynamically drifting singular regions.

[0112] By combining the final control torques of all joints, the control law sequence of the entire robot system is obtained. The torque sequence is calculated once in each control cycle and sent to the servo drives of each joint in real time to drive the robot's actual movement.

[0113] The technical solution of this disclosure integrates feedforward compensation based on the nominal dynamics model, robust feedback correction based on the dynamic sliding surface, and feedforward compensation based on disturbance prediction to generate the final control torque command. The nominal compensation term provides the basic driving force for tracking the desired trajectory; the sliding correction term, through the design of dynamic gain and boundary layer saturation function, provides strong robust convergence force and smooths the control signal; the interval disturbance compensation term actively cancels the predicted equivalent disturbance. The synergistic effect of these three components enables the control law to fully utilize model information, real-time state feedback, and look-ahead disturbance estimation. Thus, even when facing model uncertainties and equivalent disturbances caused by singular drift, it can still output accurate, stable, and highly adaptable control commands, ensuring the accuracy of trajectory tracking and system stability.

[0114] S5: Execute the final joint control torque and collect the actual response to form a closed-loop evaluation, and make online corrections to the dynamic singular interval based on the closed-loop performance.

[0115] The theoretical control law calculated in step S4 The system is safely and reliably applied to the actual robot joints, while simultaneously acquiring the system's actual response. Based on this feedback, control performance and singular states are evaluated in real time, leading to closed-loop updates of key front-end parameters. Through this closed-loop process of execution, perception, evaluation, and adjustment, the entire control system is ensured not only to theoretically handle singular drift but also to dynamically adapt and maintain stability during actual operation, thus achieving robustness throughout the entire lifecycle from design to service. This is achieved through the following sub-steps.

[0116] S5.1: Send the control torque command to the joint actuator and simultaneously measure the actual joint angle and angular velocity.

[0117] This step is the interface connecting the digital controller and the physical actuator. It is responsible for converting the calculated target torque into actual motor drive signals and simultaneously measuring the robot's real motion state, providing first-hand data for closed-loop evaluation.

[0118] First, the controller in each fixed sampling period Inside, the target torque of the i-th joint output in step S4 is... The command is sent to the corresponding servo driver. The driver's internal circuitry, based on its preset amplification factor, efficiency model, and friction compensation parameters, converts the digital command into the actual physical torque applied to the motor shaft. This conversion process can be summarized as follows: ,in It is a comprehensive drive gain coefficient that reflects the conversion relationship from command to actual torque. It is usually obtained through system calibration, and its typical value ranges from 0.9 to 1.1. Actual driving torque Directly drive the joint motor to generate movement.

[0119] Subsequently, the system uses a high-precision encoder built into the joint to measure the rotational position of the motor in real time, thereby obtaining the measured joint angle. The measured joint angular velocity is obtained by differential calculation based on the angle values ​​from two consecutive sampling periods. The calculation formula is: Sampling period The typical value range is 1-10 milliseconds. Thus, the system obtains the most realistic motion state feedback of each joint of the robot after executing control commands. and These data form the basis for evaluating the effectiveness of control and updating subsequent algorithms.

[0120] S5.2: Calculate the closed-loop tracking error, closed-loop sliding surface, and updated actual singularity metric based on measured data.

[0121] After obtaining the actual joint response, the key control and state assessment variables are recalculated, and the theoretical design values ​​are aligned with the actual operating values, thereby reconstructing closed-loop indicators for monitoring and regulation at the level of the real physical system.

[0122] First, calculate the closed-loop tracking error. Based on the measured angles and velocities, calculate the closed-loop position error for each joint. Closed-loop speed error These error values ​​more accurately reflect the system's tracking accuracy than the errors predicted by the model.

[0123] Next, the time-varying sliding mode gain, which was determined in step S3 and may still be slowly updating, is utilized. Constructing a closed-loop sliding surface Its calculation formula is consistent with the theoretical sliding surface, but it uses the measured error: The closed-loop sliding mode surface value It is the direct basis for judging whether the system is actually operating on the ideal sliding mode dynamics, and its magnitude directly reflects the comprehensive deviation between the actual trajectory and the ideal trajectory.

[0124] Meanwhile, in order to continuously monitor the actual drift of the singular region within the closed loop, it is necessary to calculate the actual drift based on all measured joint angles (denoted as vectors). Recalculate the Jacobian matrix for the robot's current actual posture. Then, singular value decomposition is performed to obtain the minimum singular value based on the actual pose. To ensure the continuity of this value and filter out measurement noise, a smoothing process similar to that in step S1.3 is performed to obtain the closed-loop singularity metric. .in This is a smoothing coefficient used for closed-loop data. Its function is similar to the smoothing coefficient β in step S1.3, and its typical value range is 0.7-0.95. As a real-time estimate of the actual singularity of the system, it is more reliable than values ​​based purely on model predictions.

[0125] S5.3: Construct a closed-loop stability index and use it to make online corrections to the upper and lower boundaries of the dynamic singular interval.

[0126] Using the closed-loop tracking error, closed-loop sliding mode surface value, and singularity metric of the actual pose obtained in the previous step, a comprehensive stability index is constructed, and based on this, the dynamic singular interval generated in step S1 is evaluated. By making reverse corrections, a feedback adjustment loop is formed, from the execution effect to the perceived parameters.

[0127] First, a closed-loop stability index based on Lyapunov's ideas is constructed. A local energy index is defined for each joint. This index combines the slip surface deviation and positional error, and the calculation formula is as follows: .in This is the error weighting coefficient, used to adjust the importance of position error in the index. A typical value range is 1-10, and this coefficient is preset based on the relative importance given to tracking error and sliding surface deviation. For multi-joint systems, it can be taken from all joints. The maximum or average value is used as a global indicator. .

[0128] To simultaneously measure control stability under a specific singularity, a closed-loop stability index is defined. Here, ε is a very small positive bias, typically ranging from 0.001 to 0.01, used to prevent the denominator from being zero. The physical meaning of this index lies in quantifying the error energy consumed by the control system under a unit singularity risk level. Its technical effect is to provide a normalized, comprehensive performance index that can be directly used for online evaluation and parameter self-tuning: numerator... The denominator comprehensively reflects the accuracy of trajectory tracking. This characterizes the inherent kinematic difficulty (singularity) of the current configuration. By monitoring... The control system can intelligently determine whether the current control parameters are effective in the face of current singular risks, thus providing a direct and quantitative decision-making basis for online correction of dynamic singular intervals. The smaller the value, the lower the tracking error energy and the more stable the closed-loop performance, even under the current near-singular attitude.

[0129] based on The upper and lower bounds of the dynamic singular interval generated in step S1 of the previous control cycle are corrected online. The correction formula is: , .in, and It is the boundary of the singular interval of the previous cycle; and It is an interval correction coefficient, whose value can be positive or negative, with a typical range of -0.5 to 0.5; It is a stability reference value set according to the expected performance. and Tuning is performed through simulation or experimentation of the closed-loop adaptive adjustment effect. This is set based on the desired trajectory tracking accuracy. In robot control, this formula constitutes an online self-calibration mechanism for dynamic singular intervals. Interval correction coefficient. and The sign and magnitude of the value determine the sensitivity and direction of the calibration: when its value is positive, the actual closed-loop stability index... Worse than expected (i.e.) The formula will increase the boundary of the singular interval, thereby improving the warning level and controller robustness against singular risks in subsequent control; conversely, when the actual performance is better than expected (i.e., When this occurs, the singular interval boundary should be appropriately reduced to avoid unnecessary conservative control and achieve optimal allocation of control resources. The updated closed-loop dynamic interval... It will be sent back to step S1 to update the dynamic singular interval for the next control cycle. .

[0130] In the technical solution of this disclosure, a theoretical control law is applied to the physical joint, and closed-loop monitoring and parameter updates are completed based on the measured joint response. By collecting the actual motion state, the closed-loop tracking error and sliding surface are recalculated, and the singularity metric is updated in combination with the measured pose, which can truly reflect the actual operating performance and singularity proximity of the system. Furthermore, these closed-loop data are used to construct stability indices and to perform reverse correction on the dynamic singularity interval at the front end, forming a feedback adjustment loop from execution effect to perceived parameters. This closed-loop process ensures that the entire control system can continuously self-evaluate and optimize during actual operation, enabling the judgment of singularity risks and the parameter settings of the controller to be dynamically calibrated based on actual performance, thereby realizing a complete robust control closed loop from theoretical design to physical implementation.

[0131] According to embodiments of this disclosure, an electronic device is also provided, which may include a processor, a communications interface, a memory, and a communication bus, wherein the processor, the communications interface, and the memory communicate with each other via the communication bus. The processor can invoke logical instructions stored in the memory to execute the methods provided in the above embodiments.

[0132] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and sold or used as independent products, and can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this disclosure, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this disclosure. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0133] On the other hand, this disclosure also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is implemented to perform the methods provided in the above embodiments.

[0134] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0135] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0136] It should be understood that the above embodiments are only used to illustrate the technical solutions of this disclosure, and not to limit them; although this disclosure has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or make equivalent substitutions for some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this disclosure.

Claims

1. A control method for a singular articulated robot system based on interval type-II fuzzy sliding mode, characterized in that, The method includes: S1. Real-time sensing and quantification of the dynamic drift of singular regions caused by changes in end-load, and construction of dynamic singular intervals; S2. Input the dynamic singular interval into the interval type II fuzzy system and output the disturbance prediction interval and the nominal disturbance prediction quantity; S3. Based on the uncertainty reflected by the disturbance prediction interval, a dynamically adjustable sliding surface is generated; S4. The nominal dynamic feedforward compensation, the correction feedback based on the sliding surface, and the feedforward disturbance compensation based on the nominal disturbance prediction are integrated to synthesize the final joint control torque. S5. Execute the final joint control torque and collect the actual response to form a closed-loop evaluation, and make online corrections to the dynamic singular interval based on the closed-loop performance.

2. The control method for singular articulated robot systems based on interval type-II fuzzy sliding mode according to claim 1, characterized in that, S1 includes: Simultaneously collect joint motion state and end-effector load parameters, calculate the increase in equivalent rotational inertia of the joint caused by the end-effector load, and calculate the singular values ​​of the Jacobian matrix based on the current robot configuration. The singular values ​​are smoothed to obtain the singularity measure; Based on the singularity metric, a numerical interval with dynamically updated upper and lower boundaries is generated, which serves as the dynamic singular interval.

3. The control method for singular articulated robot systems based on interval type-II fuzzy sliding mode according to claim 1, characterized in that, S2 includes: Extract scalar features representing the degree of singularity risk and their corresponding uncertainty widths from the dynamic singular intervals; Using the scalar features and the uncertainty width as input, the upper and lower bound estimates of the equivalent perturbation are obtained through interval type II fuzzy inference; The upper bound estimate and the lower bound estimate constitute the disturbance prediction interval, and the midpoint value is calculated as the nominal disturbance prediction amount.

4. The control method for singular articulated robot systems based on interval type-II fuzzy sliding mode according to claim 1, characterized in that, S3 includes: Based on the aforementioned disturbance prediction interval, calculate the normalized disturbance ratio, which reflects the global uncertainty level; The global dynamic contraction factor is determined based on the normalized perturbation ratio, and the local safety factor is determined based on the equivalent rotational inertia increment of each joint. By integrating the global dynamic contraction factor, the local safety factor, and the preset basic sliding mode gain, a time-varying sliding mode gain is generated for each joint; A dynamically adjustable sliding surface is constructed using the time-varying sliding mode gain and joint trajectory tracking error.

5. The control method for singular articulated robot systems based on interval type-II fuzzy sliding mode according to claim 4, characterized in that, The global dynamic contraction factor is determined based on the normalized perturbation ratio, satisfying the following relationship: ,in, The global dynamic contraction factor, The normalized perturbation ratio is given. and These are the preset minimum and maximum shrinkage coefficients, respectively; The local safety factor is determined based on the equivalent rotational inertia increment of each joint, satisfying the following relationship: ,in, Let be the local safety factor of the i-th joint. Let be the equivalent rotational inertia increment of the i-th joint. This is the preset inertia sensitivity coefficient.

6. The control method for singular articulated robot systems based on interval type-II fuzzy sliding mode according to claim 1, characterized in that, S4 includes: Based on the desired trajectory and the current value of the sliding surface, the nominal compensation torque is calculated; The sliding mode gain amplification factor is dynamically adjusted based on the disturbance prediction range and the nominal disturbance prediction amount, and the sliding mode correction torque is constructed using a saturation function; The nominal compensation torque, the sliding mode correction torque, and the feedforward disturbance compensation torque based on the nominal disturbance prediction are superimposed to obtain the final control torque of each joint.

7. The control method for singular articulated robot systems based on interval type-II fuzzy sliding mode according to claim 6, characterized in that, The sliding mode gain amplification factor is dynamically adjusted based on the disturbance prediction interval and the nominal disturbance prediction amount, satisfying the following relationship: ,in, Let be the sliding mode gain amplification factor for the i-th joint; This is the preset base value; The nominal disturbance prediction value; The width of the disturbance prediction interval; and This is the preset gain adjustment coefficient.

8. The control method for singular articulated robot systems based on interval type-II fuzzy sliding mode according to claim 1, characterized in that, S5 includes: The final joint control torque is applied to the physical joint, and the actual joint angle and angular velocity are measured simultaneously. Based on the measured data, the closed-loop tracking error, the closed-loop sliding mode surface value, and the singularity metric based on the actual pose are recalculated, and a stability index is constructed accordingly. Based on the deviation between the stability index and the preset reference value, the upper and lower boundaries of the dynamic singular interval are adjusted, and the adjusted interval is used for the next control cycle.

9. An electronic device, characterized in that, The electronic device includes a memory and at least one processor, the memory storing a computer program, and the processor executing the computer program to implement the singular system control method for articulated robots based on interval type II fuzzy sliding mode as described in any one of claims 1-8.

10. A computer storage medium, characterized in that, It stores a computer program, which, when executed, implements the singular system control method for articulated robots based on interval type II fuzzy sliding mode according to any one of claims 1-8.

Images