A non-singular segmented sliding mode adaptive time-delay control method for rope-driven robotic arms

Abstract

The application discloses a kind of non-singular segmented sliding mode self-adapting time delay control methods of rope driving mechanical arm, belong to robot control technical field, this method is by calculating tracking error;Non-singular segmented terminal sliding surface is constructed, and small error interval adopts sine-power function composite transition function, and singular problem is eliminated;And based on the diagonal gain matrix of upper and lower limit constraint of sliding mode variable multi-working condition adaptive update;Through time delay estimation, the system lumped uncertainty term is estimated using historical sampling signal, and model-free control is realized;Combined with fixed-time approaching law, the output control torque of mechanical arm is calculated.The application does not need accurate dynamics model, adaptive gain can compensate model uncertainty and external disturbance, and gain is constrained to avoid unbounded output;The sliding mode variable and tracking error of closed-loop system are fixed-time convergent to zero point neighborhood, and tracking accuracy, robustness and engineering practicability are considered.

Description

Technical Field

[0001] This invention belongs to the field of robot control technology, specifically relating to a non-singular segmented sliding mode adaptive time-delay control method for a rope-driven robotic arm. Background Technology

[0002] Rope-driven robotic arms, with their advantages of high load-to-weight ratio, large workspace, and good dexterity, are widely used in industrial automation, medical rehabilitation, and space exploration. However, the dynamics of rope-driven robotic arms are characterized by strong nonlinearity, coupling effects, transmission flexibility, and complex friction. This makes it difficult to establish accurate dynamic models in engineering, and the operation process is also susceptible to unknown external disturbances, posing risks to high-precision trajectory control.

[0003] Sliding mode control is a class of robust nonlinear control algorithms. Terminal sliding mode can achieve finite-time convergence, but traditional terminal sliding mode suffers from singularity problems, which can easily lead to unbounded control outputs. Existing non-singular terminal sliding mode can only achieve asymptotic convergence; fixed-time sliding mode can limit the convergence time to a constant independent of the initial conditions.

[0004] Time delay estimation (TDE) technology uses historical time-time signals to estimate the lumped uncertainty of the system, which can be used to construct model-free controllers. However, most traditional sliding mode controllers based on time delay estimation use fixed control gain, which is difficult to adapt to varying operating conditions; if the gain is too small, the disturbance rejection capability is insufficient, and if the gain is too large, it can easily cause chattering or even control saturation.

[0005] Therefore, there is an urgent need for a complete control scheme that simultaneously takes into account non-singularity, fixed-time convergence, model-free operation, and adaptive bounded gain constraints. Summary of the Invention

[0006] The purpose of this invention is to provide a non-singular segmented sliding mode adaptive time-delay control method for a rope-driven robotic arm. This method does not require an accurate robotic arm dynamics model, and the control gain can be adaptively adjusted online with upper and lower limit constraints set, thereby improving the system's anti-disturbance capability and trajectory tracking accuracy, while taking into account both the theoretical performance of the algorithm and its engineering feasibility.

[0007] To achieve the above objectives, the present invention provides a non-singular piecewise sliding mode adaptive time-delay control method for a rope-driven robotic arm, comprising the following steps: S1. The rope-driven robotic arm collects the actual state information of the joints, loads the preset desired trajectory and completes the controller parameter initialization, and outputs the actual state information of the joints and the desired trajectory to S2. S2. Receive the actual joint state information and desired trajectory output by S1, solve for the trajectory tracking error, and output the tracking error to S3. S3. Receive the tracking error output by S2, construct a non-singular segmented terminal sliding surface, use a segmented transition function composed of sine and power functions in a small error interval to eliminate the sliding surface singularity problem, calculate the sliding surface correlation coefficient and the segmented transition function, obtain the sliding surface output variable, and output the sliding surface output variable and the derivative of the segmented transition function to S4, S6, and S7. S4. Receive the sliding surface output variable from S3, read the adaptive auxiliary variable from the previous cycle, perform multi-condition logic operation based on the sliding surface output variable, and obtain the adaptive diagonal gain matrix with output boundary constraints after auxiliary variable update and upper and lower limit amplitude processing. Output the adaptive diagonal gain matrix to S5 and S7. S5. Receive the adaptive diagonal gain matrix output by S4, read the historical signal at the sampling delay time, estimate the system lumped uncertainty term using the historical sampling signal through time delay estimation, and output it to S7. S6. Receive the sliding surface output variable from S3, perform a fixed-time approach law operation to generate an approach control term, and output it to S7. S7 receives the adaptive diagonal gain matrix output from S4, the piecewise transition function derivative output from S3, the historical signal output from S5, the approach control term output from S6, and the desired joint acceleration; calculates the joint control torque and sends it to the robotic arm driver; stores the current cycle control signal as the delayed historical signal for the next cycle; and jumps to S1 to complete the closed-loop control.

[0008] Preferably, in S3, the piecewise transition function satisfies: ; In the formula, Output vectors for piecewise transition functions of the sliding surface; For trajectory tracking error; For the power sign function, it is defined as follows: ; The threshold for error segmentation; For power-order parameters; The first boundary continuous transition coefficient; The second boundary continuous transition coefficient; Perform element-wise sine operations on the vector; This refers to the second set of power-law adjustment coefficients for the sliding surface; The power-law adjustment coefficient of the sliding surface satisfies: ; In the formula, This refers to the first group of power-law adjustment coefficients for the sliding surface; Design parameters for the sliding surface; The norm of the tracking error vector; Standard symbolic functions; ; In the formula, Design parameters for the sliding surface.

[0009] Preferably, in S4, the adaptive diagonal gain matrix is ​​the first... The diagonal elements of the dimension satisfy: ; ; In the formula, It is an adaptive diagonal gain matrix; For the adaptive diagonal gain matrix, the first... One diagonal element; For the first The nominal gain constant of the degrees of freedom; This is the gain adjustment coefficient; For the first Degrees of freedom adaptive auxiliary variable, the range of values ​​of the adaptive auxiliary variable is constrained This refers to the upper limit of the auxiliary variable; The intermediate variables of the sliding mode criterion satisfy: ; In the formula, For the first Dimensional sliding mode intermediate operation variables; For sliding mode variables No. scalar components; For the first Power parameter of sliding mode criterion; For the first Small neighborhood threshold parameter for sliding mode; It is a small positive number.

[0010] Preferably, in S5, the estimated value of the system lumped uncertainty term satisfies: ; In the formula, for Estimate of the total uncertainty term at time step; For delayed sampling The historical control torque at any given moment; This is the adaptive diagonal gain matrix at the current time. For delay Constant-time joint acceleration signal; Sampling time.

[0011] Preferably, in S6, the fixed-time approach law satisfies: ; In the formula, For sliding mode variables The first time derivative with respect to time; This is the first gain coefficient matrix of the reaching law; This is the second gain coefficient matrix of the reaching law; This is the first power of the approximation law; This is the second power of the approach law; Output variables for the sliding surface.

[0012] Preferably, in S3, the boundary continuity transition coefficient satisfies: ; ; In the formula, It is an element-wise cosine function; It is an element-wise sine function; The output variables of the sliding surface satisfy: ; In the formula, For sliding mode variables; This is the first weighting coefficient for the sliding surface; This is the second weighting coefficient for the sliding surface.

[0013] Preferably, in S4, the rate of change of the adaptive auxiliary variable satisfies: ; In the formula, For adaptive auxiliary variables The derivative with respect to time; The rate coefficient is used as an auxiliary variable.

[0014] Preferably, in S7, the joint control torque satisfies: ; In the formula, Output the joint control torque vector at the current moment; The desired joint acceleration.

[0015] Therefore, the present invention employs the above-mentioned non-singular segmented sliding mode adaptive time-delay control method for a rope-driven robotic arm. Compared with the prior art, the technical solution of the present invention has the following beneficial effects: (1) The present invention designs a segmented non-singular terminal sliding surface and adopts a sine-power function composite transition function in the small error range to ensure that the sliding surface and its derivative are continuously differentiable throughout the entire process, effectively eliminating the singular value problem existing in traditional terminal sliding control; it achieves fixed-time convergence, and the convergence time is not constrained by the initial error condition of the system, thereby improving the trajectory tracking response speed. (2) This invention integrates time delay estimation technology and uses the system signal at historical sampling time to estimate the system lumped uncertainty term. It does not require obtaining the accurate dynamic model of the rope-driven robotic arm, thus reducing the modeling workload. It configures an adaptive gain matrix with upper and lower limit constraints and adjusts the gain in real time according to the output of the sliding surface, effectively compensating for model uncertainty and external disturbances, and improving the robustness of the system. (3) The present invention sets up multi-condition adaptive update logic, constrains the adaptive gain within a reasonable range, ensures that the time delay estimation compression condition is always valid, and avoids unbounded output of control quantity; according to Lyapunov stability analysis, the sliding mode variable and tracking error of the closed-loop system can converge to the neighborhood of zero point in a fixed time, taking into account both control accuracy and engineering implementation capability.

[0016] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating an embodiment of a non-singular segmented sliding mode adaptive time-delay control method for a rope-driven robotic arm according to the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Unless otherwise defined, the technical or scientific terms used in the present invention should have the ordinary meaning understood by those skilled in the art.

[0019] Example 1 like Figure 1 As shown, this embodiment provides a non-singular segmented sliding mode adaptive time-delay control method for a rope-driven robotic arm. It should be understood that the specific parameters, models, and protocols mentioned in this embodiment are merely examples to help those skilled in the art understand the present invention, and are not intended to limit the present invention.

[0020] robotic arm for Degrees of freedom, all vectors are The diagonal matrix is ; Sampling time; For historical delay moments; the power sign function is defined as follows: .

[0021] The present invention provides a non-singular segmented sliding mode adaptive time-delay control method for a rope-driven robotic arm, comprising the following steps: S1. Receive the actual joint status information collected by the cable-driven robotic arm sensor, load the preset desired trajectory, and complete the controller parameter initialization.

[0022] The actual joint state information and the desired trajectory are passed to step S2 for tracking error calculation.

[0023] This step completes hardware signal acquisition and controller parameter configuration. Unlike fixed-parameter offline simulation solutions, this step supports two sets of parameter configurations: one for the simulation platform and one for the physical experimental platform, adapting to both digital simulation and physical robot operating conditions.

[0024] Read the joint position vector output by the robotic arm joint sensor Joint velocity vector Joint acceleration vector Load a pre-planned smooth bounded expected trajectory Complete the initialization assignment of sliding surface parameters, reaching law parameters, adaptive gain parameters, and sampling time L.

[0025] Output the actual state of the joint and the expected trajectory data as the input data source for error calculation in step S2.

[0026] S2 receives the actual joint state information and expected trajectory output by S1, and calculates the joint trajectory tracking error and the first derivative of the error.

[0027] Calculated tracking error First derivative of error The result is passed to step S3 for non-singular segmented sliding surface calculation.

[0028] This step calculates the deviation between the actual and desired motion of the robotic arm, providing error input for sliding mode control.

[0029] The formula for calculating tracking error and the first derivative of the error is expressed as follows: ; ; In the formula, This is the joint position tracking error vector; The first derivative vector of the error; For the desired joint position; This refers to the actual joint position; For the desired joint velocity; This represents the actual joint velocity.

[0030] Output tracking error First derivative of error The data is then sent to the sliding surface calculation unit in step S3.

[0031] S3, Receive tracking error output from S2 First derivative of error Solve for the non-singular piecewise terminal sliding surface and output the sliding mode variables. .

[0032] sliding mode variables Sliding surface derivative The results are passed to steps S4, S6, and S7, which are used for adaptive gain update, reaching law calculation, and control torque solution, respectively.

[0033] This step uses a piecewise composite transition function to construct the sliding surface. Unlike the traditional single power function terminal sliding scheme, this step uses a sine-power function composite function in the small error interval to ensure that the function itself and the first derivative are continuously differentiable, completely eliminating the singularity problem of sliding control and achieving fixed-time convergence characteristics.

[0034] The solution of the sliding surface is performed in stages, including the following sub-steps: S301. Calculate the power coefficient of the sliding surface. The formula for calculating the first power adjustment coefficient is as follows: ; In the formula, This refers to the first group of power-law adjustment coefficients for the sliding surface; The design parameters for the sliding surface are as follows, with a value range of [value range missing]. ; The norm of the tracking error vector; Standard symbolic functions; The formula for calculating the second power adjustment coefficient is as follows: ; In the formula, This refers to the second set of power-law adjustment coefficients for the sliding surface; The design parameters for the sliding surface are as follows, with a value range of [value range missing]. .

[0035] S302. Solve for the piecewise transition function; the piecewise transition function is expressed as: ; In the formula, Output vectors for piecewise transition functions of the sliding surface; For the power sign function, it is defined as follows: ; The threshold for error segmentation; For power-order parameters; The first boundary continuous transition coefficient; The second boundary continuous transition coefficient; Perform element-wise sine operations on the vector; The formula for solving the boundary continuity transition coefficient is: ; ; In the formula, It is an element-wise cosine function; It is an element-wise sine function; coefficient Used to guarantee and its first derivative in Continuous at the boundary.

[0036] S303. Solve for the first derivative of the piecewise transition function, using the following formula: ; In the formula, Let be the first derivative vector of the piecewise transition function with respect to time.

[0037] S304. Calculate the sliding mode variables by combining the first derivative of the error, the power sign function term, and the piecewise transition function; the formula for calculating the non-singular piecewise terminal sliding surface is: ; In the formula, For sliding mode variables; This is the first weighting coefficient for the sliding surface; The second weighting coefficient for the sliding surface, with a value range of... .

[0038] Output sliding mode variables and derivatives of piecewise transition functions It will be sent to the next step.

[0039] S4 receives the sliding mode variable s output by S3, executes multi-condition logic, and updates the adaptive diagonal gain matrix subject to upper and lower limit constraints online. .

[0040] The updated adaptive diagonal gain matrix The time delay is passed to steps S5 and S7 for time delay estimation calculation and final control torque solution.

[0041] This step updates the gain auxiliary variable based on the state division of the sliding mode variable under multiple operating conditions. Unlike the fixed gain time delay estimation scheme, this step constrains the gain to a finite interval, ensuring that the time delay estimation compression condition continues to hold, preventing the control torque from being output without bounds, and adaptively compensating for model uncertainties and external disturbances.

[0042] The adaptive gain matrix update is performed in stages, including the following sub-steps: S401, Read the sliding mode variable. Dimensional components Read the auxiliary variables stored in the previous control cycle. Calculate the diagonal elements of the adaptive diagonal gain matrix; the formula for calculating the diagonal elements of the adaptive gain matrix is: ; ; In the formula, It is an adaptive diagonal gain matrix; For the adaptive diagonal gain matrix, the first... One diagonal element; For the first The nominal gain constant of the degrees of freedom; This is the gain adjustment coefficient, with a value of [value missing]. ; For the first Degrees of freedom adaptive auxiliary variable; the range of values ​​for the adaptive auxiliary variable is constrained. This represents the upper limit of the auxiliary variable.

[0043] S402. Calculate the intermediate variables using the following formula: ; In the formula, For the first Dimensional sliding mode intermediate operation variables; For sliding mode variables No. scalar components; For the first The power parameter of the sliding mode criterion has a range of values. ; For the first The sliding mode small neighborhood threshold parameter has a value range of 1. ; It is a small positive number.

[0044] S403. Solving for derivatives of auxiliary variables under multiple operating conditions The formula for calculating the rate of change of adaptive auxiliary variables under multiple operating conditions is as follows: ; In the formula, For adaptive auxiliary variables The derivative with respect to time; The update rate coefficient for the auxiliary variable has a range of values ​​of [value range missing]. ;according to The logic for switching and updating the interval and sliding mode variable norm criteria.

[0045] S404, to Numerical integration is used to obtain the auxiliary variable at the current time step. Forced limit to Substitute the elements into the formula for calculating the diagonal elements of the adaptive gain matrix to calculate the adaptive diagonal gain matrix at the current time. .

[0046] Output the adaptive diagonal gain matrix after the amplitude limiting update. Then, proceed to steps S5 and S7.

[0047] S5, Receive the current-time adaptive diagonal gain matrix output from S4. Read the historical signal at time delay L and calculate the estimated value of the system's lumped uncertainty term. .

[0048] Estimated value of lumped uncertainty The result is passed to step S7 for the final control torque solution.

[0049] This step uses time-delay estimation to estimate the lumped uncertainty of the system using historical time signals. Unlike model-dependent controllers that require a complete dynamic model, this step achieves model-free estimation and does not require prior model parameters of the robotic arm's inertia, friction, and gravity.

[0050] The formula for estimating the time delay of the lumped uncertainty term is expressed as: ; In the formula, for Estimate of the total uncertainty term at time step; This is the adaptive diagonal gain matrix at the current time. Sampling time; The actual joint acceleration vectors collected by the robotic arm's sensors are saved and then sampled and delayed to obtain the historical actual accelerations required for time-delay estimation. ; The joint control torque vector output in the current cycle is saved and used as the historical torque signal for the time delay estimation in the next cycle. ; Output the estimated value of the lumped uncertainty term Proceed to step S7.

[0051] S6, Receives the sliding mode variable output by S3 Perform fixed-time approach law operations to generate approach control terms.

[0052] The approach control term is passed to step S7 for solving the control torque.

[0053] This convergence law contains both sig function terms of powers greater than 1 and less than 1. Unlike ordinary linear convergence laws, this step enables the system state to reach the sliding surface in a fixed time, and the convergence time is independent of the initial error magnitude.

[0054] The formula for the fixed-time approach law is expressed as: ; In the formula, For sliding mode variables The first time derivative with respect to time; This is the first gain coefficient matrix of the reaching law, with values ​​ranging from 1 to 2. ; This is the second gain coefficient matrix of the reaching law, with values ​​ranging from... ; This is the first power of the approximation law; This is the second power of the approach law; ; ; In the formula, The design parameters for the first reaching law are given, and their range is [value range missing]. ; The design parameters for the second reaching law have a range of values. .

[0055] Output the approach control term and send it to step S7.

[0056] S7, Receives the adaptive diagonal gain matrix output from S4. S3 output S5 output historical moment control torque Delayed acceleration The approach control term of S6 output and the desired acceleration of S1 output. Calculate the control torque of the cable-driven robotic arm .

[0057] Output control torque Send to the robotic arm joint actuator; simultaneously store the current control torque. This serves as a delayed historical signal required for the next cycle; after execution, it jumps to S1 to complete one closed-loop control cycle.

[0058] This step integrates the sliding surface dynamics, adaptive gain, and time delay estimation historical information to obtain a completely model-free control output, solving the engineering problems of difficult model identification and disturbance suppression in rope-driven robotic arms.

[0059] The comprehensive calculation formula for the joint control torque of the robotic arm is as follows: ; In the formula, Output the joint control torque vector at the current moment; Let be the desired joint acceleration vector.

[0060] Output control torque to drive the cables and rotate the joints of the robotic arm; save , (Current actual joint acceleration) is used for the historical delay signal required for the time delay estimation of the next cycle; loop jump S1 continuously tracks the closed loop trajectory.

[0061] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0062] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A non-singular piecewise sliding mode adaptive time-delay control method for a rope-driven robotic arm, characterized in that, Includes the following steps: S1. The rope-driven robotic arm collects the actual state information of the joints, loads the preset desired trajectory and completes the controller parameter initialization, and outputs the actual state information of the joints and the desired trajectory to S2. S2. Receive the actual joint state information and desired trajectory output by S1, solve for the trajectory tracking error, and output the tracking error to S3. S3. Receive the tracking error output by S2, construct a non-singular segmented terminal sliding surface, use a segmented transition function composed of sine and power functions in a small error interval to eliminate the sliding surface singularity problem, calculate the sliding surface correlation coefficient and the segmented transition function, obtain the sliding surface output variable, and output the sliding surface output variable and the derivative of the segmented transition function to S4, S6, and S7. S4. Receive the sliding surface output variable from S3, read the adaptive auxiliary variable from the previous cycle, perform multi-condition logic operation based on the sliding surface output variable, and obtain the adaptive diagonal gain matrix with output boundary constraints after auxiliary variable update and upper and lower limit amplitude processing. Output the adaptive diagonal gain matrix to S5 and S7. S5. Receive the adaptive diagonal gain matrix output by S4, read the historical signal at the sampling delay time, estimate the system lumped uncertainty term using the historical sampling signal through time delay estimation, and output it to S7. S6. Receive the sliding surface output variable from S3, perform a fixed-time approach law operation to generate an approach control term, and output it to S7. S7 receives the adaptive diagonal gain matrix output from S4, the piecewise transition function derivative output from S3, the historical signal output from S5, the approach control term output from S6, and the desired joint acceleration; calculates the joint control torque and sends it to the robotic arm driver; stores the current cycle control signal as the delayed historical signal for the next cycle; and jumps to S1 to complete the closed-loop control.

2. The non-singular segmented sliding mode adaptive time-delay control method for a rope-driven robotic arm according to claim 1, characterized in that, In S3, the piecewise transition function satisfies: ； In the formula, Output vectors for piecewise transition functions of the sliding surface; For trajectory tracking error; For the power sign function, it is defined as follows: ; The threshold for error segmentation; For power-order parameters; The first boundary continuous transition coefficient; The second boundary continuous transition coefficient; Perform element-wise sine operations on the vector; This refers to the second set of power-law adjustment coefficients for the sliding surface; The power-law adjustment coefficient of the sliding surface satisfies: ； In the formula, This refers to the first group of power-law adjustment coefficients for the sliding surface; Design parameters for the sliding surface; The norm of the tracking error vector; Standard symbolic functions; ； In the formula, Design parameters for the sliding surface.

3. The non-singular segmented sliding mode adaptive time-delay control method for a rope-driven robotic arm according to claim 2, characterized in that, In S4, the adaptive diagonal gain matrix of the first... The diagonal elements of the dimension satisfy: ； ； In the formula, It is an adaptive diagonal gain matrix; For the adaptive diagonal gain matrix, the first... One diagonal element; For the first The nominal gain constant of the degrees of freedom; This is the gain adjustment coefficient; For the first Degrees of freedom adaptive auxiliary variable, the range of values ​​of the adaptive auxiliary variable is constrained This refers to the upper limit of the auxiliary variable; The intermediate variables of the sliding mode criterion satisfy: ； In the formula, For the first Dimensional sliding mode intermediate operation variables; For sliding mode variables No. scalar components; For the first Power parameter of sliding mode criterion; For the first Small neighborhood threshold parameter for sliding mode; It is a small positive number.

4. The non-singular segmented sliding mode adaptive time-delay control method for a rope-driven robotic arm according to claim 3, characterized in that, In S5, the estimated value of the system's lumped uncertainty term satisfies: ； In the formula, for Estimate of the total uncertainty term at time step; For delayed sampling The historical control torque at any given moment; This is the adaptive diagonal gain matrix at the current time. For delay Constant-time joint acceleration signal; Sampling time.

5. The non-singular segmented sliding mode adaptive time-delay control method for a rope-driven robotic arm according to claim 4, characterized in that, In S6, the fixed-time approach law satisfies: ； In the formula, For sliding mode variables The first time derivative with respect to time; This is the first gain coefficient matrix of the reaching law; This is the second gain coefficient matrix of the reaching law; This is the first power of the approximation law; This is the second power of the approach law; Output variables for the sliding surface.

6. The non-singular segmented sliding mode adaptive time-delay control method for a rope-driven robotic arm according to claim 5, characterized in that, In S3, the boundary continuity transition coefficient satisfies: ； ； In the formula, It is an element-wise cosine function; It is an element-wise sine function; The output variables of the sliding surface satisfy: ； In the formula, For sliding mode variables; This is the first weighting coefficient for the sliding surface; This is the second weighting coefficient for the sliding surface.

7. The non-singular segmented sliding mode adaptive time-delay control method for a rope-driven robotic arm according to claim 6, characterized in that, In S4, the rate of change of the adaptive auxiliary variable satisfies: ； In the formula, For adaptive auxiliary variables The derivative with respect to time; The rate coefficient is used as an auxiliary variable.

8. The non-singular segmented sliding mode adaptive time-delay control method for a rope-driven robotic arm according to claim 7, characterized in that, In S7, the joint control torque satisfies: ； In the formula, Output the joint control torque vector at the current moment; The desired joint acceleration.

9. A computer device, characterized in that, include: A processor configured to be coupled to a memory, read and execute instructions and / or program code in the memory to perform the method as described in any one of claims 1-8.

10. A computer-readable medium, characterized in that, The computer-readable medium stores computer program code that, when executed on a computer, causes the computer to perform the method as described in any one of claims 1-8.

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