Trajectory compensation method and device for mechanical arm rope traction joint and medium

Abstract

The application discloses a trajectory compensation method, equipment and medium for a mechanical arm rope traction joint, belongs to the field of trajectory tracking of a mechanical arm rope traction joint, and comprises the following steps: step 1, a kinematics model of the rope traction joint is established according to structural parameters of the rope traction joint; step 2, a dynamics model of the rope traction joint is established based on the kinematics model of the rope traction joint established in step 1, in combination with rope elasticity, damping and rope wheel friction; step 3, an excitation trajectory designed by using a finite term Fourier series is adopted, and a particle swarm algorithm is combined to identify the dynamics model of the rope traction joint established in step 2; and step 4, a compensation amount of an actual execution trajectory is calculated according to the dynamics model of the rope traction joint identified in step 3, and the rope traction joint is controlled to execute a compensated trajectory according to the compensation amount. The method significantly improves the trajectory tracking precision and execution stability of the mechanical arm.

Description

Technical Field

[0001] This invention relates to the field of trajectory tracking technology for cable traction joints of robotic arms, and more particularly to a trajectory compensation method for cable traction joints of robotic arms. Background Technology

[0002] Rope-traction joints, by allowing the drive motor to be positioned close to the base, effectively reduce the equivalent rotational inertia of the robot's end effector and its links, thereby reducing the overall load and improving the system's dynamic response performance. Simultaneously, rope-traction joints possess a degree of compliance, absorbing some impact energy through the elastic deformation of the rope during external collisions or abnormal contact, thus enhancing safety during human-robot interaction to some extent. Therefore, rope-traction mechanisms show promising application prospects in lightweight robotic arms and collaborative robots. However, the elastic deformation and damping effect of the rope itself, as well as the unavoidable friction between the rope and pulleys, can cause deviations between the actual joint output and the ideal motion model, introducing positional errors, velocity errors, and trajectory tracking errors, reducing the accuracy of the robotic arm's end effector. Existing compensation methods for rope-traction joints often rely on empirical corrections or controller parameter tuning, but they cannot quantitatively calculate the motion trajectory compensation amount, resulting in low trajectory tracking accuracy.

[0003] In view of this, the present invention is hereby proposed. Summary of the Invention

[0004] The purpose of this invention is to provide a trajectory compensation method, device, and medium for cable traction joints of robotic arms. This method considers cable elasticity, damping, and sheave friction in the dynamic model of the cable traction joint, identifies the dynamic model through excitation trajectory, and quantitatively calculates the trajectory compensation amount based on the dynamic model, thereby solving the problem of low trajectory tracking accuracy of cable traction joints.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] A trajectory compensation method for a cable-driven joint in a robotic arm includes:

[0007] Step 1: Establish the kinematic model of the cable traction joint based on its structural parameters;

[0008] Step 2: Based on the kinematic model of the rope traction joint established in Step 1, and combining the rope elasticity, damping and rope wheel friction, establish the dynamic model of the rope traction joint.

[0009] Step 3: The excitation trajectory is designed using a finite term Fourier series, and the dynamic model of the rope traction joint established in Step 2 is identified by combining it with the particle swarm optimization algorithm.

[0010] Step 4: Calculate the compensation amount of the actual trajectory based on the dynamic model of the rope traction joint identified in Step 3, and control the rope traction joint to execute the compensated trajectory according to the compensation amount.

[0011] A processing apparatus, comprising:

[0012] At least one memory for storing one or more programs;

[0013] At least one processor is capable of executing one or more programs stored in the memory, such that when the processor executes one or more programs, the processor can implement the method of the present invention.

[0014] A readable storage medium storing a computer program that, when executed by a processor, enables the implementation of the methods described in this invention.

[0015] Compared with the prior art, the trajectory compensation method, device and medium for cable traction joints of robotic arms provided by the present invention have the following advantages:

[0016] This method, based on a cable-driven joint dynamics model, models and compensates for trajectory deviations caused by cable elastic deformation, damping effects, and frictional characteristics, thereby making the compensation results more consistent with the dynamic error characteristics of actual transmission processes. Simultaneously, this method can complete trajectory correction without relying on joint position feedback, thus significantly improving the trajectory tracking accuracy and execution stability of the robotic arm while reducing sensor dependence and system complexity. Attached Figure Description

[0017] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 A flowchart is provided for a trajectory compensation method for a cable traction joint of a robotic arm, as described in an embodiment of the present invention.

[0019] Figure 2 This invention provides an overall flowchart of a trajectory compensation method for a robotic arm's rope traction joint in an embodiment of the invention.

[0020] Figure 3 This is a schematic diagram of the motion configuration of the rope traction joint in the trajectory compensation method provided in the embodiment of the present invention.

[0021] Figure 4This is a schematic diagram of the rope traction joint pulley group and rope tension in the trajectory compensation method provided in the embodiment of the present invention. Detailed Implementation

[0022] 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 a part of the embodiments of the present invention, and not all of them, and do not constitute a limitation on the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the protection scope of the present invention.

[0023] First, the following explanations are provided for the terms that may be used in this article:

[0024] The term "and / or" means that either or both can be achieved simultaneously. For example, X and / or Y means that it includes both "X" or "Y" as well as the three cases of "X and Y".

[0025] The terms "comprising," "including," "containing," "having," or other similar semantic descriptions should be interpreted as non-exclusive inclusion. For example, including a technical feature element (such as raw material, component, ingredient, carrier, dosage form, material, size, part, component, mechanism, device, step, process, method, reaction conditions, processing conditions, parameter, algorithm, signal, data, product or article of manufacture, etc.) should be interpreted as including not only the expressly listed technical feature element, but also other technical feature elements that are not expressly listed and are well-known in the art.

[0026] The term "composed of" excludes any technical features not expressly listed. When used in a claim, it closes the claim to exclude all technical features other than those expressly listed, except for associated conventional impurities. If the term appears only in a clause of a claim, it limits the claim to the elements expressly listed in that clause; elements recited in other clauses are not excluded from the overall claim.

[0027] Unless otherwise explicitly specified or limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to the internal connection between two components. Those skilled in the art can understand the specific meaning of the above terms in this document according to the specific circumstances.

[0028] The terms “center,” “longitudinal,” “lateral,” “length,” “width,” “thickness,” “up,” “down,” “front,” “back,” “left,” “right,” “vertical,” “horizontal,” “top,” “bottom,” “inner,” “outer,” “clockwise,” and “counterclockwise” indicate the current orientation or positional relationship, and are only for the convenience and simplification of description, and do not explicitly or implicitly suggest that the device or component referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this document.

[0029] The technical solution provided by this invention will be described in detail below. Contents not described in detail in the embodiments of this invention are prior art known to those skilled in the art. Where specific conditions are not specified in the embodiments of this invention, they shall be performed according to conventional conditions in the art or conditions recommended by the manufacturer. Reagents or instruments used in the embodiments of this invention whose manufacturers are not specified are all conventional products that can be purchased commercially.

[0030] like Figure 1 As shown, this invention provides a trajectory compensation method for a cable-driven joint of a robotic arm, used to improve trajectory tracking accuracy when the cable-driven joint executes a trajectory, including the following steps:

[0031] Step 1: Establish the kinematic model of the cable traction joint based on its structural parameters;

[0032] Step 2: Based on the kinematic model of the rope traction joint established in Step 1, and combining the rope elasticity, damping and rope wheel friction, establish the dynamic model of the rope traction joint.

[0033] Step 3: The excitation trajectory is designed using a finite term Fourier series, and the dynamic model of the rope traction joint established in Step 2 is identified by combining it with the particle swarm optimization algorithm.

[0034] Step 4: Calculate the compensation amount of the actual trajectory based on the dynamic model of the rope traction joint identified in Step 3, and control the rope traction joint to execute the compensated trajectory according to the compensation amount.

[0035] Preferably, in step 1 of the above method, the kinematic model of the cable traction joint is established based on the structural parameters of the cable traction joint in the following manner:

[0036] The upper and lower rope traction joints are located at the elbows of the robotic arm, and are tractioned by the front rope. With the back traction rope The system consists of two traction ropes, with the front traction rope comprising an inner front traction rope and an outer front traction rope, and the rear traction rope comprising an inner rear traction rope and an outer rear traction rope. The front traction rope... The length is Back traction rope The length is Front traction rope upper arm anchor point With the back traction rope upper arm anchor point The length between is The two traction ropes are fixed to the motor drum and the upper arm anchor point via pulley blocks. The changes in rope length on both sides are equal in magnitude but opposite in sign. The changes in rope length on both sides are related to the motor rotation angle of the drive motor drum. The following relationship formula is satisfied:

[0037] ;

[0038] in, Indicates the radius of the motor drum; , These represent the changes in the length of the front traction rope and the changes in the length of the back traction rope, respectively.

[0039] Because the absolute value of the change in length of the two traction ropes is always equal and the two traction ropes are always parallel to the line connecting the rotation axes of the two rope traction joints. Then the two cable traction joints at the elbow of the robotic arm will always maintain equal actual joint angles. This makes the entire robotic arm elbow appear The rotation angle;

[0040] Actual joint angle at the rope traction joint In the initial state, the upper half of the front traction rope is rotated relative to the line connecting the rotation axes of the two rope traction joints. initial elongation for:

[0041] ;

[0042] When the rope pulls the actual joint angle rotation angle Then, the upper part of the front traction rope rotates relative to the line connecting the two rope traction joint axes. The elongation becomes :

[0043] ;

[0044] Therefore, the line connecting the rotation axes of the two rope traction joints The following conversion relationship exists between the elongation and the actual joint angle of the rope traction joint:

[0045] ;

[0046] in, The number of traction ropes wound around the movable pulley of the pulley system;

[0047] By combining the above formulas for the elongation of the line connecting the two rope traction joint rotation axes, the conversion formula between the elongation of the line connecting the two rope traction joint rotation axes and the actual joint angle of the rope traction joint, and the formula relating the change in rope length of the two traction ropes to the motor rotation angle of the drive motor drum, we obtain the motor rotation angle as the kinematic model of the rope traction joint. Actual joint angle of the rope-traction joint The conversion relationship between them is as follows:

[0048] ;

[0049] ;

[0050] in, (•) represents the sine function; (•) represents the arcsine function.

[0051] Preferably, in step 2 of the above method, based on the kinematic model of the cable traction joint established in step 1, and in combination with the cable elasticity, damping, and sheave friction, a dynamic model of the cable traction joint is established, including:

[0052] The established dynamic model of the cable traction joint includes:

[0053] The dynamic models for the tension of the traction rope on the inner front side, the inner back side, and the frictional models for the tension of the traction rope on the outer front side and the outer back side of the traction rope at the cable traction joint are as follows:

[0054] The rope traction joint has a front pulley system and a back pulley system. Both the front and back pulley systems have two traction ropes wound around them. The actual torque acting on the rope traction joint... Represented as:

[0055] ;

[0056] in, The lever arm representing the tension of the traction rope to the traction joint axis; This indicates the tension acting on the movable pulley of the front pulley block. , This indicates the corresponding tension of the outer traction rope. The length of the outer traction rope is expressed as... express; This indicates the corresponding tension of the inner traction rope on the front side. The length of the inner traction rope on the front side is expressed as... express; This indicates the tension acting on the movable pulley on the back side of the pulley block. , This indicates the corresponding tension of the outer traction rope on the back side. The length of the outer traction rope on the back side is indicated by... express; This indicates the corresponding tension of the inner traction rope on the back side. The length of the inner traction rope on the back side is indicated by... express; (•) represents the sine function;

[0057] A dynamic model of the tension of the traction rope on the front inner side and the tension of the traction rope on the back inner side of the rope traction joint is established using an elastic-damped model.

[0058] Front inner traction rope tension The dynamic model is as follows:

[0059] ;

[0060] in, This indicates the pretension of the inner traction rope on the front side; Indicates the elastic coefficient of the inner traction rope on the front side; This indicates the damping coefficient of the inner traction rope on the front side; This indicates the change in length of the traction rope on the inner side of the front. This indicates the rate of change of the rope length of the inner traction rope on the front side;

[0061] Since the front traction rope and the back traction rope always maintain opposite motion trends, the tension of the inner back traction rope is obtained. The dynamic model is as follows:

[0062] ;

[0063] in, Indicates the elastic coefficient of the inner traction rope on the back; This indicates the change in length of the inner traction rope on the back side; This indicates the rate of change of the rope length of the inner traction rope on the back side;

[0064] Assuming the pretension forces of the front and back traction ropes are equal, and the damping coefficients are constant parameters, the elastic coefficients of the inner front traction rope and the inner back traction rope are calculated as follows: The elastic coefficient of the inner front traction rope is expressed as:

[0065] ;

[0066] in, This indicates the Young's modulus of the material of the inner traction rope on the front side; This represents the cross-sectional area of ​​the traction rope; all traction ropes have the same cross-sectional area. Since the inner traction rope on the front side and the inner traction rope on the back side satisfy the constraints... ,in, Connecting the rotation axes of the two rope traction joints The length of the inner traction rope on the back determines the elastic coefficient. The elastic modulus of the traction rope from the inside front Represented as:

[0067] ;

[0068] Based on the kinematic model of the rope traction joint in step 1, the length of the traction rope on the inner side of the front is... Actual joint angle of the rope-traction joint The relationship is represented as:

[0069] ;

[0070] During the movement of the rope-traction joint, the hysteresis and compliance characteristics of the rope traction mechanism cause a deviation between the expected joint angle and the actual joint angle, resulting in a change in the length of the traction rope on the inner side of the front. Represented as:

[0071] ;

[0072] in, This indicates the actual length of the traction rope on the inner side of the front. This indicates the expected length of the traction rope on the inner side of the front. Indicates the front traction rope upper arm anchor point With the back traction rope upper arm anchor point The length between; The actual joint angle of the rope-traction joint; Indicates the desired joint angle of the rope-traction joint; (•) represents the sine function;

[0073] Similarly, the rate of change of the length of the corresponding inner traction rope on the front side... Represented as:

[0074] ;

[0075] in, Indicates the rate of change of the length of the inner traction rope on the front side; This indicates the rate of change of the actual value of the length of the traction rope on the inner side of the front. This indicates the rate of change of the expected value of the inner traction rope length on the front side; This indicates the rate of change of the desired joint angle of the cable-driven joint; This indicates the rate of change of the actual joint angle of the rope-traction joint; (•) represents the cosine function;

[0076] By establishing frictional force models for the tension of the traction rope on the outer side and the tension of the traction rope on the inner side, and constructing a rope-pulley friction model using Capstan friction, the tension of the traction rope on the outer side is then determined. The frictional force model is expressed as:

[0077] ;

[0078] in, This indicates the coefficient of friction between the outer traction rope and the corresponding movable pulley surface. This indicates that the outermost traction rope wraps around the corresponding movable pulley surface at the corner. Indicates judgment The sign of the function indicates whether the value is positive or negative, which can determine the direction of motion of the velocity of the inner traction rope on the front. To judge The sign function of the value; due to the wrap angle Always maintain as The tension of the aforementioned frontal outer traction rope The friction force model formula simplifies to:

[0079] ;

[0080] in, The tension transmission coefficient;

[0081] Using a continuous and first-order differentiable hyperbolic tangent function (•) For symbolic functions A smooth substitution is performed to ensure the stability and identification accuracy of the dynamic model of the rope traction joint, thus obtaining the final frontal lateral traction rope tension. The friction model is as follows:

[0082] ;

[0083] in, These are parameters used to adjust the smoothness of the transition region; (•) is the hyperbolic tangent function;

[0084] Similarly, the tension of the outer traction rope on the back side is obtained. The friction model is as follows:

[0085] ;

[0086] The dynamic model of the cable traction joint, derived from the above formula, can predict the output trajectory given the input trajectory, and perform trajectory compensation based on the dynamic model of the cable traction joint in trajectory tracking tasks.

[0087] Preferably, in step 3 of the above method, the excitation trajectory in the form of a finite-term Fourier series is designed as follows:

[0088] A finite-term Fourier series design is used to identify the excitation trajectory of the dynamic model of the cable traction joint. for:

[0089] ;

[0090] Speed ​​of excitation trajectory for:

[0091] ;

[0092] acceleration of the excitation trajectory for:

[0093] ;

[0094] in, Indicates time; Indicates the first Fourier series; The number of terms in the Fourier series; and These are the amplitudes of the sine and cosine function terms, respectively. For constant terms; fundamental angular frequency , For trajectory period; (•) represents the sine function; (•) represents the cosine function;

[0095] The excitation trajectory parameters are generated through random sampling and must satisfy the following constraints:

[0096] ;

[0097] in, and These represent the maximum and minimum allowable joint angles of the rope traction joint, respectively. and These represent the upper limit of the actual rate of change of the joint angle and the upper limit of the acceleration of the rope traction joint, respectively. This represents the rate of change of the desired trajectory at the initial moment; This represents the acceleration of the desired trajectory at the initial moment; Indicates the period of the trajectory The rate of change of the expected trajectory; Indicates the period of the trajectory The acceleration of the expected trajectory.

[0098] Preferably, in step 3 of the above method, the dynamic model of the rope traction joint established in step 2 is identified by combining the particle swarm optimization algorithm in the following manner:

[0099] After the excitation trajectory is designed, it is executed on the cable traction joint. During the operation, the expected and actual joint angles of the cable traction joint are recorded. Based on the recorded expected and actual joint angles, the particle swarm optimization algorithm is used to identify the dynamic model parameters, including:

[0100] Using the dynamic model of the rope traction joint established in step 2 as a parameterized model, the Young's modulus of the front inner traction rope material is determined as the parameter to be identified in this parameterized model. Damping coefficient of the inner traction rope on the front Pretension of the inner traction rope on the front Tension transmission coefficient and parameters used to adjust the smoothness of the transition region Then, the position vector of each particle is mapped to a set of candidate parameters for a parameterized model. A fitness function is constructed based on the deviation between the experimental measurement output and the calculated output of the parameterized model. The fitness function characterizes the degree of fit between the parameterized model and the actual system under the current combination of candidate parameters.

[0101] Preferably, in the above method, during the particle swarm iteration process of identifying dynamic model parameters using the particle swarm algorithm, the velocity and position of each particle are updated based on its historical best position and global best position, and the update formula is as follows:

[0102] ;

[0103] in, Indicates the first The particle in the first Speed ​​during the next iteration; Inertial weight; Indicates the first The particle in the first Speed ​​during the next iteration; Indicates the first The individual historical best position of each particle; Indicates the first The particle in the first The position at the next iteration; This indicates the current globally optimal position; and These are individual learning factors and group learning factors, respectively. and The range of values ​​is respectively in Random numbers within; Indicates the first The particle in the first The position at the next iteration;

[0104] After each iteration, the fitness value corresponding to the current position of the particle is calculated, and the individual optimal position and the global optimal position are updated respectively. When the position of the particle exceeds the preset parameter range, the particle is subjected to boundary constraint processing to ensure that the parameter values ​​are within the allowable range. After the preset termination condition is met, the parameters corresponding to the global optimal position are output as the model identification result.

[0105] Preferably, in step 4 of the above method, based on the dynamic model of the cable traction joint identified in step 3, the motion trajectory compensation amount is calculated according to the actual dynamic model of the cable traction joint, and the compensated trajectory is executed, including:

[0106] Step 41, calculate the expected trajectory after compensation at the starting point: based on the dynamic model of the cable traction joint... Expected trajectory after time-compensation Perform calculations to make The actual trajectory of time discretization and The expected trajectory of time discretization Consistency, that is ;

[0107] exist At the initial moment of the trajectory, the robotic arm's cable traction joint is in a static state, and the cable traction joint torque is used to overcome gravity. At this time, the rate of change of the cable length and the joint velocity are both zero. Therefore, after compensation at the starting point, the expected trajectory can be directly calculated by solving the following equations:

[0108] ;

[0109] in, , , , , and They represent The moment of the rope traction joint torque, the tension on the front movable pulley, the tension on the back movable pulley, the elastic coefficient of the front inner traction rope, the elastic coefficient of the back inner traction rope, and the change in rope length of the front inner traction rope. (•) represents the sine function;

[0110] Step 42, Iterative Derivation Desired trajectory after time-compensation: Based on the dynamic model of the cable-traction joint established in step 2, during the movement of the cable-traction joint, The compensation amount of the tension on the front movable pulley and the tension on the back movable pulley at any given time satisfies the following constraint formula:

[0111] ;

[0112] in, , They represent The tension on the front pulley at any given moment The tension on the pulley on the back of the moment; express The actual trajectory discretized at time. express The desired trajectory discretized at time points; express The expected trajectory of the joint after compensation under the constant-time cable traction. (•) represents the sine function;

[0113] In the above constraint formula, the right side of the equation is determined by the actual motion state of the current cable-traction joint, while the left side depends on the actual motion state of the current cable-traction joint and... Desired trajectory after compensation of the cable traction joint Combined with step 41 The actual trajectory of time discretization and The expected trajectory of time discretization Consistent assumptions, namely The actual trajectory of time discretization Given that, the key to eliminating trajectory tracking errors lies in... The actual trajectory of time discretization Given the expected trajectory after compensation Calculations are performed to arrive at a reasonable result. The tension on the front pulley at any moment and The tension on the pulley on the back of the moment Make the above constraint formulas true;

[0114] Because the constraint formula for calculating the tensile compensation amount contains a part where the variable is multiplied by the cosine function, it is impossible to write out the analytical solution form of the variable. Therefore, Newton's iteration method is used to obtain the solution. Desired trajectory after compensation of the cable traction joint The numerical solution, let The objective function of Newton's iteration method is expressed as follows:

[0115] ;

[0116] The independent variable , express The tension on the pulley is always present. express The tension on the movable pulley on the back side is constant; therefore, Newton's iteration method is used to solve the problem. The zero point is Desired trajectory after compensation of the cable traction joint Numerical solution;

[0117] Calculated Desired trajectory after compensation of the cable traction joint Then, calculate a reasonable The tension on the front pulley at any moment and The tension on the pulley on the back of the moment To make the above equation hold, we obtain the expected trajectory after compensation.

[0118] Step 43: Perform the compensated desired trajectory obtained in step 42 on the cable traction joint.

[0119] Preferably, in step 42 of the above method, Newton's iteration method is used to solve the problem in the following manner. The expected trajectory after the zero point is compensated The numerical solution includes: first, given the function initial iteration value Initial iteration value Using the actual trajectory at the current moment and calculate the function and its first derivative The iterative values ​​are then updated according to Newton's iteration formula using the following formula:

[0120] ;

[0121] in, Indicates the first Approximate solution at the next iteration; Indicates the first Approximate solution at the next iteration;

[0122] Through continuous iteration The function value gradually approaches zero, thus obtaining the function The zero point;

[0123] When the difference between two consecutive iterations is less than a preset threshold or If the error is less than the preset error limit, stop the iteration and take the current iteration value as the approximate solution of the zero point;

[0124] To prevent the iteration process from diverging, the initial iteration value must be within a preset valid range, and this must be ensured during the iteration process. ;

[0125] Through the above process, the compensated expected trajectory is calculated at each time step. The calculation is performed, and after the iterative calculation of the entire trajectory is completed, the final compensated expected trajectory is obtained.

[0126] This invention also provides a processing apparatus, comprising:

[0127] At least one memory for storing one or more programs;

[0128] At least one processor is capable of executing one or more programs stored in the memory, such that when the processor executes one or more programs, the processor can implement the methods described above.

[0129] The present invention further provides a readable storage medium storing a computer program that, when executed by a processor, can implement the above-described method.

[0130] To more clearly demonstrate the technical solution and its effects provided by the present invention, the following detailed description of the solution provided by the embodiments of the present invention is provided with reference to specific examples.

[0131] Example 1

[0132] like Figure 1 , Figure 2 As shown, this embodiment provides a trajectory compensation method for a robotic arm's cable traction joint, used to improve the trajectory tracking accuracy of the cable traction joint, including:

[0133] Step 1: Establish the kinematic model of the cable traction joint based on its structural parameters. The cable traction joint structure located at the elbow of the robotic arm is shown below. Figure 3 As shown, where and These refer to the front traction rope and the back traction rope, respectively. The front traction rope and the back traction rope are traction ropes on both sides. The front traction rope includes the inner front traction rope and the outer front traction rope, and the back traction rope includes the inner back traction rope and the outer back traction rope. Represents line segment Length of line segment For the back traction rope upper arm anchor point With front traction rope upper arm anchor point Connecting line segments, and These represent the back traction ropes. Length of the front traction rope , This indicates the number of ropes wound around the movable pulley system. This indicates the actual value of the rope traction joint rotation angle. The traction ropes on both sides are fixed to the motor drum and the upper arm anchor point via pulley systems. The changes in rope length on both sides are equal in magnitude but opposite in sign, and are related to the motor rotation angle of the driving motor drum. The following relationship must be satisfied:

[0134] ;

[0135] in, Indicates the radius of the motor drum. , These represent the changes in rope length on the left and right sides, respectively. Since the absolute values ​​of the changes in rope length on both sides are always equal and the traction rope is always parallel to the line connecting the rotation axes of the two joints... Therefore, the upper and lower joints of the elbow always maintain equal angles. This makes the entire elbow appear The rotation angle.

[0136] In the initial state, that is At that time, the upper half of the front traction rope is relative to initial elongation for:

[0137] ;

[0138] When the rope pulls the joint to rotate After the angle, the elongation becomes :

[0139] ;

[0140] Therefore, the following relationship exists between the elongation of the traction rope and the actual joint angle of the rope traction joint:

[0141] ;

[0142] Combining the above formulas, we can determine the motor rotation angle. Actual joint angle of the rope-traction joint The conversion relationship between them is as follows:

[0143] ;

[0144] Step 2: Based on the kinematic model of the cable traction joint from Step 1, a dynamic model of the cable traction joint is modeled. A schematic diagram of the pulley system and cable tension of the cable traction joint is shown below. Figure 4 As shown. By Figure 4 It can be determined that the number of ropes wound around the movable pulley system , , , , These represent the rope lengths and corresponding tensions of the outer and inner traction ropes, respectively. , , , These represent the rope lengths and corresponding tensions of the outer and inner traction ropes on the back side, respectively. and These represent the tension forces acting on the front movable pulley and the back movable pulley, respectively.

[0145] according to Figure 4 The actual torque acting on the rope traction joint It can be represented as:

[0146] ;

[0147] in, This represents the lever arm of the tension applied to the rope traction joint axis. Since both the front and back pulley systems are tractioned by the outer and inner traction ropes, the tension on the movable pulley bearing can be expressed as:

[0148] ;

[0149] Since the traction rope is fixed to the upper arm via the anchor point on the inner traction rope, the tension of the inner traction rope can be directly calculated based on the elongation and the mechanical properties of the rope material. Consider using an elastic-damped model to dynamically model the rope, taking the tension of the inner traction rope on the front as an example. Taking the dynamic model as an example, it is represented as follows:

[0150] ;

[0151] in, This indicates the pretension of the inner traction rope on the front side. This indicates the elastic coefficient of the inner traction rope on the front side. This represents the damping coefficient of the traction rope. For ease of theoretical derivation and model analysis, the pretension of the front inner traction rope and the back inner traction rope are assumed to be equal, and the damping coefficient is a steady parameter. The elastic coefficient of the front inner traction rope can typically be expressed as:

[0152] ;

[0153] in, This indicates the Young's modulus of the material of the inner traction rope on the front side. This represents the cross-sectional area of ​​the traction rope. Since the inner traction rope on the front and the inner traction rope on the back satisfy the constraints... ,in, For line segments The length of the inner traction rope on the back side, therefore the elastic coefficient of the rope is... It can be directly from Represented as:

[0154] ;

[0155] Since the front traction rope and the back traction rope always maintain opposite motion trends, the tension of the inner back traction rope can be obtained similarly. The dynamic model is as follows:

[0156] ;

[0157] Based on the kinematic model of the rope traction joint derived in step 1, the length of the traction rope on the inner side of the front is... Actual joint angle of the rope-traction joint The relationship is represented as follows:

[0158] ;

[0159] During the movement of a rope-traction joint, the hysteresis and compliance characteristics of the rope traction mechanism often cause a deviation between the desired and actual joint angles, resulting in varying degrees of rope tension. This geometric change alters the rope tension and ultimately affects the driving torque of the rope traction joint. (The length of the traction rope on the inner side of the front is used as an example.) For example, let This indicates the actual joint angle of the rope traction joint. This indicates the desired joint angle of the rope-traction joint. Indicates the actual rope length. The desired rope length represents the change in the length of the frontal inner traction rope due to the discrepancy between the desired joint angle and the actual joint angle. It is expressed as follows:

[0160] ;

[0161] Similarly, the corresponding rate of change of rope length It is expressed as follows:

[0162] ;

[0163] The tension of the front outer traction rope and the back outer traction rope are modeled using the frictional relationship between the traction rope and the pulley. Considering the use of Capstan friction to construct the rope-pulley friction model, the tension of the front outer traction rope... The friction force model is expressed as follows:

[0164] ;

[0165] in, This represents the coefficient of friction between the traction rope and the surface of the movable pulley; This indicates that the outermost traction rope wraps around the corresponding movable pulley surface at the corner. This indicates the direction of movement of the outer traction rope. Because in... Figure 4 Under the rope traction structure shown, Always maintain as Therefore, the above formula can be further simplified as follows:

[0166] ;

[0167] Sign function When the direction of motion changes, there are discontinuous jumps; therefore, the tension transmission coefficient in the above formula will change from... Switch to immediately This introduces an impact effect into the numerical calculation and system response, thereby affecting the stability and identification accuracy of the rope traction joint dynamics model. Therefore, a continuous and first-order differentiable hyperbolic tangent function is used to smooth it out.

[0168] ;

[0169] in, This is used to adjust the smoothness of the transition area. Similarly, the frictional force model for the tension of the outer traction rope on the back can be obtained as follows:

[0170] ;

[0171] Based on the above derivation, the motion of the cable-traction joint initially originates from the tension difference in the front and rear traction ropes caused by the error between the desired joint angle and the actual joint angle. This tension is then converted into torque at the joint, thereby driving the joint motion. After establishing an accurate dynamic model of the cable-traction joint based on the above formula derivation, the output trajectory can be predicted given the input trajectory, and trajectory compensation can be performed based on this dynamic model in trajectory tracking tasks.

[0172] Step 3: Based on the cable traction joint dynamics model described in Step 2, design an excitation trajectory in the form of a finite-term Fourier series, and identify the parameters of the cable traction joint dynamics model using a particle swarm optimization algorithm, including:

[0173] Step 31: The excitation trajectory is designed using a finite-term Fourier series to identify the dynamic model of the cable traction joint, as shown below:

[0174] A finite-term Fourier series design is used to identify the excitation trajectory of the dynamic model of the cable traction joint. for:

[0175] ;

[0176] Speed ​​of excitation trajectory for:

[0177] ;

[0178] acceleration of the excitation trajectory for:

[0179] ;

[0180] in, Indicates time, Let be the number of terms in the Fourier series. and These are the amplitudes of the sine and cosine function terms, respectively. The constant term is the fundamental angular frequency. , The trajectory period is defined as follows. The excitation trajectory, in finite-term Fourier series form, possesses periodicity, smoothness, and continuity, effectively stimulating the robot's dynamic characteristics and improving data acquisition efficiency during periodic repetitive motion. The trajectory parameters are generated through random sampling and are guaranteed to satisfy the following constraints:

[0181] ;

[0182] in, and These represent the maximum and minimum values ​​of the actual joint angle of the rope traction joint, respectively. and These represent the upper limits of the actual joint angle change rate and acceleration of the rope traction joint, respectively. The last two lines of constraints indicate that the change rate and acceleration are both zero at the beginning and end of the trajectory, thus ensuring a relatively smooth start and end point.

[0183] After the excitation trajectory is designed, it is executed on the cable traction joint, and the desired joint angle of the cable traction joint is recorded during the operation. Actual joint angle of the rope-traction joint This is used for subsequent identification.

[0184] Step 32: Based on the data collected in Step 31, the particle swarm optimization algorithm is used to identify the parameters of the dynamic model. Specifically, using the rope traction joint dynamic model established in Step 2 as the parameterized model, the parameter to be identified for this parameterized model is determined to be the Young's modulus of the front inner traction rope material. Damping coefficient of the inner traction rope on the front Pretension of the inner traction rope on the front Tension transmission coefficient and parameters used to adjust the smoothness of the transition region Then, the position vector of each particle is mapped to a set of candidate model parameters. A fitness function is constructed based on the deviation between the experimental measurement output and the model calculation output to characterize the degree of fit between the model and the actual system under the current combination of candidate parameters.

[0185] During the particle swarm iteration process, the velocity and position of each particle are updated based on its historical best position and global best position. The update formula is as follows:

[0186] ;

[0187] in, Indicates the first The particle in the first Speed ​​during the next iteration; Inertial weight; Indicates the first The particle in the first Speed ​​during the next iteration; Indicates the first The individual historical best position of each particle; Indicates the first The particle in the first The position at the next iteration; This indicates the current globally optimal position; and These are individual learning factors and group learning factors, respectively. and The range of values ​​is respectively in Random numbers within; Indicates the first The particle in the first The position at the next iteration;

[0188] After each iteration, the fitness value corresponding to the particle's current position is calculated, and the individual optimal position and the global optimal position are updated respectively. When the particle's position exceeds the preset parameter range, boundary constraints are applied to ensure that the parameter values ​​are within the allowable range. After the preset termination condition is met, the parameters corresponding to the global optimal position are output as the model identification result.

[0189] Step 4: Based on the identification results of the cable traction joint dynamic model described in Step 3, calculate the motion trajectory compensation amount according to the actual cable traction joint dynamic model, and execute the compensated trajectory, including:

[0190] Step 41: Calculate the compensated desired trajectory at the starting point. Since the actual trajectory calculation and execution process typically involves representing and executing the trajectory as a discrete time series, the desired trajectory and the actual trajectory are discretized into... and The sampling period is expressed as The main task of this step is to determine the compensated desired trajectory based on the rope traction joint dynamics model. Calculations are performed to ensure that the actual trajectory matches the desired trajectory, i.e. Subsequent derivations are all based on this premise; therefore, both the actual and expected trajectories are treated using... express.

[0191] At the starting point of the trajectory, i.e. At this point, the system is in a static state, and the cable traction joint torque is mainly used to overcome gravity. Since the cable elongation velocity and joint angular velocity are both zero at this time, the compensated desired trajectory at the starting point can be directly calculated by solving the following equations:

[0192] ;

[0193] in, , , , , and They represent The moment of the rope traction joint torque, the tension on the front movable pulley, the tension on the back movable pulley, the elastic coefficient of the front inner traction rope, the elastic coefficient of the back inner traction rope, and the change in rope length of the front inner traction rope. (•) represents the sine function.

[0194] Step 42, iteratively derive the desired trajectory after compensation. Based on the dynamic model of the cable-traction joint derived in Step 2, during joint movement, The compensation amount of the tension on the front movable pulley and the tension on the back movable pulley at any given time satisfies the following constraint formula:

[0195] ;

[0196] in, , They represent The tension on the front pulley at any given moment The tension on the pulley on the back of the moment; express The actual trajectory discretized at time. express The desired trajectory discretized at time points; express The expected trajectory of the joint after compensation under the constant-time cable traction. (•) represents the sine function;

[0197] In the above constraint formula, the right side of the equation is determined by the actual motion state of the current cable-driven joint, while the left side depends on the actual motion state and the desired trajectory after compensation. Combining the assumption above that the actual trajectory matches the expected trajectory, that is... Given that, the key to eliminating trajectory tracking errors lies in... Given the expected trajectory after compensation Calculations are performed to arrive at a reasonable result. and This ensures the above equation holds true. Furthermore, since the calculation of the compensation involves the multiplication of the variable with the cosine function, the analytical solution form of the variable cannot be written. Therefore, Newton's iteration method is used to obtain the result. The numerical solution. Let The objective function of Newton's iteration method is expressed as follows:

[0198] ;

[0199] The independent variable Therefore, Newton's iterative method is used to solve the problem. The zero point is the expected trajectory after compensation. The numerical solution. Specifically, first, given the function... initial iteration value The initial iteration value here use The actual trajectory of time discretization and calculate the function and its first derivative The iterative values ​​are then updated according to Newton's iterative formula:

[0200] ;

[0201] in, Indicates the first Approximate solution at the next iteration Indicates the first The approximate solution at the second iteration. Through continuous iteration, the approximate solution is obtained. The function value gradually approaches zero, thus obtaining the function. Zero point.

[0202] When the difference between two consecutive iterations is less than a preset threshold, or When the error is less than a preset error limit, the iteration stops, and the current iteration value is taken as an approximate solution at the zero point. To avoid divergence during the iteration process, it is preferable that the initial value be within a preset effective range, and that this is maintained during the iteration process. Through the above process, the compensated expected trajectory is calculated at each time step. After performing calculations and completing iterative calculations of the entire trajectory, the final compensated joint trajectory can be obtained.

[0203] Step 43: Perform the final compensated joint trajectory on the cable-traction joint. Results show that the actual trajectory after compensation is significantly improved compared to before compensation. With the expected trajectory The error between the two sides was significantly reduced, verifying that the compensation method has a significant effect on improving trajectory tracking accuracy.

[0204] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc.

[0205] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims. The information disclosed in the background section is intended only to enhance the understanding of the overall background technology of the present invention and should not be construed as an admission or implication in any way that such information constitutes prior art known to those skilled in the art.

Claims

1. A trajectory compensation method for a cable-driven joint in a robotic arm, characterized in that, include: Step 1: Establish the kinematic model of the cable traction joint based on its structural parameters; In step 1, the kinematic model of the cable traction joint is established based on its structural parameters in the following manner: The upper and lower rope traction joints are located at the elbows of the robotic arm, and are tractioned by the front rope. With the back traction rope The system consists of two traction ropes, with the front traction rope comprising an inner front traction rope and an outer front traction rope, and the rear traction rope comprising an inner rear traction rope and an outer rear traction rope. The front traction rope... The length is Back traction rope The length is Front traction rope upper arm anchor point With the back traction rope upper arm anchor point The length between is The two traction ropes are fixed to the motor drum and the upper arm anchor point via pulley blocks. The changes in rope length on both sides are equal in magnitude but opposite in sign. The changes in rope length on both sides are related to the motor rotation angle of the drive motor drum. The following relationship formula is satisfied: ； in, Indicates the radius of the motor drum; , These represent the changes in the length of the front traction rope and the changes in the length of the back traction rope, respectively. Because the absolute value of the change in length of the two traction ropes is always equal and the two traction ropes are always parallel to the line connecting the rotation axes of the two rope traction joints. Then the two cable traction joints at the elbow of the robotic arm will always maintain equal actual joint angles. This makes the entire robotic arm elbow appear The rotation angle; Actual joint angle at the rope traction joint In the initial state, the upper half of the front traction rope is rotated relative to the line connecting the rotation axes of the two rope traction joints. initial elongation for: ； When the rope pulls the joint angle rotation angle Then, the upper part of the front traction rope rotates relative to the line connecting the two rope traction joint axes. The elongation becomes : ； Therefore, the line connecting the rotation axes of the two rope traction joints The following conversion relationship exists between the elongation and the actual joint angle of the rope traction joint: ； in, The number of traction ropes wound around the movable pulley of the pulley system; By combining the elongation of the line connecting the two rope traction joint rotation axes with the conversion relationship between the elongation of the line connecting the two rope traction joint rotation axes and the actual joint angle of the rope traction joint, and the relationship between the change in rope length of the two traction ropes and the motor rotation angle of the drive motor drum, the motor rotation angle, which serves as the kinematic model of the rope traction joint, can be obtained. Actual joint angle of the rope-traction joint The conversion relationship between them is as follows: ； ； in, (•) represents the sine function; (•) represents the arcsine function; Step 2: Based on the kinematic model of the rope traction joint established in Step 1, and combining the rope elasticity, damping and rope wheel friction, establish the dynamic model of the rope traction joint. In step 2, based on the kinematic model of the cable traction joint established in step 1, and incorporating cable elasticity, damping, and sheave friction, a dynamic model of the cable traction joint is established, including: The established dynamic model of the cable traction joint includes: The dynamic models for the tension of the traction rope on the inner front side, the inner back side, and the frictional models for the tension of the traction rope on the outer front side and the outer back side of the traction rope at the cable traction joint are as follows: The rope traction joint has a front pulley system and a back pulley system. Both the front and back pulley systems have two traction ropes wound around them. The actual torque acting on the rope traction joint... Represented as: ； in, The lever arm representing the tension of the traction rope to the traction joint axis; This indicates the tension acting on the movable pulley of the front pulley block. , This indicates the corresponding tension of the outer traction rope. The length of the outer traction rope is expressed as... express; This indicates the corresponding tension of the inner traction rope on the front side. The length of the inner traction rope on the front side is expressed as... express; This indicates the tension acting on the movable pulley on the back side of the pulley block. , This indicates the corresponding tension of the outer traction rope on the back side. The length of the outer traction rope on the back side is indicated by... express; This indicates the corresponding tension of the inner traction rope on the back side. The length of the inner traction rope on the back side is indicated by... express; (•) represents the sine function; A dynamic model of the tension of the traction rope on the front inner side and the tension of the traction rope on the back inner side of the rope traction joint is established using an elastic-damped model. Front inner traction rope tension The dynamic model is as follows: ； in, This indicates the pretension of the inner traction rope on the front side; Indicates the elastic coefficient of the inner traction rope on the front side; This indicates the damping coefficient of the inner traction rope on the front side; This indicates the change in length of the traction rope on the inner side of the front. This indicates the rate of change of the rope length of the inner traction rope on the front side; Since the front traction rope and the back traction rope always maintain opposite motion trends, the tension of the inner back traction rope is obtained. The dynamic model is as follows: ； in, Indicates the elastic coefficient of the inner traction rope on the back; This indicates the change in length of the inner traction rope on the back side; This indicates the rate of change of the rope length of the inner traction rope on the back side; Assuming the pretension forces of the front and back traction ropes are equal, and the damping coefficients are constant parameters, the elastic coefficients of the inner front traction rope and the inner back traction rope are calculated as follows: The elastic coefficient of the inner front traction rope is expressed as: ； in, This indicates the Young's modulus of the material of the inner traction rope on the front side; This represents the cross-sectional area of ​​the traction rope; all traction ropes have the same cross-sectional area. Since the inner traction rope on the front side and the inner traction rope on the back side satisfy the constraints... ,in, Connecting the rotation axes of the two rope traction joints The length of the inner traction rope on the back determines the elastic coefficient. The elastic modulus of the traction rope from the inside front Represented as: ； Based on the kinematic model of the rope traction joint in step 1, the length of the traction rope on the inner side of the front is... Actual joint angle of the rope-traction joint The relationship is represented as: ； During the movement of the rope-traction joint, the hysteresis and compliance characteristics of the rope traction mechanism cause a deviation between the expected joint angle and the actual joint angle, resulting in a change in the length of the traction rope on the inner side of the front. Represented as: ； in, This indicates the actual length of the traction rope on the inner side of the front. This indicates the expected length of the traction rope on the inner side of the front. Indicates the front traction rope upper arm anchor point With the back traction rope upper arm anchor point The length between; The actual joint angle of the rope-traction joint; Indicates the desired joint angle of the rope-traction joint; (•) represents the sine function; Similarly, the rate of change of the length of the corresponding inner traction rope on the front side... Represented as: ； in, Indicates the rate of change of the length of the inner traction rope on the front side; This indicates the rate of change of the actual value of the length of the traction rope on the inner side of the front. This indicates the rate of change of the expected value of the inner traction rope length on the front side; This indicates the rate of change of the desired joint angle of the cable-driven joint; This indicates the rate of change of the actual joint angle of the rope-traction joint; (•) represents the cosine function; Step 3: The excitation trajectory is designed using a finite term Fourier series, and the dynamic model of the rope traction joint established in Step 2 is identified by combining it with the particle swarm optimization algorithm. Step 4: Calculate the compensation amount of the actual trajectory based on the dynamic model of the rope traction joint identified in Step 3, and control the rope traction joint to execute the compensated trajectory according to the compensation amount.

2. The trajectory compensation method for a robotic arm cable traction joint according to claim 1, characterized in that, In step S2, a frictional force model for the tension of the outer traction rope and a frictional force model for the tension of the inner traction rope are established based on the frictional force relationship between the traction rope and the pulley. A rope-pulley frictional model is constructed using Capstan friction. Therefore, the tension of the outer traction rope... The frictional force model is expressed as: ； in, This indicates the coefficient of friction between the outer traction rope and the corresponding movable pulley surface. This indicates that the outermost traction rope wraps around the corresponding movable pulley surface at the corner. Indicates judgment The sign of the function indicates whether the value is positive or negative, which can determine the direction of motion of the velocity of the inner traction rope on the front. To judge The sign function of the value; due to the wrap angle Always maintain as The tension of the aforementioned frontal outer traction rope The friction force model formula simplifies to: ； in, The tension transmission coefficient; Using a continuous and first-differentiable hyperbolic tangent function for the sign function A smooth substitution is performed to ensure the stability and identification accuracy of the dynamic model of the rope traction joint, thus obtaining the final frontal lateral traction rope tension. The friction model is as follows: ； in, These are parameters used to adjust the smoothness of the transition region; (•) is the hyperbolic tangent function; Similarly, the tension of the outer traction rope on the back side is obtained. The friction model is as follows: ； Based on the above formula, the dynamic model of the cable traction joint is established, which can predict the output trajectory given the input trajectory, and perform trajectory compensation based on the dynamic model of the cable traction joint in trajectory tracking tasks.

3. The trajectory compensation method for a robotic arm cable traction joint according to claim 1, characterized in that, In step 3, the excitation trajectory in the form of a finite-term Fourier series is designed as follows: A finite-term Fourier series design is used to identify the excitation trajectory of the dynamic model of the cable traction joint. for: ； Speed ​​of excitation trajectory for: ； acceleration of the excitation trajectory for: ； in, Indicates time; Indicates the first Fourier series; The number of terms in the Fourier series; and These are the amplitudes of the sine and cosine function terms, respectively. For constant terms; fundamental angular frequency , For trajectory period; (•) represents the sine function; (•) represents the cosine function; The excitation trajectory parameters are generated through random sampling and must satisfy the following constraints: ； in, and These represent the maximum and minimum allowable joint angles of the rope traction joint, respectively. and These represent the upper limits of the joint's motion velocity and acceleration, respectively, induced by the cable. The velocity of the desired trajectory at the initial moment; This represents the acceleration of the desired trajectory at the initial moment; Indicates the period of the trajectory The speed of the expected trajectory; Indicates the period of the trajectory The acceleration of the expected trajectory.

4. The trajectory compensation method for a robotic arm cable traction joint according to claim 3, characterized in that, In step 3, the dynamic model of the rope traction joint established in step 2 is identified using the particle swarm optimization algorithm in the following manner: After the excitation trajectory is designed, it is executed on the cable traction joint. During the operation, the expected and actual joint angles of the cable traction joint are recorded. Based on the recorded expected and actual joint angles, the particle swarm optimization algorithm is used to identify the dynamic model parameters, including: Using the dynamic model of the rope traction joint established in step 2 as a parameterized model, the Young's modulus of the front inner traction rope material is determined as the parameter to be identified in this parameterized model. Damping coefficient of the inner traction rope on the front Pretension of the inner traction rope on the front Tension transmission coefficient and parameters used to adjust the smoothness of the transition region Then, the position vector of each particle is mapped to a set of candidate parameters for a parameterized model. A fitness function is constructed based on the deviation between the experimental measurement output and the calculated output of the parameterized model. The fitness function characterizes the degree of fit between the parameterized model and the actual system under the current combination of candidate parameters.

5. The trajectory compensation method for a robotic arm cable traction joint according to claim 4, characterized in that, In the particle swarm optimization (PSO) process for identifying dynamic model parameters, the velocity and position of each particle are updated based on its historical best position and global best position. The update formula is as follows: ； in, Indicates the first The particle in the first Speed ​​during the next iteration; Inertial weight; Indicates the first The particle in the first Speed ​​during the next iteration; Indicates the first The individual historical best position of each particle; Indicates the first The particle in the first The position at the next iteration; This indicates the current globally optimal position; and These are individual learning factors and group learning factors, respectively. and The range of values ​​is respectively in Random numbers within; Indicates the first The particle in the first The position at the next iteration; After each iteration, the fitness value corresponding to the current position of the particle is calculated, and the individual optimal position and the global optimal position are updated respectively. When the position of the particle exceeds the preset parameter range, the particle is subjected to boundary constraint processing to ensure that the parameter values ​​are within the allowable range. After the preset termination condition is met, the parameters corresponding to the global optimal position are output as the model identification result.

6. The trajectory compensation method for a cable traction joint of a robotic arm according to claim 5, characterized in that, In step 4, based on the dynamic model of the cable traction joint identified in step 3, the motion trajectory compensation amount is calculated according to the actual dynamic model of the cable traction joint, and the compensated trajectory is executed, including: Step 41, calculate the expected trajectory after compensation at the starting point: based on the dynamic model of the cable traction joint... Expected trajectory after time-compensation Perform calculations to make The actual trajectory of time discretization and The expected trajectory of time discretization Consistency, that is ; exist At the initial moment of the trajectory, the robotic arm's cable traction joint is in a static state, and the cable traction joint torque is used to overcome gravity. At this time, the rate of change of the cable length and the joint velocity are both zero. Therefore, after compensation at the starting point, the expected trajectory can be directly calculated by solving the following equations: ； in, , , , , and They represent The moment of the rope traction joint torque, the tension on the front movable pulley, the tension on the back movable pulley, the elastic coefficient of the front inner traction rope, the elastic coefficient of the back inner traction rope, and the change in rope length of the front inner traction rope. (•) represents the sine function; Step 42, Iterative Derivation Desired trajectory after time-compensation: Based on the dynamic model of the cable-traction joint established in step 2, during the movement of the cable-traction joint, The compensation amount of the tension on the front movable pulley and the tension on the back movable pulley at any given time satisfies the following constraint formula: ； in, , They represent The tension on the front pulley at any given moment The tension on the pulley on the back of the moment; express The actual trajectory discretized at time. express The desired trajectory discretized at time points; express The expected trajectory of the joint after compensation under the constant-time cable traction. (•) represents the sine function; In the above constraint formula, the right side of the equation is determined by the actual motion state of the current cable-traction joint, while the left side depends on the actual motion state of the current cable-traction joint and... Desired trajectory after compensation of the cable traction joint Combined with step 41 The actual trajectory of time discretization and The expected trajectory of time discretization Consistent assumptions, namely The actual trajectory of time discretization Given that, the key to eliminating trajectory tracking errors lies in... The actual trajectory of time discretization Given the expected trajectory after compensation Calculations are performed to arrive at a reasonable result. The tension on the front pulley at any moment and The tension on the pulley on the back of the moment Make the above constraint formulas true; Because the constraint formula for calculating the tensile compensation amount contains a part where the variable is multiplied by the cosine function, it is impossible to write out the analytical solution form of the variable. Therefore, Newton's iteration method is used to obtain the solution. Desired trajectory after compensation of the cable traction joint The numerical solution, let The objective function of Newton's iteration method is expressed as follows: ； The independent variable ; express The tension on the movable pulley is always present; express The tension on the movable pulley on the back side is constant; therefore, Newton's iteration method is used to solve the problem. The zero point is Desired trajectory after compensation of the cable traction joint Numerical solution; Calculated Desired trajectory after compensation of the cable traction joint Then, calculate a reasonable The tension on the front pulley at any moment and The tension on the pulley on the back of the moment To make the above equation hold, we obtain the expected trajectory after compensation. Step 43: Perform the compensated desired trajectory obtained in step 42 on the cable traction joint.

7. The trajectory compensation method for a cable-driven joint of a robotic arm according to claim 6, characterized in that, In step 42, the solution is obtained using Newton's iteration method in the following manner. The expected trajectory after the zero point is compensated The numerical solution includes: first, given the function initial iteration value Initial iteration value Using the actual trajectory at the current moment and calculate the function and its first derivative The iterative values ​​are then updated according to Newton's iteration formula using the following formula: ； in, Indicates the first Approximate solution at the next iteration; Indicates the first Approximate solution at the next iteration; Through continuous iteration The function value gradually approaches zero, thus obtaining the function The zero point; When the difference between two consecutive iterations is less than a preset threshold or If the error is less than the preset error limit, stop the iteration and take the current iteration value as the approximate solution of the zero point; To prevent the iteration process from diverging, the initial iteration value must be within a preset valid range, and this must be ensured during the iteration process. ; Through the above process, the compensated expected trajectory is calculated at each time step. The calculation is performed, and after the iterative calculation of the entire trajectory is completed, the final compensated expected trajectory is obtained.

8. A processing device, characterized in that, include: At least one memory for storing one or more programs; At least one processor is capable of executing one or more programs stored in the memory, such that when the one or more programs are executed by the processor, the processor can perform the method according to any one of claims 1-7.

9. A readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it can implement the method described in any one of claims 1-7.

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