A Precision Compensation Method for a Multi-Degree-of-Freedom Snake-Like Manipulator

Abstract

The present invention relates to a precision compensation method for a multi-degree-of-freedom snake-like robotic arm, including: constructing a robotic arm kinematic model, and solving the robotic arm kinematic model based on inverse kinematics to obtain an inverse kinematic relationship model; constructing a fixed-point compression iterative mapping model based on the inverse kinematic relationship model to obtain a configuration space deformation amount; substituting the configuration space deformation amount into the inverse kinematic model to obtain an expected trajectory after compensation for the drive space deformation, and performing real-time compensation for the deformation amount based on the expected trajectory. The present invention proposes a servo stiffness control method, which can adjust the reaction ability of the robotic arm to the load. Compared with the traditional stiffness control, this method is more suitable for the occasions where the robotic arm contacts the environment or people. Through this method, the present invention can enable the actuator to achieve precise and compliant interactive operations simultaneously, and improve the safety of the interactive operations.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-degree-of-freedom cable-driven robotic arm control, and particularly to a precision compensation method for a multi-degree-of-freedom snake-shaped robotic arm. Background Art

[0002] Due to reasons such as large structural size, low flexibility, and large driving inertial force, traditional rigid-joint robotic arms are greatly restricted in carrying out operations in narrow, complex and other restricted environments. According to the design concept of bionics, robotic arms with multi-degree-of-freedom similar to snakes have extremely strong environmental adaptability and can move flexibly in complex working environments. Such robotic arms have great practical value in detection, medical first aid, in-cabin maintenance, etc., and are important tools that can replace humans in restricted or dangerous environments. Compared with traditional robotic arms, such robotic arms have great flexibility and high performance in terms of operating space, stiffness control, and operability, and the real-time interaction between such robotic arms and the environment is stronger, and they have the ability to perform complex tasks. Since the series joints of such robotic arms are usually driven by means such as ropes and compressed gases, they have good flexibility. However, precisely because the overall structure of the robotic arm is not rigidly connected, when there is a load at the end of the robotic arm, the accuracy of the robotic arm will be reduced to a certain extent. According to the research status at home and abroad, the precise stiffness control method for snake-shaped robotic arms is not perfect, which poses a great technical challenge to the high-precision operation of robotic arms in the application process.

[0003] The methods in the prior art need to randomly assign poses and joint angles in the working space of the robotic arm, measure the actual pose and identify the error. During the measurement process, the sampling points are uncertain, and the measuring elements will also have accidental errors and systematic errors, which will affect the identified error and thus affect the positioning accuracy of the robotic arm. Moreover, the number of selected sampling points will have a significant impact on precision compensation, and the parameter measurement of the sampling points is time-consuming, and the global accuracy of this method is low.

[0004] The methods in the prior art need to select sampling points for point position error measurement and train an artificial intelligence model, but this method is more dependent on the number of sampling data points and ignores the structural characteristics and motion characteristics of the robotic arm. The research on artificial intelligence models is not yet mature enough to be widely applied to industrial robotic arms.

[0005] Based on the above research, the present invention designs a control method for precision compensation on a multi-degree-of-freedom snake-like manipulator, controls the servo stiffness of the manipulator, and simultaneously conducts modeling and analysis based on the kinematic model and dynamic model of the manipulator to estimate and compensate the end deformation in real time, significantly improving the end positioning accuracy of the manipulator. This method enables the manipulator to be both precise and compliant during use, not only meeting the structured working environment in industry but also being applicable to complex working conditions that require interaction with the environment, achieving high-precision and high-performance operation of the manipulator. Summary of the Invention

[0006] The purpose of the present invention is that multiple series joints of a multi-degree-of-freedom snake-like manipulator are usually driven by means such as ropes and compressed air. When an external force load is applied to the end of the manipulator or the manipulator body is in a cantilever state, due to the fact that the overall structure of the manipulator is not a rigid connection method, there will be a certain deformation at the end of the manipulator, resulting in a reduction in the control accuracy of the end of the manipulator. Aiming at the deficiencies in the precision control technology of the multi-degree-of-freedom snake-like manipulator, the present invention aims to provide a precision compensation method for accurately modeling and analyzing a snake-like manipulator and capable of real-time control application. This compensation method is applicable to redundant drive continuum manipulators, etc., and the modeling idea and compensation method have good generality.

[0007] To achieve the above purpose, the present invention provides the following solutions:

[0008] A precision compensation method for a multi-degree-of-freedom snake-like manipulator, comprising:

[0009] Construct a kinematic model of the manipulator, and solve the kinematic model of the manipulator based on inverse kinematics to obtain an inverse kinematic relationship model;

[0010] Based on the inverse kinematic relationship model, obtain the configuration space stiffness, construct a fixed-point compression iterative mapping model, and obtain the configuration space deformation;

[0011] Substitute the configuration space deformation into the inverse kinematic model to obtain the desired trajectory after compensating for the deformation in the drive space, and compensate for the deformation in real time based on the desired trajectory.

[0012] Preferably, establishing the kinematic model of the manipulator includes:

[0013] Obtain the connection relationship of a single joint of the snake-like manipulator, based on the single joint connection relationship, obtain an intermediate coordinate system, calculate the intermediate coordinate system, establish a joint coordinate system, and obtain the kinematic model of the manipulator;

[0014] The expression of the kinematic model of the manipulator is:

[0015]

[0016] Among them, c is cos, s is sin, L is half the length of the universal joint with a symmetric shape, and θ1 and θ2 are the generalized coordinates of the configuration space.

[0017] Preferably, obtaining the inverse kinematic model includes:

[0018] Solving the kinematic model of the robotic arm based on inverse kinematics to obtain the inverse kinematic model;

[0019] The expression of the inverse kinematic model is:

[0020] l = f(θ)

[0021] where l ∈ R 3 is the driving space coordinate, and θ ∈ R 2 is the configuration space coordinate.

[0022] Preferably, constructing the fixed-point contraction iteration mapping includes:

[0023] Performing a mechanical analysis on the snake-like robotic arm to establish a desired closed-loop system, and based on the desired closed-loop system, establishing an impedance control model;

[0024] Performing coordinated impedance control on the snake-like robotic arm based on the impedance control model and the inverse kinematic model to control the position, force, and servo stiffness of the snake-like robotic arm;

[0025] Calculating the servo stiffness to obtain the configuration space stiffness, and based on the configuration space stiffness, constructing a fixed-point contraction iteration mapping model.

[0026] Preferably, the method for establishing the desired closed-loop model is:

[0027]

[0028] where are the desired inertia, damping, and stiffness of the impedance system, e i is the position error, is the velocity error, is the acceleration error, and F ei is the component of the external load force exerted on the object pulled by the wire rope on the wire rope.

[0029] Preferably, the method for constructing the fixed-point contraction iteration mapping model is:

[0030]

[0031] where K θis the stiffness of the manipulator configuration space, Δθ = θ - θ0 is the deformation of the manipulator configuration space position, θ0 is the known nominal configuration space position, θ is the position of the manipulator configuration space after deformation, τ G (θ) is the gravitational moment of the object pulled by the driving wire, is the external moment acting on the moving platform.

[0032] Preferably, obtaining the deformation of the configuration space includes:

[0033] Based on the fixed-point compression iterative mapping model, obtain the iterative relationship of position kinematics. Based on the iterative relationship of position kinematics, obtain the actual configuration space position of the snake-shaped manipulator, and iterate the actual configuration space position to obtain the deformation of the configuration space.

[0034] Preferably, iterating the actual configuration space position includes:

[0035]

[0036] where θ0 is the known nominal configuration space position, θ is the position of the manipulator configuration space after deformation, is the inverse matrix of the stiffness of the manipulator configuration space, τ G is the gravitational moment of the object pulled by the driving wire, F e (θ k (t)) is the external moment received by the moving platform, θ k (t) and θ k+1 (t) are the k-th iteration value and the (k + 1)-th iteration value in the iterative mapping formula respectively, and the actual meaning is the joint angle of the configuration space.

[0037] Preferably, based on the desired trajectory, real-time compensation for the deformation amount includes:

[0038] Substitute the deformation of the configuration space into the inverse kinematics model, calculate the deformation of the configuration space based on the inverse kinematics model to obtain the desired trajectory of the snake-shaped manipulator after deformation compensation in the driving space, and perform coordinated impedance control on the snake-shaped manipulator based on the desired trajectory to control the servo stiffness for precision compensation.

[0039] Preferably, based on the desired trajectory, performing coordinated impedance control on the snake-shaped manipulator includes:

[0040] Based on the inverse kinematics model, adjust the driving space position to obtain the desired position in the configuration space, and inverse-solve the inverse kinematics model to obtain the wire movement distance of the snake-shaped manipulator. Measure the wire movement distance through the motor encoder to obtain the actual position;

[0041] Subtract the desired position from the actual position to obtain a position error, calculate the position error to obtain a velocity error, input the position error and the velocity error into an impedance controller, and determine the parameters of the impedance controller to obtain the driving tension of the joint actuator. Measure the steel wire of the snake-shaped manipulator through a tension sensor to obtain the real-time tension;

[0042] Based on the difference between the driving tension and the real-time tension, perform coordinated impedance control on the snake-shaped manipulator.

[0043] The beneficial effects of the present invention are as follows:

[0044] 1. The present invention proposes servo stiffness control, which can adjust the response ability of the manipulator to the load. Compared with the traditional stiffness control, this servo stiffness control is more suitable for the occasions where the manipulator contacts the environment or people. Through the servo stiffness control, the actuator can simultaneously achieve precise and compliant interaction operations, and improve the safety of the interaction operations.

[0045] 2. Through the analysis of the stiffness model of the manipulator, the servo stiffness of the configuration space can be controlled during the actual operation process, so that the manipulator has better motion performance;

[0046] 3. The present invention effectively reduces the position error at the end of the manipulator and improves the positioning accuracy at the end of the manipulator by constructing an iterative mapping to estimate the deformation amount in real time and update the trajectory after deformation compensation. Compared with the traditional calibration method, it avoids the disadvantage of being inapplicable to achieving high-precision compensation in the entire working space; through this method, the deformation amount can be compensated in real time during the application process, and good positioning accuracy can be achieved for different application scenarios.

[0047] 4. The present invention can compensate the accuracy in real time during the operation of the manipulator. The iterative solution included only requires a few iterations to achieve satisfactory accuracy. The iterative process is simple in application, simplifying the complexity of the calculation process. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0049] Figure 1 It is a flowchart of a method for precision compensation of a multi-degree-of-freedom snake-shaped manipulator according to an embodiment of the present invention;

[0050] Figure 2Deformation of the snake-shaped robotic arm according to an embodiment of the present invention;

[0051] Figure 3 Schematic diagram of a single joint parallel mechanism of a multi-degree-of-freedom snake-shaped robotic arm and homogeneous transformation matrix representation according to an embodiment of the present invention;

[0052] Figure 4 Mechanical sketch of a single joint of a multi-degree-of-freedom snake-shaped robotic arm according to an embodiment of the present invention;

[0053] Figure 5 Impedance control block diagram according to an embodiment of the present invention;

[0054] Figure 6 Drive structure of a single joint actuator according to an embodiment of the present invention. Detailed implementation manners

[0055] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0056] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0057] As Figure 2 shown, the purpose of the present invention is that multiple series joints of a multi-degree-of-freedom snake-shaped robotic arm are usually driven by means such as ropes and compressed air. When an external force load is applied to the end of the robotic arm or the robotic arm body is in a cantilever state, since the overall structure of the robotic arm is not a rigid connection method, there will be a certain deformation at the end of the robotic arm, resulting in a reduction in the control accuracy of the end of the robotic arm, as shown in the appendix Figure 2 shown. Aiming at the deficiencies in the precision control technology of multi-degree-of-freedom snake-shaped robotic arms, the present invention aims to provide a precision compensation method that can accurately model and analyze a snake-like robotic arm and can be applied in real-time control. This compensation method is applicable to redundant drive continuum robotic arms, etc., and the modeling idea and compensation method have good generality.

[0058] As Figure 1 shown, a precision compensation method for a multi-degree-of-freedom snake-shaped robotic arm includes:

[0059] Establish a kinematic model of the robotic arm, and solve the kinematic model of the robotic arm based on inverse kinematics to obtain an inverse kinematic model; based on the inverse kinematic model, construct a fixed-point contraction mapping to obtain the deformation amount of the configuration space; perform coordinated impedance control on the snake-shaped robotic arm through the deformation amount of the configuration space, and control the first servo stiffness for precision compensation, specifically:

[0060] Step 1: Establish a kinematic model of the robotic arm and solve the inverse kinematics. Specifically, establish a single joint coordinate system and obtain the homogeneous transformation matrix, and solve the relationship from the configuration space (two universal joint angles) to the drive space (the positions of three ropes) according to the kinematic relationship, that is, formula (6).

[0061] As Figure 5 shown, the schematic diagram of a single joint parallel mechanism of a multi-degree-of-freedom snake-shaped robotic arm and the representation diagram of the homogeneous transformation matrix;

[0062] This parallel mechanism is composed of two platforms connected by a two-degree-of-freedom universal joint, which is a two-degree-of-freedom mechanism, and the entire parallel structure is driven by three steel wires. In this parallel mechanism, the moving platform coordinate system is the configuration space, and the fixed platform position is connected to the driving device, which is defined as the drive space. Coordinate systems O i and O i-1 are fixedly connected to the centers of the moving platform and the fixed platform respectively (numbered in the order of gradually increasing serial numbers of the end moving coordinate systems). Among them, the Z axes of the two coordinate systems are perpendicular to the platform surface, the X axes are taken parallel to the platform surface, and their directions are selected according to the principle of convenient modeling, and the Y axes are determined according to the right-hand rule (X - Y - Z - X). When the joint angle is at zero position, the two coordinate systems should be parallel in the same direction. Translate the fixed coordinate system along the central support mechanism and rotate it around a certain axis respectively, and the intermediate coordinate system representation method as shown in Figure 5 can be obtained. Then, multiply the homogeneous transformation matrices in sequence according to the order from left to right to obtain the joint homogeneous transformation matrix shown in formula (1). Using this matrix, the coordinates of a point represented in the moving coordinate system O i can be transformed into the fixed coordinate system O i-1 .

[0063]

[0064] where L represents half of the length of the universal joint. According to Appendix Figure 3 each basic homogeneous matrix in formula (1) can be solved, and

[0065]

[0066] can be obtained, where "c" represents "cos", "s" represents "sin", L is half of the length of the universal joint with a symmetric shape, and θ1 and θ2 are the generalized coordinates of the configuration space.

[0067] Suppose the coordinates of the connection points between the wire ropes and the moving platform are represented as A i , i = 1, 2, 3. Thus, their homogeneous coordinates in the moving platform coordinate system can be respectively represented as

[0068]

[0069] Among them, the driving wire ropes are evenly distributed along the circumference of the platform, and the distance between the wire connection points and the platform center is R. φ is the angle between the line connecting point A1 and the origin O1 and the x1-axis.

[0070] Similarly, the connection points B between the wire ropes and the fixed platform i , i = 1, 2, 3 can be obtained, and their position coordinates in the fixed platform coordinate system are represented as

[0071]

[0072] Thus, the effective lengths of the three wire ropes can be obtained as

[0073]

[0074] Among them, l i , i = 1, 2, 3 is the effective rope length, and is the driving space position variable.

[0075] According to the solution of the rope lengths of the three driving ropes, the inverse kinematics model of this parallel mechanism can be represented as

[0076] l = f(θ) (6)

[0077] Among them, l ∈ R 3 is the driving space coordinate variable, and θ ∈ R 2 is the configuration space coordinate variable. Given a set of configuration space coordinates θ, a unique corresponding set of driving space rope length variables l can be obtained. Thus, the inverse kinematics model can reach the desired position in the configuration space by adjusting the driving space position. Through the inverse kinematics solution of a single joint, the mapping relationship between the end operating space and the driving space of a multi-joint manipulator can be obtained.

[0078] According to the inverse kinematics relationship in step 1, the driving space variables corresponding to the configuration coordinates θ can be obtained. Substitute the driving space variable l into step 2 for motion control. The obtained driving space variable l is the desired position, and the position error in equation (8) in which represents the desired position, and l i represents the actual position measured by the encoder. The obtained error variable can be used as an input item in the control algorithm.

[0079] Step 2: In the motion control stage, the rope position is obtained based on the configuration coordinates θ, and impedance control is used to precisely control the position and rope force. During the impedance control process, the servo stiffness of each motion unit can be controlled. Servo stiffness refers to the resistance of an object to external forces.

[0080] As Figure 4 shown, the mechanical schematic diagram of a single joint of a multi-degree-of-freedom snake-like manipulator;

[0081] According to the mechanical analysis of the single joint model, the controlled model of a single actuated joint can be expressed as

[0082]

[0083] where M (Kg) is the equivalent mass pulled by the steel wire; D (N·s / m) is the velocity damping of the steel wire transmission system; K (N / m) is the elastic coefficient of the steel wire; G is the component of the gravity of the object pulled by the steel wire on the steel wire; F ei represents the component of the external load force received by the object pulled by the steel wire rope (moving platform) on this steel wire rope; u i = F i is the driving tension of the steel wire rope, and in actual control applications, it is a unilateral pulse signal. l i is the effective length of the steel wire and is also a control variable. To improve the positioning accuracy of the platform, it is necessary to compensate for the end deformation caused by the gravity component and the external load component during control, that is, it is necessary to correct the target position of the positioning control (the effective length of the steel wire). According to this control model, is defined as the length error of the steel wire, and the desired closed-loop impedance system can be expressed as

[0084]

[0085] where are the desired inertia, damping, and stiffness of the impedance system. According to the established impedance model, adaptive impedance control and time-varying impedance control can be adopted to regulate the control system. Among them, different impedance control methods mainly make the control system achieve better accuracy, robustness, and stability by adjusting the impedance parameters of the impedance system in real time. Through the establishment of the above control model and the selection of control methods, the single joint of the manipulator can be coordinated for impedance control in the driving space. When the effective lengths of the three steel wires are accurate, it can also maintain the accurate desired servo stiffness.

[0086] As Figure 5 shown, the control block diagram established according to the above impedance model

[0087] where and is the expected position in the configuration space, that is, the two bending angles of the universal joint around the cross-axis. The moving distance of the wire rope in the driving space can be obtained through the inverse kinematic solution in Step 1. The position of the driving target is measured by the motor encoder. The difference between the actual position and the expected position is the position error. Differentiating the position error can obtain the velocity error. Taking the position error and the velocity error as the inputs of the impedance controller and determining the parameters of the impedance controller, the driving tension u i (t) of the wire rope can be obtained. In practical applications, when there is a requirement for the expected tension of the wire rope, the sum of the expected tension f i d and the driving tension calculated by the controller can be used as the new driving tension value. A tension sensor is configured on a single wire rope to measure the real-time tension of the rope. The difference between the driving tension value and the real-time tension value is used as the input of the force PID controller, and the obtained control output value is used as the driving input of the motor.

[0088] As Figure 6 shown, it is the driving structure (implementation module) of a single joint actuator

[0089] 1. The controller is the core component of the entire driving structure. The inputs are the expected position and the expected tension. Through the real-time calculation of the internal controller, the driving command and the control quantity are sent to the motor driver, and the motor driver changes the state of the motor. At the same time, the real-time position of the control target and the real-time tension of the wire rope are collected through the encoder, and the position and the tension are used as feedback items for the real-time calculation of the control algorithm.

[0090] 2. The motor driver is the connection between the controller and the servo motor. It receives the signal from the main controller, drives the motor to complete the expected operation, and has functions such as current feedback, under-voltage protection, over-current protection, and over-temperature protection;

[0091] 3. The servo motor is used to drive the rope stretching joint to complete the operation task issued by the main controller and complete the expected operation trajectory;

[0092] 4. The encoder provides the angular displacement signal in the transmission system, that is, the position feedback signal. Through the signal feedback of the encoder, the closed-loop control of the motion system can be realized.

[0093] 5. The transmitter is used to provide the excitation voltage for the tension sensor, collect, amplify, and filter the signal output by the tension sensor, and transmit the processed tension signal to the main controller. By controlling the position, force, and servo stiffness of each motion unit (referring to the unit where each rope is located) in Step 2. The servo stiffness K l is solved for the configuration space stiffness in Step 3. Among them, this servo stiffness K lRefers to the desired stiffness described by Equation (8) in Step 2. The servo stiffness of each motion unit can be controlled through the impedance control algorithm in Step 2.

[0094] Step 3:

[0095] According to the static relationship, the force balance equation between the configuration space and the driving space of the parallel mechanism is

[0096] τ θ =J T F1 (9)

[0097] For a certain point θ ∈ R in the configuration space of the parallel mechanism n At this point, when the stretching deformation of the steel wire is not considered, the micro-variation motion between the driving space and the configuration space satisfies the relationship

[0098] Δl=JΔθ (10)

[0099] Assume that the desired stiffness of the configuration space is K θ and the corresponding desired stiffness of the driving space is K l Then according to Hooke's theorem, it can be known that

[0100]

[0101] According to Equations (9), (10), and (11), it can be obtained that

[0102] J T K l Δl=K θ Δθ (12)

[0103] From this relationship, the stiffness of the configuration space can be calculated

[0104] K θ =J T K l J (13)

[0105] According to the coordinated impedance control in the driving space in Step 2, the servo stiffness of the driving space is made the desired stiffness K l , and based on the relationship (13), the stiffness of the configuration space can be calculated.

[0106] Function of this step: Calculate the stiffness of the end configuration space based on the servo stiffness of a single motion unit. Among them, the driving space has 3 units, and the driving space stiffness K l is a 3×3 matrix, and the diagonal elements are the stiffness coefficients of the impedance control of each unit. For the two angles of the universal joint bending in the configuration space, the configuration space stiffness matrix is 2×2, and the diagonal elements are the stiffnesses in each direction. The obtained configuration space stiffness K θ is substituted into Step 4.

[0107] Step 4: Construct a fixed-point contraction mapping to solve the deformation caused by the self-weight and external forces of the robotic arm. Constructing a fixed-point contraction mapping is a convergent iterative method for solving the deformation.

[0108] Based on Hooke's law, we can obtain

[0109]

[0110] where K θ is the stiffness of the robotic arm configuration space, Δθ = θ - θ0 is the deformation of the robotic arm configuration space position, θ0 is the known nominal configuration space position, θ is the position of the robotic arm configuration space after deformation, and τ G (θ) is the gravitational moment of the driving wire pulling object, is the external (load) moment acting on the moving platform. During the movement of the robotic arm, both the gravitational moment and the external moment are time-varying non-linear functions related to the robotic arm configuration. Thus, an iterative relationship based on position kinematics can be obtained through Equation (14)

[0111]

[0112] For any nominal configuration space position, the actual configuration space position can be solved through the iterative relationship. The deformation of the configuration space of a single joint can be obtained through Equation (15), and thus deformation compensation can be performed on the robotic arm in the driving space position control.

[0113] Substitute the deformation obtained in Equation (15) into Step 5

[0114] Step 5:

[0115] According to the configuration space deformation calculated in Step 4, use the inverse kinematics model (6) in Step 1 to calculate the expected trajectory after deformation compensation in the driving space, and perform driving space motion control in Step 2.

[0116] Take the calculated deformation as the feedback quantity and substitute it into the configuration space variable in Step 1, and perform real-time compensation for the deformation.

[0117] The embodiments described above are only descriptions of the preferred embodiments of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A precision compensation method for a multi-degree-of-freedom snake-like robotic arm, characterized in that, Including: Construct a kinematic model of the robotic arm, and solve the kinematic model of the robotic arm based on inverse kinematics to obtain an inverse kinematic model; Based on the inverse kinematic model, obtain the configuration space stiffness, construct a fixed-point contraction iterative mapping model, and obtain the configuration space deformation; Constructing the fixed-point contraction iterative mapping includes: Conduct a mechanical analysis of the snake-shaped robotic arm, establish a desired closed-loop system, and based on the desired closed-loop system, establish an impedance control model; Perform coordinated impedance control on the snake-shaped robotic arm based on the impedance control model and the inverse kinematic model, and control the position, force, and servo stiffness of the snake-shaped robotic arm; Calculate the servo stiffness to obtain the configuration space stiffness, and based on the configuration space stiffness, construct a fixed-point contraction iterative mapping model; The method for establishing the desired closed-loop system is: wherein, are the desired inertia, damping, and stiffness of the impedance system, e i is the position error, is the velocity error, is the acceleration error, F ei is the component of the external load force acting on the object pulled by the wire rope on the wire rope; The method for constructing the fixed-point contraction iterative mapping model is: Among them, K θ is the stiffness of the manipulator configuration space, Δθ = θ - θ0 is the deformation of the manipulator configuration space position, θ0 is the known nominal configuration space position, θ is the position of the manipulator configuration space after deformation, τ G (θ) is the gravitational moment of the driving wire pulling object, is the external moment received by the moving platform; Obtaining the configuration space deformation includes: Based on the fixed-point contraction iterative mapping model, obtain the iterative relationship of position kinematics. Based on the iterative relationship of position kinematics, obtain the actual configuration space position of the snake-shaped robotic arm, and iterate the actual configuration space position to obtain the configuration space deformation; Iterating the actual configuration space position includes: where θ0 is the known nominal configuration space position, and θ is the position of the configuration space after the manipulator deforms. is the inverse matrix of the manipulator configuration space stiffness, and τ G is the gravitational moment of the driving wire pulling object. is the external moment received by the moving platform. and are the k-th iteration value and the (k + 1)-th iteration value in the iterative mapping formula respectively, and the actual meaning is the joint angle of the configuration space. Substitute the configuration space deformation into the inverse kinematic model to obtain the desired trajectory after compensation for drive space deformation. Based on the desired trajectory, perform real-time compensation for the deformation.

2. The accuracy compensation method for the multi-degree-of-freedom snake-like robotic arm according to claim 1, characterized in that Establishing the kinematic model of the robotic arm includes: Obtain the connection relationship of a single joint of the snake-shaped robotic arm. Based on the single joint connection relationship, obtain an intermediate coordinate system, calculate the intermediate coordinate system, establish a joint coordinate system, and obtain the kinematic model of the robotic arm; The expression of the kinematic model of the robotic arm is: Where c is cos, s is sin, L is half the length of the universal joint with a symmetric shape, and θ1 and θ2 are generalized coordinates in the configuration space.

3. The accuracy compensation method for the multi-degree-of-freedom snake-like robotic arm according to claim 2, characterized in that, Obtaining the inverse kinematic model includes: Solve the kinematic model of the robotic arm based on inverse kinematics to obtain the inverse kinematic model; The expression of the inverse kinematic model is: l = f(θ) where \(l\in R\) 3 is the driving space coordinate, \(\theta\in R\) 2 is the configuration space coordinate.

4. The accuracy compensation method for the multi-degree-of-freedom snake-like robotic arm according to claim 1, characterized in that, Performing real-time compensation for the deformation based on the desired trajectory includes: Substitute the configuration space deformation into the inverse kinematic model. Based on the inverse kinematic model, calculate the configuration space deformation to obtain the desired trajectory of the snake-shaped robotic arm after compensation for drive space deformation. Based on the desired trajectory, perform coordinated impedance control on the snake-shaped robotic arm, and control the servo stiffness for precision compensation.

5. The accuracy compensation method for the multi-degree-of-freedom snake-like robotic arm according to claim 4, wherein, Performing coordinated impedance control on the snake-shaped robotic arm based on the desired trajectory includes: Based on the inverse kinematic model, adjust the drive space position to obtain the desired position in the configuration space, and inverse-solve the inverse kinematic model to obtain the wire movement distance of the snake-shaped robotic arm. Measure the wire movement distance through the motor encoder to obtain the actual position; Subtract the desired position from the actual position to obtain a position error, calculate the position error to obtain a velocity error, input the position error and the velocity error into an impedance controller, and determine the parameters of the impedance controller to obtain the driving tension of the joint actuator. Measure the steel wire of the snake-like manipulator through a tension sensor to obtain the real-time tension; Based on the difference between the driving tension and the real-time tension, perform coordinated impedance control on the snake-like manipulator.

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