Research on the linear driving characteristics of endoscopic continuous robot

Due to the way line drive, the continuous endoscope robot will have a certain lag in the process of movement, which will affect the accuracy and flexibility of the operation. In addition, the hysteresis and return difference caused by wire rope transmission will also increase the hysteresis effect of continuous robots. In this paper, the motion characteristics of the continuous endoscopic robot are analyzed, the hysteresis of the robot is modeled theoretically based on the Preisach model, and the effectiveness of the model is verified. Preisach hysteretic nonlinear hyperbola model predicts the bending changes under different positive and negative drives. The experimental results show that the maximum error between the model and the theoretical prediction is 3.18 degrees. The hysteresis model can predict the hysteresis characteristics of the continuous endoscope robot well.


Introduction
With the continuous development of industry, all kinds of machine parts move towards integration and precision development.Ensuring the normal and efficient operation of the machine has become an increasingly important issue.As a kind of testing equipment, the endoscope can reach the narrow gap that the human eye cannot reach by inserting without destroying or disassembling the original instrument, observing the defective parts in the parts, and feeding back to the display system in real-time.Therefore, you can grasp the internal situation of the equipment, and determine the maintenance program [1] .Nowadays, endoscopes have been widely used in medical treatment, aviation and aerospace, new energy, military and police anti-terrorism nuclear power maintenance, and other industries.Figure 1 shows the endoscope in the maintenance of aviation equipment.With the development of medical surgery [2] , medical instruments should also be continuously developed, especially in minimally invasive surgery, and surgical operating tools are becoming more and more sophisticated; In industry, precision instruments and a variety of large equipment are more and more refined, overhaul and maintenance also need the continuous support of equipment, and the endoscope is also with the development of medical and industrial development in the continuous development.The continuous robot provides many potential advantages over the traditional rigid link robot in the application [3] , including through the realization of a certain movement trajectory in the complex environment, and the robot can follow the environmental contact activities along its length, etc.These advantages make the continuous robot continuous development.
The operation of the endoscope is mainly driven by the line, relying on the lens of the end of the operator to work.As the position changes in the work, it needs to rely on the bending movement of the bending part to reach the designated working position.At present, the common structure of the bending part is shown [4] in Figure 2. The steel wire rope can be stretched to achieve bending in two directions, which requires the endoscopic robot to maintain operational accuracy and operational flexibility in both industrial and medical applications.In the driving process, the bending recovery of the fixed wire and the elastic deformation of the driving wire during the stretching process will have a certain impact on the movement of the robot, resulting in a certain lag in the movement of the continuous robot.In addition, the hysteresis and return difference caused by the wire rope transmission will also aggravate the hysteresis effect of the continuous robot.Figure 2. A common structure of the curved end of an endoscope [4] .

Kinematic characteristic analysis of wire drive
Given the motion hysteresis characteristics of continuous robots, the method of measurement and analysis of experimental data is adopted.According to the method of previous experiments, the drive line is stretched positively and negatively by controlling the steering gear, and the end position Angle of the continuous robot in the forward and reverse recovery process is captured through image processing.Due to the small structure size of the continuous robot, the installation preload in the actual installation test process is subject to the tension of the drive wire.The experimental diagram is as Figure 3 and Figure 4:  The driving disc installed on the steering gear is 20 mm in diameter.Through the stretching of the steering gear, the bending Angle of the head and the driving quantity of the forward bending and reverse drawing are obtained.The theoretical driving curve has been calculated in the forward and inverse kinematics part, as shown in Figure 5. Figure 5 shows that the bending Angle in the test process of forward stretching and reverse recovery has obvious deviation, and the bending Angle in the forward stretching is below the reverse recovery.Compared with the theoretical driving curve, the bending Angle has obvious hysteresis [5] .The main bending Angle lag is distributed in the second half of the driving stretch, and the change in the bending Angle is not obvious when the driving displacement is small.The analysis shows that it may be related to the deformation caused by the stretching of the driving line.In the second half of the driving stretch, the tensile force is large, the hysteresis is more obvious, and the recovery process of positive and negative stretching may be related to the initial state.From the overall view of the image, the process of forward stretching and reverse recovery can be approximately regarded as forming a hysteresis loop [6] .Given the above phenomenon, it is difficult to control the continuous robot.Hysteresis model analysis should be carried out for the continuous robot, so the hysteresis error can be reduced in the use of the continuous robot and more accurate control can be achieved.

Hysteresis characteristics analysis of continuous robot based on the Preisach model
Preisach hysteresis model is widely used in the simulation of hysteresis and loss characteristics of power equipment because of its high precision and fast operation speed.The model can be regarded as a series of results with hysteresis unit superposition [7] .The application of the model to study the linear driving hysteresis characteristics of continuous robots has the advantages of simplicity and convenience.

Preisach hysteresis model
The basic principle of the Preisach model is regarded as the result of a series of weighted Relay operators superimposed, each generator can show a local memory lag, superimposed together to show the global memory [8] .The model can be expressed as Formula (1).
( ) ( )  ( ) Where, ( ) utis the input, ( ) Each hysteresis unit is a pair of switching quantities ( ) ,  to determine [9] ,  and  is the upper and lower switching value;   , so each hysteresis unit is a determined point in the Preisach half plane = , as shown in Figure 6. is a saturation value of the input.When the input signal is zero, the whole system has no input history, then the integral interval of the entire region is zero, obviously the integral result is zero, then all hysteresis generators are 0. With an increase in the input signal, when the input signal rises 1 u , drawing a line parallel  to each other, this region is divided into two regions 0 S and S + , as shown in Figure 7 (b).At this time, the integral interval is S + , then the larger the input signal is, the larger the integral interval will be.S + When the input signal rises, the geometric division is completed ( ) ut.However, when the signal descends, the integration area is not simply the area formed by moving from the 1 u down to the 2 u , but as shown in Figure 7 (c), a straight line  is made parallel to it, and the front line 1 u is moved from right to left to form a trapezoidal area S + ..As long as the memory erasability and secondary loop consistency hysteresis process are satisfied, the Preisach model can be used for modeling and analysis.The memory erasability reflects that the output of the hysteretic system is not only affected by the current input but also by the historical dominant extreme value of the input.The secondary ring consistency refers to the closed track formed by the input signal in a certain range, monotonically increasing from a certain value to a certain value, and then monotonically decreasing from the value to the original value.The secondary ring consistency shows that the shape of the secondary ring and the main ring formed in a certain range is the same.Most hysteresis models have secondary loop consistency, but the hyperbolic function hysteresis model used in this chapter does not have secondary loop consistency.It is obvious that the driving process of a continuous robot is similar to that of piezoelectric ceramics, and this model can be introduced into the hysteresis analysis of a continuous robot [11] .

Establishment of hysteresis model of continuous robot
According to the characteristics reflected in Figure 1, the hyperbolic nonlinear model describing Preisach hysteresis is adopted in this paper.The hysteresis main ring established by Badel with hyperbolic function is shown as [12] : Where, 1 a , 2 a , 1 b , 2 b , 1 c , and 2 c ; the six parameters are the parameters of driver response identification.1 f is the rising section of the hysteresis curve and 2 f is the falling section of the hysteresis curve.This model has memory erasability, and the requirement is that the model must pass through the origin (0,0).As can be seen from Formula (2), compared with the basic model of Formula ( 6), this model is simpler and requires fewer parameters.Only the data on the main ring is needed to complete the driver design.
To verify the validity of the hyperbolic function model, the drive displacement of the stretch section of the steering gear is taken as the target input, and the bending Angle of the continuous robot is taken as the target output.The fitting toolbox in MATLAB is used to identify the parameters of the experimental data measured [13][14] .Levenberg-Marquardt algorithm is used to solve each parameter in Formula (2), to obtain the linear driving hysteresis model of the continuous robot.The values of the obtained parameters are shown in Table 1, and the images are shown in Figure 8.To verify the hysteresis model, a series of drive input sequences are selected, and the simulation results are compared with the experimental results.As can be seen from Table 2, the maximum error value of the bending Angle obtained after parameter identification fitting is 3.18, the mathematical expectation of error is 1.033, and the standard deviation is 1.0039.The maximum error value of theoretical bending is 7.78, the mathematical expectation is 2.887, and the standard deviation is 3.0445.Compared with the previous theoretical model, it is obvious that the error is reduced, and the standard deviation of the error is smaller.According to the results in the table, the predicted results of the model are similar to the experimental results, indicating that the hyperbolic Preisach model can accurately predict the driving bending of the continuous robot, and the model can be used as a part of the control system of the continuous robot to reduce its motion hysteresis.

Conclusion
In this chapter, the main reasons for hysteresis are analyzed by structural characteristics, and the hysteresis characteristics of continuous robots are analyzed.The application principle of the Preisach basic model is introduced, the hysteresis model of the robot is modeled by using the hyperbolic Preisach model, the parameters of the model are identified by experimental data, and the main loop curve of the prediction model is obtained.Finally, comparing the error of the prediction results and the experimental results, the results show that the hysteresis model has a good prediction result for the hysteresis characteristics of a continuous robot, and the maximum error of the prediction result is 3.18 degrees.

Figure 4 .
Figure 4. Schematic diagram of the experimental layout.The driving disc installed on the steering gear is 20 mm in diameter.Through the stretching of the steering gear, the bending Angle of the head and the driving quantity of the forward bending and reverse drawing are obtained.The theoretical driving curve has been calculated in the forward and inverse kinematics part, as shown in Figure5.Figure5shows that the bending Angle in the test process of forward stretching and reverse recovery has obvious deviation, and the bending Angle in the forward stretching is below the reverse recovery.Compared with the theoretical driving curve, the bending Angle has obvious hysteresis[5] .The main bending Angle lag is distributed in the second half of the driving stretch, and the change in the bending Angle is not obvious when the driving displacement is small.The analysis shows that it may be related to the deformation caused by the stretching of the driving line.In the second half of the driving stretch, the tensile force is large, the hysteresis is more obvious, and the recovery process of positive and negative stretching may be related to the initial state.From the overall view of the image, the process of forward stretching and reverse recovery can be approximately regarded as forming a hysteresis loop[6] .Given the above phenomenon, it is difficult to control the continuous robot.Hysteresis model analysis should be carried out for the continuous robot, so the hysteresis error can be reduced in the use of the continuous robot and more accurate control can be achieved.

Figure 5 .
Figure 5.The bending Angle change of a continuous robot during a stretching process.
is the output, ( ) ,    is the weight function of the hysteresis unit γ  , and  ( ) γ ut  is the Relay operator.

Figure 6 .
Figure 6.A simple hysteresis generator.The classic Preisach model can be described in Figure 7.As shown in Figure 7 (a), 0 is a saturation value of the input.When the input signal is zero, the whole system has no input history, then the integral interval of the entire region is zero, obviously the integral result is zero, then all hysteresis generators are 0. With an increase in the input signal, when the input signal rises 1 u , drawing a line

Figure 7 .
Figure 7. Geometric description of the Preisach model.Preisach has two important features, namely memory erasability and secondary loop singleness[10] .As long as the memory erasability and secondary loop consistency hysteresis process are satisfied, the Preisach model can be used for modeling and analysis.The memory erasability reflects that the output of the hysteretic system is not only affected by the current input but also by the historical dominant extreme value of the input.The secondary ring consistency refers to the closed track formed by the input signal in a certain range, monotonically increasing from a certain value to a certain value, and then monotonically decreasing from the value to the original value.The secondary ring consistency shows

Figure 8 .
Figure 8.The hysteresis curve of a continuous robot.Table 1. Hysteresis model parameter identification values.

Table 1 .
Hysteresis model parameter identification values.

Table 2 .
Comparison of theoretical and experimental bending angles after fitting.