Mixed control scheme for accurate control of robotic flexible endoscope

Abstract

Tendon-driven endoscopes are mainly used in the current practice. Their flexible bodies may change frequently during the processes of biopsy, endoscopic mucosal resection or endoscopic submucosal dissection. These changes lead to backlash hysteresis and nonlinear friction effects, which make it difficult to achieve accurate control. To address this problem, a mixed control scheme based on the combination of discrete and continuous models was proposed and quantitatively compared with a conventional feedback control scheme, a feedforward control scheme and an adaptive control scheme. These experiments were conducted using a robotic gastroscope. The results showed that our control scheme can achieve more accurate tracking performance when the configuration changes frequently, with mean square error of tracking performance decreased by 50–75%.

Introduction

Flexible endoscopy is considered as an effective minimally invasive clinical procedure that aims to perform the internal body examinations and treatments via the natural body openings. The procedures of biopsy, endoscopic mucosal resection (EMR) and endoscopic submucosal dissection (ESD) are frequently performed during endoscopy to remove lesions. As shown in Figure 1, a physician must use both hands to manipulate a standard endoscope to achieve four degrees of freedom (DOFs): rotation, bending along two perpendicular axes and pushing/pulling. ¹ There are two main drawbacks of this operation style: (a) This operation is not intuitive and it is difficult for physicians to perform accurate treatments inside human’s body. According to the American Society for Gastrointestinal Endoscopy, the acceptable size of polyps for biopsy ranges from 2 mm to 8 mm. With EMR, a lesion is always removed with a snare so its size is always limited to 20 mm. In comparison, larger mucosa is dissected using an electrosurgical knife in a freehand manner in ESD. ESD has higher rate of en bloc resection but is more time-consuming. ² If the operation error was more than 2–3 mm, the blood vessel or varicose vein during these procedures would be damaged, which causes sudden bleeding. Perforation rates of 22–63% were reported during gastric and esophageal ESD even with experienced physicians. ³ This shows that it is hard to perform these procedures accurately in practice (the desired clinical accuracy should be more than 1 mm). (b) This operation is awkward and can cause pain or injury in the thumb, wrist, neck and back. ⁴

Figure 1.

Physicians use both hands to operate endoscope during (a) gastroscopy and (b) colonoscopy.

These drawbacks mainly come from the flexible body of endoscope in the current clinical routine. As shown in Figure 2, the flexible body typically consists of two groups of tendon-sheath systems (TSSs) that transmit tension to the bending section; a TSS is a commonly used and convenient mechanism for transmission of force through paths that are time-varying and highly spatially constrained. As the endoscope passes through a natural orifice, its profile will change depending on the operational manoeuvers through which it is directed. The time-varying operational path and the presence of the encircling structure of the TSS induce nonlinear friction effects and hysteresis phenomena. These difficulties in manoeuverability have resulted in quite unintuitive operations of procedures inside human’s body with endoscopes.

Figure 2.

The insertion section usually consists of two groups of TSSs which are responsible for DOF-1 and DOF-2 (left portion); the bending section consists of two groups of tendons (right portion). TSS: tendon–sheath system; DOF: degree of freedom.

Recently, many researchers have become interested in robotics technology to overcome these challenges and facilitate endoscopic surgeries. For example, Allemann et al. ⁵ used a motorized gastroscope to evaluate the use of a joystick interface, and Reilink et al. ⁶ designed a stationary motorized colonoscope with haptic guidance. A remote-controlled duodenoscope has been introduced, ⁷ and Fang et al. ⁸ proposed a motorized rhino endoscope that can be freely manipulated. Other groups have studied robotic flexible endoscopes based on completely new designs. ^9,10 These robotic flexible endoscopes all possess a basic structure similarly as shown in Figure 3. The mechanical control section is replaced with a motor drive system and a lightweight master control device, such as a joystick. The slave component typically has four DOFs.

Figure 3.

The comparison between a traditional flexible endoscope (upper portion) and a robotic flexible endoscope (bottom portion).

Although robotic technology can help decrease the physical discomfort of manipulating the endoscope, current studies do not completely address the problem of precisely controlling the tip position of the endoscope. This is a challenging problem because of backlash hysteresis and nonlinear friction effects. This is also one important reason why all types of flexible tendon-driven endoscopes are operated manually in current practice. ¹¹

Two well-known approaches exist for modelling and controlling TSSs, namely, the discrete static and the continuous dynamic methods. Since Kaneko et al. ¹² proposed the first static model of a single-tendon system; many researchers have used lumped mass model elements to model TSSs, such as Palli and Melchiorri, ¹³ Chen et al. ¹⁴ and Low et al. ¹⁵ A set of partial differential equations were proposed by Agrawal et al. ^16,17 to model the nonlinearity of TSSs. However, static approaches have some limitations. First, the computation becomes more complicated as more TSS elements are added to increase accuracy. Second, these models require information regarding the configuration of the sheath along the endoscope, which is often difficult to obtain in practice. Finally, with the use of the Coulomb friction model, discontinuous phenomena arise; these models cannot describe pre-sliding status or zero-velocity status. As an alternative approach to describe TSSs, Do et al. ^{18 –22} introduced novel dynamic friction models, in which continuous backlash hysteresis models were used. This continuous approach can achieve high accuracy without increasing computational cost because the TSS is modelled as a single element with nonlinear friction and hysteresis. The tendon configurations need not be known in advance but should remain fixed or vary only moderately. In addition, this approach solves the discontinuity problem encountered in static models.

For a more complete description of the characteristics of TSSs, it is promising to adopt continuous dynamic models. In terms of related control methods, many controllers for natural orifice transluminal endoscopic surgery (NOTES) with moderately varying configurations have been introduced. These controllers are well suited for their intended applications: During the surgical process, no changes in configuration occur once the flexible body of endoscope is held without deformation in the patient’s body. However, this condition does not apply in our endoscopic system, which is a prototype for robotic gastroscope or colonoscope. Unlike the variable stiffness required in NOTES to ensure platform stability for surgeries, a gastroscope or colonoscope should always be flexible because in biopsy, EMR or ESD, a wider working region is always needed. In this case, the adoption of robotic technology is expected to improve the accuracy and manoeuverability of these operations, meaning that the tip-tracking performance should be guaranteed without requiring the entire configuration to remain fixed.

In this study, a mixed control scheme for robotic flexible endoscope is proposed to achieve the goal of tracking the desired movement of the tip accurately (the largest error is less than 1 mm), with the body of the endoscope moving freely. After the physician decides the target for the biopsy or the range of EMR or ESD, the whole system will work automatically to track the target or the path for surgical tool. This strategy shows great potential in avoiding bleeding and perforation, in achieving a higher rate of en bloc resection and in decreasing the procedure time during the interventional treatment stages of these surgeries. This tracking method is based on the combination of the discrete static and the continuous dynamic models. To date, no applications mixing these two approaches for the design of precise motion control scheme have been reported.

In the following sections, the mixed control scheme is proposed, beginning with the reference to existing methods for the nonlinearity of TSSs. Subsequently, our experimental platform is described. After this, evaluation experiments are described. The results are then presented and discussed separately. Finally, a conclusion is presented.

Theoretical background

Discrete and continuous models for the nonlinearity of TSSs

A complete TSS is usually considered as the accumulation of many infinitesimal TSS segments in the discrete static model, as shown in Figure 4(a). The curvature of TSS ${\kappa }_i=1/r_i$ is arbitrary and may even be time-varying; as a result, it is difficult to calculate the output driving force T_out of a flexible configuration. The studies of Wang et al. ^{23, 24} and Sun et al. ²⁵ proposed a solution to remove κ_i by defining Φ_L as the sum of all convex curve angles φ_i along the TSS, thereby enabling the estimation of the TSS configuration in practice

$T_{\text{out}}=\{\begin{array}{l}{T}_{\text{in}}\exp \{-\mu {\Phi }_L\zeta \}-P,{\Phi }_L<{\Phi }_0\\ T_0,{\Phi }_L\ge {\Phi }_0\end{array}$

1

Figure 4.

(a) TSS is usually modelled as the accumulation of many infinitesimal segments in the discrete static model. (b) TSS is usually modelled as a single element with nonlinearity in the continuous dynamic model. TSS: tendon–sheath system.

where μ is the coefficient of friction and ζ is the direction index indicating the case of sliding. L is the length of the tendon along the entire insertion section, T _in is the tension applied at the beginning of the TSS and T₀ is the pre-tension. Φ₀ is defined as the location at which T _in can be effectively transmitted. P is the length penalty.

Since the discrete static model adopts the Coulomb friction model, it suffers from the problem of discontinuity. To completely describe the backlash hysteresis nonlinearity, the continuous dynamic model is needed. This method usually models the TSS as one element, as shown in Figure 4(b). To model nonlinear effect, various types of Bouc-Wen models ^{18 –20} and Dahl models ^21–22 have been used. Do et al. ²² proposed a promising modified Dahl model as follows

$\dot{z}=-\beta {\dot{\chi }}_{\text{in}}-\alpha \left|{\dot{\chi }}_{\text{in}}\right|z$

2

${\chi }_{\text{out}}=c{\chi }_{\text{in}}+z+{\chi }_{\text{offset}}$

3

where z is an internal state; α, c and β are factors; and χ_in and χ_out denote the input and output displacement of the TSS, respectively. χ_offest arises from the difference between the estimated and experimental results. They also proposed a feedforward control scheme and an adaptive control scheme based on this model.

Mixed control scheme for varying configurations

Although the controllers based on the continuous dynamic model can accurately estimate the backlash hysteresis, they must satisfy some conditions in advance. Only in the case of a constant configuration, the feedforward control scheme exhibits accurate tracking performance. When part of the tendon-sheath configuration changes, a period of 3 s is needed for the adaptive control scheme to converge to the new parameters. ²² Neither of these controllers is suitable for the application of a robotic gastroscope or colonoscope, in which the overall configuration of the TSSs varies more widely and frequently because of the movements of the patient, the doctor or the intra-corporeal organs during the biopsy, EMR or ESD procedure.

However, the flexible characteristics of the discrete static model (equation (1)) can be exploited to improve the performance of existing methods. In this study, the mixed control scheme is proposed to address the problem of frequently changing configurations. In the literature, the Dahl model is often simplified for easier numerical implementation as follows ²⁶

$\dot{z}={\dot{\chi }}_{\text{in}}-{\sigma }_0\left|{\dot{\chi }}_{\text{in}}\right|z/F_c$

4

$S_{\text{out}}={\sigma }_{0}z$

5

where σ₀ is the asperity stiffness and F_c is the Coulomb friction. S_out is the output of the system model, which is interpreted as the friction force. S_out in equation (5) can be expressed as follows

$S_{\text{out}}=T_{\text{in}}-T_{\text{out}}$

6

From equation (1), ${\chi }_{\text{out}}=S_{\text{out}}/{\sigma }_0$ , and in equations (3) and (6), the output displacement of TSS can be estimated through the tension information of TSS

${\chi }_{\text{out}}=\frac{\left(T_{\text{in}}\left(1-\exp \left\{\mu {\Phi }_L\zeta \right\}\right)+P\right)}{{\sigma }_0}$

7

Thus, the desired output displacement of the TSS, χ_ref, can be approached through the force control at the proximal end of the TSS. The mixed control scheme can be explained as follows

$T_{\text{in,ctrl}}=\frac{\left({\sigma }_0{\chi }_{\text{ref}}-P\right)}{\left(1-\exp \left\{-\mu {\Phi }_L\zeta \right\}\right)},\Delta {\Phi }_L\ne 0$

8

${\chi }_{\text{in,ctrl}}={\chi }_{\text{FF,adaptive}},\Delta {\Phi }_L=0$

9

where T_in,ctrl and χ_in,ctrl are the control signal of input tension and the control signal of input displacement, respectively; χ_FF,adaptive is generated from the adaptive control scheme. ²² When a change in configuration is detected ( $\Delta {\Phi }_L\ne 0$ ), the mixed control scheme relies on the discrete static model to track the desired output displacement. When the change is complete ( $\Delta {\Phi }_L=0$ ), the adaptive control laws based on the continuous dynamic model are used to track the desired position.

Filters are very important to ensure the performance of control schemes. Three major types of filters can be implemented: set point filters, denoted by F_r; process output filters, denoted by F_p; and load disturbance filters, denoted by F_d. In our case, because the set point or reference signal does not often change stepwise, the specific set point filters are not implemented to cope with overshoot. This can provide additional benefits for the dynamic response of our system. The measurable load disturbance signal, $\Delta {\Phi }_L$ , is used to overcome the problem of lag in the TSSs. Process output filters play a key role in ensuring the performance of our system. A second-order filter,F_second, is implemented followed by a lead/lag filter,F_lead-lag

$\{\begin{array}{l}{F}_{\text{second}}=\frac{1}{\left(\frac{1+s{T}_f+s^2{T}_f^2}{2}\right)}\\ F_{\text{lead-lag}}=\frac{\left(1+s{T}_{lp}\right)}{1+s{T}_{\text{lead-lag}}}\\ F_p=F_{\text{second}}·F_{\text{lead-lag}}\end{array}$

10

where T_f is the filter-time constant of F_second, $T_{lp}=T_f$ , and T_lead-lag is the new time constant. F_p is designed not only to ensure a low noise level in the signals from the torque sensors and rotary encoders but also to reduce the introduced delay.

The block diagrams for the conventional feedback control scheme, the feedforward control scheme and the adaptive control scheme ²² are illustrated in Figure 5(a) to (c), respectively. The proposed mixed control scheme is depicted in Figure 5(d). $e_r(t)$ is the tracking error at the time t and χ_real is the actual output displacement of the TSSs during the evaluation of control schemes. For the brushless DC (BLDC) motor loop, a saturation function is implemented to maintain the controller output within the working range of the motors.

Figure 5.

Four structures of control schemes. The conventional feedback control scheme, the feedforward control scheme, the adaptive control scheme and the proposed mixed control scheme.

Experimental material and methods

The evaluation experiments were conducted based on a robotic flexible endoscope. The input driving force and input displacement of the TSS were measured by different sensors at the proximal end of system. The output driving force and output displacement of the TSS were measured indirectly by the angle-detecting system (ADS) at the distal side of endoscope. The methods for evaluating control schemes are then described subsequently.

Robotic flexible endoscope

The system is based on a standard gastroscope (VME-98; AoHua Photoelectricity Endoscope Co., Ltd, Shanghai, China) as shown in panels (a) and (b) of Figure 6. This gastroscope can be replaced with a standard colonoscope (VME-1300; AoHua Photoelectricity Endoscope Co., Ltd) for further thorough evaluation of the controllers. Three BLDC motors (B3657 M; Hengdrive Electric, Shenzhen, China) were used to drive the flexible endoscope in three DOFs. Three pairs of torque sensors (0.01-Nm resolution, ZH08; Zhonghang Kedian Measurement & Control Technology, Beijing, China) and rotary encoders (12-bit resolution; Wufeng Electronic Technology, Shandong, China) were installed between the motors and the mechanical drive system. The diameter of reel rounded by wire is 10 mm. So the accuracy of the measurement module was considered as 0.01 mm. A controller board was also included to collect position data and torque signals and to control the motors; this board consisted primarily of a microcontroller unit (STM32F103ZET; ST, Italy and France) and a complex programmable logic device (EPM1270; Altera, San Jose, California, USA). A personal computer (PC) collected the information from the controller board via a RS-232 connection.

Figure 6.

(a) Experimental platform and (b) schematic of the robotic gastroscope, which consists of four parts: motor drive system, ADS, a modified gastrosocpe and a desktop. ADS: angle-detecting system.

The insertion section of the gastroscope was mounted on a piece of cork board with several plastic supports to allow the endoscope to assume various configurations. There were two groups of TSSs consisting of tendons 0.5 mm in diameter and sheaths with inner diameter of 0.6 mm and outer diameter of 0.8 mm.

The proposed control schemes were designed to estimate backlash hysteresis phenomena and nonlinear friction effects without using output feedback at the distal end for compensation. However, to evaluate the accuracy of control schemes, information regarding the displacement and driving force at the tip must be collected during experiments. Unlike many researchers’ platforms that provide sufficient space on the distal side for installation of encoders or load cells, such as a pulley wound with tendons, a spring structure or a gripper, similar sensors cannot be installed at the end of a gastroscope or a colonoscope because a commercial endoscope has limited additional space at the tip for these sensors.

To evaluate the control schemes with the least possible interference, the ADS is proposed to collect displacement and driving force information from the tip of endoscope. Three modules (modules 1–3) were installed on the bending and insertion sections of the endoscope, as shown in the left portion of Figure 7. Each module was based on a motion sensor (MPU-9250; InvenSense, San Jose, California, USA) with three integrated sensors: a 3-axis gyroscope, a 3-axis accelerometer and a 3-axis magnetometer. The on-chip and run-time calibration firmware of the MPU-9250 was used to monitor each module’s accuracy. A Kalman filter was also implemented on the PC to address the problem of gyroscope drift. All calculations were performed in real time at 10–12 Hz on a desktop with an Intel® Core™ i5-3470 3.2 GHz CPU (Lenove ThinkCentre M92p 3218).

Figure 7.

ADS consists of three modules (modules 1–3). Modules 1 and 2 were installed at the ends of the bending section to collect different θ. θ has the relationship to T_out and χ_out at the distal end of TSS. Module 3 was installed at the proximal end of TSS and used to collect Φ_L with module 2. T_in and χ_in were also collected. Different surgical tools (biopsy forcep, snare and electrosurgical knife) were installed for different experiments. ADS: angle-detecting system; TSS: tendon–sheath system.

It is important to measure the displacement and force information at the bending section to study the nonlinear effects of TSSs. To obtain this information, we used the endoscope only with a bending section and two modules (modules 1–2), as shown in the right portion of Figure 7. First, the bending section was moved separately through its maximum ranges of DOF-1 and DOF-2. During this motion, T_out, χ_out and the bending angle θ of DOF-1 or DOF-2 for the bending section were recorded in a lookup table. The lookup table was used for reference during the evaluation of the control schemes, part of which is shown in Figure 8. The difference value between module 2 and module 3 was used to calculate Φ_L. The ADS continuously monitored the orientations of MPU-9250; more accurate results could be achieved if more modules were installed inside the body of the insertion section.

Figure 8.

The modified gastroscope (right portion of Figure 7) is moved in DOF-1 and DOF-2. The tension and displacement of its tendons are considered as T_out and χ_out of TSS. These data, as well as θ, were collected via controller board and ADS simultaneously. DOF: degree of freedom; TSS: tendon–sheath system; ADS: angle-detecting system.

In this implementation, the ADS communicated with the controller board via inter-mixed circuit (I²C). This could be implemented as a wireless connection (e.g. with Zigbee module) in the future. In addition, the MPU-9250 is one of the world’s smallest 9-axis motion sensors, with a 3 × 3 × 1 mm³ quad flat no-leads package. This means that it is also possible to adopt similar approaches in real practice.

To evaluate the proposed mixed control scheme in the endoscopes in their real working conditions, different surgical tools were installed on the endoscope. As shown in Figure 7, a biopsy forceps (FD-6C-1.B; Olympus, Japan) was placed inside its body, which makes it work as it would during biopsy procedure. In addition, a snare (SD-7C-1.B; Olympus) for EMR and an electrosurgical knife (KD-620LR; Olympus) for ESD were installed on the gastroscope or colonoscope for corresponding experiments. Installation of these tools simulates the real response of the tips of the endoscopes during different surgeries.

Experimental evaluation of control schemes for flexible configurations

The parameters of the discrete static model (equation (1)) and the continuous dynamic model (equations (2) and (3)) were validated at first.

In terms of the validation of the discrete static model, several custom endoscopes were prepared with TSSs of different lengths: 0.04 (bending section only), 0.25, 0.5, 0.75 and 1 m (see Figure 9). Various configurations of all insertion sections (Φ_L = 48°, Φ_L = 90°, Φ_L = 180° and Φ_L = 450°) were implemented. The robotic endoscope was moved in different directions, while T_in and θ were recorded separately by the torque sensors and the ADS in real time. T_out was then calculated from the prepared lookup table. μ was estimated by applying equation (1) to the experimental results from the pulling phase for T_out. This process was repeated five times with different TSSs; results from the same batch exhibited only slight variations (standard deviation of 3.16%), yielding a value of μ = 0.131. The length penalty was calculated using the logarithmic regression, yielding $P=0.077\text{log}(L)\zeta +0.288\zeta$ . The parameters of the continuous dynamic model were predicted using the Nelder–Mead simplex method. ²¹

Figure 9.

To validate referenced models, flexible endoscopes with five different lengths of insertion section were used from 0.04 m to 1 m.

The control schemes for flexible configurations were then compared with three other methods: the conventional feedback control scheme, the feedforward control scheme and the adaptive control scheme.

An overview of the experimental set-up is illustrated in Figure 10. For evaluation purposes, χ_ref at the distal end of the endoscope was generated randomly by the PC and was the same for all of the schemes. χ_real was obtained via the lookup table. The torque sensors and optical encoders on the proximal side were used to collect T_in and χ_in for the controllers.

Figure 10.

The whole experimental set-up.

Each control scheme experiment lasted 40 s, and a TSS of L = 1 m was used. To simulate the configuration changes that occur during biopsy, ESD or EMR using a gastroscope or colonoscope, Φ_L was initially set to 160° and was modified manually with the assistance of the ADS three times during the experiments: from 160° to 90°, from 90° to 45° and from 45° to 180°. This manual adjustment of the accumulated angle was performed quickly at the same time for each experiment. For the backlash hysteresis model for the feedforward control scheme, the parameters chosen were those obtained from the offline calibration during the validation of the continuous dynamic model, with L = 1 m and Φ_L = 160°. For the adaptive control laws, the parameters of the backlash hysteresis model for the dynamic and mixed control scheme were obtained from the offline learning results for a TSS, with L = 1 m and Φ_L = 180°. Three trials were conducted in each experiment. For clarity, only one trial with motion in DOF-1 is displayed. In order to thoroughly evaluate a number of endoscopes, a total of 20 subjects were used for the experiments: 10 gastroscopes from different manufacturing batches and 10 colonoscopes from different manufacturing batches. A modified gastroscope and a modified colonoscope were used to generate corresponding lookup tables, with a biopsy forcep, a snare or an electrosurgical knife installed. The four control schemes were then evaluated under the motion in the two DOFs simultaneously. A number of experiments were conducted with each combination of endoscope type and surgical tool. The two endoscope types were the gastroscope and colonoscope, respectively. The three surgical tools that were used were the biopsy forcep, the snare and the electrosurgical knife, respectively.

Results

In this study, different control schemes were compared quantitatively. Figure 11 shows that the output of the conventional feedback control scheme always lags behind the reference input because of friction effects. This lag is also due to the fact that the error becomes larger when Φ_L increases (with a maximum amplitude of 4.6 mm). The outputs of TSSs cannot follow the commanded displacements, particularly when a commanded displacement changes direction. This is the result of hysteresis phenomena. When disturbances are introduced, quick changes of the output can be observed clearly.

Figure 11.

Experimental results of the conventional feedback control scheme.

By contrast, the feedforward control scheme demonstrates better tracking performance before the first disturbance (from 160° to 90°), as displayed in Figure 12, with a significant reduction from mean square error (MSE) from 0.18 to 0.02. The main reason is that the parameters were optimized offline with the same configuration (Φ_L = 160°). However, as more disturbances are introduced, this controller suffers larger tracking errors, which are most severe during the third period (after the second disturbance: from 90° to 45°), with MSE = 0.42. Clear over-control phenomena can be observed during these periods. Subsequently, the tracking performance improves again when Φ_L becomes 180°. The overall performance suffers, with MSE = 0.13.

Figure 12.

Experimental results of the feedforward control scheme.

The results of the adaptive control scheme show a large error (with a maximum amplitude of 1 mm) through the first 3.5 s, as shown in Figure 13. Because the initial parameters of the controller came from offline learning with a different configuration (Φ_L = 180°), the adaptive laws and tracking error require this long to converge to the new values. After this initial period and before the first introduced disturbance (from 160° to 90°), the tracking performance demonstrates accurate tracking results. However, when a disturbance is introduced, the adaptive controller once again requires 3–4 s to converge. This influences the overall tracking accuracy, which is characterized by the values of MSE = 0.05.

Figure 13.

Experimental results of the dynamic control scheme.

In the case of the proposed mixed control scheme with the same initial parameters as the adaptive controller, no distinct error was observed during the initial stage of the experiment, as shown in Figure 14. Then, before the first introduced disturbance (from 160° to 90°), the tracking performance improved. Despite the introductions of three disturbances, only a moderate reduction of tracking accuracy was observed during the first 2 s after each disturbance. As a result, this control strategy ensures good overall accuracy, with MSE = 0.02. It can be observed from the displacement error in this trial as shown in Figure 15 that only the adaptive control scheme and the mixed control scheme can adapt to changing conditions, while the latter shows smaller tracking errors (the largest error is less than 1 mm).

Figure 14.

Experimental results of the mixed control scheme for the motion along DOF-1. DOF: degree of freedom.

Figure 15.

The overall $e_r(t)$ of the trial (Figures 11 to 14)

The MSE of thorough evaluation using gastroscopes and colonoscope from different batches is summarized as boxplots in Figure 16. These figures display the tracking results of the simulated biopsy (a biopsy forcep installed), the simulated EMR (a snare installed) and the simulated ESD (an electrosurgical knife installed) for each of the four conditions, for both gastroscopes and colonoscopes.

Figure 16.

The MSE of tracking results (χ_ref and χ_real) for the thorough evaluation experiments. MSE: mean square error.

Three two-way mixed analysis of variance was performed for all the subjects. These were done on the simulated biopsy, the simulated EMR and the simulated ESD, with the controller (the conventional feedback control scheme, the feedforward control scheme, the adaptive control scheme and the mixed control scheme) as a factor and endoscopes (gastroscope and colonoscope) as a between-subject factor.

As shown in Table 1, there is a significant influence of controller on tracking performance because the significant factor in all the experiments is less than 0.001. The adoption of our mixed control scheme can decrease the MSE by 50–75% compared with traditional methods. Furthermore, the analysis revealed no significant controller × endoscope interaction or endoscope effect for the biopsy, the EMR and the ESD, which means that the choice of gastroscope or colonoscope does not influence the tracking performance of a particular controller.

Table 1.

The two-way mixed ANOVA of the tracking results of all subjects during experiments for biopsy, EMR and ESD.

	Experiments for biopsy		Experiments for EMR		Experiments for ESD
	F	Sig.	F	Sig.	F	Sig.
Controllers	179.739	<0.001	313.943	<0.001	532.002	<0.001
Endoscopes	0.767	0.393	0.314	0.582	1.904	0.14
Controllers × Endoscopes	0.291	0.832	0.462	0.71	0.511	0.484

ANOVA: analysis of variance; EMR: endoscopic mucosal resection; ESD: endoscopic submucosal dissection.

Discussion

The results from Figures 11 to 16 suggest that it is not advantageous to use the conventional feedback control scheme for TSSs because the nonlinear characteristics of the system will always cause the output to lag with respect to the desired trajectory. The feedforward control scheme was designed to address this problem. It can be implemented easily because it can be derived directly from the inverse of a modified Dahl model, and it also demonstrates good tracking results when the configuration is the same as that used for offline learning.

However, when a larger Φ_L is introduced as a disturbance in the experiments, the conventional feedback control scheme has a larger error, and the feedforward control scheme has poor performance when the accumulated angle Φ_L is quite different from the one it used for offline learning. It is natural to implement some adaptive laws for variable configurations.

The adaptive control scheme can adjust its parameters to adapt to different working conditions. However, it requires 3–4 s to converge, during which time the actual output of TSSs may vary significantly because of nonlinear effects. In comparison, the proposed mixed control scheme has a smaller error in tracking performance before convergence. When the configuration changes ( $\Delta {\Phi }_L\ne 0$ ), a quick estimate of output displacement can be obtained via equation (7). Our experiments show that this method yields a good estimate of the nonlinear friction when Φ_L is provided. During the initial time before parameter convergence occurs, the error in the tracking performance can thus be limited. However, this discrete static model is simplified for flexible configurations, and all the dynamic characteristics of TSSs do not depend only on curvature; therefore, accurate tracking performance can be achieved only when the hysteresis model can be well estimated. When the configuration is no longer changing ( $\Delta {\Phi }_L=0$ ), the adaptive control laws are used to update these parameters.

In summary, the conventional feedback control scheme has the poorest tracking performance since it ignores the nonlinearity of TSSs. The feedforward control scheme can predict the nonlinearity of TSSs, but it is sensitive to changing configurations. The adaptive control scheme is capable of adapting to varying configurations but needs time to recover from disturbances. The mixed control scheme is able to solve these problems via the combination of the discrete static model and the continuous dynamic model. In addition, although the natural response of endoscope may be changed because of the installation of different surgical devices, such as a snare or electrosurgical knife, the mixed control scheme always achieves the best tracking performance, followed by the adaptive control scheme, the feedforward control scheme and the conventional feedback control scheme. In terms of the system usability, since all the experiments were conducted without any physician involved, the difficulty of training for the robotic endoscope with the mixed control scheme remains unknown. In the next phase of our research, physicians will be invited to take part in the experiments for the usability of whole system. Besides, in order to evaluate the clinical applicability of this research, ex vivo and in vivo experimental investigations will also be undertaken using real procedures in the future. For example, we will evaluate the duration time of ESD with different control schemes. The flexible body varies at the same time.

Conclusions

Robotic flexible endoscopes can free physicians from the need to perform frequent complex manipulations and may assist in performing complex surgeries. However, the challenge of accurately steering flexible systems is a hindrance to the adoption of this technology. To ensure accurate tracking performance of a robotic gastroscope or colonoscope at all time in variable configurations, we have proposed a mixed control scheme based on the combination of the discrete static model and the continuous dynamic model. Experimentally, the proposed control scheme had improved tracking performance under varying configurations.

This study also proposed an indirect method of determining the tension and displacement at the distal end by means of motion sensors, which is also possible in real practice.