Endoscopy based surgical operations involved confined spaces with complex anatomy. Therefore, excellent bending and higher flexibility are crucial requirements for efficient endoscopy. Among the available endoscopes, the joint-type comprising of articulated rigid joints are commonly used. It is integrated with a surgical robot system to preciously control its movements. Presently, several precise models such as the constant-curvature model have been developed to improve the control accuracy. Even though most of these kinematic models have been used to effectively describe the deformation of such endoscopes, they have proved to be ineffective for joint-type flexible endoscopes. This is because they ignore the effect of internal friction and thus, they cannot accurately show the required shapes.
To this end, a collaborative effort by Shenyang Institute of Automation researchers: Dr. Yuanyuan Zhou, Professor Zhidong Wang, Professor Zhongtao Zhang, and Professor Hao Liu developed a novel nonlinear bending model to describe the shape of the joint-type endoscope tip under cable tensions based on the elastic deformation and internal friction force. The main aim was to overcome the inefficiencies of the previous models and improve the use of endoscopy in surgical operations. Their research work is currently published in the journal, Advanced Robotics.
The model comprised of a rubber tube and metal net at each joint. They were approximated as tubes undergoing elastic deformation and therefore, they were assigned equivalent bending stiffness. On the other hand, the moment balance equation at each joint was modeled by taking into account the internal friction force along with the normal, friction and tension forces. The friction coefficient and bending stiffness were calibrated experimentally.
The novelty of the nonlinear model was validated by performing a group of experiments. Two major innovations for the joint-type flexible endoscope were brought out. First, by taking into account the internal friction force, the modeling accuracy was significantly improved as compared to models that neglected the effects of the internal friction forces. Secondly, this model does not require many and time-consuming computations. With only a few linear equations, it improves the computational efficiency. Finally, the results of the experiments and the prediction of the models were compared. This provided more insights on the hysteresis from the bending shape and the model accuracy.
The experimental result closely confirmed the model predictions. During bending and unbending phases, the model’s tip position errors were 1.48 ± 0.99 mm and 1.68 ± 0.91 mm while the bending angles errors were -5.50±2.54° and 1.68±3.66° respectively. Consequently, the hysteresis of the bending shape was observed in both the model and experiments and was noted to be very common in cable-driven flexible robots. The hysteresis effect was attributed to the internal friction force.
In summary, the scholars successfully modeled a bending section of a joint-type flexible endoscope based on elastic deformation and internal friction. The model is less complex and has good computational efficiency and thus suitable for real-time control. In particular, Professor Hao Liu, the corresponding author in a statement to Advances in Engineering emphasized this work is supported by the National Key R&D Program of China (2017YFC0110902) and used in the single port laparoscopic robot control.
Zhou, Y., Jiang, G., Zhang, C., Wang, Z., Zhang, Z., & Liu, H. (2019). Modeling of a joint-type flexible endoscope based on elastic deformation and internal friction. Advanced Robotics, 33(19), 985-995.