Concentric tube robots (CTRs) are a promising prospect for minimally invasive surgery due to their inherent compliance and ability to navigate in constrained environments. Existing mechanics-based kinematic models typically neglect friction, clearance, and torsion between each pair of contacting tubes, leading to large positioning errors in medical applications. In this paper, an improved kinematic modeling method is developed. The effect of clearance on tip position during concentric tube assembly is compensated by the database method. The new kinematic model is mechanic-based, and the impact of friction moment and torsion on tubes is considered. Integrating the infinitesimal torsion of the concentric tube robots eliminates the errors caused by the interaction force between the tubes. A prototype is built, and several experiments with kinematic models are designed. The results indicate that the error of tube rotations is less than 2 mm. The maximum error of the feeding experiment does not exceed 0.4 mm. The error of the new modeling method is lower than that of the previous kinematic model. This paper has substantial implications for the high-precision and real-time control of concentric tube robots.

Background: Suturing and knotting in Natural Orifice Transluminal Endoscopic Surgery (NOTES) requires the robot not only to be able to work with multiple manipulators but also to have a high degree of dexterity. However, little attention has been paid to the design and enhancement of dexterity in multi-manipulated robots. Methods:In this paper, the dexterity of a new dual-manipulator collaborative continuum robot in collaborative space is analyzed and enhanced. A kinematic model of the continuum robot was developed. The dexterity function of the robot is evaluated based on the concepts of the low-Degree-of-Freedom Jacobian matrix.Then an Adaptive Parameter Gray Wolf Coupled Cuckoo Optimization Algorithm with faster convergence and higher accuracy is innovatively proposed to optimize the objective function. Finally, experiments demonstrate that the dexterity of the optimized continuum robot is enhanced. Results:The optimization results show that the optimized dexterity is 24.91% better than the initial state. Conclusion:Through the work of this paper, the robot for NOTES can perform suturing and knot more dexterously, which has significant implications for the treatment of digestive tract diseases. K E Y W O R D Scontinuum robots, dexterity, low-DOF Jacobian matrix, robot for NOTES | INTRODUCTIONSuturing and knotting in traditional Natural Orifice Transluminal Endoscopic Surgery (NOTES) is mainly done by endoscopy and human hands. 1 In NOTES, suturing is usually made with purse strings, which are easy to operate, the surface after suturing is smooth and promotes healing. Currently, the purse-string method is implemented with titanium clips, which are easily operated and accurately positioned. However, they suffer from the problem of dislodging easily, causing wound dehiscence and rebleeding. Therefore, new types of