Adaptive control for enhancing tracking performances of flexible tendon–sheath mechanism in natural orifice transluminal endoscopic surgery (NOTES)

• Compensation control schemes for tendon–sheath system are developed.
• Hysteresis model parameters are identified and optimized for feedforward.
• Compensation with feedforward scheme is used for control purpose.
• Compensation with nonlinear adaptive scheme is developed for control purpose.
• The proposed models and control structure are validated satisfactorily.

Tendon–sheath mechanism (TSM) has inherent advantages in the development of flexible robotic systems because of its simplicity, safety, flexibility, and ease of transmission. However, the control of TSM is challenging due to the presence of nonlinearities, namely friction, backlash-like hysteresis and the time-varying configuration of the TSM during its operations. Existing studies of TSM found in the literature only address tendon transmission under the assumption of fixed configuration and a complex inverse model of backlash is required. In order to flexibly use the system in a wider range of applications, the aforementioned nonlinear effects have to be characterized for the purpose of compensation. In this paper, we endeavor to address these issues by presenting a series of controller strategies, namely a feedforward control scheme under the assumption of known backlash-like hysteresis profile, and an adaptive control scheme to characterize the nonlinearities with unknown backlash hysteresis and uncertainties. The proposed control schemes do not require information of the tendon–sheath configurations, which is challenging to obtain in practice, in the compensation structures. In the absence of output position feedback, a simple direct inverse model-based feedforward has been used that efficiently reduce the tracking errors. The feedforward compensation does not require any complex algorithm for the inverse model. In the presence of output position feedback, a nonlinear adaptive controller has been developed to enhance the tracking performances of the TSM regardless of the random change in the tendon–sheath configurations during compensation. In addition, exact values of the model parameters are not required. They are estimated online during the operations. A dedicated experimental setup is introduced to validate the proposed control approaches. The results show that the proposed control schemes significantly improve the tracking performances for the TSM in the presence of uncertainties and time-varying configurations during the operations. There is a significant decrease of 0.0158 rad2 (before compensation) to smaller value of 0.0012 rad2 (use feedforward control) and 8.2815 × 10−5 rad2 (use nonlinear controller) after compensation.