Recent study shows that tendon-sheath system (TSS) has great potential in the development of surgical robots for endoscopic surgery. It is able to deliver adequate power in a light-weight and compact package. And the flexibility and compliance of the tendon-sheath system make it capable of adapting to the long and winding path in the flexible endoscope. However, the main difficulties in precise control of such system fall on the nonlinearities of the system behavior and absence of necessary sensory feedback at the surgical end-effectors. Since accurate position control of the tool is a prerequisite for efficacy, safety and intuitive user-experience in robotic surgery, in this paper we propose a system modeling approach for motion compensation. Based on a bidirectional actuated system using two separate tendon-sheaths, motion transmission is firstly characterized. Two types of positional errors due to system backlash and environment loading are defined and modeled. Then a model-based feedforward compensation method is proposed for open-loop control, giving the system abilities to adjust according to changes in the transmission route configuration without any information feedback from the distal end. A dedicated experimental platform emulating a bidirectional TSS robotic system for endoscopic surgery is built for testing. Proposed positional errors are identified and verified. The performance of the proposed motion compensation is evaluated by trajectory tracking under different environment loading conditions. And the results demonstrate that accurate position control can be achieved even if the transmission route configuration is updated. 
Modeling and motion compensation of a bidirectional tendon-sheath actuated system for robotic endoscopic surgery