Electronic Thesis and Dissertation Repository

Degree

Doctor of Philosophy

Program

Electrical and Computer Engineering

Supervisor

Ilia G. Polushin

2nd Supervisor

Rajni V. Patel

Joint Supervisor

Abstract

Tendon-based transmission is a common approach for transferring motion and forces in surgical robots. In spite of design simplicity and compactness that comes with the tendon drives, there exists a number of issues associated with the tendon-based transmission. In particular, the elasticity of the tendons and the frictional interaction between the tendon and the routing result in substantially nonlinear behavior. Also, in surgical applications, the distal joints of the robot and instruments cannot be sensorized in most cases due to technical limitations. Therefore, direct measurement of forces and use of feedback motion/force control for compensation of uncertainties in tendon-based motion and force transmission are not possible. However, force/motion estimation and control in tendon-based robots are important in view of the need for haptic feedback in robotic surgery and growing interest in automatizing common surgical tasks.

One possible solution to the above-described problem is the development of mathematical models for tendon-based force and motion transmission that can be used for estimation and control purposes. This thesis provides analysis of force and motion transmission in tendon-pulley based surgical robots and addresses various aspects of the transmission modeling problem. Due to similarities between the quasi-static hysteretic behavior of a tendon-pulley based da Vinci® instrument and that of a typical tendon-sheath mechanism, a distributed friction approach for modeling the force transmission in the instrument is developed. The approach is extended to derive a formula for the apparent stiffness of the instrument. Consequently, a method is developed that uses the formula for apparent stiffness of the instrument to determine the stiffness distribution of the tissue palpated. The force transmission hysteresis is further investigated from a phenomenological point of view. It is shown that a classic Preisach hysteresis model can accurately describe the quasi-static input-output force transmission behavior of the da Vinci® instrument.

Also, in order to describe the distributed friction effect in tendon-pulley mechanisms, the creep theory from belt mechanics is adopted for the robotic applications. As a result, a novel motion transmission model is suggested for tendon-pulley mechanisms. The developed model is of pseudo-kinematic type as it relates the output displacement to both the input displacement and the input force. The model is subsequently used for position control of the tip of the instrument. Furthermore, the proposed pseudo-kinematic model is extended to compensate for the coupled-hysteresis effect in a multi-DOF motion. A dynamic transmission model is also suggested that describes system’s response to high frequency inputs. Finally, the proposed motion transmission model was used for modeling of the backlash-like hysteresis in RAVEN II surgical robot.

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