Modeling of Force and Motion Transmission in Tendon-Driven Surgical Robots

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

Shape Memory Alloy Actuators and Sensors for Applications in Minimally Invasive Interventions

Reduced access size in minimally invasive surgery and therapy (MIST) poses several restriction on the design of the dexterous robotic instruments. The instruments should be developed that are slender enough to pass through the small sized incisions and able to effectively operate in a compact workspace. Most existing robotic instruments are operated by big actuators, located outside the patient’s body, that transfer forces to the end effector via cables or magnetically controlled actuation mechanism. These instruments are certainly far from optimal in terms of their cost and the space they require in operating room. The lack of adequate sensing technologies make it very challenging to measure bending of the flexible instruments, and to measure tool-tissue contact forces of the both flexible and rigid instruments during MIST. Therefore, it requires the development of the cost effective miniature actuators and strain/force sensors. Having several unique features such as bio-compatibility, low cost, light weight, large actuation forces and electrical resistivity variations, the shape memory alloys (SMAs) show promising applications both as the actuators and strain sensors in MIST. However, highly nonlinear hysteretic behavior of the SMAs hinders their use as actuators. To overcome this problem, an adaptive artificial neural network (ANN) based Preisach model and a model predictive controller have been developed in this thesis to precisely control the output of the SMA actuators. A novel ultra thin strain sensor is also designed using a superelastic SMA wire, which can be used to measure strain and forces for many surgical and intervention instruments. A da Vinci surgical instrument is sensorized with these sensors in order to validate their force sensing capability