The following simulation results were produced with a inverse kinetostatics formula- tion (inputs of pose and wrench) to initialize q and τ along with the matrices needed
Figure 5.3: The desired compliance of the manipulator was scaled from Cd= 3C to Cd= 8C and a constant force of 1.1 N was applied on the end effector in the positive x direction. Different simulations for the desired compliance matrices are shown here.
for calculation of Kp. A forward kinetostatics formulation (inputs of q and wrench) was used to apply a force to the end effector and measure the displacement.
Passive Stiffness Controller Position Convergence
The passive stiffness controller solves for new actuation forces or link lengths with a
constant Kp matrix based on the current pose of the manipulator. The convergence
of the controller onto the correct pose for the desired stiffness is measured in the number of times the robot plant model is provided new actuation variables and solved for the pose. The figure shows results for 6 different desired stiffness behaviors and the position convergence for each was simulated with a robot plant in the form of
a forward kinetostatic model. Results are shown in Figure 5.3. The dotted line
represents the displacement desired when the force is placed on the end effector. This is calculated by multiplying the x component of the Cdmatrix (the first diagonal) by
law is simply Equation (5.5). In the simulation with Cd= 8C, an additional damping term is required for convergence. The control law is of the form
τ = α(τd− Kp(q − qd)) + (1 − α)τold (5.12)
where τold is the previous input to the robot plant.
All of the simulations produced actuation forces of less than 3 N. This demon- strates that the control law is achievable with modest motor effort.
Chapter 6
Continuum Robot Tool
Manipulators for Colonoscopy
In chapters 3 and 4, kinematic modeling and design analyses of continuum robots
were developed. These results provide the means by which to analyze a particular concentric tube robot for a surgical task. This chapter outlines the task goals and requirements, development of a robotically enhanced colonoscope, challenges with actuation via a long transmission section of the colonoscope, and the resulting design and construction of a prototype sufficient for bench-top evaluation.
Colonoscopy is a procedure where a colonoscope (endoscope specifically sized for the colon) is introduced via the rectum and navigated by a surgeon to view and sample patient tissue to test for abnormal or cancerous growths. A standard colonoscope has a light source, a camera, air ports that insufflate, or pump air into, the colon, and tool channels. These tools channels are used to introduce a variety of components into the working area of the colonoscope which is defined by the field of view of the camera. Currently, these tools are extremely flexible with only 2 degrees of freedom (insertion and grasping). The flexibility of these tools increases the difficulty of complex tissue removal. Surgeons have to manipulate the entire colonoscope in order to change the direction and reach of these tools. Moving the scope in this way increases the risk to
the patient for tissue damage or even perforation. The goal of the continuum robot tool manipulators is to increase the dexterity of the currently available tools and allow for complex tool manipulation without moving the colonoscope. The design requires incorporation of current tools and minimal changes in colonoscope functionality.
Due to the size constraints and the need for an open lumen with which to pass currently available tools, concentric tube robots are the most logical choice for the tool manipulator. As previously described, these robots consist of flexible pre-curved
tubes that are routed concentrically. The most suitable material is super-elastic
Nitinol due to it’s high elastic stress-strain range and the ability to set pre-curved shapes with relative ease.
6.1
Design Specifications
A literature review of the relevant anatomy and surgical techniques provided insight into the workspace and force requirements needed for the physical guidelines
and constraints of the colon. Specifically, we have established (1) a volumetric
representation of the desired workspace that our instrument manipulator design must exhibit, (2) a stiffness requirement specifying the maximum allowable deflection that the instruments can exhibit under typical forces during submucosal dissection, (3) size constraints on the instrument manipulators such that they can be deployed through tool-port channels in currently available endoscopes, and (4) an accuracy requirement for effective surgical teleoperation.
Workspace Volume: The colon is approximately 130-150 centimeters long and
5 centimeters wide on average (188; 189). Since the desired operation is with a
stationary colonoscope tip, the desired workspace for the tool manipulators needs to cover the largest local stage lesions encountered. We estimate that this workspace is 4-6 centimeters in diameter and 8-10 centimeters in length. This cylindrical volume will be the desired workspace specification for our endoscopic robot.
Forces and Stiffness: The force application required during endoscopic submu- cosal dissection consists of applying traction to displace the mucosal and submucosal layers away from the musculature in order to dissect the tissue. This pull force has
been measured on average to be 2.5 Newtons with a maximum of 5 Newtons (177).
The force required for perforation of the colon wall has also been measured and has a great degree of variability based on the location and tissue condition. In a study with porcine bowel segments, the perforation force averaged 13.5 Newtons with a range of
7-19 Newtons (190). Considering these force magnitudes and the small scale of the
procedure, we can specify a desired tool displacement of less than 1 millimeter per 5 Newtons of force. Therefore, the output stiffness requirement for our robot will be 5 N/mm.
Tube Sizes: A standard colonoscope measures 1700 mm in length, 11-15 mm in
diameter and has 1-2 working channels for tools. These tool ports measure between
2.8 and 4.2 mm with most measuring around 3.8 mm (191). This measurement will
dictate the sizes of our concentric tubes.
Accuracy: We can specify the required positional accuracy of the robot based
on the suggested negative margins (amount of normal tissue removed along with cancerous tissue) of 2-5 mm to decrease the recurrence of cancerous lesions (192). Based on this margin requirement, a reasonable accuracy goal for our robot’s end- effector position is less than 1 mm.