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RCM-Constrained Manipulator Trajectory Tracking Using Differential Kinematics Control

Omar Rayyan, Vinicius Gonçalves, Nikolaos Evangeliou, Anthony Tzes

TL;DR

An approach for controlling surgical robotic systems, while complying with the Remote Center of Motion (RCM) constraint in Robot-Assisted Minimally Invasive Surgery (RA-MIS), and introduces a manipulability index of the robot which considers the RCM-error that it is used to find a starting configuration.

Abstract

This paper proposes an approach for controlling surgical robotic systems, while complying with the Remote Center of Motion (RCM) constraint in Robot-Assisted Minimally Invasive Surgery (RA-MIS). In this approach, the RCM-constraint is upheld algorithmically, providing flexibility in the positioning of the insertion point and enabling compatibility with a wide range of general-purpose robots. The paper further investigates the impact of the tool's insertion ratio on the RCM-error, and introduces a manipulability index of the robot which considers the RCM-error that it is used to find a starting configuration. To accurately evaluate the proposed method's trajectory tracking within an RCM-constrained environment, an electromagnetic tracking system is employed. The results demonstrate the effectiveness of the proposed method in addressing the RCM constraint problem in RA-MIS.

RCM-Constrained Manipulator Trajectory Tracking Using Differential Kinematics Control

TL;DR

An approach for controlling surgical robotic systems, while complying with the Remote Center of Motion (RCM) constraint in Robot-Assisted Minimally Invasive Surgery (RA-MIS), and introduces a manipulability index of the robot which considers the RCM-error that it is used to find a starting configuration.

Abstract

This paper proposes an approach for controlling surgical robotic systems, while complying with the Remote Center of Motion (RCM) constraint in Robot-Assisted Minimally Invasive Surgery (RA-MIS). In this approach, the RCM-constraint is upheld algorithmically, providing flexibility in the positioning of the insertion point and enabling compatibility with a wide range of general-purpose robots. The paper further investigates the impact of the tool's insertion ratio on the RCM-error, and introduces a manipulability index of the robot which considers the RCM-error that it is used to find a starting configuration. To accurately evaluate the proposed method's trajectory tracking within an RCM-constrained environment, an electromagnetic tracking system is employed. The results demonstrate the effectiveness of the proposed method in addressing the RCM constraint problem in RA-MIS.
Paper Structure (12 sections, 12 equations, 7 figures)

This paper contains 12 sections, 12 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Methodology
  3. Mathematical Notation
  4. Forward and Differential Kinematics for the RCM-Constraint
  5. Controller Design
  6. Comparison with Other Approaches
  7. The Effect of the Tool Insertion
  8. Selecting the Starting Configuration
  9. Experimental Studies
  10. Experimental Setup
  11. Results and Accuracy Evaluation
  12. Conclusions

Figures (7)

  • Figure 1: Illustration of the RCM-constraint.
  • Figure 2: Geometric illustration of the fact that $\|d\mathbf{p}_E\|/\|d\mathbf{p}_T\| = (L-\lambda)/\lambda = \rho$. If $\|d\mathbf{p}_E\|$ and $\|d\mathbf{p}_T\|$ are small, the two triangles formed are very close to be right triangles, similar to each other, and thus, $\|d\mathbf{p}_E\|/(L-\lambda) = \|d\mathbf{p}_T\|/\lambda$.
  • Figure 3: Initial Configuration of the Manipulator ($\mathbf{p}_{T,0}$) in the setup environment
  • Figure 4: Tool-Tip Position Visualization using the forward-kinematics model and the Aurora device measurement
  • Figure 5: Tool-Tip Position Error evaluated using the forward-kinematics model and the Aurora device measurement
  • ...and 2 more figures