Continuum Robot Shape Estimation Using Magnetic Ball Chains

TL;DR

The use of magnetic ball chains are proposed as a means of generating shape-specific magnetic fields that can be detected by an external array of Hall effect sensors that could be inserted inside the lumen of any continuum robot to provide real-time shape feedback.

Abstract

Shape sensing of medical continuum robots is important both for closed-loop control as well as for enabling the clinician to visualize the robot inside the body. There is a need for inexpensive, but accurate shape sensing technologies. This paper proposes the use of magnetic ball chains as a means of generating shape-specific magnetic fields that can be detected by an external array of Hall effect sensors. Such a ball chain, encased in a flexible polymer sleeve, could be inserted inside the lumen of any continuum robot to provide real-time shape feedback. The sleeve could be removed, as needed, during the procedure to enable use of the entire lumen. To investigate this approach, a shape-sensing model for a steerable catheter tip is derived and an observability and sensitivity analysis are presented. Experiments show maximum estimation errors of 7.1% and mean of 2.9% of the tip position with respect to total length.

Figures (7)

• Figure 1: Magnetic ball chain shape sensing. (a) The sensor is comprised of a chain of spherical permanent magnets encased in a flexible sleeve which is inserted in a robot's lumen. (b) An external array of Hall effect sensors measures the combined magnetic field of all balls from which the shape of the robot is computed.
• Figure 2: Schematic representation of magnetic ball chain with plane ($\phi$) and angle of bending ($\psi$) parameters. Two possible sensor array locations (I and II) are shown.
• Figure 3: Contour plots of shape observability as measured by reciprocal condition number, $\chi$, for the two sensor array configurations shown in Fig. \ref{['fig:schematic']}. Here, $\chi$ is expressed as a percentage.
• Figure 4: Maximum tip position error (percentage of robot length) as a function of bending angle, $\psi$, for three noise levels in Configuration I (See Fig. \ref{['fig:schematic']}).
• Figure 5: Maximum tip position error (percentage of robot length) as a function of bending angle, $\psi$, for 3 noise levels in Configuration II (See Fig. \ref{['fig:schematic']}).