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.
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