On the inseparable nature of sensor selection, sensor placement, and state estimation for continuum robots or “where to put your sensors and how to use them”

When designing continuum robots for applications that require sensing, designers are faced with the problems of deciding what sensors to use, where they should be placed, and how best to use the information they provide. In this paper, we describe how a differential representation of a continuum robot's kinematic equations that govern its states (e.g., shape) can be used to simultaneously address these problems under the guidance of statistical state estimation. We identify how state estimation and sensing-system design (i.e., sensor selection and placement) are inherently coupled problems, which leads us to formulate sensing-system design as an optimization problem governed by the results of statistical estimation. As a case-study, the methods described herein are used to design a magnetic sensing system for concentric-tube robots.