Magnet-tipped, elastic rods can be steered by an external magnetic field to perform surgical tasks. Such rods could be useful for a range of new medical applications because they do not require either pull wires or other bulky mechanisms that are problematic in small anatomical regions. However, current magnetic rod steering systems are large and expensive. Here, we describe a method to guide a rod using a robot-manipulated magnet located near a patient. We solve for rod deflections by combining permanent-magnet models with a Kirchhoff elastic rod model and use a resolved-rate approach to compute trajectories. Experiments show that three-dimensional trajectories can be executed accurately without feedback and that the system's redundancy can be exploited to avoid obstacles.

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.