Optimizing curvature sensor placement for fast, accurate shape sensing of continuum robots

Robot control requires the rapid computation of robot shape, which for continuum robots typically involves solving complex mechanics-based models. Furthermore, shape computation based on kinematic input variables can be inaccurate due to parameter errors and model simplification. An alternate approach is to compute the shape in real-time from a set of sensors positioned along the length of the robot that provide measurements of local curvature, e.g., optical fiber Bragg gratings. This paper proposes a general framework for selecting the number and placement of such sensors with respect to arclength so as to compute the forward kinematic solution accurately and quickly. The approach is based on defining numerically-efficient shape reconstruction models parameterized by sensor number and location. Optimization techniques are used to find the sensor locations that minimize shape and tip error between a reconstruction model and a mechanics-based model. As a specific example, several reconstruction models are proposed and compared for concentric tube robots. These results indicate that the choice of reconstruction model as well as sensor placement can have a substantial effect on robot shape estimation.