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.

Motion planning for robots subject to holonomic constraints typically involves planning on constraint manifolds. In this paper we present the Tangent Space Rapidly Exploring Random Tree (TS-RRT) algorithm for planning on constraint manifolds. The key idea is to construct random trees not on the constraint manifold itself, but rather on tangent space approximations to the constraint manifold. Curvature-based methods are developed for constructing bounded tangent space approximations, as well as procedures for random node generation and bidirectional tree extension. Extensive numerical experiments suggest that the TS-RRT algorithm, despite its increased preprocessing and bookkeeping, outperforms existing constrained planning algorithms for a wide range of benchmark planning problems.

We propose a framework for online generation of efficient gaits on uneven terrain. A set of dynamically optimal leg swing motion primitives for irregular terrains is first constructed offline-this is done by generating minimum torque motions for various starting and ending ground configurations, extracting dominant principal components, and forming basis functions. Gaits are then generated online via linear interpolation of the principal component basis functions, using a distance metric on SO(3) to select the components. The algorithm is verified via dynamic simulations involving the STriDER, a three legged passive-walking robot. Our results show that gaits using only knee-actuated leg swings are able to traverse uneven terrain of bounded variation.