The Kinematics of Constant Curvature Continuum Robots Through Three Segments
Yucheng Li, David H. Myszka, Andrew P. Murray
Abstract
This letter investigates the mathematical relationships between the positions and orientations at the segment tips of a piecewise constant curvature (PCC) continuum robot with up to three segments. For one-segment, a reachability criterion is proposed, simplifying the calculation of the neighboring orientation. For two-segments, a reachability criterion is proposed and the redundancy of its inverse kinematics solution is found, establishing a circle of tip locations. For three-segments, the redundancy of the inverse kinematics includes tips that lie on a sphere providing a closed-form solution to the inverse kinematics problem. These relationships are derived from the unique characteristics of the bisecting plane of a single segment. The degenerate cases for the solutions are also addressed. These outcomes stem from a specific PCC parametrization, with implications extending to the general PCC model. Note that this study is grounded solely in simulation.