Piecewise constant curvature is a popular kinematics framework for continuum
robots. Computing the model parameters from the desired end pose, known as the
inverse kinematics problem, is fundamental in manipulation, tracking and
planning tasks. In this paper, we propose an efficient multi-solution solver to
address the inverse kinematics problem of 3-section constant-curvature robots
by bridging both the theoretical reduction and numerical correction. We derive
analytical conditions to simplify the original problem into a one-dimensional
problem. Further, the equivalence of the two problems is formalised. In
addition, we introduce an approximation with bounded error so that the one
dimension becomes traversable while the remaining parameters analytically
solvable. With the theoretical results, the global search and numerical
correction are employed to implement the solver. The experiments validate the
better efficiency and higher success rate of our solver than the numerical
methods when one solution is required, and demonstrate the ability of obtaining
multiple solutions with optimal path planning in a space with obstacles.Comment: Robotics: Science and Systems 202