Forward Kinematics and Control of a Segmented Tunable-Stiffness 3-D Continuum Manipulator

In this work, we consider the problem of controlling the end effector position of a continuum manipulator through local stiffness changes. Continuum manipulators offer the advantage of continuous deformation along their lengths, and recent advances in smart material actuators further enable local compliance changes, which can affect the manipulator's bulk motion. However, leveraging local stiffness change to control motion remains lightly explored. We build a kinematic model of a continuum manipulator as a sequence of segments consisting of symmetrically arranged springs around the perimeter of every segment, and we show that this system has a closed form solution to its forward kinematics. The model includes common constraints such as restriction of torsional or shearing movement. Based on this model, we propose a controller on the spring stiffnesses for a single segment and provide provable guarantees on convergence to a desired goal position. The results are verified in simulation and compared to physical hardware.