Linear Kinematics for General Constant Curvature and Torsion Manipulators

We present a novel general model that unifies the kinematics of constant curvature and constant twist continuum manipulators. Combining this kinematics with energy-based physics, we derive a linear mapping from actuator configuration to manipulator deformation that is analogous to traditional robot forward kinematics. Our model generalizes across manipulators with different sizes, types of bending, and types of actuators, without the need for parameter re-fitting. The combination of generality and linearity makes the model useful for control and planning algorithms. Finally, our model is shown to be accurate through experimental validation on manipulators with pneumatic artificial muscles.