  Continuum robots are typically slender and flexible with infinite freedoms in
theory, which poses a challenge for their control and application. The shape
sensing of continuum robots is vital to realise accuracy control. This letter
proposed a novel general real-time shape sensing framework of continuum robots
based on the piecewise polynomial curvature (PPC) kinematics model. We
illustrate the coupling between orientation and position at any given location
of the continuum robots. Further, the coupling relation could be bridged by the
PPC kinematics. Therefore, we propose to estimate the shape of continuum robots
through orientation estimation, using the off-the-shelf orientation sensors,
e.g., IMUs, mounted on certain locations. The approach gives a valuable
framework to the shape sensing of continuum robots, universality, accuracy and
convenience. The accuracy of the general approach is verified in the
experiments of multi-type physical prototypes.
