Continuum robotics has rapidly become a rich and diverse area of research, with many designs and applications demonstrated. Despite this diversity in form and purpose, there exists remarkable similarity in the fundamental simplified kinematic models that have been applied to continuum robots. However, this can easily be obscured – especially to a newcomer to the field – by the different applications, coordinate frame choices, and analytical formalisms employed. In this paper we review several modeling approaches in a common frame and notational convention, illustrating that for piecewise constant curvature, they produce identical results. This discussion elucidates what has been articulated in different ways by a number of researchers in the past several years, namely that that constant curvature kinematics can be considered as consisting of two separate submappings – one that is general and applies to all continuum robots, and another that is robot-specific. These mappings...
Robert J. Webster III, Bryan A. Jones