On the Kinematic Model of Continuum Robots with Spatially Varying Nonlinear Stiffness

In this paper, we propose a laser-patterned monolithic tube with varying structural properties along the length as a core for building compact, customizable continuum devices with an inner working channel. The backbone of these robots can achieve the commonly desired distally increasing curvature through two means: varying pattern shape and varying pattern distribution. To characterize this nonlinear variation of structural properties like bending rigidity along the length and with change in strain, we use the Cosserat rod theory to estimate bending stiffness from the (computer vision based) measured shape of the robot under various simple known loading conditions. The dependence of bending stiffness on arc-length and strain is conveniently depicted as a 3D surface plot.