Planar Conformal Deformation of Robotic S-Isothermic Surface

Robotic surfaces can design the space they cover by deforming and can be used in laparoscopic surgery to secure a surgical field space. In medical applications, a coordinate transformation is crucial to cooperate with other robots. However, allowing shear in the robot surfaces' deformations makes accurate coordinate transformations difficult. Robotic S-isothermic surfaces, given their mathematics, are only slightly deform in shear. In a system that combines this robot with rigid-body robots, each coordinate system can be entirely unified in the orthogonal coordinate system, simplifying the control. However, it has not been thoroughly investigated whether the deformed robot's local coordinate system is Cartesian or not. In this study, we use a rubber-like resin robotic S-isothermic surface and demonstrate that its deformation in a plane is conformal. We also show that when the deformation to the desired shape is small, there are conformal parameters close to the shape even during the deformation.