Distortion-free Robotic Surface-drawing using Conformal Mapping

Abstract

We present a robotic pen-drawing system that is capable of faithfully reproducing pen art on an unknown surface. Our robotic system relies on an industrial, seven-degree-of freedom manipulator that can be both position- and impedance-controlled. In order to estimate a rough geometry of the target, continuous surface, we first generate a point cloud of the surface using an RGB-D camera, which is filtered to remove outliers and calibrated to the physical canvas surface. Then, our control algorithm physically reproduces digital drawing on the surface by impedance-controlling the manipulator. Our impedance-controlled drawing algorithm compensates for the uncertainty and incompleteness inherent to a point-cloud estimation of the drawing surface. Moreover, since drawing 2D vector pen art on a 3D surface requires surface parameterization that does not destroy the original 2D drawing, we rely on the least squares conformal mapping. Specifically, the conformal map reduces angle distortion during surface parameterization. As a result, our system can create distortion-free and complicated pen drawings on general surfaces with many unpredictable bumps robustly and faithfully.