Skeleton-Guided Rolling-Contact Kinematics for Arbitrary Point Clouds via Locally Controllable Parameterized Curve Fitting

Rolling contact kinematics plays a vital role in dexterous manipulation and rolling-based locomotion. Yet, in practical applications, the environments and objects involved are often captured as discrete point clouds, creating substantial difficulties for traditional motion control and planning frameworks that rely on continuous surface representations. In this work, we propose a differential geometry-based framework that models point cloud data for continuous rolling contact using locally parameterized representations. Our approach leverages skeletonization to define a rotational reference structure for rolling interactions and applies a Fourier-based curve fitting technique to extract and represent meaningful controllable local geometric structure. We further introduce a novel 2D manifold coordinate system tailored to arbitrary surface curves, enabling local parameterization of complex shapes. The governing kinematic equations for rolling contact are then derived, and we demonstrate the effectiveness of our method through simulations on various object examples.