Related papers: A note on synthesizing geodesic based contact curv…
Reasoning about rolling and sliding contact, or roll-slide contact for short, is critical for dexterous manipulation tasks that involve intricate geometries. But existing works on roll-slide contact mostly focus on continuous shapes with…
A complete treatment of the intersections of two geodesics on the surface of an ellipsoid of revolution is given. With a suitable metric for the distances between intersections, bounds are placed on their spacing. This leads to fast and…
Moving our hands smoothly is essential to execute ordinary tasks, such as carrying a glass of water without spilling. Past studies have revealed a natural tendency to generate smooth trajectories when moving the hand from one point to…
We give a complete answer to the question of when two curves in two different Riemannian manifolds can be seen as trajectories of rolling one manifold on the other without twisting or slipping. We show that up to technical hypotheses, a…
The goal of this study is to provide a method for computing the following: Given a network of curves in 3d (satisfying a condition at the intersection points), compute efficiently a smooth surface such that the curves are geodesics on it.…
A large number of powerful, high-quality, and open-source simulation packages exist to efficiently perform molecular dynamics simulations, and their prevalence has greatly accelerated discoveries across a wide range of scientific domains.…
The theory of geodesic regression aims to find a geodesic curve which is an optimal fit to a given set of data. In this article we restrict ourselves to the Riemannian manifold of positive definite operators (matrices) on a Hilbert space of…
Contact-based motion planning for manipulation, object exploration or balancing often requires finding sequences of fixed and sliding contacts and planning the transition from one contact in the environment to another. However, most…
The problem of a disc and a ball rolling on a horizontal plane without slipping is considered. Differential constrained equations are shown to be integrated when the trajectory of the point of contact is taken in a form of the natural…
We give an accessible introduction and elaboration on the methods used in obtaining a geodesic, which is the curve of shortest length connecting two points lying on the surface of a function. This is found through computing what's known as…
This paper explores an eclectic range of path-planning methodologies engineered for rolling surfaces. Our focus is on the kinematic intricacies of rolling contact systems, which are investigated through a motion planning lens. Beyond…
This letter studies a distributed collision avoidance control problem for a group of rigid bodies on a sphere. A rigid body network, consisting of multiple rigid bodies constrained to a spherical surface and an interconnection topology, is…
The consideration of the so-called rotation minimizing frames allows for a simple and elegant characterization of plane and spherical curves in Euclidean space via a linear equation relating the coefficients that dictate the frame motion.…
3D grasp synthesis generates grasping poses given an input object. Existing works tackle the problem by learning a direct mapping from objects to the distributions of grasping poses. However, because the physical contact is sensitive to…
Barrier potentials gained popularity as a means for robust contact handling in physical modeling and for modeling self-avoiding shapes. The key to the success of these approaches is adherence to geometric constraints, i.e., avoiding…
We define "robotic contact juggling" to be the purposeful control of the motion of a three-dimensional smooth object as it rolls freely on a motion-controlled robot manipulator, or "hand." While specific examples of robotic contact juggling…
The geodesic total curvature of rectifiable spherical curves is analyzed. We extend to the case of high dimension spheres the explicit formula that holds true for curves supported into the 2-sphere. For this purpose, we take advantage of…
Modeling contact between deformable solids is a fundamental problem in computer animation, mechanical design, and robotics. Existing methods based on $C^0$-discretizations -- piece-wise linear or polynomial surfaces -- suffer from…
In this paper, we investigate the ruled surfaces generated by a straight line according to rotation minimizing frame (RMF). Using this frame of a straight line, we obtained the necessary and sufficient conditions when the ruled surface is…
This paper presents the first kinematic modeling of tendon-driven rolling-contact joint mechanisms with general contact surfaces subject to external loads. We derived the kinematics as a set of recursive equations and developed efficient…