arXiv subjects

Abhilash Nayak

Publications and source records attributed to Abhilash Nayak.

5 recordsLinked to original sources

arXiv2026

A Simple Gripper Interface for Simulator-Agnostic Cloth Manipulation

This paper presents a grasping model for cloth manipulation specifically tailored to ease the deployment of robotic control methods. The model is robust, fast and easy to implement avoiding at the same time contact and friction considerations between the gripper and the cloth in favor of simple positional constraints. The gripper is described by its pose, jaw state, and an attached grasping volume. Two kinds of grasping volumes are considered: an axis-aligned box to simulate a pinch grasping and a square pyramidal volume to simulate point grasping. When the gripper closes, the discrete cloth positions lying inside this volume are selected, stored in the local gripper frame, and then transported with the gripper motion. A simple squeezing step is also included to progressively move the selected cloth positions toward the center of the grasping region, avoiding an instantaneous displacement at closure. The model can be used in any simulator as it only requires access to discrete cloth positions and a mechanism for imposing target positions as constraints. We implement our grasping model in conjunction with a constraint-based inextensible cloth simulator, where grasping is implemented as moving positional equality constraints coupled with stretch, shear, collision, and table contact projection steps. The same gripper trajectory is applied on a robot arm to fold a real piece of cloth, serving as a simple bridge between simulation and physical cloth manipulation and showcasing the realism and practicality of our idealized grasping model.

cs.RO↗

arXiv2026

C-space Analysis using Tropical Geometry

Configuration space~(C-space) of a mechanism is a real variety describing the set of feasible configurations that it can attain. To understand the behavior of a mechanism, it is crucial to identify and scrutinize especially the singular points of its C-space. They usually appear when the variety intersects itself, leading to different branches of motion. There exist many approaches to detect those intersections if they are transversal. However, the problem remains challenging if there are tangential, cuspidal, inter-dimensional or a combination of these intersections. This paper exploits an approach acquired from tropical geometry to analyze the neighborhood of any point on C-spaces of 1-degree-of-freedom~(\emph{dof}) mechanisms. This is done by finding the approximate rational parametrization of the curve(s) passing through the given point using Puiseux series. The proposed approach is shown to succesfully detect the transversal branchings in two foldable four bar mechanisms and a cusp in the configuration curve of the double Watt mechanism.

cs.RO↗

arXiv2026

Singularity Analysis for the Perspective-Four and Five-Line Problems

This paper deals with image-based visual servoing and pose estimation by observing four and five lines. Our main interest is to determine the relative configurations of the camera and the observed lines that lead to problems in control and stability. Since it is equivalent to finding the singularities of the corresponding Jacobian matrix, we use tools from computational algebraic geometry to seek configurations such that all of its minors vanish simultaneously. By choosing a suitable basis for this matrix, we revisit the problem in the case of three lines to show that one type of the singularities is when the camera lies on the hyperboloid of one sheet uniquely defined by the lines. This result is further exploited to prove that the one-dimensional singularities, if any, in the case of $n$ lines appear when the camera lies on the transversals to the observed lines. Thus, by forcing the transversals to be complex, we can avoid the aforementioned type of singularities in the case of four lines although the algebra shows that there can always be up to 10 inevitable singular locations of the camera for the other type of singularity. For five lines, we find out that there are no singularities in the generic case. The singularities are also characterized for four and five lines with orthogonality and parallelism constraints. Furthermore, a visual servoing library is used to conduct some simulated experiments to substantiate the theoretical results. As expected, we observe problems in control in the vicinity of a singularity as well as increased errors in pose estimation.

cs.RO↗

arXiv2026

Inverse kinematic solution for generic 3R positional robots using Conformal Geometric Algebra

The inverse kinematics of generic 3R robots has been investigated through multiple approaches, mainly algebraic methods involving the solution of certain equation sets. Previous geometric interpretations of the solution, characterized as the intersection of a pair of conics have been confined to the joint-space domain. In this article, we study the Inverse Kinematic Model (IKM) of 3R robots, using the advantages of Conformal Geometric Algebra (CGA) to provide further insights on its kinematic properties. Our approach directly yields a univariate polynomial in terms of theta_2 without the need to eliminate theta_1 and theta_3 by reframing the problem as the intersection of two circles, which are fundamental elements within this algebraic framework.

cs.RO↗

arXiv2026

Geometric analysis of generic 3R robots, and necessary and sufficient conditions for a class of orthogonal robots to have four IKS

The kinematic analysis of a generic 3R robot has been investigated with multiple approaches in the past. The algebraic approaches have established concrete results but are unfortunately limited to special classes or architectural simplifications. Geometric approaches on the other hand have extended the analysis to generic robots while also providing an intuitive understanding of their kinematic properties. We use the best of both approaches to present the kinematic analysis of a generic 3R robot, using the inverse kinematic model inherited from a method based on conformal geometric algebra. The paper discusses a generic framework to study the conditions for a 3R robot to have four inverse kinematic solutions (IKS) and allows to study the distribution of IKS as seen in workspace. The necessary and sufficient conditions for a class of orthogonal robots are presented using the proposed approach.

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