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Relative pose estimation is crucial for various computer vision applications, including Robotic and Autonomous Driving. Current methods primarily depend on selecting and matching feature points prone to incorrect matches, leading to poor…
Many works in collaborative robotics and human-robot interaction focuses on identifying and predicting human behaviour while considering the information about the robot itself as given. This can be the case when sensors and the robot are…
Robots coexisting with humans in their environment and performing services for them need the ability to interact with them. One particular requirement for such robots is that they are able to understand spatial relations and can place…
It is argued that, for motion in a central force field, polar reciprocals of trajectories are an elegant alternative to hodographs. The principal advantage of polar reciprocals is that the transformation from a trajectory to its polar…
In this short note, we provide the well-posedness for an hyperbolic-hyperbolic-elliptic system of PDEs describing the motion of collision free-plasma in magnetic fields. The proof combines a pointwise estimate together with a bootstrap type…
We present an approach for detecting and estimating the 3D poses of objects in images that requires only an untextured CAD model and no training phase for new objects. Our approach combines Deep Learning and 3D geometry: It relies on an…
We develop a novel method for finding bifurcations for nonlinear systems of equations based on directly finding bifurcations through saddle points of extended quotients. The method is applied to find the saddle-node bifurcation point for…
We use "generalized" version of total variation, coarea formulas, isoperimetric inequalities to obtain sharp estimates for solutions (and for their gradients) to anisotropic elliptic equations with a lower order term, comparing them with…
Straight lines are common features in human made environments, which makes them a frequently explored feature for control applications. Many control schemes, like Visual Servoing, require the 3D parameters of the features to be estimated.…
Robotic learning in simulation environments provides a faster, more scalable, and safer training methodology than learning directly with physical robots. Also, synthesizing images in a simulation environment for collecting large-scale image…
For general quadratically-constrained quadratic programming (QCQP), we propose a parabolic relaxation described with convex quadratic constraints. An interesting property of the parabolic relaxation is that the original non-convex feasible…
This paper presents a method for pose estimation of off-road vehicles moving over uneven terrain. It determines the contact points between the wheels and the terrain, assuming rigid contacts between an arbitrary number of wheels and ground.…
Relative pose estimation provides a promising way for achieving object-agnostic pose estimation. Despite the success of existing 3D correspondence-based methods, the reliance on explicit feature matching suffers from small overlaps in…
We explore convex shapes $S$ in the Euclidean plane which have the following property: there is a circle $C$ such that the angle between the two tangents from any point of $C$ to $S$ is constant equal to $\alpha$. A dynamical formulation…
Algorithms for the computation of geodesics on an ellipsoid of revolution are given. These provide accurate, robust, and fast solutions to the direct and inverse geodesic problems and they allow differential and integral properties of…
In this work, we present an adaptation of the classical stereographic projection, originally formulated for the sphere, now considering the context of the ellipsoid and the elliptic paraboloid. We begin by constructing the stereographic…
We first review the definition of the angle between subspaces and how it is computed using matrix algebra. Then we introduce the Grassmann and Clifford algebra description of subspaces. The geometric product of two subspaces yields the full…
We address the problem, not of the determination -- which usually needs numerical methods -- but of an accurate analytical estimation of the distance of a raw elasticity tensor to cubic symmetry and to orthotropy. We point out that there…
Ellipse and ellipsoid fitting has been extensively researched and widely applied. Although traditional fitting methods provide accurate estimation of ellipse parameters in the low-noise case, their performance is compromised when the noise…
We investigate several topics of triangle geometry in the elliptic and in the extended hyperbolic plane, such as: centers based on orthogonality, centers related to circumcircles and incircles, radical centers and centers of similitude,…