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This paper presents a novel approach for collision avoidance in optimal and model predictive control, in which the environment is represented by a large number of points and the robot as a union of padded polygons. The conditions that none…
For elliptic interface problems with discontinuous coefficients, the maximum accuracy order for compact 9-point finite difference scheme in irregular points is three [7]. The discontinuous coefficients usually have abrupt jumps across the…
Motivated by finding an effective way to compute the algebraic complexity of the nearest point problem for algebraic models, we introduce an efficient method for detecting the limit points of the stratified Morse trajectories in a small…
Many topics in planetary studies demand an estimate of the collision probability of two objects moving on nearly Keplerian orbits. In the classic works of \"Opik (1951) and Wetherill (1967), the collision probability was derived by…
We present a new algorithm, trimed, for obtaining the medoid of a set, that is the element of the set which minimises the mean distance to all other elements. The algorithm is shown to have, under certain assumptions, expected run time…
Most existing distance metric learning methods assume perfect side information that is usually given in pairwise or triplet constraints. Instead, in many real-world applications, the constraints are derived from side information, such as…
We consider the problem of minimizing a convex function over the intersection of finitely many simple sets which are easy to project onto. This is an important problem arising in various domains such as machine learning. The main difficulty…
The modern optical telescopes produce a huge number of asteroid observations, that are grouped into very short arcs (VSAs), each containing a few observations of the same object in one single night. To decide whether two VSAs, collected in…
Given $n$ points in a circular region $C$ in the plane, we study the problems of moving the $n$ points to its boundary to form a regular $n$-gon such that the maximum (min-max) or the sum (min-sum) of the Euclidean distances traveled by the…
The search of high-order periodic orbits has been typically restricted to problems with symmetries that help to reduce the dimension of the search space. Well-known examples include reversible maps with symmetry lines. The present work…
This paper presents an analysis of optimal impact strategies to deflect potentially dangerous asteroids. To compute the increase in the minimum orbit intersection distance of the asteroid due to an impact with a spacecraft, simple…
We introduce a new method to perform preliminary orbit determination for space debris on low Earth orbits (LEO). This method works with tracks of radar observations: each track is composed by $n\ge 4$ topocentric position vectors per pass…
This paper presents a novel method for reformulating non-differentiable collision avoidance constraints into smooth nonlinear constraints using strong duality of convex optimization. We focus on a controlled object whose goal is to avoid…
Let $f \colon \mathcal{M} \to \mathbb{R}$ be a Lipschitz and geodesically convex function defined on a $d$-dimensional Riemannian manifold $\mathcal{M}$. Does there exist a first-order deterministic algorithm which (a) uses at most…
We compute the closest convex piecewise linear-quadratic (PLQ) function with minimal number of pieces to a given univariate piecewise linear-quadratic function. The Euclidean norm is used to measure the distance between functions. First, we…
In this paper, we discuss an efficient algorithm for computing the growth distance between two compact convex sets with representable support functions. The growth distance between two sets is the minimum scaling factor such that the sets…
This paper describes novel and fast, simple and robust algorithm with O(N) expected complexity which enables to decrease run-time needed to find an exact maximum distance of two points in E2. The proposed algorithm has been evaluated…
The collision avoidance constraints are prominent as non-convex, non-differentiable, and challenging when defined in optimization-based motion planning problems. To overcome these issues, this paper presents a novel non-conservative…
Problems that require the parameterization of closed contours arise frequently in computer vision applications. This article introduces a new curve parameterization algorithm that is able to fit a closed curve to a set of points while being…
The minimum regularized covariance determinant method (MRCD) is a robust estimator for multivariate location and scatter, which detects outliers by fitting a robust covariance matrix to the data. Its regularization ensures that the…