Related papers: Minimum Orbital Intersection Distance: Asymptotic …
The distance of closest approach of hard particles is a key parameter of their interaction and plays an important role in the resulting phase behavior. For non-spherical particles, the distance of closest approach depends on orientation,…
It has recently been shown by Egal et al. (2017) that some types of existing meteor in-atmosphere trajectory estimation methods may be less accurate than others, particularly when applied to high precision optical measurements. The…
In the domain of Space Situational Awareness (SSA), the challenges pertaining to orbit determination and catalog correlation are notably pronounced, partly attributable to the escalating presence of non-cooperative satellites engaging in…
Optimization-based methods are commonly applied in autonomous driving trajectory planners, which transform the continuous-time trajectory planning problem into a finite nonlinear program with constraints imposed at finite collocation…
This work introduces two Monte Carlo (MC)-based sampling methods, known as line sampling and subset simulation, to improve the performance of standard MC analyses in the context of asteroid impact risk assessment. Both techniques sample the…
The shortest distance between the first $n$ iterates of a typical point can be quantified with a log rule for some dynamical systems admitting Gibbs measures. We show this in two settings. For topologically mixing Markov shifts with at most…
Probabilistic collision detection (PCD) is essential in motion planning for robots operating in unstructured environments, where considering sensing uncertainty helps prevent damage. Existing PCD methods mainly used simplified geometric…
In automated driving, crash mitigation is crucial to ensure passenger safety. Accurate avoidance requires precise knowledge of the object's position and orientation. However, sensor noise and occlusions often result in tracking and…
Various packing problems and simulations of hard and soft interacting particles, such as microscopic models of nematic liquid crystals, reduce to calculations of intersections and pair interactions between ellipsoids. When constrained to a…
We give a short introduction to Pade approximation (rational approximation to a function with close contact at one point) and to Hermite-Pade approximation (simultaneous rational approximation to several functions with close contact at one…
In modern production facilities industrial robots and humans are supposed to interact sharing a common working area. In order to avoid collisions, the distances between objects need to be measured conservatively which can be done by a…
The quantitative characterization of amplitudes and periods of perturbations in orbital elements can help to our understanding the minor bodies dynamics, especially in case motion in vicinity of resonances. The main goal of this study is to…
For two multisets $S$ and $T$ of points in $[\Delta]^2$, such that $|S| = |T|= n$, the earth-mover distance (EMD) between $S$ and $T$ is the minimum cost of a perfect bipartite matching with edges between points in $S$ and $T$, i.e.,…
When an asteroid has a few observations over a short time span the information contained in the observational arc could be so little that a full orbit determination may be not possible. One of the methods developed in recent years to…
An analytical formulation for collision avoidance maneuvers involving a spacecraft and a space debris is presented, including solutions for the maximum deviation and minimum collision probability cases. Gauss' planetary equations and…
We present a practical approach to solving distance-based optimization problems using optical computing hardware. The objective is to minimize an energy function defined as the weighted sum of squared differences between measured distances…
In order to avoid collisions with space debris, the near Earth orbit must be continuously scanned by either ground- or spaced-based facilities. For the low Earth orbit, radar telescopes are the workhorse for this task, especially due to…
The apparent close encounters of two satellites in the plane of the sky, called mutual approximations, have been suggested as a different type of astrometric observation to refine the moons' ephemerides. The main observables are the central…
This paper explores the problem of analytically approximating the orbital state for a subset of orbits in a rotating potential with oblateness and ellipticity perturbations. This is done by isolating approximate differential equations for…
This paper shows how to find lower bounds on, and sometimes solve globally, a large class of nonlinear optimal control problems with impulsive controls using semi-definite programming (SDP). This is done by relaxing an optimal control…