Related papers: Computing the Instantaneous Collision Probability …

This research introduces two efficient methods to estimate the collision risk of planned trajectories in autonomous driving under uncertain driving conditions. Deterministic collision checks of planned trajectories are often inaccurate or…

State estimation for hybrid systems that undergo intermittent contact with their environments, such as extraplanetary robots and satellites undergoing docking operations, is difficult due to the discrete uncertainty propagation during…

This paper presents a robust linear method for impact probability estimation of near-Earth asteroids with the Earth. This method is a significantly modified and improved method, which uses a special curvilinear coordinate system associated…

We introduce a fast, high-precision algorithm for calculating intersections between great circle arcs and lines of constant latitude on the unit sphere. We first propose a simplified intersection point formula with improved speed and…

In surface diffusion, one of the key observables is the so-called intermediate scattering function which is measured directly from the surface technique called Helium spin echo. In this work, we show that this function can be seen as a…

Probability of coincidental clustering among the orbits of comets, asteroids and meteoroids depends on many factors like: the size of the orbital sample searched for clusters or the size of the identified group, it is different for groups…

We developed a modification to the calculation of the two-point correlation function commonly used in the analysis of large scale structure in cosmology. An estimator of the two-point correlation function is constructed by contrasting the…

An orbiting `photon clock' is proposed to test directly the relativity of simultaneity of special relativity. This is done by comparison of the arrival times at a ground station of three microwave signals transmitted by two satellites…

In this work, we study probability functions associated with Gaussian mixture models. Our primary focus is on extending the use of spherical radial decomposition for multivariate Gaussian random vectors to the context of Gaussian mixture…

First passage distributions of semi-Markov processes are of interest in fields such as reliability, survival analysis, and many others. The problem of finding or computing first passage distributions is, in general, quite challenging. We…

The motion of satellite constellations similar to GPS and Galileo is numerically simulated and, then, the region where bifurcation (double positioning) occurs is appropriately represented. In the cases of double positioning, the true…

In this paper, we formulate a novel trajectory optimization scheme that takes into consideration the state uncertainty of the robot and obstacle into its collision avoidance routine. The collision avoidance under uncertainty is modeled here…

Conjunction analysis and maneuver planning for spacecraft collision avoidance remains a manual and time-consuming process, typically involving repeated forward simulations of hand-designed maneuvers. With the growing density of satellites…

Typically we can deliver astrometric positions of natural satellites with errors in the 50-150 mas range. Apparent distances from mutual phenomena, have much smaller errors, less than 10 mas. However, this method can only be applied during…

When the problem of boson sampling was first proposed, it was assumed that little or no photon collisions occur. However, modern experimental realizations rely on setups where collisions are quite common, i.e. the number of photons $M$…

This paper introduces a novel motion planning algorithm for stochastic scenarios. We extend the concept of a navigation function to such scenarios. Our main idea is to consider both the Gaussian distribution probabilities of the players'…

Spacecraft collision avoidance procedures have become an essential part of satellite operations. Complex and constantly updated estimates of the collision risk between orbiting objects inform the various operators who can then plan risk…

We consider the safety evaluation of discrete time, stochastic systems over a finite horizon. Therefore, we discuss and link probabilistic invariance with reachability as well as reach-avoid problems. We show how to efficiently compute…

This work presents a sequential convex program method to compute fuel-optimal collision avoidance maneuvers for long-term encounters. The low-thrust acceleration model is used to account for the control, but the method can compute…

Image matching is a fundamental problem in Computer Vision with direct applications in robotics, remote sensing, and geospatial data analysis. We present an analytical and experimental evaluation of classical local feature-based image…