Related papers: A Method for Calculating Collision Probability Bet…
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…
Real-time safety systems are crucial components of intelligent vehicles. This paper introduces a prediction-based collision risk assessment approach on highways. Given a point mass vehicle dynamics system, a stochastic forward reachable set…
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…
Intelligent devices for supporting persons with vision impairment are becoming more widespread, but they are lacking behind the advancements in intelligent driver assistant system. To make a first step forward, this work discusses the…
The amount of debris in orbit has increased significantly over the years. With the recent growth of interest in space exploration, conjunction assessment has become a central issue. One important metric to evaluate conjunction risk is the…
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…
As mobile robots and autonomous vehicles become increasingly prevalent in human-centred environments, there is a need to control the risk of collision. Perceptual modules, for example machine vision, provide uncertain estimates of object…
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…
Summary: In the past decade both scientists and laymen have probably heard at least once through the newspapers, TV and Internet that a new asteroid has been discovered with non-zero (sometimes "high") probability of collision with the…
One often-used approximation in the study of binary compact objects (i.e., black holes and neutron stars) in general relativity is the instantaneously circular orbit assumption. This approximation has been used extensively, from the…
Direct collisions between finite-sized particles occur commonly in many areas of astrophysics. Such collisions are typically mediated by chaotic, bound gravitational interactions involving small numbers of particles. An important…
Collision detection plays an important role in simulation, control, and learning for robotic systems. However, no existing method is differentiable with respect to the configurations of the objects, greatly limiting the sort of algorithms…
Consider two balls with radius $r>0$ whose centers are at a distance $2$, positioned symmetrically with respect to the origin in ${\mathbb{R}}^d$. Suppose that the initial velocities are independent standard normal vectors. When $r\to0$,…
The dynamical interaction of minor bodies (such as comets or asteroids) with planets plays an essential role in the planetary system's architecture and evolution. As a result of these interactions, structures like the Kuiper belt and the…
The probability of detecting a planetary companion of a lensing star during a microlensing event toward the Galactic center, averaged over all relevant event and galactic parameters, when the planet-star mass ratio $q=0.001$ has a maximum…
We present a method for guaranteed collision detection with toleranced motions. The basic idea is to consider the motion as a curve in the 12-dimensional space of affine displacements, endowed with an object-oriented Euclidean metric, and…
Motivated by a heat radiative transport equation, we consider a particle undergoing collisions in a space-time domain and propose a method to sample its escape time, space and direction from the domain. The first step of the procedure is an…
Our knowledge about the "cold" Universe often relies on molecular spectra. A general property of such spectra is that the energy level populations are rarely at local thermodynamic equilibrium. Solving the radiative transfer thus requires…
We give a lower bound for the non-collision probability up to a long time T in a system of n independent random walks with fixed obstacles on the two-dimensional lattice. By `collision' we mean collision between the random walks as well as…
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…