Related papers: Minimum Orbital Intersection Distance: Asymptotic …
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…
Reachability analysis of hybrid systems has been used as a safety verification tool to assess offline whether the state of a system is capable of remaining within a designated safe region for a given time horizon. Although it has been…
Optimal Transport (OT) based distances are powerful tools for machine learning to compare probability measures and manipulate them using OT maps. In this field, a setting of interest is semi-discrete OT, where the source measure $\mu$ is…
In this paper, we aim to provide a statistical theory for object matching based on the Gromov-Wasserstein distance. To this end, we model general objects as metric measure spaces. Based on this, we propose a simple and efficiently…
Given a finite metric space $(V,d)$, an approximate distance oracle is a data structure which, when queried on two points $u,v \in V$, returns an approximation to the the actual distance between $u$ and $v$ which is within some bounded…
The main problem is to understand and to find periodic symmetric orbits in the $n$-body problem, in the sense of finding methods to prove or compute their existence, and more importantly to describe their qualitative and quantitative…
The method of asymptotic expansions is used to build an approximation scheme relevant to celestial mechanics in relativistic theories of gravitation. A scalar theory is considered, both as a simple example and for its own sake. This theory…
Metrics on the space of sets of trajectories are important for scientists in the field of computer vision, machine learning, robotics, and general artificial intelligence. However, existing notions of closeness between sets of trajectories…
We present the results of our investigation on the use of the two-body integrals to compute preliminary orbits by linking too short arcs of observations of celestial bodies. This work introduces a significant improvement with respect to the…
A novel algorithm is presented for the estimation of collision probabilities between dynamic objects with uncertain trajectories, where the trajectories are given as a sequence of poses with Gaussian distributions. We propose an adaptive…
Modeling the orbital dynamics of objects in galactic disks is crucial to understanding the stability and evolution of disk galaxies. While studies of galactic orbits are largely dominated by $N$-body simulations, perturbative analytical…
We propose an adaptation of the semilinear algorithm for the prediction of the impact corridor on ground of an Earth-impacting asteroid. The proposed algorithm provides an efficient tool, able to reliably predict the impact regions at fixed…
We present a simple choice of integration variables that can be used to exploit the near-integrable character of problems in celestial mechanics. The approach is based on the well-known principle of variation of parameters: instead of…
Autonomous driving systems require a quick and robust perception of the nearby environment to carry out their routines effectively. With the aim to avoid collisions and drive safely, autonomous driving systems rely heavily on object…
In this paper we introduce an optical approximation into the theory of impedance calculation, one valid in the limit of high frequencies. This approximation neglects diffraction effects in the radiation process, and is conceptually…
The article considers minimization of the expectation of convex function. Problems of this type often arise in machine learning and a number of other applications. In practice, stochastic gradient descent (SGD) and similar procedures are…
A framework is introduced for sequentially solving convex stochastic minimization problems, where the objective functions change slowly, in the sense that the distance between successive minimizers is bounded. The minimization problems are…
By quantifying the distance between two collider events, one can triangulate a metric space and reframe collider data analysis as computational geometry. One popular geometric approach is to first represent events as an energy flow on an…
Digital co-addition of astronomical images is a common technique for increasing signal-to-noise and image depth. A modification of this simple technique has been applied to the detection of minor bodies in the Solar System: first stationary…
To be applicable to real world scenarios trajectory planning schemes for mobile autonomous systems must be able to efficiently deal with obstacles in the area of operation. In the context of optimization based trajectory planning and…