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Not only is the geometry of rock fragments often well approximated by ideal convex polyhedra having few faces and vertices, but these numbers carry vital geophysical information on the fragmentation process. Despite their significance, the…
The distance geometry problem asks to find a realization of a given simple edge-weighted graph in a Euclidean space of given dimension K, where the edges are realized as straight segments of lengths equal (or as close as possible) to the…
Optimal control problems are formulated and efficient computational procedures are proposed for combined orbital and rotational maneuvers of a rigid body in three dimensions. The rigid body is assumed to act under the influence of forces…
Most of the optimal guidance problems can be formulated as nonconvex optimization problems, which can be solved indirectly by relaxation, convexification, or linearization. Although these methods are guaranteed to converge to the global…
The sum of elliptic integrals simultaneously determines orbits in thr Kepler problem and the addition of divisors on elliptic curves. Periodic motion of a body in physical space is defined by symmetries, whereas periodic motion of divisors…
We construct a highly-symmetric periodic orbit of eight bodies in three dimensions. In this orbit, each body collides with its three nearest neighbors in a regular periodic fashion. Regularization of the collisions in the orbit is achieved…
We consider the ideal orientation problem in planar graphs. In this problem, we are given an undirected graph $G$ with positive edge lengths and $k$ pairs of distinct vertices $(s_1, t_1), \dots, (s_k, t_k)$ called terminals, and we want to…
We study the problem of recovering the relative positions of objects moving along the real line based only on pairwise collision data. While interaction-based sensing systems arise naturally in a variety of practical settings, a systematic…
This thesis presents an innovative framework for the automated detection and characterization of galactic bars, pivotal structures in spiral galaxies, using the YOLO-OBB (You Only Look Once with Oriented Bounding Boxes) model. Traditional…
Images are an important source of information for spacecraft navigation and for three-dimensional reconstruction of observed space objects. Both of these applications take the form of a triangulation problem when the camera has a known…
A new approach is presented for the problem of optimal impulsive rendezvous of a spacecraft in an inertial frame near a circular orbit in a Newtonian gravitational field. The total characteristic velocity to be minimized is replaced by a…
Autonomous systems often employ multiple LiDARs to leverage the integrated advantages, enhancing perception and robustness. The most critical prerequisite under this setting is the estimating the extrinsic between each LiDAR, i.e.,…
In this work, we study the periodic orbits in the spatial isosceles three-body problem. These periodic orbits form a one-parameter set with a rotation angle $\theta$ as the parameter. Some new phenomenons are discovered by applying our…
Gaia's astrometric solution aims to determine at least five parameters for each star, together with appropriate estimates of their uncertainties and correlations. This requires at least five distinct observations per star. In the early data…
Absolute pose estimation is a fundamental problem in computer vision, and it is a typical parameter estimation problem, meaning that efforts to solve it will always suffer from outlier-contaminated data. Conventionally, for a fixed…
In this paper, we propose an advanced methodology for the detection of 3D objects and precise estimation of their spatial positions from a single image. Unlike conventional frameworks that rely solely on center-point and dimension…
We propose to estimate 3D human pose from multi-view images and a few IMUs attached at person's limbs. It operates by firstly detecting 2D poses from the two signals, and then lifting them to the 3D space. We present a geometric approach to…
Inertial odometry is an attractive solution to the problem of state estimation for agile quadrotor flight. It is inexpensive, lightweight, and it is not affected by perceptual degradation. However, only relying on the integration of the…
Since Intersection-over-Union (IoU) based optimization maintains the consistency of the final IoU prediction metric and losses, it has been widely used in both regression and classification branches of single-stage 2D object detectors.…
A moment approach for orbit determinations of astrometric binaries from astrometric observations alone has been recently studied for a low signal-to-noise ratio (Iwama et al. 2013, PASJ, 65, 2). With avoiding a direct use of the…