Active Estimation of 3D Lines in Spherical Coordinates

Straight lines are common features in human made environments, which makes them a frequently explored feature for control applications. Many control schemes, like Visual Servoing, require the 3D parameters of the features to be estimated. In order to obtain the 3D structure of lines, a nonlinear observer is proposed. However, to guarantee convergence, the dynamical system must be coupled with an algebraic equation. This is achieved by using spherical coordinates to represent the line's moment vector, and a change of basis, which allows to introduce the algebraic constraint directly on the system's dynamics. Finally, a control law that attempts to optimize the convergence behavior of the observer is presented. The approach is validated in simulation, and with a real robotic platform with a camera onboard.Comment: Accepted in 2019 American Control Conference (ACC) (Final Version

A multi-spacecraft view of a giant filament eruption during 26/27 September 2009

We analyze multi-spacecraft observations of a giant filament eruption that occurred during 26 and 27 September 2009. The filament eruption was associated with a relatively slow coronal mass ejection (CME). The filament consisted of a large and a small part, both parts erupted nearly simultaneously. Here we focus on the eruption associated with the larger part of the filament. The STEREO satellites were separated by about 117 degree during this event, so we additionally used SoHO/EIT and CORONAS/TESIS observations as a third eye (Earth view) to aid our measurements. We measure the plane-of-sky trajectory of the filament as seen from STEREO-A and TESIS view-points. Using a simple trigonometric relation, we then use these measurements to estimate the true direction of propagation of the filament which allows us to derive the true R=R_sun v/s time profile of the filament apex. Furthermore, we develop a new tomographic method that can potentially provide a more robust three-dimensional reconstruction by exploiting multiple simultaneous views. We apply this method also to investigate the 3D evolution of the top part of filament. We expect this method to be useful when SDO and STEREO observations are combined. We then analyze the kinematics of the eruptive filament during its rapid acceleration phase by fitting different functional forms to the height-time data derived from the two methods. We find that, for both methods, an exponential function fits the rise profile of the filament slightly better than parabolic or cubic functions. Finally, we confront these results with the predictions of theoretical eruption models.Comment: 16 pages, 9 figures, to appear in Astrophysical Journa

Active Estimation of Distance in a Robotic Vision System that Replicates Human Eye Movement

Many visual cues, both binocular and monocular, provide 3D information. When an agent moves with respect to a scene, an important cue is the different motion of objects located at various distances. While a motion parallax is evident for large translations of the agent, in most head/eye systems a small parallax occurs also during rotations of the cameras. A similar parallax is present also in the human eye. During a relocation of gaze, the shift in the retinal projection of an object depends not only on the amplitude of the movement, but also on the distance of the object with respect to the observer. This study proposes a method for estimating distance on the basis of the parallax that emerges from rotations of a camera. A pan/tilt system specifically designed to reproduce the oculomotor parallax present in the human eye was used to replicate the oculomotor strategy by which humans scan visual scenes. We show that the oculomotor parallax provides accurate estimation of distance during sequences of eye movements. In a system that actively scans a visual scene, challenging tasks such as image segmentation and figure/ground segregation greatly benefit from this cue.National Science Foundation (BIC-0432104, CCF-0130851

A fast multipole method for stellar dynamics

The approximate computation of all gravitational forces between $N$ interacting particles via the fast multipole method (FMM) can be made as accurate as direct summation, but requires less than $\mathcal{O}(N)$ operations. FMM groups particles into spatially bounded cells and uses cell-cell interactions to approximate the force at any position within the sink cell by a Taylor expansion obtained from the multipole expansion of the source cell. By employing a novel estimate for the errors incurred in this process, I minimise the computational effort required for a given accuracy and obtain a well-behaved distribution of force errors. For relative force errors of $\sim10^{-7}$, the computational costs exhibit an empirical scaling of $\propto N^{0.87}$. My implementation (running on a 16 core node) out-performs a GPU-based direct summation with comparable force errors for $N\gtrsim10^5$.Comment: 21 pages, 15 figures, accepted for publication in Journal for Computational Astrophysics and Cosmolog

Role of hydrodynamic flows in chemically driven droplet division

We study the hydrodynamics and shape changes of chemically active droplets. In non-spherical droplets, surface tension generates hydrodynamic flows that drive liquid droplets into a spherical shape. Here we show that spherical droplets that are maintained away from thermodynamic equilibrium by chemical reactions may not remain spherical but can undergo a shape instability which can lead to spontaneous droplet division. In this case chemical activity acts against surface tension and tension-induced hydrodynamic flows. By combining low Reynolds-number hydrodynamics with phase separation dynamics and chemical reaction kinetics we determine stability diagrams of spherical droplets as a function of dimensionless viscosity and reaction parameters. We determine concentration and flow fields inside and outside the droplets during shape changes and division. Our work shows that hydrodynamic flows tends to stabilize spherical shapes but that droplet division occurs for sufficiently strong chemical driving, sufficiently large droplet viscosity or sufficiently small surface tension. Active droplets could provide simple models for prebiotic protocells that are able to proliferate. Our work captures the key hydrodynamics of droplet division that could be observable in chemically active colloidal droplets

Estimation of width and inclination of a filament sheet using He II 304 A observations by STEREO/EUVI

The STEREO mission has been providing stereoscopic view of the filament eruptions in EUV wavelengths. The most extended view during filament eruptions is seen in He II 304 \AA observations, as the filament spine appears darker and sharper. The projected filament width appears differently when viewed from different angles by STEREO satellites. Here, we present a method for estimating the width and inclination of the filament sheet using He II 304 \AA\ observations by STEREO-A and B satellites from the two viewpoints. The width of the filament sheet, when measured from its feet to its apex, gives estimate of filament height above the chromosphere.Comment: 9 pages, 2 figures, in Annales Geophysica

Global axis shape of magnetic clouds deduced from the distribution of their local axis orientation

Coronal mass ejections (CMEs) are routinely tracked with imagers in the interplanetary space while magnetic clouds (MCs) properties are measured locally by spacecraft. However, both imager and insitu data do not provide direct estimation on the global flux rope properties. The main aim of this study is to constrain the global shape of the flux rope axis from local measurements, and to compare the results from in-situ data with imager observations. We perform a statistical analysis of the set of MCs observed by WIND spacecraft over 15 years in the vicinity of Earth. With the hypothesis of having a sample of MCs with a uniform distribution of spacecraft crossing along their axis, we show that a mean axis shape can be derived from the distribution of the axis orientation. In complement, while heliospheric imagers do not typically observe MCs but only their sheath region, we analyze one event where the flux-rope axis can be estimated from the STEREO imagers. From the analysis of a set of theoretical models, we show that the distribution of the local axis orientation is strongly affected by the global axis shape. Next, we derive the mean axis shape from the integration of the observed orientation distribution. This shape is robust as it is mostly determined from the global shape of the distribution. Moreover, we find no dependence on the flux-rope inclination on the ecliptic. Finally, the derived shape is fully consistent with the one derived from heliospheric imager observations of the June 2008 event. We have derived a mean shape of MC axis which only depends on one free parameter, the angular separation of the legs (as viewed from the Sun). This mean shape can be used in various contexts such as the study of high energy particles or space weather forecast.Comment: 13 pages, 12 figure