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In this paper, we solve the complete coordination problem of robotic fiber positioners using supervisory control theory. In particular, we model positioners and their behavioral specifications as discrete-event systems by the discretization of their motion spaces. We synthesize a coordination supervisor associated with a specific set of positioners. In particular, the coordination supervisor includes the solutions to the complete coordination problem of its corresponding positioners. Then, we use the backtracking forcibility technique of supervisory control theory to present an algorithm based on a completeness condition to solve the coordination problem similar to a reconfiguration problem. We illustrate the functionality of our method using an example.

Astrobot swarms are used to capture astronomical signals to generate the map of the observable universe for the purpose of dark energy studies. The convergence of each swarm in the course of its coordination has to surpass a particular threshold to yield a satisfactory map. The current coordination methods do not always reach desired convergence rates. Moreover, these methods are so complicated that one cannot formally verify their results without resource-demanding simulations. Thus, we use support vector machines to train a model which can predict the convergence of a swarm based on the data of previous coordination of that swarm. Given a fixed parity, i.e., the rotation direction of the outer arm of an astrobot, corresponding to a swarm, our algorithm reaches a better predictive performance compared to the state of the art. Additionally, we revise our algorithm to solve a more generalized convergence prediction problem according to which the parities of astrobots may differ. We present the prediction results of a generalized scenario, associated with a 487-astrobot swarm, which are interestingly efficient and collision-free given the excessive complexity of this scenario compared to the constrained one.

This paper introduces the emerging field of astrobotics, that is, a recently-established branch of robotics to be of service to astrophysics and observational astronomy. We first describe a modern requirement of dark matter studies, i.e., the generation of the map of the observable universe, using astrobots. Astrobots differ from conventional two-degree-of-freedom robotic manipulators in two respects. First, the dense formation of astrobots give rise to the extremely overlapping dynamics of neighboring astrobots which make them severely subject to collisions. Second, the structure of astrobots and their mechanical specifications are specialized due to the embedded optical fibers passed through them. We focus on the coordination problem of astrobots whose solutions shall be collision-free, fast execution, and complete in terms of the astrobots' convergence rates. We also illustrate the significant impact of astrobots assignments to observational targets on the quality of coordination solutions To present the current state of the field, we elaborate the open problems including next-generation astrophysical projects including 20,000 astrobots, and other fields, such as space debris tracking, in which astrobots may be potentially used

The data throughput of massive spectroscopic surveys in the course of each observation is directly coordinated with the number of optical fibers which reach their target. In this paper, we evaluate the safety and the performance of the astrobots coordination in SDSS-V by conducting various experimental and simulated tests. We illustrate that our strategy provides a complete coordination condition which depends on the operational characteristics of astrobots, their configurations, and their targets. Namely, a coordination method based on the notion of cooperative artificial potential fields is used to generate safe and complete trajectories for astrobots. Optimal target assignment further improves the performance of the used algorithm in terms of faster convergences and less oscillatory movements. Both random targets and galaxy catalog targets are employed to observe the coordination success of the algorithm in various target distributions. The proposed method is capable of handling all potential collisions in the course of coordination. Once the completeness condition is fulfilled according to initial configuration of astrobots and their targets, the algorithm reaches full convergence of astrobots. Should one assign targets to astrobots using efficient strategies, convergence time as well as the number of oscillations decrease in the course of coordination. Rare incomplete scenarios are simply resolved by trivial modifications of astrobots swarms' parameters., Comment: https://link.springer.com/article/10.1007/s10686-020-09687-4

Astrobots are robotic artifacts whose swarms are used in astrophysical studies to generate the map of the observable universe. These swarms have to be coordinated with respect to various desired observations. Such coordination are so complicated that distributed swarm controllers cannot always coordinate enough astrobots to fulfill the minimum data desired to be obtained in the course of observations. Thus, a convergence verification is necessary to check the suitability of a coordination before its execution. However, a formal verification method does not exist for this purpose. In this paper, we instead use machine learning to predict the convergence of astrobots swarm. In particular, we propose a weighted $k$-NN-based algorithm which requires the initial status of a swarm as well as its observational targets to predict its convergence. Our algorithm learns to predict based on the coordination data obtained from previous coordination of the desired swarm. This method first generates a convergence probability for each astrobot based on a distance metric. Then, these probabilities are transformed to either a complete or an incomplete categorical result. The method is applied to two typical swarms including 116 and 487 astrobots. It turns out that the correct prediction of successful coordination may be up to 80% of overall predictions. Thus, these results witness the efficient accuracy of our predictive convergence analysis strategy.

Robotic fiber positioners play a vital role in the generation of massive spectroscopic surveys. The more complete a positioners set is coordinated, the more information its corresponding spectrograph receives during an observation. The complete coordination problem of positioners sets is studied in this paper. We first define the local and the global completeness problems and determine their relationship. We then propose a new artificial potential field according to which the convergences of a positioner and its neighboring positioners are cooperatively taken into account. We also discover the required condition for a complete coordination. We finally explain how the modifications of some of the parameters of a positioners set may resolve its incompleteness coordination scenarios. We verify our accomplishments using simulations.

Robotics have recently contributed to cosmological spectroscopy to automatically obtain the map of the observable universe using robotic fiber positioners. For this purpose, an assignment algorithm is required to assign each robotic fiber positioner to a target associated with a particular observation. The assignment process directly impacts on the coordination of robotic fiber positioners to reach their assigned targets. In this paper, we establish an optimal target assignment scheme which simultaneously provides the fastest coordination accompanied with the minimum of colliding scenarios between robotic fiber positioners. In particular, we propose a cost function by whose minimization both of the cited requirements are taken into account in the course of a target assignment process. The applied simulations manifest the improvement of convergence rates using our optimal approach. We show that our algorithm scales the solution in quadratic time in the case of full observations. Additionally, the convergence time and the percentage of the colliding scenarios are also decreased in both supervisory and hybrid coordination strategies.

DESI (Dark Energy Spectroscopic Instrument) is a Stage IV ground-based dark energy experiment that will study baryon acoustic oscillations (BAO) and the growth of structure through redshift-space distortions with a wide-area galaxy and quasar redshift survey. To trace the underlying dark matter distribution, spectroscopic targets will be selected in four classes from imaging data. We will measure luminous red galaxies up to $z=1.0$. To probe the Universe out to even higher redshift, DESI will target bright [O II] emission line galaxies up to $z=1.7$. Quasars will be targeted both as direct tracers of the underlying dark matter distribution and, at higher redshifts ($ 2.1 < z < 3.5$), for the Ly-$\alpha$ forest absorption features in their spectra, which will be used to trace the distribution of neutral hydrogen. When moonlight prevents efficient observations of the faint targets of the baseline survey, DESI will conduct a magnitude-limited Bright Galaxy Survey comprising approximately 10 million galaxies with a median $z\approx 0.2$. In total, more than 30 million galaxy and quasar redshifts will be obtained to measure the BAO feature and determine the matter power spectrum, including redshift space distortions.

DESI (Dark Energy Spectropic Instrument) is a Stage IV ground-based dark energy experiment that will study baryon acoustic oscillations and the growth of structure through redshift-space distortions with a wide-area galaxy and quasar redshift survey. The DESI instrument is a robotically-actuated, fiber-fed spectrograph capable of taking up to 5,000 simultaneous spectra over a wavelength range from 360 nm to 980 nm. The fibers feed ten three-arm spectrographs with resolution $R= \lambda/\Delta\lambda$ between 2000 and 5500, depending on wavelength. The DESI instrument will be used to conduct a five-year survey designed to cover 14,000 deg$^2$. This powerful instrument will be installed at prime focus on the 4-m Mayall telescope in Kitt Peak, Arizona, along with a new optical corrector, which will provide a three-degree diameter field of view. The DESI collaboration will also deliver a spectroscopic pipeline and data management system to reduce and archive all data for eventual public use.

The next generation of large-scale spectroscopic survey experiments such as DESI, will use thousands of fiber positioner robots packed on a focal plate. In order to maximize the observing time with this robotic system we need to move in parallel the fiber-ends of all positioners from the previous to the next target coordinates. Direct trajectories are not feasible due to collision risks that could undeniably damage the robots and impact the survey operation and performance. We have previously developed a motion planning method based on a novel decentralized navigation function for collision-free coordination of fiber positioners. The navigation function takes into account the configuration of positioners as well as their envelope constraints. The motion planning scheme has linear complexity and short motion duration (~2.5 seconds with the maximum speed of 30 rpm for the positioner), which is independent of the number of positioners. These two key advantages of the decentralization designate the method as a promising solution for the collision-free motion-planning problem in the next-generation of fiber-fed spectrographs. In a framework where a centralized computer communicates with the positioner robots, communication overhead can be reduced significantly by using velocity profiles consisting of a few bits only. We present here the discretization of velocity profiles to ensure the feasibility of a real-time coordination for a large number of positioners. The modified motion planning method that generates piecewise linearized position profiles guarantees collision-free trajectories for all the robots. The velocity profiles fit few bits at the expense of higher computational costs., Comment: SPIE Astronomical Telescopes + Instrumentation 2014 in Montr\'eal, Quebec, Canada. arXiv admin note: substantial text overlap with arXiv:1312.1644

In the large-scale, Dark Energy Spectroscopic Instrument (DESI), thousands of fiber positioners will be used. Those are robotic positioners, with two axis, and having the size of a pen. They are tightly packed on the focal plane of the telescope. Dedicated micro-robots have been developed and they use 4mm brushless DC motors. To simplify the implementation and reduce the space occupancy, each actuator will integrate its own electronic control board. This board will be used to communicate with the central trajectory generator, manage low level control tasks and motor current feeding. In this context, we present a solution for a highly compact electronic. This electronic is composed of two layers. The first is the power stage that can drive simultaneously two brushless motors. The second one consists of a fast microcontroller and deals with different control tasks: communication, acquisition of the hall sensor signals, commutation of the motors phases, and performing position and current regulation. A set of diagnostic functions are also implemented to detect failure in the motors or the sensors, and to sense abnormal load change that may be the result of two robots colliding., Comment: 7 pages, 10 figures, SPIE Digital Library

Some of the next generation massive spectroscopic survey projects, such as DESI and PFS, plan to use thousands of fiber positioner robots packed at a focal plane to quickly move in parallel the fiber-ends from the previous to the next target points. The most direct trajectories are prone to collision that could damage the robots and impact the survey operation. We thus present here a motion planning method based on a novel decentralized navigation function for collision-free coordination of fiber positioners. The navigation function takes into account the configuration of positioners as well as the actuator constraints. We provide details for the proof of convergence and collision avoidance. Decentralization results in linear complexity for the motion planning as well as dependency of motion duration with respect to the number of positioners. Therefore the coordination method is scalable for large-scale spectrograph robots. The short in-motion duration of positioner robots (~2.5 seconds using typical actuator constraints), will thus allow the time dedicated for observation to be maximized.

In the spectra of pulsating stars, especially Mira stars, the detection of intense hydrogen emission lines has been explained by a radiative shock wave, periodically propagating throughout the atmosphere. Previous observation of the Mira star omicron Ceti around a bright maximum of light led to the detection of a strong linear polarization associated to Balmer emissions, although the origin of this phenomenon is not fully explained yet. With the help of spectropolarimetry, we propose to investigate the nature of shock waves propagating throughout the stellar atmosphere and present, for omicron Ceti (the prototype of Mira stars), a full observational study of hydrogen emission lines formed in the radiative region of such a shock. Using the instrument NARVAL, we performed a spectropolarimetric monitoring of omicron Ceti during three consecutive pulsation cycles. All Stokes parameters were systematically collected, with a particular emphasis on the maxima of luminosity, i.e. when a radiative shock wave is supposed to emerge from the photosphere and propagate outward. On Balmer lines, over a large part of the luminosity cycle, we report detections in Stokes spectra which are evolving with time. These signatures appear to be strongly correlated to the presence of an intense shock wave responsible for the hydrogen emission lines. We establish that those lines are polarized by a process inherent to the mechanism responsible for the emission line formation: the shock wave itself. Two mechanisms are considered: a global one that implies a polarization induced by convective cells located around the photosphere and a local one that implies a charge separation due to the passage of the shock wave, inducing an electrical current. Combined with the existing turbulence, this may generate a magnetic field, hence polarization., Comment: 11 pages, 9 figures; Astronomy and Astrophysics 2011, preprint online