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We present a conceptual design for a fiber positioning system for multi-object high-resolution spectroscopy, designed to be compatible with the upcoming large telescopes with a wide field of view. The design incorporates multiple Atmospheric Dispersion Correctors (ADCs) and tip-tilt mirrors that receive non-telecentric input from individual targets and direct it to the ADCs. Here, we introduce a mechanical design for the fiber positioner that accommodates the optics and operates in a curved focal plane with a Radius of Curvature (R) of 3m. This mechanical design provides four degrees of freedom to access the focal volume, enhancing targeting efficiency. The proposed design and an efficient target allocation algorithm ensure a targeting efficiency of approximately 80-100% for a primary observation session. We also present a methodology for target assignment, positioning, and quantification based on sequential and Monte Carlo (MC) algorithms. This method has been tested on realistic fields with varying target densities to validate its performance.

We introduce a novel approach for safe control design based on the density function. A control density function (CDF) is introduced to synthesize a safe controller for a nonlinear dynamic system. The CDF can be viewed as a dual to the control barrier function (CBF), a popular approach used for safe control design. While the safety certificate using the barrier function is based on the notion of invariance, the dual certificate involving the density function has a physical interpretation of occupancy. This occupancy-based physical interpretation is instrumental in providing an analytical construction of density function used for safe control synthesis. The safe control design problem is formulated using the density function as a quadratic programming (QP) problem. In contrast to the QP proposed for control synthesis using CBF, the proposed CDF-based QP can combine both the safety and convergence conditions to target state into single constraints. Further, we consider robustness against uncertainty in system dynamics and the initial condition and provide theoretical results for robust navigation using the CDF. Finally, we present simulation results for safe navigation with single integrator and double-gyre fluid flow-field examples, followed by robust navigation using the bicycle model and autonomous lane-keeping examples.

In fiber-based spectroscopy within telescopes, a prevailing limitation has been the necessity to align the fiber diameter with the telescope's seeing conditions, often characterized by the Full Width at Half Maximum of the point spread function. This alignment constraint captures around 50 \% of the incoming flux from any point source. Furthermore, the challenge is compounded when high-resolution spectroscopy is in play, as it often demands a minute slit width, further exacerbating flux loss. The essence of this paper lies in a comprehensive exploration, accomplished through theoretical simulations, of strategies aimed at enhancing the coupling efficiency of high-resolution spectrographs. The primary objective is to bolster the flux capture without compromising the critical aspect of spectral resolution. This research endeavors to unlock the potential for more effective utilization of high-resolution spectrographs to study celestial objects., Comment: 7 pages, 6 figures, 4 tables. Submitted to proceedings of the SPIE Astronomical Telescopes + Instrumentation 2024

The 2.34m Vainu Bappu Telescope (VBT) is a reflecting telescope that operates in two modes, prime focus and cassegrain focus, and is equipped with two instruments. In prime focus mode, the telescope has the F-number of f/3.25, and the High-Resolution Echelle Spectrograph (HRES) is employed through optical fiber. On the other hand, in cassegrain focus mode, the F-number is f/13, and the OMR Spectrograph (OMRS) is mounted for low and medium-resolution spectroscopy. Currently, the VBT faces a limitation: either the OMRS or the HRES can be used due to the switch in the heavy secondary mirror. To overcome this, we present a novel method enabling the OMRS to operate from prime mode alongside the HRES. The fiber setup for OMRS is optimized with a 25-lenslet + fiber-based Integral Field Unit (IFU) capable of observing both point and extended sources. The optimized lenslet, fiber, and fore optics design is undergoing lab testing. Our approach allows seamless operation of both spectrographs on the same night, enhancing the observational capabilities of astronomical studies with VBT., Comment: 7 pages, 6 figures, 2 tables. Submitted to proceedings of the SPIE Astronomical Telescopes + Instrumentation 2024

A novel method to reconstruct the energy of hadronic showers in the CMS High Granularity Calorimeter (HGCAL) is presented. The HGCAL is a sampling calorimeter with very fine transverse and longitudinal granularity. The active media are silicon sensors and scintillator tiles readout by SiPMs and the absorbers are a combination of lead and Cu/CuW in the electromagnetic section, and steel in the hadronic section. The shower reconstruction method is based on graph neural networks and it makes use of a dynamic reduction network architecture. It is shown that the algorithm is able to capture and mitigate the main effects that normally hinder the reconstruction of hadronic showers using classical reconstruction methods, by compensating for fluctuations in the multiplicity, energy, and spatial distributions of the shower's constituents. The performance of the algorithm is evaluated using test beam data collected in 2018 prototype of the CMS HGCAL accompanied by a section of the CALICE AHCAL prototype. The capability of the method to mitigate the impact of energy leakage from the calorimeter is also demonstrated., Comment: Prepared for submission to JINST

The Spectroscopic Investigation of Nebular Gas (SING) is a near-ultraviolet (NUV) low-resolution spectrograph payload designed to operate in the NUV range, 1400 $\unicode{x212B}$ -- 2700 $\unicode{x212B}$, from a stable space platform. SING telescope has a primary aperture of 298 mm, feeding the light to the long-slit UV spectrograph. SING has a field of view (FOV) of 1$^{\circ}$, achieving a spatial resolution of 1.33 arc minute and spectral resolution of 3.7 $\unicode{x212B}$ ($R\sim600$) at the central wavelength. SING employs a micro-channel plate (MCP) with a CMOS readout-based photon-counting detector. The instrument is designed to observe diffuse sources such as nebulae, supernova remnants, and the interstellar medium (ISM) to understand their chemistry. SING was selected by the United Nations Office for Outer Space Affairs to be hosted on the Chinese Space Station. The instrument will undergo qualification tests as per the launch requirements. In this paper, we describe the hardware design, optomechanical assembly, and calibration of the instrument.

We consider the problem of navigating a nonlinear dynamical system from some initial set to some target set while avoiding collision with an unsafe set. We extend the concept of density function to control density function (CDF) for solving navigation problems with safety constraints. The occupancy-based interpretation of the measure associated with the density function is instrumental in imposing the safety constraints. The navigation problem with safety constraints is formulated as a quadratic program (QP) using CDF. The existing approach using the control barrier function (CBF) also formulates the navigation problem with safety constraints as QP. One of the main advantages of the proposed QP using CDF compared to QP formulated using CBF is that both the convergence/stability and safety can be combined and imposed using the CDF. Simulation results involving the Duffing oscillator and safe navigation of Dubin car models are provided to verify the main findings of the paper.

This paper presents a motion planning algorithm for quadruped locomotion based on density functions. We decompose the locomotion problem into a high-level density planner and a model predictive controller (MPC). Due to density functions having a physical interpretation through the notion of occupancy, it is intuitive to represent the environment with safety constraints. Hence, there is an ease of use to constructing the planning problem with density. The proposed method uses a simplified model of the robot into an integrator system, where the high-level plan is in a feedback form formulated through an analytically constructed density function. We then use the MPC to optimize the reference trajectory, in which a low-level PID controller is used to obtain the torque level control. The overall framework is implemented in simulation, demonstrating our feedback density planner for legged locomotion. The implementation of work is available at \url{https://github.com/AndrewZheng-1011/legged_planner}, Comment: arXiv admin note: text overlap with arXiv:2306.15830

Highly multiplexed spectroscopic surveys have changed the astronomy landscape in recent years. However, these surveys are limited to low and medium spectral resolution. High spectral resolution spectroscopy is often photon starved and will benefit from a large telescope aperture. Multiplexed high-resolution surveys require a wide field of view and a large aperture for a suitable large number of bright targets. This requirement introduces several practical difficulties, especially for large telescopes, such as the future ELTs. Some of the challenges are the need for a wide field atmospheric dispersion corrector and to deal with the curved non-telecentric focal plane. Here, we present a concept of Multi-Object Spectroscopy (MOS) mode for TMT High-Resolution Optical Spectrograph (HROS), we have designed an atmospheric dispersion corrector for individual objects that fit inside a fiber positioner. We present the ZEMAX design and the performance of the atmospheric dispersion corrector for all elevations accessible by TMT.

The advent of the silicon photomultiplier has allowed the development of highly segmented calorimeters using plastic scintillator as the active media, with photodetectors embedded in the calorimeter, in dimples in the plastic. To reduce the photodetector's dark current and radiation damage, the high granularity calorimeter designed for the high luminosity upgrade of the CMS detector at CERN's Large Hadron Collider will be operated at a temperature of about -30$^\circ$C. Due to flammability considerations, a low oxygen environment is being considered. However, the radiation damage to the plastic scintillator during irradiation in this operating environment needs to be considered. In this paper, we present measurements of the relative decrease of light output during irradiation of small plastic scintillator tiles read out by silicon photomultipliers. The irradiations were performed using a $^{60}\mathrm{Co}$ source both to produce the tiles' light and as a source of ionizing irradiation at dose rates of 0.3, 1.3, and $1.6\,$Gy/hr, temperatures of -30, -15, -5, and 0$^\circ$C, and with several different oxygen concentrations in the surrounding atmosphere. The effect of the material used to wrap the tile was also studied. Substantial temporary damage, which annealed when the sample was warmed, was seen during the low-temperature irradiations, regardless of the oxygen concentration and wrapping material. The relative light loss was largest with 3M$^{\tiny \textrm{TM}}$ Enhanced Specular Reflector Film wrapping and smallest with no wrapping, although due to the substantially higher light yield with wrapping, the final light output is largest with wrapping. The light loss was less at warmer temperatures. Damage with $3\%$ oxygen was similar to that in standard atmosphere. Evidence of a plateau in the radical density was seen for the 0$^\circ$C data.

The paper is about the computation of the principal spectrum of the Koopman operator (i.e., eigenvalues and eigenfunctions). The principal eigenfunctions of the Koopman operator are the ones with the corresponding eigenvalues equal to the eigenvalues of the linearization of the nonlinear system at an equilibrium point. The main contribution of this paper is to provide a novel approach for computing the principal eigenfunctions using a path-integral formula. Furthermore, we provide conditions based on the stability property of the dynamical system and the eigenvalues of the linearization towards computing the principal eigenfunction using the path-integral formula. Further, we provide a Deep Neural Network framework that utilizes our proposed path-integral approach for eigenfunction computation in high-dimension systems. Finally, we present simulation results for the computation of principal eigenfunction and demonstrate their application for determining the stable and unstable manifolds and constructing the Lyapunov function.

This paper presents a novel approach for safe control synthesis using the dual formulation of the navigation problem. The main contribution of this paper is in the analytical construction of density functions for almost everywhere navigation with safety constraints. In contrast to the existing approaches, where density functions are used for the analysis of navigation problems, we use density functions for the synthesis of safe controllers. We provide convergence proof using the proposed density functions for navigation with safety. Further, we use these density functions to design feedback controllers capable of navigating in cluttered environments and high-dimensional configuration spaces. The proposed analytical construction of density functions overcomes the problem associated with navigation functions, which are known to exist but challenging to construct, and potential functions, which suffer from local minima. Application of the developed framework is demonstrated on simple integrator dynamics and fully actuated robotic systems.

In this paper, we propose a novel data-driven approach for learning and control of quadrotor UAVs based on the Koopman operator and extended dynamic mode decomposition (EDMD). Building observables for EDMD based on conventional methods like Euler angles (to represent orientation) is known to involve singularities. To address this issue, we employ a set of physics-informed observables based on the underlying topology of the nonlinear system. We use rotation matrices to directly represent the orientation dynamics and obtain a lifted linear representation of the nonlinear quadrotor dynamics in the SE(3) manifold. This EDMD model leads to accurate prediction and can be generalized to several validation sets. Further, we design a linear model predictive controller (MPC) based on the proposed EDMD model to track agile reference trajectories. Simulation results show that the proposed MPC controller can run as fast as 100 Hz and is able to track arbitrary reference trajectories with good accuracy. Implementation details can be found in \url{https://github.com/sriram-2502/KoopmanMPC_Quadrotor}.

This paper presents the implementation of off-road navigation on legged robots using convex optimization through linear transfer operators. Given a traversability measure that captures the off-road environment, we lift the navigation problem into the density space using the Perron-Frobenius (P-F) operator. This allows the problem formulation to be represented as a convex optimization. Due to the operator acting on an infinite-dimensional density space, we use data collected from the terrain to get a finite-dimension approximation of the convex optimization. Results of the optimal trajectory for off-road navigation are compared with a standard iterative planner, where we show how our convex optimization generates a more traversable path for the legged robot compared to the suboptimal iterative planner.

This paper presents a state-of-the-art optimal controller for quadruped locomotion. The robot dynamics is represented using a single rigid body (SRB) model. A linear time-varying model predictive controller (LTV MPC) is proposed by using linearization schemes. Simulation results show that the LTV MPC can execute various gaits, such as trot and crawl, and is capable of tracking desired reference trajectories even under unknown external disturbances. The LTV MPC is implemented as a quadratic program using qpOASES through the CasADi interface at 50 Hz. The proposed MPC can reach up to 1 m/s top speed with an acceleration of 0.5 m/s2 executing a trot gait. The implementation is available at https:// github.com/AndrewZheng-1011/Quad_ConvexMPC