A methodology for robust optimization of low-thrust trajectories in multi-body environments

Issued as final reportThales Alenia Spac

Precomputing Process Noise Covariance for Onboard Sequential Filters

Process noise is often used in estimation filters to account for unmodeled and mismodeled accelerations in the dynamics. The process noise covariance acts to inflate the state covariance over propagation intervals, increasing the uncertainty in the state. In scenarios where the acceleration errors change significantly over time, the standard process noise covariance approach can fail to provide effective representation of the state and its uncertainty. Consider covariance analysis techniques provide a method to precompute a process noise covariance profile along a reference trajectory, using known model parameter uncertainties. The process noise covariance profile allows significantly improved state estimation and uncertainty representation over the traditional formulation. As a result, estimation performance on par with the consider filter is achieved for trajectories near the reference trajectory without the additional computational cost of the consider filter. The new formulation also has the potential to significantly reduce the trial-and-error tuning currently required of navigation analysts. A linear estimation problem as described in several previous consider covariance analysis publications is used to demonstrate the effectiveness of the precomputed process noise covariance, as well as a nonlinear descent scenario at the asteroid Bennu with optical navigation

Multi-Shooting Differential Dynamic Programming for Hybrid Systems using Analytical Derivatives

Differential Dynamic Programming (DDP) is a popular technique used to generate motion for dynamic-legged robots in the recent past. However, in most cases, only the first-order partial derivatives of the underlying dynamics are used, resulting in the iLQR approach. Neglecting the second-order terms often slows down the convergence rate compared to full DDP. Multi-Shooting is another popular technique to improve robustness, especially if the dynamics are highly non-linear. In this work, we consider Multi-Shooting DDP for trajectory optimization of a bounding gait for a simplified quadruped model. As the main contribution, we develop Second-Order analytical partial derivatives of the rigid-body contact dynamics, extending our previous results for fixed/floating base models with multi-DoF joints. Finally, we show the benefits of a novel Quasi-Newton method for approximating second-order derivatives of the dynamics, leading to order-of-magnitude speedups in the convergence compared to the full DDP method.Comment: https://www.youtube.com/watch?v=C0h6mEpcnA

Vascular Insulin Resistance May Contribute to Health Disparities in People from the Rio Grande Valley

Microvascular blood flow (MBF) increases postprandially in skeletal muscle in response to insulin to aid in myocyte glucose delivery. This MBF response is considered a measure of vascular insulin resistance and can be impaired with altered meal composition, obesity, type 2 diabetes mellitus (T2DM), and insulin resistance. Current studies indicate this MBF response to a mixed meal challenge (MMC) may identify vascular insulin resistance before typically-presenting serum biomarkers of insulin resistance, as it displays more sensitivity than when using an oral glucose challenge (OGC). However, it is unknown if healthy adults residing in the Rio Grande Valley (RGV), an area with a 3x higher prevalence of T2DM vs the national average, demonstrate impaired MBF responses similar to those seen in overt insulin resistance. PURPOSE: To determine microvascular responses in apparently healthy individuals of the RGV between OGC and MMC. METHODS: 17 healthy participants from the RGV (age 25±6 yrs, BMI 25±3 kg/m2, fat mass % 29±9%, and android fat % 31±10.4%) without hypertension, T2DM, or dyslipidemia were administered a MMC and OGC on two separate occasions. Forearm skeletal muscle MBF (measured as acoustic intensity/second (AI/s)) was recorded pre- and 1-hour postprandial via contrast-enhanced ultrasound (CEU). RESULTS: MMC pre- vs. post-prandial demonstrated a 0.59 fold reduction (1.6101 vs. 0.6548 AI/s, 95% CI [-.2871, 3.5073] and [0.887, 1.2209], respectively). OGC pre- vs. post-prandial MBF had a 0.18 fold reduction (1.6734 vs. 1.3693 AI/s, 95% CI [.3755, 2.9714] and [.4725, 2.2661], respectively). MBF in skeletal muscle demonstrated no significant difference between MMC and OGC groups (Mean square= 2.378, F(1, 48) = .320, p = 0.574). CONCLUSION: Unlike healthy Caucasians, apparently healthy residents of the RGV display impaired microvascular responses to MMC, similar to using an OGC, suggesting early vascular insulin resistance. As this population displays significant health disparities for chronic diseases such as T2DM, obesity, and Alzheimer’s, it is plausible that early vascular insulin resistance noted in this population significantly contributes to the increased incidence of these chronic diseases. Additional research is needed to identify mechanisms explaining this population\u27s etiology of impaired MBF responses and vascular insulin resistance

Extremely Metal-Poor Stars. VII. The Most Metal-Poor Dwarf, CS 22876-032

We report high-resolution, high-signal-to-noise, observations of the extremely metal-poor double-lined spectroscopic binary CS 22876-032. The system has a long period : P = 424.7 $\pm$ 0.6 days. It comprises two main sequence stars having effective temperatures 6300 K and 5600 K, with a ratio of secondary to primary mass of 0.89 $\pm$ 0.04. The metallicity of the system is [Fe/H] = -3.71 $\pm$ 0.11 $\pm$ 0.12 (random and systematic errors) -- somewhat higher than previous estimates. We find [Mg/Fe] = 0.50, typical of values of less extreme halo material. [Si/Fe], [Ca/Fe], and [Ti/Fe], however, all have significantly lower values, ~ 0.0-0.1, suggesting that the heavier elements might have been underproduced relative to Mg in the material from which this object formed. In the context of the hypothesis that the abundance patterns of extremely metal-poor stars are driven by individual enrichment events and the models of Woosley and Weaver (1995), the data for CS 22876-032 are consistent with its having been enriched by a zero-metallicity supernova of mass 30 M$_{\odot}$. As the most metal-poor near-main-sequence-turnoff star currently known, the primary of the system has the potential to strongly constrain the primordial lithium abundance. We find A(Li) (= log(N(Li)/N(H)) + 12.00) = 2.03 $\pm$ 0.07, which is consistent with the finding of Ryan et al. (1999) that for stars of extremely low metallicity A(Li) is a function of [Fe/H].Comment: 27 pages, 9 figures, accepted for publication in The Astrophysical Journal, Sept. 1, 2000 issu

Exploiting Lunar Natural and Augmented Thermal Environments for Exploration and Research

Near the poles of the Moon, there are permanently shadowed craters whose surface temperatures never exceed 100 K. Craters within craters, commonly referred to as double-shaded craters, have areas where even colder regions exist with, in many cases, temperatures that should never exceed 50 K. The presence of water ice possibly existing in permanently shaded areas of the moon has been hypothesized, discussed, and studied since Watson et al. [1] predicted the possibility of ice on the moon. Ingersoll et al. [2] estimated that the maximum sublimation rate for ice is less than 1 cm per billion years for these types of environments. These potential ice stores have many uses for lunar exploration, potentially providing precious water and rocket fuel for any human exploration or future colonization. The temperatures within these regions offer unprecedented high-vacuum cryogenic environments, which in their natural state could support cryogenic applications such as high-temperature superconductors and associated devices that could be derived. The potential application of naturally occurring cryogenic environments in conjunction with simple methods to augment these environments to achieve even colder temperatures opens the potential use of many additional cryogenic techniques. Besides ice stores and the potential for continuous solar illumination for power production, the unique cryogenic conditions at the lunar poles provide an environment that could reduce the power, weight, and total mass that would have to be carried from the Earth to the Moon for lunar exploration and research

Electronic nematic order in the normal state of strontium ruthenate

Despite significant achievements in characterizing the properties of Sr$_2$RuO$_4$ over the last three decades, the precise nature of its electronic ground state is still unresolved. In this work, we provide a missing piece of the puzzle by uncovering evidence of electronic nematic order in the normal state of Sr$_2$RuO$_4$, revealed by ultrafast time-resolved optical dichroism measurements of uniaxially strained thin films. This nematic order, whose domains are aligned by the strain, spontaneously breaks the four-fold rotational symmetry of the crystal. The temperature dependence of the dichroism resembles an Ising-like order parameter, and optical pumping induces a coherent oscillation of its amplitude mode. A microscopic model of intra-unit-cell nematic order is presented, highlighting the importance of Coulomb repulsion between neighboring oxygen $p$-orbitals. The existence of electronic nematic order in the normal state of Sr$_2$RuO$_4$ may have consequences for the form and mechanism of superconductivity in this material