Recursive mass matrix factorization and inversion: An operator approach to open- and closed-chain multibody dynamics

This report advances a linear operator approach for analyzing the dynamics of systems of joint-connected rigid bodies.It is established that the mass matrix M for such a system can be factored as M=(I+H phi L)D(I+H phi L) sup T. This yields an immediate inversion M sup -1=(I-H psi L) sup T D sup -1 (I-H psi L), where H and phi are given by known link geometric parameters, and L, psi and D are obtained recursively by a spatial discrete-step Kalman filter and by the corresponding Riccati equation associated with this filter. The factors (I+H phi L) and (I-H psi L) are lower triangular matrices which are inverses of each other, and D is a diagonal matrix. This factorization and inversion of the mass matrix leads to recursive algortihms for forward dynamics based on spatially recursive filtering and smoothing. The primary motivation for advancing the operator approach is to provide a better means to formulate, analyze and understand spatial recursions in multibody dynamics. This is achieved because the linear operator notation allows manipulation of the equations of motion using a very high-level analytical framework (a spatial operator algebra) that is easy to understand and use. Detailed lower-level recursive algorithms can readily be obtained for inspection from the expressions involving spatial operators. The report consists of two main sections. In Part 1, the problem of serial chain manipulators is analyzed and solved. Extensions to a closed-chain system formed by multiple manipulators moving a common task object are contained in Part 2. To retain ease of exposition in the report, only these two types of multibody systems are considered. However, the same methods can be easily applied to arbitrary multibody systems formed by a collection of joint-connected regid bodies

Kinematic functions for the 7 DOF robotics research arm

The Robotics Research Model K-1207 manipulator is a redundant 7R serial link arm with offsets at all joints. To uniquely determine joint angles for a given end-effector configuration, the redundancy is parameterized by a scalar variable which corresponds to the angle between the manipulator elbow plane and the vertical plane. The forward kinematic mappings from joint-space to end-effector configuration and elbow angle, and the augmented Jacobian matrix which gives end-effector and elbow angle rates as a function of joint rates, are also derived

Spatial operator algebra framework for multibody system dynamics

The Spatial Operator Algebra framework for the dynamics of general multibody systems is described. The use of a spatial operator-based methodology permits the formulation of the dynamical equations of motion of multibody systems in a concise and systematic way. The dynamical equations of progressively more complex grid multibody systems are developed in an evolutionary manner beginning with a serial chain system, followed by a tree topology system and finally, systems with arbitrary closed loops. Operator factorizations and identities are used to develop novel recursive algorithms for the forward dynamics of systems with closed loops. Extensions required to deal with flexible elements are also discussed

Eclipse Ice Core Accumulation and Stable Isotope Variability as an Indicator of North Pacific Climate

The high accumulation rate and negligible amount of melt at Eclipse Icefield (3017 m) in the Saint Elias Range of Yukon, Canada, allows for the preservation of a high-resolution isotopic and glaciochemical records valuable for reconstruction of climatic variables. Each of the three Eclipse ice cores have a well-constrained depth–age scale with dozens of reference horizons over the twentieth century that permits an exceptional level of confi- dence in the results of the current calibration exercise. Stacked time series of accumulation and stable isotopes were divided into cold and warm seasons and seasons of extreme high and extreme low accumulation and stable isotope values (eight groups). For each group, season-averaged composites of 500-hPa geopotential height grids, and the individual seasons that constitute them, were analyzed to elucidate common anomalous flow patterns. This analysis shows that the most fractionated isotopes and lowest accumulation cold seasons reflect a more zonal height pattern in the North Pacific associated with negative Pacific–North American (PNA) and Pacific decadal oscillation (PDO) indices. Conversely, the least fractionated isotopes and highest accumulation cold seasons are associated with a positive PNA pattern. Although only a maximum of approximately 20% of the total number of accumulation and stable isotope seasons exhibit a relatively consistent relationship with 500-hPa geopotential height patterns, these results support the hypothesis that the most extreme accumulation and extreme isotope cold-season values in the Saint Elias Mountains are related to consistent atmospheric circulation and oceanic sea surface temperature patterns

Seasonal deuterium excess in a Tien Shan ice core: Influence of moisture transport and recycling in Central Asia

Stable water isotope (δ18O, δD) data from a high elevation (5100 masl) ice core recovered from the Tien Shan Mountains, Kyrgyzstan, display a seasonal cycle in deuterium excess (d = δD − 8*δ18O) related to changes in the regional hydrologic cycle during 1994–2000. While there is a strong correlation (r2 = 0.98) between δ18O and δD in the ice core samples, the regression slope (6.9) and mean d value (23.0) are significantly different than the global meteoric water line values. The resulting time-series ice core d profile contains distinct winter maxima and summer minima, with a yearly d amplitude of ∼15–20‰. Local-scale processes that may affect d values preserved in the ice core are not consistent with the observed seasonal variability. Data from Central Asian monitoring sites in the Global Network of Isotopes in Precipitation (GNIP) have similar seasonal d changes. We suggest that regional-scale hydrological conditions, including seasonal changes in moisture source, transport, and recycling in the Caspian/Aral Sea region, are responsible for the observed spatial and temporal d variability

Ice core evidence for a second volcanic eruption around 1809 in the Northern Hemisphere

A volcanic signal observed in ice cores from both polar regions six years prior to Tambora is attributed to an unknown tropical eruption in 1809. Recovery of dacitic tephra from the 1809 horizon in a Yukon ice core (Eclipse) that is chemically distinct from andesitic 1809 tephra found in Antarctic ice cores indicates a second eruption in the Northern Hemisphere at this time. Together with the similar magnitude and timing of the 1809 volcanic signal in the Arctic and Antarctic, this could suggest a large tropical eruption produced the sulfate and Antarctic tephra and a minor Northern Hemisphere eruption produced the Eclipse tephra. Nonetheless, the possibility that there were coincidental eruptions of similar magnitude in both hemispheres, rather than a single tropical eruption, should not be discounted. Correctly attributing the source of the 1809 volcanic signal has important implications for modeling the magnitude and latitudinal distribution of volcanic radiative forcing

Ice core paleovolcanic records from the St. Elias Mountains, Yukon, Canada

We previously reported a record of regionally significant volcanic eruptions in the North Pacific using an ice core from Eclipse Icefield (St. Elias Mountains, Yukon, Canada). The acquisition of two new ice cores from Eclipse Icefield, along with the previously available Eclipse Icefield and Mount Logan Northwest Col ice cores, allows us to extend our record of North Pacific volcanism to 550 years before present using a suite of four ice cores spanning an elevation range of 3–5 km. Comparison of volcanic sulfate flux records demonstrates that the results are highly reproducible, especially for the largest eruptions such as Katmai (A.D. 1912). Correlation of volcanic sulfate signals with historically documented eruptions indicates that at least one-third of the eruptions recorded in St. Elias ice cores are from Alaskan and Kamchatkan volcanoes. Although there are several moderately large (volcanic explosivity index (VEI) ≥ 4) eruptions recorded in only one core from Eclipse Icefield, the use of multiple cores provides signals in at least one core from all known VEI ≥ 4 eruptions in Alaska and Kamchatka since A.D. 1829. Tephrochronological evidence from the Eclipse ice cores documents eruptions in Alaska (Westdahl, Redoubt, Trident, and Katmai), Kamchatka (Avachinsky, Kliuchevoskoi, and Ksudach), and Iceland (Hekla). Several unidentified tephra-bearing horizons, with available geochemical evidence suggesting Alaskan and Kamchatkan sources, were also found. We present a reconstruction of annual volcanic sulfate loading for the North Pacific troposphere based on our ice core data, and we provide a detailed assessment of the atmospheric and climatic effects of the Katmai eruption

Flow dynamics of an accumulation basin: a case study of upper Kahiltna Glacier, Mount McKinley, Alaska

We interpreted flow dynamics of the Kahiltna Pass Basin accumulation zone on Mount McKinley, Alaska, USA, using 40, 100 and 900 MHz ground-penetrating radar profiles and GPS surface velocity measurements. We found dipping, englacial surface-conformable strata that experienced vertical thickening as the glacier flowed westward from a steep, higher-velocity (60 m a–1) region into flat terrain associated with a 908 bend in the glacier and lower velocities (15 m a–1) to the south. Stratigraphy near the western side of the basin was surface-conformable to 170 m depth and thinned as flow diverged southward, down-glacier. We found complex strata beneath the conformable stratigraphy and interpret these features as buried crevasses, avalanche debris and deformed ice caused by up-glacier events. We also suggest that basin dimensions, bed topography and the sharp bend each cause flow extension and compression, significantly contributing to conformable and complex strata thickness variations. Our findings show that surface-conformable stratigraphy continuous with depth and consistent strata thicknesses cannot be assumed in accumulation basins, because local and upglacier terrain and flow dynamics can cause structural complexities to occur under and within surfaceconformable layers

High level language-based robotic control system

This invention is a robot control system based on a high level language implementing a spatial operator algebra. There are two high level languages included within the system. At the highest level, applications programs can be written in a robot-oriented applications language including broad operators such as MOVE and GRASP. The robot-oriented applications language statements are translated into statements in the spatial operator algebra language. Programming can also take place using the spatial operator algebra language. The statements in the spatial operator algebra language from either source are then translated into machine language statements for execution by a digital control computer. The system also includes the capability of executing the control code sequences in a simulation mode before actual execution to assure proper action at execution time. The robot's environment is checked as part of the process and dynamic reconfiguration is also possible. The languages and system allow the programming and control of multiple arms and the use of inward/outward spatial recursions in which every computational step can be related to a transformation from one point in the mechanical robot to another point to name two major advantages

Melt regimes, internal stratigraphy, and flow dynamics of three glaciers in the Alaska Range

We used ground-penetrating radar (GPR), GPS and glaciochemistry to evaluate melt regimes and ice depths, important variables for mass-balance and ice-volume studies, of Upper Yentna Glacier, Upper Kahiltna Glacier and the Mount Hunter ice divide, Alaska. We show the wet, percolation and dry snow zones located below 2700 m a.s.l., at 2700 to 3900 m a.s.l. and above 3900 m a.s.l., respectively. We successfully imaged glacier ice depths upwards of 480 m using 40–100 MHz GPR frequencies. This depth is nearly double previous depth measurements reached using mid-frequency GPR systems on temperate glaciers. Few Holocene-length climate records are available in Alaska, hence we also assess stratigraphy and flow dynamics at each study site as a potential ice-core location. Ice layers in shallow firn cores and attenuated glaciochemical signals or lacking strata in GPR profiles collected on Upper Yentna Glacier suggest that regions below 2800 m a.s.l. are inappropriate for paleoclimate studies because of chemical diffusion, through melt. Flow complexities on Kahiltna Glacier preclude ice-core climate studies. Minimal signs of melt or deformation, and depth–age model estimates suggesting 4815 years of ice on the Mount Hunter ice divide (3912 m a.s.l.) make it a suitable Holocene-age ice-core location