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Identification of motion parameters of a rigid body from its orthogonal and perspective projections

An estimate is made of the motion parameters, namely, linear and angular velocities, of a rigid body rotating and translating in three-space. The authors assume that the velocities are constant and that the motion is not completely observable. They consider two separate cases of partial observations corresponding to the orthogonal and the perspective projections, respectively. If (x, y, z) is the Cartesian coordinate of the three-space, the authors assume in the first case that the projection of the motion on the x-y plane is observed. If (r, theta, phi) is the polar coordinates of the three-space, they assume in the second case that the parameter vector (theta, phi) is observed. The use of both of these cases to estimate the motion parameters is discussed.

Ganguly, S.

Back to the Future: Consistency-Based Trajectory Tracking

Given a model of a physical process and a sequence of commands and observations received over time, the task of an autonomous controller is to determine the likely states of the process and the actions required to move the process to a desired configuration. We introduce a representation and algorithms for incrementally generating approximate belief states for a restricted but relevant class of partially observable Markov decision processes with very large state spaces. The algorithm presented incrementally generates, rather than revises, an approximate belief state at any point by abstracting and summarizing segments of the likely trajectories of the process. This enables applications to efficiently maintain a partial belief state when it remains consistent with observations and revisit past assumptions about the process' evolution when the belief state is ruled out. The system presented has been implemented and results on examples from the domain of spacecraft control are presented.

Kurien, James

Observability of discretized partial differential equations

It is shown that complete observability of the discrete model used to assimilate data from a linear partial differential equation (PDE) system is necessary and sufficient for asymptotic stability of the data assimilation process. The observability theory for discrete systems is reviewed and applied to obtain simple observability tests for discretized constant-coefficient PDEs. Examples are used to show how numerical dispersion can result in discrete dynamics with multiple eigenvalues, thereby detracting from observability.

Cohn, Stephen E.

Clustering with Missing Values: No Imputation Required

Clustering algorithms can identify groups in large data sets, such as star catalogs and hyperspectral images. In general, clustering methods cannot analyze items that have missing data values. Common solutions either fill in the missing values (imputation) or ignore the missing data (marginalization). Imputed values are treated as just as reliable as the truly observed data, but they are only as good as the assumptions used to create them. In contrast, we present a method for encoding partially observed features as a set of supplemental soft constraints and introduce the KSC algorithm, which incorporates constraints into the clustering process. In experiments on artificial data and data from the Sloan Digital Sky Survey, we show that soft constraints are an effective way to enable clustering with missing values.

constraints

Galaxy and cluster redshift observations in the Sextans-Leo region

Redshift observations of 30 clusters in the direction of the Sextans-Leo supercluster candidate are reported. The observations are part of a program which involves mapping the universe's large-scale structure, and include North Galactic Cap Abell clusters, Abell clusters that have only been partially observed, and unmeasured poor Zwicky clusters. Three large superclusters are identified in the region which surround an apparent void that is open on one side towards the galaxy void in Bootes. The minimum dimensions of the void are given, and one of the superclusters is identified based on it resemblance to Coma/A1367. The emptiness of the Bootes void and the void of Bahcall and Soneira (1982) are redefined by the positions determined for five clusters observed in other portions of the northern cap. Additionally, some galaxies appear to be within the bounds of the Sextans-Leo void.

Batuski, David J.

Solar Wind Electron Interaction with the Dayside Lunar Surface and Crustal Magnetic Fields: Evidence for Precursor Effects

Electron distributions measured by Lunar Prospector above the dayside lunar surface in the solar wind often have an energy dependent loss cone, inconsistent with adiabatic magnetic reflection. Energy dependent reflection suggests the presence of downward parallel electric fields below the spacecraft, possibly indicating the presence of a standing electrostatic structure. Many electron distributions contain apparent low energy (<100 eV) upwardgoing conics (58% of the time) and beams (12% of the time), primarily in regions with non-zero crustal magnetic fields, implying the presence of parallel electric fields and/or wave-particle interactions below the spacecraft. Some, but not all, of the observed energy dependence comes from the energy gained during reflection from a moving obstacle; correctly characterizing electron reflection requires the use of the proper reference frame. Nonadiabatic reflection may also play a role, but cannot fully explain observations. In cases with upward-going beams, we observe partial isotropization of incoming solar wind electrons, possibly indicating streaming and/or whistler instabilities. The Moon may therefore influence solar wind plasma well upstream from its surface. Magnetic anomaly interactions and/or non-monotonic near surface potentials provide the most likely candidates to produce the observed precursor effects, which may help ensure quasi-neutrality upstream from the Moon.

Solar

Kinematics of NGC 4826: A sleeping beauty galaxy, not an evil eye

A recent high resolution H I study of the Sab galaxy NGC 4826 (1992) reveals that the sense of rotation of the neutral gas reverses from the inner to the outer disk. The present paper reports on optical spectra at high velocity resolution in four position angles in NGC 4826, which cover the region of the gas reversal and which reveal a high degree of complexity. In the inner disk, which includes the prominent dusty lane, the stars and gas rotate in concert, and the spiral arms trail (for the adopted geometry). Arcs of ionized gas are observed partially encircling the nucleus; expansion velocities reach 400 km/s. At distances just beyond the prominent dust lane, the ionized gas exhibits a rapid, orderly velocity fall and within 500 parsecs it has reversed from 180 km/s prograde to 200 km/s retrograde; it also has a component radial toward the nucleus of over 100 km/s. The stars, however, continue their prograde rotation. Beyond this transition zone, the neutral gas continues its retrograde rotation, stellar velocities are prograde, but the sense of the almost circular arms is not established. Because of its kinematical complexity as well as its proximity, NGC 4826 is an excellent early-type galaxy in which to observe the long term effects of gas acquistion or a galaxy merger on a disk galaxy.

Rubin, Vera C.

An Adaptive Technique for a Redundant-Sensor Navigation System

An on-line adaptive technique is developed to provide a self-contained redundant-sensor navigation system with a capability to utilize its full potentiality in reliability and performance. The gyro navigation system is modeled as a Gauss-Markov process, with degradation modes defined as changes in characteristics specified by parameters associated with the model. The adaptive system is formulated as a multistage stochastic process: (1) a detection system, (2) an identification system and (3) a compensation system. It is shown that the sufficient statistics for the partially observable process in the detection and identification system is the posterior measure of the state of degradation, conditioned on the measurement history.

Chien, T. T.

Temperature and velocity profiles in sooting free boundary layer flames

Temperature and velocity profiles are presented for cyclohexane, n-heptane, and iso-octane free, laminar, boundary layer, sooting, diffusion flames. Temperatures are measured with 3 mil Pt/Pt-13 percent Rh thermocouples. Corrected gas temperatures are derived by performing an energy balance of convection to and radiation from the thermocouple bead incorporating the variation of air conductivity and platinum emissivity with temperature. Velocities are measured using laser doppler velocimetry techniques. Profiles are compared with previously reported analytic temperature and velocity fields. Comparison of theoretical and experimental temperature profiles suggests improvement in the analytical treatment is needed, which accounts more accurately for the local soot radiation. The velocity profiles are in good agreement, with the departure of the theory from observation partially due to the small fluctuations inherent in these free flows.

Ang, J. A.

Qualitative Discovery in Medical Databases

Implication rules have been used in uncertainty reasoning systems to confirm and draw hypotheses or conclusions. However a major bottleneck in developing such systems lies in the elicitation of these rules. This paper empirically examines the performance of evidential inferencing with implication networks generated using a rule induction tool called KAT. KAT utilizes an algorithm for the statistical analysis of empirical case data, and hence reduces the knowledge engineering efforts and biases in subjective implication certainty assignment. The paper describes several experiments in which real-world diagnostic problems were investigated; namely, medical diagnostics. In particular, it attempts to show that: (1) with a limited number of case samples, KAT is capable of inducing implication networks useful for making evidential inferences based on partial observations, and (2) observation driven by a network entropy optimization mechanism is effective in reducing the uncertainty of predicted events.

Maluf, David A.

Markov Tracking for Agent Coordination

Partially observable Markov decision processes (POMDPs) axe an attractive representation for representing agent behavior, since they capture uncertainty in both the agent's state and its actions. However, finding an optimal policy for POMDPs in general is computationally difficult. In this paper we present Markov Tracking, a restricted problem of coordinating actions with an agent or process represented as a POMDP Because the actions coordinate with the agent rather than influence its behavior, the optimal solution to this problem can be computed locally and quickly. We also demonstrate the use of the technique on sequential POMDPs, which can be used to model a behavior that follows a linear, acyclic trajectory through a series of states. By imposing a "windowing" restriction that restricts the number of possible alternatives considered at any moment to a fixed size, a coordinating action can be calculated in constant time, making this amenable to coordination with complex agents.

Washington, Richard

Making the Impossible Possible: Strategies for Fast POMDP Monitoring

Systems modeled as partially observable Markov decision processes (POMDPs) can be tracked quickly with three restrictions: all actions are grouped together, the out-degree of each system state is bounded by a constant, and the number of non-zero elements in the belief state is bounded by a (different) constant. With these restrictions, the tracking algorithm operates in constant time and linear space. The first restriction assumes that the action itself is unobservable. The second restriction defines a subclass of POMDPs that covers however a wide range of problems. The third restriction is an approximation technique that can lead to a potentially vexing problem: an observation may be received that has probability according to the restricted belief state. This problem of impossibility will cause the belief state to collapse. In this paper we discuss the tradeoffs between the constant bound on the belief state and the quality of the solution. We concentrate on strategies for overcoming the impossibility problem and demonstrate initial experimental results that indicate promising directions.

Washington, Richard

Optimal Limited Contingency Planning

For a given problem, the optimal Markov policy over a finite horizon is a conditional plan containing a potentially large number of branches. However, there are applications where it is desirable to strictly limit the number of decision points and branches in a plan. This raises the question of how one goes about finding optimal plans containing only a limited number of branches. In this paper, we present an any-time algorithm for optimal k-contingency planning. It is the first optimal algorithm for limited contingency planning that is not an explicit enumeration of possible contingent plans. By modelling the problem as a partially observable Markov decision process, it implements the Bellman optimality principle and prunes the solution space. We present experimental results of applying this algorithm to some simple test cases.

Meuleau, Nicolas

Hybrid Discrete-Continuous Markov Decision Processes

This paper proposes a Markov decision process (MDP) model that features both discrete and continuous state variables. We extend previous work by Boyan and Littman on the mono-dimensional time-dependent MDP to multiple dimensions. We present the principle of lazy discretization, and piecewise constant and linear approximations of the model. Having to deal with several continuous dimensions raises several new problems that require new solutions. In the (piecewise) linear case, we use techniques from partially- observable MDPs (POMDPS) to represent value functions as sets of linear functions attached to different partitions of the state space.

Feng, Zhengzhu

Learning Grasp Strategies Composed of Contact Relative Motions

Of central importance to grasp synthesis algorithms are the assumptions made about the object to be grasped and the sensory information that is available. Many approaches avoid the issue of sensing entirely by assuming that complete information is available. In contrast, this paper proposes an approach to grasp synthesis expressed in terms of units of control that simultaneously change the contact configuration and sense information about the object and the relative manipulator-object pose. These units of control, known as contact relative motions (CRMs), allow the grasp synthesis problem to be recast as an optimal control problem where the goal is to find a strategy for executing CRMs that leads to a grasp in the shortest number of steps. An experiment is described that uses Robonaut, the NASA-JSC space humanoid, to show that CRMs are a viable means of synthesizing grasps. However, because of the limited amount of information that a single CRM can sense, the optimal control problem may be partially observable. This paper proposes expressing the problem as a k-order Markov Decision Process (MDP) and solving it using Reinforcement Learning. This approach is tested in a simulation of a two-contact manipulator that learns to grasp an object. Grasp strategies learned in simulation are tested on the physical Robonaut platform and found to lead to grasp configurations consistently.

Platt, Robert, Jr.

Eta Car: The Good, the Bad and the Ugly of Nebular and Stellar Confusion

Observations in the far-UV provide a unique opportunity to investigate the very massive star Eta Car and its hot binary companion, Eta Car B. Eta Car was observed with FUSE over a large portion of the 5.54 year spectroscopic period before and after the 2003.5 minimum. The observed spectrum is defined by strong stellar wind signatures, primarily from Eta Car A, complicated by the strong absorptions of the ejecta surrounding Eta Car plus interstellar absorption. The Homunculus and Little Homunculus are massive bipolar ejecta historically associable with LBV outbursts in the 1840s and the 1890s and are linked to absorptions at -513 and -146 km/s, respectively. The FUSE spectra are confused by the extended nebulosity and thermal drifting of the FUSE co-pointed instruments. Interpretation is further complicated by two B-stars sufficiently close to h Car to be included most of the time in the large FUSE aperture. Followup observations partially succeeded in obtaining spectra of at least one of these B-stars through the smaller apertures, allowing potential separation of the B-star contributions and h Car. A complete analysis of all available spectra is currently underway. Our ultimate goals are to directly detect the hot secondary star if possible with FUSE and to identify the absorption contributions to the overall spectrum especially of the stellar members and the massive ejecta.

Gull, T.R.

Comparison of Statistical Estimation Techniques for Mars Entry, Descent, and Landing Reconstruction from MEDLI-like Data Sources

Flight data from an entry, descent, and landing (EDL) sequence can be used to reconstruct the vehicle's trajectory, aerodynamic coefficients and the atmospheric profile experienced by the vehicle. Past Mars missions have contained instruments that do not provide direct measurement of the freestream atmospheric conditions. Thus, the uncertainties in the atmospheric reconstruction and the aerodynamic database knowledge could not be separated. The upcoming Mars Science Laboratory (MSL) will take measurements of the pressure distribution on the aeroshell forebody during entry and will allow freestream atmospheric conditions to be partially observable. This data provides a mean to separate atmospheric and aerodynamic uncertainties and is part of the MSL EDL Instrumentation (MEDLI) project. Methods to estimate the flight performance statistically using on-board measurements are demonstrated here through the use of simulated Mars data. Different statistical estimators are used to demonstrate which estimator best quantifies the uncertainties in the flight parameters. The techniques demonstrated herein are planned for application to the MSL flight dataset after the spacecraft lands on Mars in August 2012.

Dutta, Soumyo