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The linearity of the equations of motion of dynamical systems such as spacecraft or manipulators when controlled by acceleration commands is exploited in generating exact fast maneuvers. A simulated robot example thereof is examined, with advantages and limitations of the proposed design approach discussed in its context.
The relative position and relative proper motion of the radio sources 3C 345 and NRAO 512 are estimated from four sets of VLBI observations spread out over the period from October 1971 to May 1974. The use of phase-connection techniques yields the separation, in 1950.0 coordinates, of the centers of brightness of the compact components of the two sources. An upper bound of 0.0005 arcsec/yr is placed on the relative proper motion (70% estimated confidence limits). Bounds that can be placed on the distances to the two sources are considered, prospects for improvement in the determination of relative position and proper motion of these sources are discussed, and other possible applications of the basic technique are described.
A kinematic model for southern California, based on late-Quaternary slip rates and orientations of major faults in the region, is proposed. Internally consistent motions are determined assuming that these faults bound rigid blocks. Relative to North America, most of California west of the San Andreas fault is moving parallel to the San Andreas fault through the Transverse Ranges and not parallel to the motion of the Pacific plate. The velocities of the blocks are calculated along several paths in southern California that begin in the Mojave Desert and end off the California coast. A path that crosses the western Transverse Ranges accumulates the accepted relative North America-Pacific plate velocity, whereas paths to the north and south result in a significant missing component of motion, implying the existence of a zone of active deformation in southern California.
The general relativistic motion of a particle in a bounded orbit around a central mass M is derived with the aid of the Schwarzschild field of M. A quadrature gives the central angle as a quasi-periodic function of an effective true anomaly. The mean rate of advance of the pericenter is investigated. Classical and general relativistic orbiters with the same initial conditions are compared, taking into account the treatment of the general relativistic effect by means of a differential correction. General relativistic variations are discussed, giving attention to the variation of the eccentric anomaly and the variation of the central angle.
The computational problem of inverse kinematics and inverse dynamics of robot manipulators by taking advantage of parallelism and pipelining architectures is discussed. For the computation of inverse kinematic position solution, a maximum pipelined CORDIC architecture has been designed based on a functional decomposition of the closed-form joint equations. For the inverse dynamics computation, an efficient p-fold parallel algorithm to overcome the recurrence problem of the Newton-Euler equations of motion to achieve the time lower bound of O(log sub 2 n) has also been developed.
Robotics research has begun to address the modeling and implementation of a wide variety of unstructured tasks. Examples include automated navigation, platform servicing, custom fabrication and repair, deployment and recovery, and science exploration. Such tasks are poorly described at onset; the workspace layout is partially unfamiliar, and the task control sequence is only qualitatively characterized. The robot must model the workspace, plan detailed physical actions from qualitative goals, and adapt its instantaneous control regimes to unpredicted events. Developing robust representations and computational approaches for these sensing, planning, and control functions is a major challenge. The underlying domain constraints are very general, and seem to offer little guidance for well-bounded approximation of object shape and motion, manipulation postures and trajectories, and the like. This generalized modeling problem is discussed, with an emphasis on the role of sensing. It is also discussed that unstructured tasks often have, in fact, a high degree of underlying physical symmetry, and such implicit knowledge should be drawn on to model task performance strategies in a methodological fashion. A group-theoretic decomposition of the workspace organization, task goals, and their admissible interactions are proposed. This group-mechanical approach to task representation helps to clarify the functional interplay of perception and control, in essence, describing what perception is specifically for, versus how it is generically modeled. One also gains insight how perception might logically evolve in response to needs of more complex motor skills. It is discussed why, of the many solutions that are often mathematically admissible to a given sensory motor-coordination problem, one may be preferred over others.
The horizontal air motions accompanying the development of a planetary wave critical layer are presently investigated on the sphere, in terms of wave amplitude, the characteristics of the zonal flow, and dissipation. While attention is given to adiabatic motions, which should furnish an upper bound on the redistribution of conserved quantities by eddy stirring, nonconservative processes may be important in determining how large a role eddy stirring actually plays in the redistribution of atmospheric constituents. Nonconservative processes may also influence tracer distributions by directly affecting dynamics.
For space based robots in which the base is free to move, motion planning and control is complicated by uncertainties in the inertial properties of the manipulator and its load. A new adaptive control method is presented for space based robots which achieves globally stable trajectory tracking in the presence of uncertainties in the inertial parameters of the system. A partition is made of the fifteen degree of freedom system dynamics into two parts: a nine degree of freedom invertible portion and a six degree of freedom noninvertible portion. The controller is then designed to achieve trajectory tracking of the invertible portion of the system. This portion consist of the manipulator joint positions and the orientation of the base. The motion of the noninvertible portion is bounded, but unpredictable. This portion consist of the position of the robot's base and the position of the reaction wheel.
A control method is presented that achieves globally stable trajectory tracking in the presence of uncertainties in the inertial parameters of the system. The 15-DOF system dynamics are divided into two components: a 9-DOF invertible portion and 6-DOF noninvertible portion. A controller is then designed to achieve trajectory tracking of the invertible portion of the system, which consists of the manipulator-joint positions and the orientation of the base. The motion of the noninvertible portion is bounded but otherwise unspecified. This portion of the system consists of the position of the robot's base and the position of the reaction wheels. A simulation is presented to demonstrate the effectiveness of the controller. A quadratic polynomial is used to generate the desired trajectory to illustrate the trajectory-tracking capability of the controller.
The Goldstone Solar System RADAR (GSSR) group at JPL produced a Digital Elevation Model (DEM) of the lunar south pole using data obtained in 2006. This model has 40-meter horizontal resolution and about 5-meter relative vertical accuracy. This paper uses that Digital Elevation Model to compute average solar illumination and Earth visibility near the lunar south pole. This data quantifies solar power and Earth communications resources at proposed lunar base locations. The elevation data were converted into local terrain horizon masks, then converted into selenographic latitude and longitude coordinates. The horizon masks were compared to latitude, longitude regions bounding the maximum Sun and Earth motions relative to the moon. Proposed lunar south pole base sites were examined in detail, with the best site showing multi-year averages of solar power availability of 92% and Direct-To-Earth (DTE) communication availability of about 50%. Results are compared with a theoretical model, and with actual sun and Earth visibility averaged over the years 2009 to 2028. Results for the lunar North pole were computed using the GSSR DEM of the lunar North pole produced in 1997. The paper also explores using a heliostat to reduce the photovoltaic power system mass and complexity.
In this paper the equations of motion of a formation consisting of n spacecraft in Earth orbit are derived via Lagrange's equations. The equations of motion of the formation are developed with respect to both (1) a bound Keplerian reference orbit, and (2) a specific spacecraft in the formation. The major orbital perturbations acting on a formation in low Earth orbit are also included in the analysis. In contrast to the traditional approach based on the balance of linear momentum, the use of Lagrange's equations leads to a high-level matrix derivation of the formation equations of motion. The matrix form of the nonlinear motion equations is then linearized about a bound Keplerian reference orbit. Next, it is demonstrated that under the assumption of a circular reference orbit, the linearized equations of motion reduce to the well-known Hill-Clohessy-Wiltshire equations. The resulting linear and nonlinear dynamic equations lead to maximal physical insight into the structure of formation dynamics, and are ideally suited for use in the design and validation of formation guidance and control laws.
Coronal magnetic fields are twisted up by motion of their footpoints in the photosphere. When the twist exceeds a critical amount, kink-ballooning instabilities occur. These instabilities are studied numerically, in long, thin, axially bounded magnetic fields. Nonlinearly, the three-dimensional kinking motion compresses magnetic flux, forming a current sheet. Magnetic energy can be dissipated at a rate orders of magnitude greater than without the current sheets. The energy of footpoint motion can then go into coronal heating, via Ohmic dissipation in the current sheets.
The tip clearance flows of transonic compressor rotors are important because they have a significant impact on rotor and stage performance. While numerical simulations of these flows are quite sophisticated. they are seldom verified through rigorous comparisons of numerical and measured data because these kinds of measurements are rare in the detail necessary to be useful in high-speed machines. In this paper we compare measured tip clearance flow details (e.g. trajectory and radial extent) with corresponding data obtained from a numerical simulation. Recommendations for achieving accurate numerical simulation of tip clearance flows are presented based on this comparison. Laser Doppler Velocimeter (LDV) measurements acquired in a transonic compressor rotor, NASA Rotor 35, are used. The tip clearance flow field of this transonic rotor was simulated using a Navier-Stokes turbomachinery solver that incorporates an advanced k-epsilon turbulence model derived for flows that are not in local equilibrium. Comparison between measured and simulated results indicates that simulation accuracy is primarily dependent upon the ability of the numerical code to resolve important details of a wall-bounded shear layer formed by the relative motion between the over-tip leakage flow and the shroud wall. A simple method is presented for determining the strength of this shear layer.
The tip clearance flows of transonic compressor rotors have a significant impact on rotor and stage performance. Although numerical simulations of these flows are quite sophisticated, they are seldom verified through rigorous comparisons of numerical and measured data because, in high-speed machines, measurements acquired in sufficient detail to be useful are rare. Researchers at the NASA Glenn Research Center at Lewis Field compared measured tip clearance flow details (e.g., trajectory and radial extent) of the NASA Rotor 35 with results obtained from a numerical simulation. Previous investigations had focused on capturing the detailed development of the jetlike flow leaking through the clearance gap between the rotating blade tip and the stationary compressor shroud. However, we discovered that the simulation accuracy depends primarily on capturing the detailed development of a wall-bounded shear layer formed by the relative motion between the leakage jet and the shroud.
We use a global hybrid code kinetic model to demonstrate how kinetic processes at the bow shock and within the foreshock can dramatically modify the solar wind just before its interaction with the magnetosphere. During periods of steady radial interplanetary magnetic field (IMF) orientation, the foreshock fills with a diffuse population of suprathermal ions. The ions generate cavities marked by enhanced temperatures, depressed densities, and diminished magnetic field strengths that convect antisunward into the bow shock with the solar wind flow. Tangential discontinuities marked by inward-pointing electric fields and normals transverse to the Sun-Earth line generate hot flow anomalies marked by hot tenuous plasmas bounded by outward propagating shocks. When the motional electric field in the magnetosheath points inward towards the Earth, a solitary bow shock appears. For typical IMF orientations, the solitary shocks should appear at poorly sampled high latitudes, but for strongly northward or southward IMF orientations the solitary shocks should appear on the flanks of the magnetosphere. Although quasi-perpendicular, solitary shocks should be marked by turbulent magnetosheath flows, often directed towards the Sun-Earth line, and abrupt spike-like enhancements in the density and magnetic field strength at the shock. Finally,we show how flux transfer events generated between parallel subsolar reconnection lines are destroyed upon encountering the magnetopause at latitudes above the cusp.
This project extends the study of the structure of wall-bounded flows using the topological properties of eddying motions as developed by Chong et al. (1990), Soria et al. (1992, 1994), and as recently extended by Blackburn et al. (1996) and Chacin et al. (1996). In these works, regions of flow which are focal in nature are identified by being enclosed by an isosurface of a positive small value of the discriminant of the velocity gradient tensor. These regions resemble the attached vortex loops suggested first by Theodorsen (1955). Such loops are incorporated in the attached eddy model versions of Perry & Chong (1982), Perry et al. (1986), and Perry & Marusic (1995), which are extensions of a model first formulated by Townsend (1976). The DNS data of wall bounded flows studied here are from the zero pressure gradient flow of Spalart (1988) and the boundary layer with separation and reattachment of Na & Moin (1996). The flow structures are examined from the viewpoint of the attached eddy hypothesis.
Analytic error bounds are presented for the solutions of approximate models for self-excited near-symmetric rigid bodies. The error bounds are developed for analytic solutions to Euler's equations of motion. The results are applied to obtain a simplified analytic solution for Eulerian rates and angles. The results of a sample application of the range and error bound expressions for the case of the Galileo spacecraft experiencing transverse torques demonstrate the use of the bounds in analyses of rigid body spin change maneuvers.
Coherent structures in turbulent shear flows were studied extensively by several techniques, including the VITA technique which selects rapidly accelerating or decelerating regions in the flow. The evolution of a localized disturbance in a laminar boundary layer shows strong similarity to the evolution of coherent structures in a turbulent-wall bounded flow. Starting from a liftup-sweep motion, a strong shear layer develops which shares many of the features seen in conditionally-sampled turbulent velocity fields. The structure of the shear layer, Reynolds stress distribution, and wall pressure footprint are qualitatively the same, indicating that the dynamics responsible for the structure's evolution are simple mechanisms dependent only on the presence of a high mean shear and a wall and independent of the effects of local random fluctuations and outer flow effects. As the disturbance progressed, the development of streak-like-high- and low-speed regions associated with the three-dimensionality.