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At least 469 records · Page 26

Application of Pressure-Sensitive Paint to Rotorcraft

In this presentation, a plan to develop methods for applying pressure-sensitive paint to rotorcraft will be described. These methods are needed because flows over rotor blades are typically very complex and poorly understood and because conventional methods for measuring unsteady pressures on rotor blades (using unsteady pressure transducers provide grossly inadequate spatial resolution. Since PSP is a surface, rather than a point, measurement technique, it has the potential to significantly increase the spatial resolution )f pressure measurements on rotor blades. PSP techniques currently in use at Ames were developed for measuring steady pressures on rigid, complex airplane configurations in large, production wind tunnels. Applying PSP to rotorcraft requires a significant departure from these techniques. First and most importantly new, fast-responding and self-referencing pressure paints are required. The paints must be fast (98% response in 1-5 msec) to resolve flow unsteadiness; they must be self-referencing (or "binary") to account for changes in incident light intensity due to deflection of flexible rotors. Self-referencing paints have been used at Ames for some time; however, these paints have response times that are far too long for unsteady applications. Flash illumination is required to resolve flow unsteadiness and to minimize image blurring due to relative motion between the model and the camera. Current practice at Ames is to use continuous illumination Finally, "in situ" paint calibration versus measurements by pressure transducers, which is current Ames practice, is not practical because of the difficulty and expense of installing transducers in rotor blades. Instead, the paint must be calibrated "a priori" in a calibration chamber. A sequence of five experiments that systematically isolates and addresses the problems involved in making PSP measurements on rotor blades has been planned. These are: (1) measurements on a rigid rotor in hover; (2) measurements on a flexible rotor in hover; measurements of paint response time in a calibration apparatus; (4) measurements on a rigid, two-dimensional oscillating airfoil; and (5) measurements on a flexible rotor in forward flight. Experiments were recently conducted at Ames where PSP measurements were made on a rigid oscillating airfoil (experiment type 4) and on a flexible rotor in hover (experiment type 2). Preliminary results from these experiments will be discussed.

Schairer, Edward T.↗

Contributions of orbital mechanics to conducting experiments in space

Orbital mechanics as a discipline is principally concerned with solving the set of equations for analyzing the motion of a satellite under various conditions. This activity on the surface may not seem crucial to conducting experiments in space, but it provides insights into the way in which forces may influence these experiments. More directly, for experiments concerned with external targets, it provides predictions of the satellites's position and velcoity verus time, enabling extensive preflight planning and resulting in optimum use of on-orbit time.

Mullins, L. D.↗

Minimizing attitude control fuel in space manipulator systems

Techniques are presented for finding space manipulator motions which result in reduced spacecraft dynamic disturbances. Although a spacecraft's attitude control reaction jets can compensate for these disturbances, reaction jet fuel is a limited resource and excessive disturbances would limit the life of a space manipulator. A graphical tool called the Enhanced Disturbance Map (EDM) is presented and is demonstrated as an aid in developing planning and control algorithms to solve this complex problem.

Dubowsky, Steven↗

Motion of Drops on Surfaces with Wettability Gradients

A liquid drop present on a solid surface can move because of a gradient in wettability along the surface, as manifested by a gradient in the contact angle. The contact angle at a given point on the contact line between a solid and a liquid in a gaseous medium is the angle between the tangent planes to the liquid and the solid surfaces at that point and is measured within the liquid side, by convention. The motion of the drop occurs in the direction of increasing wettability. The cause of the motion is the net force exerted on the drop by the solid surface because of the variation of the contact angle around the periphery. This force causes acceleration of an initially stationary drop, and leads to its motion in the direction of decreasing contact angle. The nature of the motion is determined by the balance between the motivating force and the resisting hydrodynamic force from the solid surface and the surrounding gaseous medium. A wettability gradient can be chemically induced as shown by Chaudhury and Whitesides who provided unambiguous experimental evidence that drops can move in such gradients. The phenomenon can be important in heat transfer applications in low gravity, such as when condensation occurs on a surface. Daniel et al have demonstrated that the velocity of a drop on a surface due to a wettability gradient in the presence of condensation can be more than two orders of magnitude larger than that observed in the absence of condensation. In the present research program, we have begun to study the motion of a drop in a wettability gradient systematically using a model system. Our initial efforts will be restricted to a system in which no condensation occurs. The experiments are performed as follows. First, a rectangular strip of approximate dimensions 10 x 20 mm is cut out of a silicon wafer. The strip is cleaned thoroughly and its surface is exposed to the vapor from an alkylchlorosilane for a period lasting between one and two minutes inside a desiccator. This is done using an approximate line source of the vapor in the form of a string soaked in the alkylchlorosilane. Ordinarily, many fluids, including water, wet the surface of silicon quite well. This means that the contact angle is small. But the silanized surface resists wetting, with contact angles that are as large as 100 degs. Therefore, a gradient of wettability is formed on the silicon surface. The region near the string is highly hydrophobic, and the contact angle decreases gradually toward a small value at the hydrophilic end away from this region. The change in wettability occurs over a distance of several mm. The strip is placed on a platform within a Plexiglas cell. Drops of a suitable liquid are introduced on top of the strip near the hydrophobic end. An optical system attached to a video camera is trained on the drop so that images of the moving drop can be captured on videotape for subsequent analysis. We have performed preliminary experiments with water as well as ethylene glycol drops. Results from these experiments will be presented in the poster. Future plans include the refinement of the experimental system so as to permit images to be recorded from the side as well as the top, and the conduct of a systematic study in which the drop size is varied over a good range. Experiments will be conducted with different fluids so as to obtain the largest possible range of suitably defined Reynolds and Capillary numbers. Also, an effort will be initiated on theoretical modeling of this motion. The challenges in the development of the theoretical description lie in the proper analysis of the region in the vicinity of the contact line, as well as in the free boundary nature of the problem. It is known that continuum models assuming the no slip condition all the way to the contact line fail by predicting that the stress on the solid surface becomes singular as the contact line is approached. One approach for dealing with this issue has been to relax the no-slip boundary condition using the Navier model. Molecular dynamics simulations of the contact line region show that for a non-polar liquid on a solid surface, the no-slip boundary condition is in fact incorrect near the contact line. Furthermore, the same simulations also show that the usual relationship between stress and the rate of deformation breaks down in the vicinity of the contact line. In developing continuum theoretical models of the system, we shall accommodate this knowledge to the extent possible.

Subramanian, R. Shankar↗

The ILRS: Approaching 20 Years and Planning for the Future

The International Laser Ranging Service (ILRS) was established by the International Association of Geodesy (IAG) in 1998 to support programs in geodesy, geophysics, fundamental constants and lunar research, and to provide the International Earth Rotation Service with data products that are essential to the maintenance and improvement in the International Terrestrial Reference Frame (ITRF), the basis for metric measurements of changes in the Earth and Earth–Moon system. Other scientific products derived from laser ranging include precise geocentric positions and motions of ground stations, satellite orbits, components of Earth’s gravity field and their temporal variations, Earth Orientation Parameters, precise lunar ephemerides and information about the internal structure of the Moon. Laser ranging systems are already measuring the one-way distance to remote optical receivers in space and are performing very accurate time transfer between remote sites in the Earth and in Space. The ILRS works closely with the IAG’s Global Geodetic Observing System. The ILRS develops (1) the standards and specifications necessary for product consistency, and (2) the priorities and tracking strategies required to maximize network efficiency. The service collects, merges, analyzes, archives and distributes satellite and lunar laser ranging data to satisfy a variety of scientific, engineering, and operational needs and encourages the application of new technologies to enhance the quality, quantity, and cost effectiveness of its data products. The ILRS works with (1) new satellite missions in the design and building of retroreflector targets to maximize data quality and quantity, and (2) science programs to optimize scientific data yield. Since its inception, the ILRS has grown to include forty laser ranging stations distributed around the world. The ILRS stations track more than ninety satellites from low Earth orbit (LEO) to the geosynchronous orbit altitude as well as retroreflector arrays on the surface of the Moon. Applications have been expanded to include time transfer, asynchronous ranging for targets at extended ranges, free space quantum telecommunications, and the tracking of space debris. Laser ranging technology is moving to lower energy, higher repetition rates (kHz), single-photon-sensitive detectors, shorter pulse widths, shorter normal point intervals for faster data acquisition, and increased pass interleaving, automated to autonomous operation with remote access, and embedded software for real-time updates and decision making. An example of pass interleaving is presented for the Yarragadee station (see Fig. 4); tracking of LEO satellites is often accommodated during break in LEO and GNSS passes. New satellites arrays provide more compact targets and work continues on the development of lighter less expensive arrays for satellites and the moon. The service now provides operational ITRF products including daily/ weekly station positions and daily resolution Earth orientation products; the flow of weekly combination of satellite orbit files for LAGEOS/Etalon-1 and -2 has recently been established. New products are under testing through a pilot project on systematic error monitoring currently underway. The article will give an overview of activities underway within the service, paths forward presently envisioned, and current issues and challenges.

Laser retroreflectors↗

Filaments in and between galaxy clusters at low and mid-frequency with the SKA

Context. Understanding the magnetised Universe is a major challenge in modern astrophysics, and cosmic magnetism has been acknowledged as one of the key scientific drivers of the most ambitious radio instrument ever planned, the Square Kilometre Array. Aims. With this work, we aim to investigate the potential of the Square Kilometre Array and its precursors and pathfinders in the study of magnetic fields in galaxy clusters and filaments through diffuse synchrotron radio emission. Galaxy clusters and filaments of the cosmic web are indeed unique laboratories in which to investigate turbulent fluid motions and large-scale magnetic fields in action, and much of what is known about magnetic fields in galaxy clusters comes from sensitive radio observations. Methods. Based on cosmological magneto-hydrodynamic simulations, we predict radio properties (total intensity and polarisation) of a pair of galaxy clusters connected by a cosmic-web filament. Results. We use our theoretical expectations to explore the potential of polarimetric observations to study large-scale structure magnetic fields in the frequency ranges 50–350 MHz and 950–1760 MHz. We also present predictions for galaxy cluster polarimetric observations with the Square Kilometre Array precursors and pathfinders, such as the LOw frequency ARray 2.0 and the MeerKAT+ telescope. Conclusions. Our findings point out that polarisation observations are particularly powerful for the study of large-scale magnetic fields, since they are not significantly affected by confusion noise. The unprecedented sensitivity and spatial resolution of the intermediatefrequency radio telescopes make them the favourite instruments for the study of these sources through polarimetric data, potentially allowing us to understand if the energy density of relativistic electrons is in equipartition with the magnetic field or rather coupled with the thermal gas density. Our results show that low-frequency instruments also represent a precious tool to study diffuse synchrotron emission in total intensity and polarisation.

79 ASTRONOMY AND ASTROPHYSICS↗

Model Development and Testing for THEMIS Controlled Mars Mosaics

As part of our work [1] to develop techniques and procedures to create regional and eventually global THEMIS mosaics of Mars, we are developing algorithms and software to photogrammetrically control THEMIS IR line scanner camera images. We have found from comparison of a limited number of images to MOLA digital image models (DIMs) [2] that the a priori geometry information (i.e. SPICE [3]) for THEMIS images generally allows their relative positions to be specified at the several pixel level (e.g. approx.5 to 13 pixels). However a need for controlled solutions to improve this geometry to the sub-pixel level still exists. Only with such solutions can seamless mosaics be obtained and likely distortion from spacecraft motion during image collection removed at such levels. Past experience has shown clearly that such mosaics are in heavy demand by users for operational and scientific use, and that they are needed over large areas or globally (as opposed to being available only on a limited basis via labor intensive custom mapping projects). Uses include spacecraft navigation, landing site planning and mapping, registration of multiple data types and image sets, registration of multispectral images, registration of images with topographic information, recovery of thermal properties, change detection searches, etc.

Archinal, B. A.↗

Tagged Short-Range Correlations for Medium to Heavy Ions at an Electron Ion Collider

Understanding short-range correlations between pairs of nucleons in the nucleus is an important nuclear physics topic that can address longstanding mysteries in nuclear physics such as the behavior of dense nuclear systems and the modification of parton distributions. As a collider and with a large acceptance detector, the Jefferson Lab version of the Electron Ion Collider has unique capabilities that are complementary to previous short-range correlation studies, most notably the ability to more fully reconstruct the final state. Optimization of the collider’s detector to maximally exploit these capabilities called for important extensions of existing simulation tools. For this one year laboratory directed research and development project, we upgraded the benchmark electron-nucleon event generator for lepto-production simulation code Benchmark eA Generator for LEptoproduction (BeAGLE) to be able to handle tagged medium-to-heavy nucleons. This included updating the code to correctly handle Fermi motion of nucleons in the nucleus as well as the large momentum caused by short-range correlations. In addition, we also investigated the possibility of improved kinematic reconstruction methods for electron nucleon collisions and looked at pair-spectator tagging of short-range correlations with the Jefferson Lab electron ion collider design. The project progressed very much as planned.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

The rationale and suggested approaches for research geosynchronous satellite measurements for severe storm and mesoscale investigations

The measurements from current and planned geosynchronous satellites provide quantitative estimates of temperature and moisture profiles, surface temperature, wind, cloud properties, and precipitation. A number of significant observation characteristics remain, they include: (1) temperature and moisture profiles in cloudy areas; (2) high vertical profile resolution; (3) definitive precipitation area mapping and precipitation rate estimates on the convective cloud scale; (4) winds from low level cloud motions at night; (5) the determination of convective cloud structure; and (6) high resolution surface temperature determination. Four major new observing capabilities are proposed to overcome these deficiencies: a microwave sounder/imager, a high resolution visible and infrared imager, a high spectral resolution infrared sounder, and a total ozone mapper. It is suggested that the four sensors are flown together and used to support major mesoscale and short range forecasting field experiments.

Shenk, W. E.↗

Improving Scientific Capabilities in Space in the 21st Century: The NASA New Millennium Program

NASA's New Millennium Program (NMP) has been chartered to identify and validate in space emerging, revolutionary technologies that will enable less costly, more capable future science missions. The program utilizes a unique blend of science guidance and industry partnering to ferret out technology solutions to enable science capabilities in space which are presently technically infeasible, or unaffordable. Those technologies which present an unacceptably high risk to future science missions (whether small PI-led or operational) are bundled into technology validation missions. These missions seek to validate the technologies in a manner consistent with their future uses, thus reducing the associated risk to the first user, and obtaining meaningful science data as well. The Space Readiness Coherent Lidar Experiment (SPARCLE) was approved as the second NMP Earth Observing mission (EO2) in October 1997, and assigned to Marshall Space Flight Center for implementation. Leading up to mission confirmation, NMP sponsored a community workshop in March 1996 to draft Level-1 requirements for a doppler wind lidar mission, as well as other space-based lidar missions (such as DIAL). Subsequently, a study group was formed and met twice to make recommendations on how to perform a comparison of coherent and direct detection wind lidars in space. These recommendations have guided the science validation plan for the SPARCLE mission, and will ensure that future users will be able to confidently assess the risk profile of future doppler wind missions utilizing EO2 technologies. The primary risks to be retired are: (1) Maintenance of optical alignments through launch and operations on orbit, and (2) Successful velocity estimation compensation for the Doppler shift due to the platform motion, and due to the earth's rotation. This includes the need to account for all sources of error associated with pointing control and knowledge. The validation objectives are: (1) Demonstrate measurement of tropospheric winds from space using a scanning coherent Doppler lidar technique that scales to meet future research (e.g. ESSP) and operational (e.g. NPOESS) mission requirements. Specifically, produce and validate LOS wind data with single shot accuracy of 1-2 m/s in regions of high signal-to-noise ratio (SNR), and low atmospheric wind turbulence and wind shear, (2) Collect the atmospheric and instrument performance data in various scanning modes necessary to validate and improve instrument performance models that will enable the definition of future missions with greater confidence. Such data include aerosol backscatter data over much of the globe, and high SNR data such as that from surface returns, and (3) Produce a set of raw instrument data with which advanced signal processing techniques can be developed. This objective will permit future missions to better understand how to extract wind information from low backscatter regions of the atmosphere.

Raymond, Carol A.↗

U.S. IMERG Status

The U.S. Science Team’s Integrated Multi-satellitE Retrievals for the Global Precipitation Measurement (GPM) mission (IMERG) product provides estimates of surface precipitation rate and related information on a global 0.1° half-hour grid. It is run three times at increasingly longer latency and higher information input to serve different communities. This presentation will briefly summarize the major upgrades included in Version 07. The Goddard Profiling (GPROF) algorithm (applied to passive microwave sensor data from the GPM virtual constellation) and the Combined Radar-Radiometer Algorithm (CORRA) that provide input to IMERG V07 are both improved, and the new Precipitation Estimation from Remotely Sensed Information Using Artificial Neural Networks–Dynamic Infrared Rain Rate (PDIR) algorithm is being applied to infrared data, which employs an additional, warmer infrared temperature threshold than the previous infrared scheme and a deep neural network. V07 has improved bias performance as a result of calibrations that now employ the entire swath widths of CORRA and GPROF GPM Microwave Imager precipitation estimates. As well, time continuity in precipitation features is improved as a result of changes to the Kalman filter that approximately preserve the local histogram of precipitation rates (Scheme for Histogram Adjustment with Ranked Precipitation Estimates in the Neighborhood, or SHARPEN), and that better account for differences in sensor performance. A long-standing bug in the geolocation that shifted grid values 0.1° to the east in the latitude band 70°N-S has been corrected. Other changes in V07 include a hierarchical selection among motion vector sources to address deficiencies in the precipitation propagation near orography, an update to the precipitation phase specification for improved consistency with current inputs, and a renewed effort to implement climatological gauge adjustment to the near-real-time Runs. Early evaluations of V07 IMERG show interesting behavior across the TRMM orbit boost that is highly relevant to the planned orbit boost for the GPM Core observatory.

GPM↗

The g-code file

The slicing process for additive manufacturing (AM) involves many steps, including slicing the object to be printed and fitting toolpaths to each resulting layer. The toolpaths define the trajectories that the machine must follow during printing to construct the object. Once the slicing is complete and all toolpaths have been found and properly planned, this data must be transferred to the 3D printer in a way the printer can use to construct the object. This is achieved by exporting a file, usually a g-code file, from the slicing software. The g-code file is a text-based file that contains instructions for the machine, controlling the system and defining the motions for each toolpath. The file, which often contains thousands of lines of code, is mostly composed of numbers that command positions for axis motions. This chapter will outline the contents of a g-code file, discuss various commands and their implementation, then provide example codes and files for object construction.

Roschli, Alex↗

Distributed Parameter Analysis of Pressure and Flow Disturbances in Rocket Propellant Feed Systems

A digital distributed parameter model for computing the dynamic response of propellant feed systems is formulated. The analytical approach used is an application of the wave-plan method of analyzing unsteady flow. Nonlinear effects are included. The model takes into account locally high compliances at the pump inlet and at the injector dome region. Examples of the calculated transient and steady-state periodic responses of a simple hypothetical propellant feed system to several types of disturbances are presented. Included are flow disturbances originating from longitudinal structural motion, gimbaling, throttling, and combustion-chamber coupling. The analytical method can be employed for analyzing developmental hardware and offers a flexible tool for the calculation of unsteady flow in these systems.

UNSTEADY FLOW↗

Ageostrophic winds and vertical motion fields accompanying upper level jet streak propagation during the Red River Valley tornado outbreak

Preliminary results are shown relating the ageostrophic wind field, through the terms of a semigeostrophic wind equation (assuming adiabatic conditions and the geostrophic momentum approximation) to both air parcel trajectories and their vertical motion fields computed from the parcels' displacement on isentropic surfaces, with respect to pressure. The analysis of results considers both upper-level (324 K) ageostrophic fields and low-level (304 K) fields. Preliminary results tend to support Uccellini and Johnson's (1979) hypothesis concerning upper-level-jet/low-level-jet (ULJ/LLJ) coupling in the exit region of the ULJ. Future plans are described briefly for research intended to clarify the mechanism behind ULJ streak propagation, LLJ development and their relationship to the initiation of severe convection.

Moore, J. T.↗

Orbital Maintenance for the Wide Field Infrared Survey Telescope: The Effects of Solar Radiation Pressure and Navigation Accuracies on Station Keeping

The Wide-Field Infrared Survey Telescope (WFIRST), a NASA observatory designed to investigate dark energy and astrophysics, is planned for a launch in 2025 to orbit the Sun-Earth L2 (SEL2) Libration Point. Due to the instability of the SEL2 environment, WFIRST must perform maneuvers to remain in its mission orbit. This paper investigates how different error sources affect the resulting stationkeeping delta v for WFIRST. We study how Solar Radiation Pressure (SRP) modeling affects WFIRST's orbital motion and stability, and how SRP combined with Orbit Determination (OD) errors drive the stationkeeping maneuver magnitudes. Our goal is to determine the best way to model WFIRST's SRP so that we minimize its impact on total stationkeeping delta v required over the mission lifetime.

Radiation↗

Radioactive Source Localization via Bayesian Particle Filter

In the event of a misplaced radioactive source or other emergency situation, measuring a radiation field, mapping its distribution, and determining a source location are essential tasks to ameliorating the situation. However, radiation fields may be extremely hazardous to human surveyors and minimizing received radiation doses is just as essential. Robots appear to be a potential solution to these problems. Beyond simply measuring radiation, the robot's computer processing capabilities offer a way to apply complex data analysis methods to radiation measurements in real-time. Methods which predict likely source locations can then feed this information into other processes, potentially improving path planning and enabling more efficient measurements. Given a robot mounted with a gamma-ray detector, can we: develop a methodology to account for detector performance across a wide range of source angles, distances, and photon energies? operate an autonomously navigating robot to effectively survey and characterize an area of interest? implement a data analysis method, conventionally used in measurements of motion, for source localization purposes? An open-source TurtleBot 3 robot, running Robot Operating System (ROS) on Ubuntu 16.04 LTS, was fitted with a Kromek GR1{sup R} Cadmium Zinc Telluride (CZT) solid-state gamma-ray detector. As a part of ROS, the packages OpenSlam, gmapping, and amcl were used to perform Simultaneous Localization and Mapping (SLAM), determining the robot's position and mapping the surrounding area. Data was acquired via Lidar mounted on top the TurtleBot 3. Detector Calibration Fit: The equation was fit to 365 counts of various energies, distances, and angles. A MATLAB{sup R} program was written to simulate measurements taken a robot on a random walk, with count data and positions discretized into finite element pixels. Using this program, a sample of 100 runs was performed on a map with a simulated source at the center, with a total of 200 of 2 pixels each. Similarly, multiple runs of the filter were performed on recorded robot measurement data. In both simulation and real tests, when corrected for errors (particles placed outside of bounds or on the robot, and simulation-specific errors), corresponding t-tests of predicted x and y-coordinates were within a 95% confidence interval of the actual position. For the real trial, these positions are slightly skewed right in the x-axis as the robot remained mainly to the left side of the source within the sample area. These simulations demonstrate potential validity for the usage of a particle filter as method of radioactive source localization. In the future, true real-time implementation and data fusion may further augment the performance of the robot to localize lost sources. Additionally, identification of multiple sources, determination of source types, and usage of a collimator are areas to potentially be explored.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

The Ponape ST radar

In May, 1984, a 50-MHz ST radar was installed on the island of Ponape in the western equatorial Pacific (7 deg N, 158 deg E) by the Aeronomy Laboratory of NOAA. The radar consists of a 100 m x 100 m array with a single, vertically directed, beam and is initially transmitting micro sec. (2.25 km) pulses. The radar is operating continuously, with Doppler spectra being recorded at approximately 1 1/2 minute intervals and sent to Boulder for later analysis. One of the principal goals of the radar is to measure vertical motions in the troposphere and lower stratosphere at a location which is within the intertropical convergence zone during part of the year. First results, during generally fair weather conditions, show detectable echoes up to about 21 km with the tropopause at 17-18 km. Once daily balloon soundings are available locally from a NOAA Weather Service Office on the island, it is planned that this radar will be joined in the coming year by two others with oblique as well as vertical beams on two yet-to-be-selected equatorial islands as part of the TOGA (Tropical Oceans Global Atmosphere) program.

Carter, D. A.↗

Kinematics, controls, and path planning results for a redundant manipulator

The inverse kinematics solution, a modal position control algorithm, and path planning results for a 7 degree of freedom manipulator are presented. The redundant arm consists of two links with shoulder and elbow joints and a spherical wrist. The inverse kinematics problem for tip position is solved and the redundant joint is identified. It is also shown that a locus of tip positions exists in which there are kinematic limitations on self-motion. A computationally simple modal position control algorithm has been developed which guarantees a nearly constant closed-loop dynamic response throughout the workspace. If all closed-loop poles are assigned to the same location, the algorithm can be implemented with very little computation. To further reduce the required computation, the modal gains are updated only at discrete time intervals. Criteria are developed for the frequency of these updates. For commanding manipulator movements, a 5th-order spline which minimizes jerk provides a smooth tip-space path. Schemes for deriving a corresponding joint-space trajectory are discussed. Modifying the trajectory to avoid joint torque saturation when a tip payload is added is also considered. Simulation results are presented.

Gretz, Bruce↗