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NASA NTRS1989

Real-time neuromorphic algorithms for inverse kinematics of redundant manipulators

The paper presents an efficient neuromorphic formulation to accurately solve the inverse kinematics problem for redundant manipulators. The approach involves a dynamical learning procedure based on a novel formalism in neural network theory: the concept of 'terminal' attractors. Topographically mapped terminal attractors are used to define a neural network whose synaptic elements can rapidly encapture the inverse kinematics transformations, and, subsequently generalize to compute joint-space coordinates required to achieve arbitrary end-effector configurations. Unlike prior neuromorphic implementations, this technique can also systematically exploit redundancy to optimize kinematic criteria, e.g., torque optimization. Simulations on 3-DOF and 7-DOF redundant manipulators, are used to validate the theoretical framework and illustrate its computational efficacy.

Barhen, Jacob↗

NASA NTRS1989

A case study using kinematic quantities derived from a triangle of VHF Doppler wind profilers

Horizontal divergence, relative vorticity, kinematic vertical velocity, and geostrophic and ageostrophic winds are computed from Colorado profiler network data to investigate an upslope snowstorm in northeastern Colorado. Horizontal divergence and relative vorticity are computed using the Gauss and Stokes theorems, respectively. Kinematic vertical velocities are obtained from the surface to 9 km by vertically integrating the continuity equation. The geostrophic and ageostrophic winds are computed by applying a finite differencing technique to evaluate the derivatives in the horizontal equations of motion. Comparison of the synoptic-scale data with the profiler network data reveals that the two datasets are generally consistent. Also, the profiler-derived quantities exhibit coherent vertical and temporal patterns consistent with conceptual and theoretical flow fields of various meteorological phenomena. It is suggested that the profiler-derived quantities are of potential use to weather forecasters in that they enable the dynamic and kinematic interpretation of weather system structure to be made and thus have nowcasting and short-term forecasting value.

Carlson, Catherine A.↗

NASA NTRS1989

Laboratory studies of wave-current interaction - Kinematics of the strong interaction

Controlled laboratory experiments have been conducted to study the kinematics of wave-current interactions. The results confirm the conservation of waves under the steady state condition. The data also show that the kinematic effect of the current on waves can be treated as a simple Doppler shift. After the Doppler correction, the kinematics of the waves (either breaking or nonbreaking) follow the linear theory very well.

Lai, Ronald J.↗

NASA NTRS1990

Kinematic modeling of the galaxy. II - Two samples of high proper motion stars

The paper analyzes two independent surveys, due to Fouts and Sandage and to Carney and Latham, of high proper motion stars with photoelectric photometry and line-of-sight velocity information. A purely kinematic study of both samples indicates that a two-component classical (disk + spheroid) model of the Galaxy is inadequate to represent the kinematics of stars in the solar neighborhood. A component with intermediate kinematic properties (old disk) is required. An asymmetric drift of 50 + or - 15 km/s and principal velocity dispersions of (66, 37, 38) + or - 10 km/s are determined, in good agreement with the results of the metallicity-based analysis of Sandage and Fouts and of Carney and collaborators. The density of this component is poorly constrained, and is 10 percent + or - 5 percent of the local disk density for the same color range; the scale height is less than 1 kpc.

Casertano, Stefano↗

NASA NTRS1991

Resolved rate and torque control schemes for large scale space based kinematically redundant manipulators

Resolved rate control of kinematically redundant ground based manipulators is a challenging problem. The structural, actuator, and control loop frequency characteristics of industrial grade robots generally allow operation with resolved rate control; a rate command is achievable with good accuracy. However, space based manipulators are different, typically have less structural stiffness, more motor and joint friction, and lower control loop cycle frequencies. These undesirable characteristics present a considerable Point of Resolution (POR) control problem for space based, kinematically redundant manipulators for the following reason: a kinematically redundant manipulator requires an arbitrary constraint to solve for the joint rate commands. A space manipulator will not respond to joint rate commands because of these characteristics. A space based manipulator simulation, including free end rigid body dynamics, motor dynamics, motor striction/friction, gearbox backlash, joint striction/friction, and Space Station Remote Manipulator System type configuration parameters, is used to evaluate the performance of a documented resolved rate control law. Alternate schemes which include torque control are also evaluated.

Robert W Bailey↗

NASA NTRS1990

An adaptive inverse kinematics algorithm for robot manipulators

An adaptive algorithm for solving the inverse kinematics problem for robot manipulators is presented. The algorithm is derived using model reference adaptive control (MRAC) theory and is computationally efficient for online applications. The scheme requires no a priori knowledge of the kinematics of the robot if Cartesian end-effector sensing is available, and it requires knowledge of only the forward kinematics if joint position sensing is used. Computer simulation results are given for the redundant seven-DOF robotics research arm, demonstrating that the proposed algorithm yields accurate joint angle trajectories for a given end-effector position/orientation trajectory.

Colbaugh, R.↗

NASA NTRS1990

Kinematic analysis of 7 DOF anthropomorphic arms

A kinematic analysis of anthropomorphic seven-degree-of-freedom serial link spatial manipulators with revolute joints is presented. To uniquely determine joint angles for a given end-effector position and orientation, the redundancy is parameterized by a scalar variable which corresponds to the angle between the arm plane and a reference plane. The forward kinematic mappings from joint-space to end-effector coordinates and arm angle and the augmented Jacobian matrix which gives end-effector and arm angle rates as functions of joint rates are given. Conditions under which the augmented Jacobian becomes singular are given and are shown to correspond to the arm being either at a kinematically singular configuration or at a nonsingular configuration for which the arm angle ceases to parameterize the redundancy.

Kreutz-Delgado, K.↗

NASA NTRS1992

The kinematics of the extended gas in the Seyfert galaxy NGC 3516

Long-slit spectroscopy of the extended gas in the Seyfert galaxy NGC 3516 reveals considerable substructure in the narrow emission lines with several kinematically distinct components visible in H-alpha and N II lambda 6583. The velocity measurements cover almost all of the 3 kpc scale, Z-shaped emission-line structure seen in narrow-band images and suggest that a significant rotational component is present. At large radii, strong deviations from this rotation are observed, indicating that a radial component of motion to the gas is also required to adequately describe the velocity field. There is a clear antisymmetry in these deviations with the velocities being blueshifted with respect to 'normal' galactic rotation on the southwest side of the nucleus and redshifted with respect to it on the northeast side. Although several models can be invoked to explain the observed velocities, the symmetries in the kinematics and emission-line morphology are most easily explained by a bent bipolar mass outflow from the nucleus. In this simple model, gas is ejected out of the plane of the stellar disk and is then slowed by gravitational forces. As the gas trajectory begins to bend, significant velocity deviations are produced. These observations provide some of the best kinematic evidence for mass outflow, although indirect arguments suggest they may be a common feature in many Seyfert galaxies.

Mulchaey, John S.↗

NASA NTRS1992

Kinematic analysis of the ARID manipulator

The kinematic structure of the ARID manipulator lends itself to simple forward and inverse kinematics analysis. The purpose of this paper is to fully document and verify an existing analysis. The symbolic software package MATHEMATICA was used to produce and verify the equations presented here. In the analysis to follow, the standard Devenit-Hartenberg kinematic parameters of the ARID were employed.

Doty, Keith L↗

NASA NTRS1992

A feasibility study of hand kinematics for EVA analysis using magnetic resonance imaging

A new method of analyzing the kinematics of joint motion is developed. Magnetic Resonance Imaging (MRI) offers several distinct advantages. Past methods of studying anatomic joint motion have usually centered on four approaches. These methods are x-ray projection, goniometric linkage analysis, sonic digitization, and landmark measurement of photogrammetry. Of these four, only x-ray is applicable for in vivo studies. The remaining three methods utilize other types of projections of inter-joint measurements, which can cause various types of error. MRI offers accuracy in measurement due to its tomographic nature (as opposed to projection) without the problems associated with x-ray dosage. Once the data acquisition of MR images was complete, the images were processed using a 3D volume rendering workstation. The metacarpalphalangeal (MCP) joint of the left index finger was selected and reconstructed into a three-dimensional graphic display. From the reconstructed volumetric images, measurements of the angles of movement of the applicable bones were obtained and processed by analyzing the screw motion of the MCP joint. Landmark positions were chosen at distinctive locations of the joint at fixed image threshold intensity levels to ensure repeatability. The primarily two dimensional planar motion of this joint was then studied using a method of constructing coordinate systems using three (or more) points. A transformation matrix based on a world coordinate system described the location and orientation of a local target coordinate system. Future research involving volume rendering of MRI data focusing on the internal kinematics of the hand's individual ligaments, cartilage, tendons, etc. will follow. Its findings will show the applicability of MRI to joint kinematics for gaining further knowledge of the hand-glove (power assisted) design for extravehicular activity (EVA).

Dickenson, Rueben D.↗

NASA NTRS1992

Kinematic analysis of 7-DOF manipulators

This article presents a kinematic analysis of seven-degree-of-freedom serial link spatial manipulators with revolute joints. To uniquely determine the joint angles for a given end-effector position and orientation, the redundancy is parameterized by a scalar variable that defines the angle between the arm plane and a reference plane. The forward kinematic mappings from joint space to end-effector coordinates and arm angle and the augmented Jacobian matrix that gives end-effector and arm angle rates as functions of joint rates are presented. Conditions under which the augmented Jacobian becomes singular are also given and are shown to correspond to the arm being either at a kinematically singular configuration or at a nonsingular configuration for which the arm angle ceases to parameterize the redundancy.

Kreutz-Delgado, Kenneth↗

NASA NTRS1993

Kinematics and control of a fully parallel force-reflecting hand controller for manipulator teleoperation

Design of a parallel force-reflecting hand controller that implements a friction- and inertia canceling control loop about the entire mechanism based on wrench sensing in the mechanism handgrip is discussed. Kinematics of the controller under consideration is analyzed and results are presented using a closed-form solution for the inverse kinematics and Newton-Raphson's method for the forward kinematics. Results indicate that the force control scheme based on a handgrip force sensor provides smaller steady-state errors than the scheme without a handigrip sensor.

Bryfogle, Mark D.↗

NASA NTRS1994

Fault tolerant kinematic control of hyper-redundant manipulators

Hyper-redundant spatial manipulators possess fault-tolerant features because of their redundant structure. The kinematic control of these manipulators is investigated with special emphasis on fault-tolerant control. The manipulator tasks are viewed in the end-effector space while actuator commands are in joint-space, requiring an inverse kinematic algorithm to generate joint-angle commands from the end-effector ones. The rate-inverse kinematic control algorithm presented in this paper utilizes the pseudoinverse to accommodate for joint motor failures. An optimal scale factor for the robust inverse is derived.

Bedrossian, Nazareth S.↗

NASA NTRS1999

A Kinematic Link Between Boxy Bulges, Stellar Bars, and Nuclear Activity in NGC 3079 and NGC 4388

We present direct kinematic evidence for bar streaming in two active galaxies with boxy stellar bulges. The Hawaii Imaging Fabry-Perot Interferometer was used on the Canada-France-Hawaii 3.6-m telescope and the University of Hawaii 2.2-m telescope to derive the two-dimensional velocity field of the line-emitting gas in the disks of the Sc galaxy NGC 3079 and the Sb galaxy NGC 4388. In contrast to previous work based on long-slit data, the detection of the bar potential from the Fabry-Perot data does not rely on the existence of inner Lindblad resonances or strong bar-induced shocks. Simple kinematic models which approximate the intrinsic gas orbits as nonintersecting, inclined elliptical annuli that conserve angular momentum characterize the observed velocity fields. In NGC 3079, bar streaming motions with moderately eccentric orbits (e = b/a approx. 0.7) aligned along PA = 130 deg. intrinsic to the disk (PA = 97 deg. on the sky) are detected out to R(sub b) = 3.6 kpc. The orbits become increasingly circular beyond that radius (e = 1 at R(sub d) approx. = 6 kpc). The best model for NGC 4388 includes highly eccentric orbits (e approx. 0.3) for R(sub) less than or equal to 1.5 kpc which are aligned along PA = 135 deg. intrinsic to the disk (PA = 100 deg. on the sky). The observed "spiral arms" are produced by having the orbits become increasingly circular from the ends of the bar to the edge of the disk (R(sub d) approx. = 5 kpc), and the intrinsic bar PA shifting from 135 deg. to 90 deg.. Box-shaped bulges in both NGC 3079 and NGC 4388 are confirmed using new near-infrared images to reduce dust obscuration. Morphological analysis of starlight in these galaxies is combined with the gas kinematics derived from the Fabry-Perot spectra to test evolutionary models of stellar bars that involve transitory boxy bulges, and to quantify the importance of such bars in fueling active nuclei. Our data support the evolutionary bar models, but fail to prove convincingly that the stellar bars in NGC 3079 and NGC 4388 directly trigger or sustain the nuclear activity.

Veilleux, S.↗

NASA NTRS2000

An Indirect Mixed-Sensitivity Approach to Microgravity Vibration Isolation: The Exploitation of Kinematic Coupling In Frequency-weighting Design-Filter Selections

Many space-science experiments need an active isolation system to provide them with the requisite microgravity environment. The isolation systems planned for use with the International Space Station have been appropriately modeled using relative position relative velocity, and acceleration states. In theory, frequency-weighting design filters can be applied to these state-space models, in order to develop optimal H2 or mixed-norm controllers with desired stability and performance characteristics. In practice, however, the kinematic coupling among the various states can lead, through the associated frequency-weighting-filters, to conflicting demands on the Riccati design "machinery." The results can be numerically ill-conditioned regulator and estimator Riccati equations and/or reduced intuition in the design process. In addition, kinematic coupling can result in a redundancy in the demands imposed by the frequency weights. Failure properly to account for this type of coupling can lead to an unnecessary increase in controller dimensionality and, in turn, controller complexity. This paper suggests a rational approach to the assignment of frequency-weighting design filters, in the presence of the kinematic coupling among states that exists in the microgravity vibration isolation problem.

Hampton, R. David↗

NASA NTRS2000

An Indirect Mixed-Sensitivity Approach to Microgravity Vibration Isolation: The Exploitation of Kinematic Coupling In Frequency-Weighting Design-Filter Selections

Many space science experiments need an active isolation system to provide them with the requisite microgravity environment. The isolation systems planned for use with the International Space Station have been appropriately modeled using relative position, relative velocity, and acceleration states. In theory, frequency design filters can be applied to these state-space models, in order to develop optimal H, or mixed-norm controllers with desired stability- and performance characteristics. In practice. however, the kinematic coupling among the various states can lead, through the associated frequency-weighting-filters, to conflicting demands on the Riccati design "machinery." The results can be numerically ill-conditioned regulator and estimator Riccati equations and/or reduced intuition in the design process. In addition, kinematic coupling can result in a redundancy in the demands imposed by the frequency weights. Failure properly to account for this type of coupling can lead to an unnecessary increase in controller dimensionality and, in turn, controller complexity. This paper suggests a rational approach to the assignment of frequency weighting design filters, in the presence of the kinematic coupling among states that exists in the microgravity vibration isolation problem.

Hampton, R. David↗

NASA NTRS2004

Direct and Inverse Kinematics of a Novel Tip-Tilt-Piston Parallel Manipulator

Closed-form direct and inverse kinematics of a new three degree-of-freedom (DOF) parallel manipulator with inextensible limbs and base-mounted actuators are presented. The manipulator has higher resolution and precision than the existing three DOF mechanisms with extensible limbs. Since all of the manipulator actuators are base-mounted; higher payload capacity, smaller actuator sizes, and lower power dissipation can be obtained. The manipulator is suitable for alignment applications where only tip, tilt, and piston motions are significant. The direct kinematics of the manipulator is reduced to solving an eighth-degree polynomial in the square of tangent of half-angle between one of the limbs and the base plane. Hence, there are at most 16 assembly configurations for the manipulator. In addition, it is shown that the 16 solutions are eight pairs of reflected configurations with respect to the base plane. Numerical examples for the direct and inverse kinematics of the manipulator are also presented.

Tahmasebi, Farhad↗

NASA NTRS2005

Kinematics of a New High Precision Three Degree-of-Freedom Parallel Manipulator

Closed-form direct and inverse kinematics of a new three degree-of-freedom (DOF) parallel manipulator with inextensible limbs and base-mounted actuators are presented. The manipulator has higher resolution and precision than the existing three DOF mechanisms with extensible limbs. Since all of the manipulator actuators are base-mounted; higher payload capacity, smaller actuator sizes, and lower power dissipation can be obtained. The manipulator is suitable for alignment applications where only tip, tilt, and piston motions are significant. The direct kinematics of the manipulator is reduced to solving an eighth-degree polynomial in the square of tangent of half-angle between one of the limbs and the base plane. Hence, there are at most sixteen assembly configurations for the manipulator. In addition, it is shown that the sixteen solutions are eight pairs of reflected configurations with respect to the base plane. Numerical examples for the direct and inverse kinematics of the manipulator are also presented.

Tahmasebi, Farhad↗