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At least 109 records · Page 6

GRAIL Refinements to Lunar Seismic Structure

The present ]day internal structure of the Moon provides insight not only into its own formation and evolution, but also that of all rocky planetary bodies. The most direct way to probe a planet fs interior structure is through seismology. As part of the Apollo lunar missions, four seismometers were deployed on the nearside surface of the Moon between the years 1969 and 1972. These instruments operated continuously until 1977, forming the only substantial extraterrestrial seismic data set in existence. These data have been used to constrain various aspects of the seismic velocity and density structure of the Moon. Typical 1-D models recognize a 30-60 km thick crust overlying a nearly constant ]velocity mantle, and extend to a depth of approximately 1000 km, below which the lack of penetrating moonquake ray ]paths precludes the seismic determination of deeper structure. Previously, the lack of observed moonquakes from the far side of the Moon has been used to infer the presence of a highly attenuating (possibly molten) core. Indirect geophysical measurements such as moment of inertia, magnetic induction, lunar laser ranging, and elemental abundances of mare basalts also place varying constraints on core size and state. In combination with seismic studies, these indirect measurements have been used to arrive at a commonly accepted model of the Moon's deepest interior that includes a solid inner and fluid outer core, overlain by a partial melt boundary layer. We recently applied modern array seismology techniques to the Apollo data and revealed detailed core structure, including the first direct confirmation of the presence of a solid inner core. Our study focused on the identification of core ]reflected phases in deep moonquake seismograms. The resulting model of the Moon fs innermost structure was found to be consistent with the commonly accepted model. However, the modeled layer radii may vary by tens of kilometers, as is expected when accounting for uncertainties such as moonquake location, timing errors, and potential seismic heterogeneities. In addition, the modeled velocities may vary with a 1-to-1 trade ]off with the modeled reflector depth. The GRAIL (Gravity Recovery and Interior Laboratory) mission, launched in Sept. 2011, placed two nearly identical spacecraft in lunar orbit. The two satellites make extremely high-resolution measurements of the lunar gravity field, which can be used to constrain the interior structure of the Moon using a "crust to core" approach. GRAIL fs constraints on crustal thickness, mantle structure, core radius and stratification, and core state (solid vs. molten) will complement seismic investigations in several ways. Here we present a progress report on our efforts to advance our knowledge of the Moon fs internal structure using joint gravity and seismic analyses. We will focus on methodology, including 1) refinements to the seismic core constraint accomplished through array processing of Apollo seismic data, made by applying a set of travel time corrections based on GRAIL structure estimates local to each Apollo seismic station; 2) modeling deep lunar structure through synthetic seismograms, to test whether the seismic core model can reproduce the core reflections observed in the Apollo seismograms; and 3) a joint seismic and gravity inversion in which we attempt to fit a family of seismic structure models with the gravity constraints from GRAIL, resulting in maps of seismic velocities and densities that vary from a nominal model both laterally and with depth.

Weber, Renee↗

A complete analytical solution for the inverse instantaneous kinematics of a spherical-revolute-spherical (7R) redundant manipulator

Using a method based upon resolving joint velocities using reciprocal screw quantities, compact analytical expressions are generated for the inverse solution of the joint rates of a seven revolute (spherical-revolute-spherical) manipulator. The method uses a sequential decomposition of screw coordinates to identify reciprocal screw quantities used in the resolution of a particular joint rate solution, and also to identify a Jacobian null-space basis used for the direct solution of optimal joint rates. The results of the screw decomposition are used to study special configurations of the manipulator, generating expressions for the inverse velocity solution for all non-singular configurations of the manipulator, and identifying singular configurations and their characteristics. Two functions are therefore served: a new general method for the solution of the inverse velocity problem is presented; and complete analytical expressions are derived for the resolution of the joint rates of a seven degree of freedom manipulator useful for telerobotic and industrial robotic application.

Podhorodeski, R. P.↗

Dynamic analysis of astronaut motions in microgravity: Applications for Extravehicular Activity (EVA)

Simulations of astronaut motions during extravehicular activity (EVA) tasks were performed using computational multibody dynamics methods. The application of computational dynamic simulation to EVA was prompted by the realization that physical microgravity simulators have inherent limitations: viscosity in neutral buoyancy tanks; friction in air bearing floors; short duration for parabolic aircraft; and inertia and friction in suspension mechanisms. These limitations can mask critical dynamic effects that later cause problems during actual EVA's performed in space. Methods of formulating dynamic equations of motion for multibody systems are discussed with emphasis on Kane's method, which forms the basis of the simulations presented herein. Formulation of the equations of motion for a two degree of freedom arm is presented as an explicit example. The four basic steps in creating the computational simulations were: system description, in which the geometry, mass properties, and interconnection of system bodies are input to the computer; equation formulation based on the system description; inverse kinematics, in which the angles, velocities, and accelerations of joints are calculated for prescribed motion of the endpoint (hand) of the arm; and inverse dynamics, in which joint torques are calculated for a prescribed motion. A graphical animation and data plotting program, EVADS (EVA Dynamics Simulation), was developed and used to analyze the results of the simulations that were performed on a Silicon Graphics Indigo2 computer. EVA tasks involving manipulation of the Spartan 204 free flying astronomy payload, as performed during Space Shuttle mission STS-63 (February 1995), served as the subject for two dynamic simulations. An EVA crewmember was modeled as a seven segment system with an eighth segment representing the massive payload attached to the hand. For both simulations, the initial configuration of the lower body (trunk, upper leg, and lower leg) was a neutral microgravity posture. In the first simulation, the payload was manipulated around a circular trajectory of 0.15 m radius in 10 seconds. It was found that the wrist joint theoretically exceeded its ulnal deviation limit by as much as 49. 8 deg and was required to exert torques as high as 26 N-m to accomplish the task, well in excess of the wrist physiological limit of 12 N-m. The largest torque in the first simulation, 52 N-m, occurred in the ankle joint. To avoid these problems, the second simulation placed the arm in a more comfortable initial position and the radius and speed of the circular trajectory were reduced by half. As a result, the joint angles and torques were reduced to values well within their physiological limits. In particular, the maximum wrist torque for the second simulation was only 3 N-m and the maximum ankle torque was only 6 N-m.

Newman, Dava J.↗

An optimal resolved rate law for kindematically redundant manipulators

The resolved rate law for a manipulator provides the instantaneous joint rates required to satisfy a given instantaneous hand motion. When the joint space has more degrees of freedom than the task space, the manipulator is kinematically redundant and the kinematic rate equations are underdetermined. These equations can be locally optimized, but the resulting pseudo-inverse solution was found to cause large joint rates in some case. A weighting matrix in the locally optimized (pseudo-inverse) solution is dynamically adjusted to control the joint motion as desired. Joint reach limit avoidance is demonstrated in a kinematically redundant planar arm model. The treatment is applicable to redundant manipulators with any number of revolute joints and to nonplanar manipulators.

Bourgeois, B. J.↗

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↗

Joint physics-based and data-driven time-lapse seismic inversion: Mitigating data scarcity

In carbon capture and sequestration (CCS), developing rapid and effective imaging techniques is crucial for real-time monitoring of the spatial and temporal dynamics of CO 2 propagation during/after injection. With continuing improvements in computational power and data storage, data-driven techniques based on machine learning (ML) have been effectively applied to seismic inverse problems. In particular, ML helps alleviate the ill-posedness and high computational cost of full-waveform inversion (FWI). However, such data-driven inversion techniques require massive high-quality training data sets to ensure prediction accuracy, which hinders their application to time-lapse monitoring of CO 2 sequestration. We propose an efficient “hybrid” time-lapse workflow that combines physics-based FWI and data-driven ML inversion. The scarcity of the available training data is addressed by developing a new data-generation technique with physics constraints. The method is vali dated on a synthetic CO 2 -sequestration model based on the Kimberlina storage reservoir in California. The proposed approach is shown to synthesize a large volume of high-quality, physically realistic training data, which is critically important in accurately characterizing the CO 2 movement in the reservoir. In conclusion, the developed hybrid methodology can also simultaneously predict the variations in velocity and saturation and achieve high spatial resolution in the presence of realistic noise in the data.

58 GEOSCIENCES↗

Inversion of Multiangular Polarimetric Measurements Over Open and Coastal Ocean Waters: A Joint Retrieval Algorithm for Aerosol and Water-Leaving Radiance Properties

Ocean color remote sensing is a challenging task over coastal waters due to the complex optical properties of aerosols and hydrosols. In order to conduct accurate atmospheric correction, we previously implemented a joint retrieval algorithm, hereafter referred to as the Multi-Angular Polarimetric Ocean coLor (MAPOL) algorithm, to obtain the aerosol and water-leaving signal simultaneously. The MAPOL algorithm has been validated with synthetic data generated by a vector radiative transfer model, and good retrieval performance has been demonstrated in terms of both aerosol and ocean water optical properties (Gao et al., 2018). In this work we applied the algorithm to airborne polarimetric measurements from the Research Scanning Polarimeter (RSP) over both open and coastal ocean waters acquired in two field campaigns: the Ship-Aircraft Bio-Optical Research (SABOR) in 2014 and the North Atlantic Aerosols and Marine Ecosystems Study (NAAMES) in 2015 and 2016. Two different yet related bio-optical models are designed for ocean water properties. One model aligns with traditional open ocean water bio-optical models that parameterize the ocean optical properties in terms of the concentration of chlorophyll a. The other is a generalized bio-optical model for coastal waters that includes seven free parameters to describe the absorption and scattering by phytoplankton, colored dissolved organic matter, and nonalgal particles. The retrieval errors of both aerosol optical depth and the water-leaving radiance are evaluated. Through the comparisons with ocean color data products from both in situ measurements and the Moderate Resolution Imaging Spectroradiometer (MODIS), and the aerosol product from both the High Spectral Resolution Lidar (HSRL) and the Aerosol Robotic Network (AERONET), the MAPOL algorithm demonstrates both flexibility and accuracy in retrieving aerosol and water-leaving radiance properties under various aerosol and ocean water conditions.

Gao, Meng↗

An optimal resolved rate law for kinematically redundant manipulators

The resolved rate law for a manipulator provides the instantaneous joint rates required to satisfy a given instantaneous hand motion. When the joint space has more degrees of freedom than the task space, the manipulator is kinematically redundant and the kinematic rate equations are underdetermined. These equations can be locally optimized, but the resulting pseudo-inverse solution has been found to cause large joint rates in some cases. A weighting matrix in the locally optimized (pseudo-inverse) solution is dynamically adjusted to control the joint motion as desired. Joint reach limit avoidance is demonstrated in a kinematically redundant planar arm model. The treatment is applicable to redundant manipulators with any number of revolute joints and to non-planar manipulators.

Bourgeois, B. J.↗

Topology Hierarchy of Transition Metal Dichalcogenides Built from Quantum Spin Hall Layers

The evolution of the physical properties of 2D material from monolayer limit to the bulk reveals unique consequences from dimension confinement and provides a distinct tuning knob for applications. Monolayer 1T'-phase transition metal dichalcogenides (1T'-TMDs) with ubiquitous quantum spin Hall (QSH) states are ideal 2D building blocks of various 3D topological phases. However, the stacking geometry has been previously limited to the bulk 1T'-WTe 2 type. Here, the novel 2M-TMDs consisting of translationally stacked 1T'-monolayers are introduced as promising material platforms with tunable inverted bandgaps and interlayer coupling. By performing advanced polarization-dependent angle-resolved photoemission spectroscopy as well as first-principles calculations on the electronic structure of 2M-TMDs, a topology hierarchy is revealed: 2M-WSe 2 , MoS 2 , and MoSe 2 are weak topological insulators (WTIs), whereas 2M-WS 2 is a strong topological insulator (STI). Further demonstration of topological phase transitions by tunning interlayer distance indicates that band inversion amplitude and interlayer coupling jointly determine different topological states in 2M-TMDs. Finally, it is proposed that 2M-TMDs are parent compounds of various exotic phases including topological superconductors and promise great application potentials in quantum electronics due to their flexibility in patterning with 2D materials.

36 MATERIALS SCIENCE↗

Reliable fusion of control and sensing in intelligent machines

Although robotics research has produced a wealth of sophisticated control and sensing algorithms, very little research has been aimed at reliably combining these control and sensing strategies so that a specific task can be executed. To improve the reliability of robotic systems, analytic techniques are developed for calculating the probability that a particular combination of control and sensing algorithms will satisfy the required specifications. The probability can then be used to assess the reliability of the design. An entropy formulation is first used to quickly eliminate designs not capable of meeting the specifications. Next, a framework for analyzing reliability based on the first order second moment methods of structural engineering is proposed. To ensure performance over an interval of time, lower bounds on the reliability of meeting a set of quadratic specifications with a Gaussian discrete time invariant control system are derived. A case study analyzing visual positioning in robotic system is considered. The reliability of meeting timing and positioning specifications in the presence of camera pixel truncation, forward and inverse kinematic errors, and Gaussian joint measurement noise is determined. This information is used to select a visual sensing strategy, a kinematic algorithm, and a discrete compensator capable of accomplishing the desired task. Simulation results using PUMA 560 kinematic and dynamic characteristics are presented.

Mcinroy, John E.↗

Basic Operational Robotics Instructional System

The Basic Operational Robotics Instructional System (BORIS) is a six-degree-of-freedom rotational robotic manipulator system simulation used for training of fundamental robotics concepts, with in-line shoulder, offset elbow, and offset wrist. BORIS is used to provide generic robotics training to aerospace professionals including flight crews, flight controllers, and robotics instructors. It uses forward kinematic and inverse kinematic algorithms to simulate joint and end-effector motion, combined with a multibody dynamics model, moving-object contact model, and X-Windows based graphical user interfaces, coordinated in the Trick Simulation modeling environment. The motivation for development of BORIS was the need for a generic system for basic robotics training. Before BORIS, introductory robotics training was done with either the SRMS (Shuttle Remote Manipulator System) or SSRMS (Space Station Remote Manipulator System) simulations. The unique construction of each of these systems required some specialized training that distracted students from the ideas and goals of the basic robotics instruction.

Todd, Brian Keith↗

Modeling and Simulation Efforts to Support Improved Comfort in ARGOS

BACKGROUND: The Active Response Gravity Offload System (ARGOS) provides an analog environment for extravehicular activity (EVA) testing and training. Discomfort has been observed during longer suited test sessions. While the subject’s core is offloaded during surface EVA evaluations, his/her arms experience full Earth gravity and can become overly fatigued, especially during suited tests which involve reaching and prolonged arm extensions. A device (ARGOS Negation of Gravitational Effects on the Limbs: ANGEL) to offload the weight of the arms and suit sleeves is being developed by JSC’s Flight Systems Branch, and here we present preliminary modeling of that device using the open-source biomechanical tool OpenSim [1,2] with an in-house developed plugin. We analyze a series of motions performed by a single shirt-sleeved subject with goals of characterizing the device, validating the model, and predicting whether reduced gravity conditions (i.e., lunar gravity (Lg) or Martian gravity (Mg)) can be accurately simulated with the device, as well as providing comfort to the ARGOS user. METHODS AND RESULTS: To model the offload device, we augment the OpenSim human model topology with the offload mechanism components and joints, using CAD models to represent the mechanism graphically. The joint angles of the device are either obtained from (1) inverse kinematics (IK) using motion capture markers on the various components of the device or (2) calculated in the OpenSim plugin by modeling how the components configure themselves under the offloading spring tension given a particular IK-derived arm position. Given the joint angles of the device, the resulting force on the arm is computed by the plugin and applied as an external load in inverse dynamics (ID) in order to enable study of overall shoulder joint torques as well as offload achieved. We verify the calculated joint angles by using the inverse kinematic data and the forces from manual measurements of the spring both independently and integrated within the device. We found that calculated joint angles generally represent the angles measured and computed with IK, supporting a possible analysis workflow inputting human motion data and observing system behavior under varied design parameters. In two different device configurations in which the maximum applied force was 131 N, our current model accurately captured force with a difference of 2-3 N from measured loads. Though our initial test was performed with a shirt-sleeve subject, arm weights were added to emulate the weight of the suit sleeve and the subject was positioned in a test stand with a Mark-III Hard Upper Torso (HUT) and Portable Life Support System (PLSS) mockup. Arm range of motion tasks were performed outside of the HUT, inside the HUT, and inside the HUT while using the device. A variety of other upper body tasks were completed as well. In summary, we have developed a model to investigate and verify an upper limb offload device currently in development. We believe this model will be a valuable tool not only for device characterization but also to predict proper configurations to simulate Lg or Mg conditions, investigate range of motion concerns, predict limitations such as internal collisions and contacts, and inform future design improvements.

L B Nilsson↗

Kinematic equations for control of the redundant eight-degree-of-freedom advanced research manipulator 2

The forward position and velocity kinematics for the redundant eight-degree-of-freedom Advanced Research Manipulator 2 (ARM2) are presented. Inverse position and velocity kinematic solutions are also presented. The approach in this paper is to specify two of the unknowns and solve for the remaining six unknowns. Two unknowns can be specified with two restrictions. First, the elbow joint angle and rate cannot be specified because they are known from the end-effector position and velocity. Second, one unknown must be specified from the four-jointed wrist, and the second from joints that translate the wrist, elbow joint excluded. There are eight solutions to the inverse position problem. The inverse velocity solution is unique, assuming the Jacobian matrix is not singular. A discussion of singularities is based on specifying two joint rates and analyzing the reduced Jacobian matrix. When this matrix is singular, the generalized inverse may be used as an alternate solution. Computer simulations were developed to verify the equations. Examples demonstrate agreement between forward and inverse solutions.

Williams, Robert L., II↗

Software for Simulating a Complex Robot

RoboSim (Robot Simulation) is a computer program that simulates the poses and motions of the Robonaut a developmental anthropomorphic robot that has a complex system of joints with 43 degrees of freedom and multiple modes of operation and control. RoboSim performs a full kinematic simulation of all degrees of freedom. It also includes interface components that duplicate the functionality of the real Robonaut interface with control software and human operators. Basically, users see no difference between the real Robonaut and the simulation. Consequently, new control algorithms can be tested by computational simulation, without risk to the Robonaut hardware, and without using excessive Robonaut-hardware experimental time, which is always at a premium. Previously developed software incorporated into RoboSim includes Enigma (for graphical displays), OSCAR (for kinematical computations), and NDDS (for communication between the Robonaut and external software). In addition, RoboSim incorporates unique inverse-kinematical algorithms for chains of joints that have fewer than six degrees of freedom (e.g., finger joints). In comparison with the algorithms of OSCAR, these algorithms are more readily adaptable and provide better results when using equivalent sets of data.

Goza, S. Michael↗

Microseismic at HFTS2: A Story of Three Stimulated Wells

A microseismic data set was acquired at Hydraulic Fracturing Test Site 2 (HFTS2) in the Delaware Basin (Texas, USA) by the HFTS2 consortium as a part of data-collection program designed to help maximize the efficiency of hydraulic fracturing, understand the impacts of nearby depleted zones, and increase the production of hydrocarbons. Advanced methods of microseismic monitoring applied at HFTS2 include 1) native synchronization of five monitor arrays, 2) real-time location of microseismic events, 3) joint event hypocenter/ velocity-model inversion that locates microseismic events simultaneously with constructing azimuthally anisotropic velocity models, 4) high-resolution reservoir imaging, utilizing microseismic events as downhole sources. HFTS2 microseismic data set illustrated the influence of geologic complexity, variations in treatment designs, and the presence of parent wells on the efficiency of hydraulic fracturing. Three Wolfcamp wells, Boxwood 1H, 2H, and 4H, were stimulated sequentially, exhibiting very different patterns of microseismicity. When the Boxwood 1H well is stimulated, its toe stages quickly reacted to the presence of depleted Bitterroot section to the east of the Boxwood pad, extending microseismic events over 3,000 ft to the east. This behavior changes dramatically after the treatment passes the Bitterroot section at the toe, and the heel stages in 1H showed tight microseismic grouping around the stimulated well, indicative of treatment of virgin reservoir rock. The Boxwood 2H demonstrates this same pattern of behavior between the toe and heel stages of the well, suggesting that the depleted Bitterroot section remains easier to refracture than adjacent non-depleted rock. Microseismic activity associated with Boxwood 4H treatment is distinctly different from those in Boxwood wells 1H and 2H. The events generated during stimulation of 4H are hardly influenced by the depleted Bitterroot section and fill the space between the previously stimulated 1H and 2H wells. Altogether, microseismic patterns suggest that treatment fluids tend to find the weakest passages through geologic formations, and the relative well positions and treatment sequence have a significant impact on fracture geometry, as indicated by microseismic event locations.

58 GEOSCIENCES↗

Seismic Monitoring near Ithaca, New York, Reveals Nonuniform Distribution of Microseismicity in an Intraplate Region

Abstract Cornell University intends to use a deep direct-use geothermal system to heat its Ithaca, New York, campus. In preparation for this project, the Cornell Seismic Network has been monitoring the background seismicity in this intraplate region since 2019. From January 2020 to June 2023, 95 events were detected within 20 km of the proposed geothermal well site, with local magnitudes ranging from −1.02 to 0.56. None of these events appear in regional or national catalogs. Events locate in a narrow geographic band, with one-fourth exhibiting multimodal hypocentral probability peaks both near the surface and at 1–4 km depth. We relocate events with a joint hypocenter and 1D velocity model inversion, in addition to a fully nonlinear method, and then compare observations with synthetic waveforms. Together, these approaches provide strong evidence for >95% of events locating at the surface or within the 3-km-thick sedimentary sequence. We explore how anthropogenic activity and regional topographic stress may contribute to frequent surficial events. This information is critical for characterizing the background microseismicity for comparison during future geothermal operations. Ithaca’s geology of Paleozoic sediments overlying Precambrian crystalline basement is typical of many continental interiors, so these results also provide insight into intraplate microseismicity patterns.

Geochemistry & Geophysics↗

Efficient mapping algorithms for scheduling robot inverse dynamics computation on a multiprocessor system

Two efficient mapping algorithms for scheduling the robot inverse dynamics computation consisting of m computational modules with precedence relationship to be executed on a multiprocessor system consisting of p identical homogeneous processors with processor and communication costs to achieve minimum computation time are presented. An objective function is defined in terms of the sum of the processor finishing time and the interprocessor communication time. The minimax optimization is performed on the objective function to obtain the best mapping. This mapping problem can be formulated as a combination of the graph partitioning and the scheduling problems; both have been known to be NP-complete. Thus, to speed up the searching for a solution, two heuristic algorithms were proposed to obtain fast but suboptimal mapping solutions. The first algorithm utilizes the level and the communication intensity of the task modules to construct an ordered priority list of ready modules and the module assignment is performed by a weighted bipartite matching algorithm. For a near-optimal mapping solution, the problem can be solved by the heuristic algorithm with simulated annealing. These proposed optimization algorithms can solve various large-scale problems within a reasonable time. Computer simulations were performed to evaluate and verify the performance and the validity of the proposed mapping algorithms. Finally, experiments for computing the inverse dynamics of a six-jointed PUMA-like manipulator based on the Newton-Euler dynamic equations were implemented on an NCUBE/ten hypercube computer to verify the proposed mapping algorithms. Computer simulation and experimental results are compared and discussed.

Lee, C. S. G.↗

Control of a flexible bracing manipulator: Integration of current research work to realize the bracing manipulator

All research results about flexible manipulator control were integrated to show a control scenario of a bracing manipulator. First, dynamic analysis of a flexible manipulator was done for modeling. Second, from the dynamic model, the inverse dynamic equation was derived, and the time domain inverse dynamic method was proposed for the calculation of the feedforward torque and the desired flexible coordinate trajectories. Third, a tracking controller was designed by combining the inverse dynamic feedforward control with the joint feedback control. The control scheme was applied to the tip position control of a single link flexible manipulator for zero and non-zero initial condition cases. Finally, the contact control scheme was added to the position tracking control. A control scenario of a bracing manipulator is provided and evaluated through simulation and experiment on a single link flexible manipulator.

Kwon, Dong-Soo↗