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NASA NTRS1990

Users Manual for the NASA Lewis Ice Accretion Prediction Code (LEWICE)

LEWICE is an ice accretion prediction code that applies a time-stepping procedure to calculate the shape of an ice accretion. The potential flow field is calculated in LEWICE using the Douglas Hess-Smith 2-D panel code (S24Y). This potential flow field is then used to calculate the trajectories of particles and the impingement points on the body. These calculations are performed to determine the distribution of liquid water impinging on the body, which then serves as input to the icing thermodynamic code. The icing thermodynamic model is based on the work of Messinger, but contains several major modifications and improvements. This model is used to calculate the ice growth rate at each point on the surface of the geometry. By specifying an icing time increment, the ice growth rate can be interpreted as an ice thickness which is added to the body, resulting in the generation of new coordinates. This procedure is repeated, beginning with the potential flow calculations, until the desired icing time is reached. The operation of LEWICE is illustrated through the use of five examples. These examples are representative of the types of applications expected for LEWICE. All input and output is discussed, along with many of the diagnostic messages contained in the code. Several error conditions that may occur in the code for certain icing conditions are identified, and a course of action is recommended. LEWICE has been used to calculate a variety of ice shapes, but should still be considered a research code. The code should be exercised further to identify any shortcomings and inadequacies. Any modifications identified as a result of these cases, or of additional experimental results, should be incorporated into the model. Using it as a test bed for improvements to the ice accretion model is one important application of LEWICE.

Ruff, Gary A.↗

DOE OSTI2023

Illustration of bunch merge simulation in RHIC

Following are examples of a 4 to 2 to 1 merge of proton bunches in RHIC obtained by running the simulation code rhic2mrg23. As the code runs, the user is prompted to enter several numbers. For these examples, RF harmonic number 1440.0 is entered. An RF frequency of 112.597 696 626 MHz at this harmonic is entered. This gives a proton energy of 100 GeV. The merge simulation starts with a uniform distribution of unbunched protons. 2.0 eV-s is entered for the longitudinal emittance of the distribution. The code will recommend a voltage to capture the unbunched protons into 4 harmonic 1440 buckets. A capture voltage of 142.390 kV is recommended. 144.0 kV is entered. It is desirable to capture the protons as “adiabatically” as possible. A capture time of 3318 ms is recommended by the code. 3320.0 ms is entered. A 4 to 2 merge time of 1659 ms is recommended by the code. 1660.0 ms is entered. A 2 to 1 merge time twice that of the 4 to 2 merge is recommended by the code. 3320.0 ms is entered. The code requests a “time fraction” FQMRG to be entered. This is a number (from 0.1 to 1.0) that determines the time at which data are recorded during the 4 to 2 merge. The number 0.5 is entered. This encodes the recording of data halfway through the 4 to 2 merge.

43 PARTICLE ACCELERATORS↗

NASA NTRS1989

An assessment of multibody simulation tools for articulated spacecraft

A survey of multibody simulation codes was conducted in the spring of 1988, to obtain an assessment of the state of the art in multibody simulation codes from the users of the codes. This survey covers the most often used articulated multibody simulation codes in the spacecraft and robotics community. There was no attempt to perform a complete survey of all available multibody codes in all disciplines. Furthermore, this is not an exhaustive evaluation of even robotics and spacecraft multibody simulation codes, as the survey was designed to capture feedback on issues most important to the users of simulation codes. We must keep in mind that the information received was limited and the technical background of the respondents varied greatly. Therefore, only the most often cited observations from the questionnaire are reported here. In this survey, it was found that no one code had both many users (reports) and no limitations. The first section is a report on multibody code applications. Following applications is a discussion of execution time, which is the most troublesome issue for flexible multibody codes. The representation of component flexible bodies, which affects both simulation setup time as well as execution time, is presented next. Following component data preparation, two sections address the accessibility or usability of a code, evaluated by considering its user interface design and examining the overall simulation integrated environment. A summary of user efforts at code verification is reported, before a tabular summary of the questionnaire responses. Finally, some conclusions are drawn.

Man, Guy K.↗

NASA NTRS2001

Transient Reliability Analysis Capability Developed for CARES/Life

The CARES/Life software developed at the NASA Glenn Research Center provides a general-purpose design tool that predicts the probability of the failure of a ceramic component as a function of its time in service. This award-winning software has been widely used by U.S. industry to establish the reliability and life of a brittle material (e.g., ceramic, intermetallic, and graphite) structures in a wide variety of 21st century applications.Present capabilities of the NASA CARES/Life code include probabilistic life prediction of ceramic components subjected to fast fracture, slow crack growth (stress corrosion), and cyclic fatigue failure modes. Currently, this code can compute the time-dependent reliability of ceramic structures subjected to simple time-dependent loading. For example, in slow crack growth failure conditions CARES/Life can handle sustained and linearly increasing time-dependent loads, whereas in cyclic fatigue applications various types of repetitive constant-amplitude loads can be accounted for. However, in real applications applied loads are rarely that simple but vary with time in more complex ways such as engine startup, shutdown, and dynamic and vibrational loads. In addition, when a given component is subjected to transient environmental and or thermal conditions, the material properties also vary with time. A methodology has now been developed to allow the CARES/Life computer code to perform reliability analysis of ceramic components undergoing transient thermal and mechanical loading. This means that CARES/Life will be able to analyze finite element models of ceramic components that simulate dynamic engine operating conditions. The methodology developed is generalized to account for material property variation (on strength distribution and fatigue) as a function of temperature. This allows CARES/Life to analyze components undergoing rapid temperature change in other words, components undergoing thermal shock. In addition, the capability has been developed to perform reliability analysis for components that undergo proof testing involving transient loads. This methodology was developed for environmentally assisted crack growth (crack growth as a function of time and loading), but it will be extended to account for cyclic fatigue (crack growth as a function of load cycles) as well.

Nemeth, Noel N.↗

DOE OSTI2025

FY25 status report on the addition of candidate materials in Class B Code Case

This report provides the time-dependent allowable stress calculation strategy leveraging the limited creep rupture tests data generated to support the allowable stress for 100,000 hours in American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code (BPVC), Section II, Part D. A variable confidence index procedure to extrapolate material properties to support 500,000 hours design life is discussed. Time-dependent allowable stresses for Class B component design and analysis are presented for Grade 1 and Grade 2 of Alloy 625. The presented data extrapolation and allowable stress calculation method will support new material addition using limited creep rupture data in the new ASME Boiler and BPVC, Section III, Division 5, Class B rules.

Part D↗

DOE OSTI2022

Global gyrokinetic simulations of ASDEX Upgrade up to the transport timescale with GENE–Tango

An accurate description of turbulence up to the transport timescale is essential for predicting core plasma profiles and enabling reliable calculations for designing advanced scenarios and future devices. Here, we exploit the gap separation between turbulence and transport timescales and couple the global gyrokinetic code GENE to the transport-solver Tango, including kinetic electrons, collisions, realistic geometries, toroidal rotation and electromagnetic effects for the first time. This approach overcomes gyrokinetic codes' limitations and enables high-fidelity profile calculations in experimentally relevant plasma conditions, significantly reducing the computational cost. We present numerical results of GENE–Tango for two ASDEX Upgrade discharges, one of which exhibits a pronounced peaking of the ion temperature profile not reproduced by TGLF–ASTRA. We show that GENE–Tango can correctly capture the ion temperature peaking observed in the experiment. By retaining different physical effects in the GENE simulations, e.g., collisions, toroidal rotation and electromagnetic effects, we show that the ion temperature profile's peaking can be linked to electromagnetic effects of submarginal (stable) KBM modes. Furthermore, based on these results, the expected GENE–Tango speedup for the ITER standard scenario is larger than two orders of magnitude compared to a single gyrokinetic simulation up to the transport timescale, possibly making first-principles ITER simulations feasible on current computing resources.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

ARCS: Agentic Retrieval-Augmented Code Synthesis with Iterative Refinement

Agentic Retrieval-Augmented Code Synthesis with Iterative RefinementIn supercomputing, efficient and optimized code generation is essential to leverage high-performance systems effectively. We have developed Agentic Retrieval-Augmented Code Synthesis (ARCS), an advanced framework for accurate, robust, and efficient code generation, completion, and translation. ARCS integrates Retrieval-Augmented Generation (RAG) with Chain-of-Thought (CoT) reasoning to systematically break down and iteratively refine complex programming tasks. An agent-based RAG mechanism retrieves relevant code snippets, while real-time execution feedback drives the synthesis of candidate solutions. This process is formalized as a state-action search tree optimization, balancing code correctness with editing efficiency. Evaluations on the Geeks4Geeks and HumanEval benchmarks demonstrate that ARCS significantly outperforms traditional prompting methods in translation and generation quality. By enabling scalable and precise code synthesis, ARCS offers transformative potential for automating and optimizing code development in supercomputing applications, enhancing computational resource utilization

Bhattarai, Manish [Los Alamos National Labs]↗

NASA NTRS1992

Moment method analysis of linearly tapered slot antennas: Low loss components for switched beam radiometers

A Moment Method Model for the radiation pattern characterization of single Linearly Tapered Slot Antennas (LTSA) in air or on a dielectric substrate is developed. This characterization consists of: (1) finding the radiated far-fields of the antenna; (2) determining the E-Plane and H-Plane beamwidths and sidelobe levels; and (3) determining the D-Plane beamwidth and cross polarization levels, as antenna parameters length, height, taper angle, substrate thickness, and the relative substrate permittivity vary. The LTSA geometry does not lend itself to analytical solution with the given parameter ranges. Therefore, a computer modeling scheme and a code are necessary to analyze the problem. This necessity imposes some further objectives or requirements on the solution method (modeling) and tool (computer code). These may be listed as follows: (1) a good approximation to the real antenna geometry; and (2) feasible computer storage and time requirements. According to these requirements, the work is concentrated on the development of efficient modeling schemes for these type of problems and on reducing the central processing unit (CPU) time required from the computer code. A Method of Moments (MoM) code is developed for the analysis of LTSA's within the parameter ranges given.

Koeksal, Adnan↗

NASA NTRS1997

Visualization of Unsteady Computational Fluid Dynamics

The current compute environment that most researchers are using for the calculation of 3D unsteady Computational Fluid Dynamic (CFD) results is a super-computer class machine. The Massively Parallel Processors (MPP's) such as the 160 node IBM SP2 at NAS and clusters of workstations acting as a single MPP (like NAS's SGI Power-Challenge array and the J90 cluster) provide the required computation bandwidth for CFD calculations of transient problems. If we follow the traditional computational analysis steps for CFD (and we wish to construct an interactive visualizer) we need to be aware of the following: (1) Disk space requirements. A single snap-shot must contain at least the values (primitive variables) stored at the appropriate locations within the mesh. For most simple 3D Euler solvers that means 5 floating point words. Navier-Stokes solutions with turbulence models may contain 7 state-variables. (2) Disk speed vs. Computational speeds. The time required to read the complete solution of a saved time frame from disk is now longer than the compute time for a set number of iterations from an explicit solver. Depending, on the hardware and solver an iteration of an implicit code may also take less time than reading the solution from disk. If one examines the performance improvements in the last decade or two, it is easy to see that depending on disk performance (vs. CPU improvement) may not be the best method for enhancing interactivity. (3) Cluster and Parallel Machine I/O problems. Disk access time is much worse within current parallel machines and cluster of workstations that are acting in concert to solve a single problem. In this case we are not trying to read the volume of data, but are running the solver and the solver outputs the solution. These traditional network interfaces must be used for the file system. (4) Numerics of particle traces. Most visualization tools can work upon a single snap shot of the data but some visualization tools for transient problems require dealing with time.

Haimes, Robert↗

NASA NTRS1984

Sensor Radiance for a Midlatitude Atmospheric Model

The Herman radiative transfer code which iteratively traces solar radiance through a discrete number of scattering angles and many atmospheric layers was transferred to a personnal computer to reduce time in recompiling the source code. The code was then used to predict what ground reflectance would saturate the TM sensor output given a standard midlatitude atmospheric model. Output radiance is tabulated for the first four bands. Plots show radiance at the sensor as a function of solar zenith angle from a visibility of 40 km; solar zenith angle as a function of time of year for four latitudes over a typical portion of the descending node of a LANDSAT orbit; and values of ground reflectance required to saturate the TM sensor from three different aerosol loading conditions (corresponding to about 20 km, 40 km. and greater than 100 km visibility).

Source record↗

NASA NTRSDate not supplied

Flexible Data and Frame Synchronization Structure for the LunaNet PNT Signal

A LunaNet Lunar Augmented Navigation Service (LANS) is being developed to enable a position, navigation, and timing service for future Lunar operations. The signal includes two components. An in-phase data channel signal is spread by a 1.023 MCPS ranging code that provides a high-rate data message at 250 bps and is encoded by a strong Low Density Parity Check (LDPC) code. A pilot channel with a 5.115 MCPS spreading code is also provided. The pilot code is configured with a secondary (overlay) code that does not currently provide absolute time or frame Synchronization as is the case for L1C. This work shows the advantage of implementing an overlay structure that provides absolute time for the LunaNet LANS signal structure known as the Augmented Forward Signal (AFS). The LunaNet AFS structure was developed to service two classes of user receivers. The first class is a low-complexity user receiver that only receives the 1.023 MCPS signal and does not use the 5.115 MCPS pilot channel. For this class of user, a data frame Sync word is needed. The second class of receiver is a high-end receiver that can processes both data and pilot channels to take advantage of the higher chip rate pilot channel for enhanced robustness and improved accuracy. In the current draft LunaNet LANS AFS design, these users must employ the frame Sync word in the data channel and obtain absolute time after decoding the AFS navigation message. The signal structure would greatly benefit from the addition of a pilot overlay structure that provides absolute time and robust frame Sync for high-end users as done for L1C. To provide a more robust and interoperable AFS structure, this work summarizes a study and recommends alternatives for a new overlay code on the pilot channel that provides absolute time and a Sync word approach on the data channel. The overlay code and Sync word are designed to allow for flexible and robust data synchronization for both low- complexity and high-end user receivers. The new overlay code structure permits frame synchronization performance that is as good as or better than the L1 C signal, while enabling a determination of absolute time upon frame Sync to aid high-end assisted LANS AFS user receivers at low signal to noise levels. We also present the design of rate-matched 5G new radio (5GNR) LDPC codes that fit within the current 6000-symbol frame size along with a time of interval (TOI) word, frame ID (FID) word, and the remaining LunaNet AFS data message blocks. The paper describes and demonstrates robust frame Synchronization performance of the overlay code and Synch word approaches. The results are described in terms of probability of missed detection and probability of false alarm for a correct frame Synchronization at low Eb/No levels expected for decoding the TOI word and LDPC encoded data. Advantages of the proposed data Synchronization structure will be described along with use cases for low-end and high-end receivers. Practical implementation considerations will also be described.

LunaNet↗

DOE OSTI2019

An Energy Consistent Discretization of the Nonhydrostatic Equations in Primitive Variables

We derive a formulation of the nonhydrostatic equations in spherical geometry with a Lorenz staggered vertical discretization. The combination conserves a discrete energy in exact time integration when coupled with a mimetic horizontal discretization. The formulation is a version of Dubos and Tort (2014, https://doi.org/10.1175/MWR-D-14-00069.1) rewritten in terms of primitive variables. It is valid for terrain following mass or height coordinates and for both Eulerian or vertically Lagrangian discretizations. The discretization relies on an extension to Simmons and Burridge (1981, https://doi.org/10.1175/1520-0493(1981)109<0758:AEAAMC>2.0.CO;2) vertical differencing, which we show obeys a discrete derivative product rule. This product rule allows us to simplify the treatment of the vertical transport terms. Energy conservation is obtained via a term-by-term balance in the kinetic, internal, and potential energy budgets, ensuring an energy-consistent discretization up to time truncation error with no spurious sources of energy. We demonstrate convergence with respect to time truncation error in a spectral element code with a horizontal explicit vertically implicit implicit-explicit time stepping algorithm.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1989

Application of a full-potential solver to bending-torsion flutter in cascades

A two-dimensional, unsteady, full-potential cascade aerodynamic code has been used for flutter calculations. The code, which uses a time-marching implicit scheme with internal Newton-iterations at each time step, allows oscillatory blade motions with phase lag between adjacent blades to be modeled using a single inter-blade passage. This aerodynamic code has been used with a two-degrees-of-freedom typical section structural model to determine the aeroelastic stability of a bladed disk. The unsteady pressure results calculated from the aerodynamic code have been verified by comparison with results from the linear and linearized potential theories. Flutter results have been presented for two cases. A comparison with linear theory shows identical trends; however, the present calculations show a lower flutter frequency.

Bakhle, Milind A.↗

NASA NTRS1993

Reliability enhancement of Navier-Stokes codes through convergence enhancement

Reduction of total computing time required by an iterative algorithm for solving Navier-Stokes equations is an important aspect of making the existing and future analysis codes more cost effective. Several attempts have been made to accelerate the convergence of an explicit Runge-Kutta time-stepping algorithm. These acceleration methods are based on local time stepping, implicit residual smoothing, enthalpy damping, and multigrid techniques. Also, an extrapolation procedure based on the power method and the Minimal Residual Method (MRM) were applied to the Jameson's multigrid algorithm. The MRM uses same values of optimal weights for the corrections to every equation in a system and has not been shown to accelerate the scheme without multigriding. Our Distributed Minimal Residual (DMR) method based on our General Nonlinear Minimal Residual (GNLMR) method allows each component of the solution vector in a system of equations to have its own convergence speed. The DMR method was found capable of reducing the computation time by 10-75 percent depending on the test case and grid used. Recently, we have developed and tested a new method termed Sensitivity Based DMR or SBMR method that is easier to implement in different codes and is even more robust and computationally efficient than our DMR method.

Choi, K.-Y.↗

NASA NTRSDate not supplied

Flexible Data and Frame Synchronization Structure for the LunaNet PNT Signal

A LunaNet Lunar Augmented Navigation Service (LANS) is being developed to enable a position, navigation, and timing service for future Lunar operations [1]. The signal includes two components. An in-phase data channel signal is spread by a 1.023 MCPS ranging code that provides a high-rate data message at 250 bps and is encoded by a strong Low Density Parity Check (LDPC) code. A pilot channel with a 5.115 MCPS spreading code is also provided. The pilot code is configured with a secondary (overlay) code that does not currently provide absolute time or frame Synchronization as is the case for L1C [2] [3]. This work shows the advantage of implementing an overlay structure that provides absolute time for the LunaNet LANS signal structure known as the Augmented Forward Signal (AFS). The LunaNet AFS structure was developed to service two classes of user receivers. The first class is a low-complexity user receiver that only receives the 1.023 MCPS signal and does not use the 5.115 MCPS pilot channel. For this class of user, a data frame Sync word is needed. The second class of receiver is a high-end receiver that can processes both data and pilot channels to take advantage of the higher chip rate pilot channel for enhanced robustness and improved accuracy. In the current draft LunaNet LANS AFS design, these users must employ the frame Sync word in the data channel and obtain absolute time after decoding the AFS navigation message [2]. The signal structure would greatly benefit from the addition of a pilot overlay structure that provides absolute time and robust frame Sync for high-end users as done for L1C [3]. To provide a more robust and interoperable AFS structure, this work summarizes a study and recommends alternatives for a new overlay code on the pilot channel that provides absolute time and a Sync word approach on the data channel. The overlay code and Sync word are designed to allow for flexible and robust data synchronization for both low- complexity and high-end user receivers. The new overlay code structure permits frame synchronization performance that is as good as or better than the L1 C signal, while enabling a determination of absolute time upon frame Sync to aid high-end assisted LANS AFS user receivers at low signal to noise levels. We also present the design of rate-matched 5G new radio (5GNR) LDPC codes that fit within the current 6000-symbol frame size along with a time of interval (TOI) word, frame ID (FID) word, and the remaining LunaNet AFS data message blocks. The paper describes and demonstrates robust frame Synchronization performance of the overlay code and Synch word approaches. The results are described in terms of probability of missed detection and probability of false alarm for a correct frame Synchronization at low Eb/No levels expected for decoding the TOI word and LDPC encoded data. Advantages of the proposed data Synchronization structure will be described along with use cases for low-end and high-end receivers. Practical implementation considerations will also be described.

Philip Dafesh↗

DOE OSTI2020

Choosing the Best Modeling Platform for Radiological Risk Assessment Models - 20468

Radiological risk assessments, in the form of performance or safety assessments, are often required under regulations or guidance for remediation of contaminated land, decommissioning of contaminated buildings or structures, and radioactive waste disposal. These risk assessments are usually supported by fate and transport models that address decay and ingrowth of radionuclides, as well as their movement through engineered systems and the natural environment. These models are often projected thousands, or more, years into the future, largely because the radioactive species change through decay and ingrowth, and hence the magnitude of the radioactive effect changes with time. There are many computer codes that are available to address this type of modeling. They range from addressing specific pathways or processes such as infiltration of water, groundwater, surface water, air, biota, diffusion and advection of water and gases, to those that try to couple all processes together to evaluate the impact of fate and transport through the entire system to places in space and time to which access is assumed. These different types of codes are sometimes separated with the monikers process-level and systems-level codes, although it is often not clear that this separation does justice to the capabilities of the many codes that are available to evaluate fate and transport of radionuclides. The focus of this paper is the latter group of modeling codes. Several systems level modeling codes exist and are used. There are differences between these codes in terms of utility, flexibility, complexity and cost. The purpose of this paper is to compare a few of these codes in the context of work currently being performed by the International Atomic Energy Agency (IAEA) Modeling and Data for Radiological Impact Assessments (MODARIA) II Working Group 1 (WG1). The MODARIA II WG1's main focus is how stakeholder engaged decision analysis can, or should, be applied to radiological contamination problems so that better, longstanding, sustainable, solutions are reached. However, the WG1 also recognizes the potential impact of the modeling tools that are chosen to address radiological risk, which is often a primary objective of decision making for radiological problems. Other objectives might also be important, such as constraining costs, obtaining financing, minimizing impact on ecosystems, saving cultural resources, saving jobs, farmland, environmental justice, etc., in a full decision analysis for a given radiological contamination problem, but none of these other objectives have the same types of complex modeling needs as minimize radiological dose. Consequently, a further focus of WG1 is to evaluate the potential impacts on decision making of the choice of fate and transport, and risk assessment, modeling codes that are used to support decision making. The WG1 will produce a report at the end of 2020 that will focus on an approach to effective decision making and stakeholder engagement. The report will also consider the role that performance assessment modeling should play in the decision-making process, including the impact of the choice of modeling tools or computer codes on risk-informed decision making. Several sites around the World have been made available by Member States for these model comparisons, and several modeling tools have been considered. However, the focus of this paper is on two of the sites, one in Belgium and one in Ukraine, and on three of the tools: NORMALYSA (NORM And Legacy Site Assessment); GoldSim{sup C}, and AMBER{sup C}. The final report from this working group will also cover other modeling tools, including RESRAD, and PC-Cream{sup R}. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2023

Validation of time-dependent shift using the pulsed sphere benchmarks

The detailed behavior of neutrons in a rapidly changing time-dependent physical system is a challenging computational physics problem, particularly when using Monte Carlo methods on heterogeneous high-performance computing architectures. A small number of algorithms and code implementations have been shown to be performant for time-independent (fixed source and k-eigenvalue) Monte Carlo, and there are existing simulation tools that successfully solve the time-dependent Monte Carlo problem on smaller computing platforms. To bridge this gap, a time-dependent version of ORNL’s Shift code has been recently developed. Shift’s history-based algorithm on CPUs, and its event-based algorithm on GPUs, have both been observed to scale well to very large numbers of processors, which motivated the extension of this code to solve time-dependent problems. The validation of this new capability requires a comparison with time-dependent neutron experiments. Lawrence Livermore National Laboratory’s (LLNL) pulsed sphere benchmark experiments were simulated in Shift to validate both the time-independent as well as new time-dependent features recently incorporated into Shift. A suite of pulsed-sphere models was simulated using Shift and compared to the available experimental data and simulations with MCNP. Overall results indicate that Shift accurately simulates the pulsed sphere benchmarks, and that the new time-dependent modifications of Shift are working as intended. Validated exascale neutron transport codes are essential for a wide variety of future multiphysics applications.

Palmer, Camille J.↗

NASA NTRS1989

Approximate minimum-time trajectories for 2-link flexible manipulators

Powell's nonlinear programming code, VF02AD, was used to generate approximate minimum-time tip trajectories for 2-link semi-rigid and flexible manipulator movements in the horizontal plane. The manipulator is modeled with an efficient finite-element scheme for an n-link, m-joint system with horizontal-plane bending only. Constraints on the trajectory include boundary conditions on position and energy for a rest-to-rest maneuver, straight-line tracking between boundary positions, and motor torque limits. Trajectory comparisons utilize a change in the link stiffness, EI, to transition from the semi-rigid to flexible case. Results show the level of compliance necessary to excite significant modal behavior. Quiescence of the final configuration is examined with the finite-element model.

Eisler, G. R.↗