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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Visualization techniques to aid in the analysis of multi-spectral astrophysical data sets

The goal of this project was to support the scientific analysis of multi-spectral astrophysical data by means of scientific visualization. Scientific visualization offers its greatest value if it is not used as a method separate or alternative to other data analysis methods but rather in addition to these methods. Together with quantitative analysis of data, such as offered by statistical analysis, image or signal processing, visualization attempts to explore all information inherent in astrophysical data in the most effective way. Data visualization is one aspect of data analysis. Our taxonomy as developed in Section 2 includes identification and access to existing information, preprocessing and quantitative analysis of data, visual representation and the user interface as major components to the software environment of astrophysical data analysis. In pursuing our goal to provide methods and tools for scientific visualization of multi-spectral astrophysical data, we therefore looked at scientific data analysis as one whole process, adding visualization tools to an already existing environment and integrating the various components that define a scientific data analysis environment. As long as the software development process of each component is separate from all other components, users of data analysis software are constantly interrupted in their scientific work in order to convert from one data format to another, or to move from one storage medium to another, or to switch from one user interface to another. We also took an in-depth look at scientific visualization and its underlying concepts, current visualization systems, their contributions, and their shortcomings. The role of data visualization is to stimulate mental processes different from quantitative data analysis, such as the perception of spatial relationships or the discovery of patterns or anomalies while browsing through large data sets. Visualization often leads to an intuitive understanding of the meaning of data values and their relationships by sacrificing accuracy in interpreting the data values. In order to be accurate in the interpretation, data values need to be measured, computed on, and compared to theoretical or empirical models (quantitative analysis). If visualization software hampers quantitative analysis (which happens with some commercial visualization products), its use is greatly diminished for astrophysical data analysis. The software system STAR (Scientific Toolkit for Astrophysical Research) was developed as a prototype during the course of the project to better understand the pragmatic concerns raised in the project. STAR led to a better understanding on the importance of collaboration between astrophysicists and computer scientists.

Brugel, Edward W.↗
NASA NTRS1993

Visualization techniques to aid in the analysis of multispectral astrophysical data sets

The goal of this project was to support the scientific analysis of multi-spectral astrophysical data by means of scientific visualization. Scientific visualization offers its greatest value if it is not used as a method separate or alternative to other data analysis methods but rather in addition to these methods. Together with quantitative analysis of data, such as offered by statistical analysis, image or signal processing, visualization attempts to explore all information inherent in astrophysical data in the most effective way. Data visualization is one aspect of data analysis. Our taxonomy as developed in Section 2 includes identification and access to existing information, preprocessing and quantitative analysis of data, visual representation and the user interface as major components to the software environment of astrophysical data analysis. In pursuing our goal to provide methods and tools for scientific visualization of multi-spectral astrophysical data, we therefore looked at scientific data analysis as one whole process, adding visualization tools to an already existing environment and integrating the various components that define a scientific data analysis environment. As long as the software development process of each component is separate from all other components, users of data analysis software are constantly interrupted in their scientific work in order to convert from one data format to another, or to move from one storage medium to another, or to switch from one user interface to another. We also took an in-depth look at scientific visualization and its underlying concepts, current visualization systems, their contributions and their shortcomings. The role of data visualization is to stimulate mental processes different from quantitative data analysis, such as the perception of spatial relationships or the discovery of patterns or anomalies while browsing through large data sets. Visualization often leads to an intuitive understanding of the meaning of data values and their relationships by sacrificing accuracy in interpreting the data values. In order to be accurate in the interpretation, data values need to be measured, computed on, and compared to theoretical or empirical models (quantitative analysis). If visualization software hampers quantitative analysis (which happens with some commercial visualization products), its use is greatly diminished for astrophysical data analysis. The software system STAR (Scientific Toolkit for Astrophysical Research) was developed as a prototype during the course of the project to better understand the pragmatic concerns raised in the project. STAR led to a better understanding on the importance of collaboration between astrophysicists and computer scientists. Twenty-one examples of the use of visualization for astrophysical data are included with this report. Sixteen publications related to efforts performed during or initiated through work on this project are listed at the end of this report.

Brugel, E. W.↗
NASA NTRS2008

NASA Crew Exploration Vehicle, Thermal Protection System, Lessons Learned

The Orion (CEV) thermal protection system (TPS) advanced development project (ADP) was initiated in late 2006 to reduce developmental risk by significant investment in multiple heat shield architectural solutions that can meet the needs both the Low Earth orbit (LEO) and Lunar return missions. At the same time, the CEV TPS ADP was also charged with developing a preliminary design for the heat shield to meet the PDR requirement and at the time of the PDR, transfer the design to Lockheed- Martin, the prime contractor. We reported on the developmental activities of the first 18 months at the IPPW5 in Bordeaux, France, last summer. In June 08, at the time of the IPPW6, the CEV TPS ADP would have nearly completed the preparation for the Orion PDR and would be close to the original three-year mark. We plan to report on the progress at the Atlanta workshop. In the past year, Orion TPS ADP investment in TPS Technology, especially in PICA ablative Heat-shield design, development, testing and engineering (DDTE) has paid off in enabling MSL mission to switch from SLA 561 V heat shield to PICA heat shield. CEV TPS ADP considered SLA 561 V as a candidate for LEO missions and our testing identified failure modes in SLA and as a result, we dropped SLA for further evaluation. This close synergy between two projects is a highly visible example of how investment in technology areas can and does benefit multiple missions. In addition, CEV TPS ADP has been able to revive the Apollo ablative system namely AVCOAT honeycomb architecture as an alternate to the baseline PICA architecture and we plan to report the progress we have made in AVCOAT. CEV TPS ADP has invested considerable resources in developing analytical models for PICA and AVCOAT, material property measurements that is essential to the design of the heat-shield, in arcjet testing, in understanding the differences between different arc jet facilities, namely NASA Ames, NASA JSC and Air Force's AEDC, and in Non-Destructive Evaluation (NDE), and in integration of and manufacturing heat shield as a system. The capabilities of the two heat shield systems including failure modes via testing and analysis, once established, can serve the Probe Community and future mission designers to inner and outer planetary exploration very well. For example, missions to Venus, Mars and Titan can use either one of the system by selecting the mission design parameters that utilizes the full characteristics of these system to make use of system efficiency that will result in reduced heat shield mass, system robustness that will enhance mission success and cost. We plan to present significant progresses of the past three years and highlight the significant contributions CEV TPS ADP Project has made to advance the state of the art in Thermal Protection System technology that has and will continue to benefit future entry probe missions.

NASA Crew Exploration Vehicle↗
NASA NTRS1989

Distortion and regulation characterization of a Mapham inverter

Output-voltage total harmonic distortion (THD) of a 20-kHz, 6-kVA Mapham resonant inverter is characterized as a function of its switching-to-resonant frequency ratio, f(s)/f(r), using the EASY5 Engineering Analysis System. EASY5 circuit simulation results are compared with hardware test results to verify the accuracy of the simulations. The effects of load on the THD versus f(s)/f(r) is investigated for resistive, leading, and lagging power factor load impedances. The effect of the series output capacitor on the Mapham inverter output-voltage distortion and inherent load regulation is characterized under loads of various power factors and magnitudes. An optimum series capacitor value which improves the inherent load regulation to better than 3 percent is identified. The optimum series capacitor value is different from the value predicted from a modeled frequency domain analysis. An explanation is proposed which takes into account the conduction overlap in the inductor pairs during steady-state inverter operation, which decreases the effective inductance of a Mapham inverter. A fault protection and current limit method is discussed which allows the Mapham inverter to operate into a short circuit, even when the inverter resonant circuit becomes overdamped.

Sundberg, Richard C.↗
NASA NTRS2010

NASA Tech Briefs, February 2010

Topics covered include: Insulation-Testing Cryostat With Lifting Mechanism; Optical Testing of Retroreflectors for Cryogenic Applications; Measuring Cyclic Error in Laser Heterodyne Interferometers; Self-Referencing Hartmann Test for Large-Aperture Telescopes; Measuring a Fiber-Optic Delay Line Using a Mode-Locked Laser; Reconfigurable Hardware for Compressing Hyperspectral Image Data; Spatio-Temporal Equalizer for a Receiving-Antenna Feed Array; High-Speed Ring Bus; Nanoionics-Based Switches for Radio-Frequency Applications; Lunar Dust-Tolerant Electrical Connector; Compact, Reliable EEPROM Controller; Quad-Chip Double-Balanced Frequency Tripler; Ka-Band Waveguide Two-Way Hybrid Combiner for MMIC Amplifiers; Radiation-Hardened Solid-State Drive; Use of Nanofibers to Strengthen Hydrogels of Silica, Other Oxides, and Aerogels; Two Concepts for Deployable Trusses; Concentric Nested Toroidal Inflatable Structures; Investigating Dynamics of Eccentricity in Turbomachines; Improved Low-Temperature Performance of Li-Ion Cells Using New Electrolytes; Integrity Monitoring of Mercury Discharge Lamps; White-Light Phase-Conjugate Mirrors as Distortion Correctors; Biasable, Balanced, Fundamental Submillimeter Monolithic Membrane Mixer; ICER-3D Hyperspectral Image Compression Software; and Context Modeler for Wavelet Compression of Spectral Hyperspectral Images.

Source record↗
NASA NTRS1989

Distortion and regulation characterization of a Mapham inverter

Output voltage Total Harmonic Distortion (THD) of a 20kHz, 6kVA Mapham resonant inverter is characterized as a function of its switching-to-resonant frequency ratio, f sub s/f sub r, using the EASY5 engineering analysis system. EASY5 circuit simulation results are compared with hardware test results to verify the accuracy of the simulations. The effects of load on the THD versus f sub s/f sub r ratio is investigated for resistive, leading, and lagging power factor load impedances. The effect of the series output capacitor on the Mapham inverter output voltage distortion and inherent load regulation is characterized under loads of various power factors and magnitudes. An optimum series capacitor value which improves the inherent load regulation to better than 3 percent is identified. The optimum series capacitor value is different than the value predicted from a modeled frequency domain analysis. An explanation is proposed which takes into account the conduction overlap in the inductor pairs during steady-state inverter operation, which decreases the effective inductance of a Mapham inverter. A fault protection and current limit method is discussed which allows the Mapham inverter to operate into a short circuit, even when the inverter resonant circuit becomes overdamped.

Sundberg, Richard C.↗
NASA NTRS2004

Novel Microstructures for Polymer-Liquid Crystal Composite Materials

There are a number of interface-dominated composite materials that contain a liquid crystalline (LC) phase in intimate contact with an isotropic phase. For example, polymer- dispersed liquid crystals, used in the fabrication of windows with switchable transparency, consist of micron size LC droplets dispersed in an isotropic polymer matrix. Many other types of liquid crystal composite materials can be envisioned that might have outstanding optical properties that could be exploited in novel chemical sensors, optical switches, and computer displays. This research project was based on the premise that many of these potentially useful LC composite materials can only be fabricated under microgravity conditions where gravity driven flows are absent. In the ground-based research described below, we have focused on a new class of LC composites that we call thermotropic- lyotropic liquid crystal systems (TLLCs). TLLCs consist of nanosize droplets of water dispersed in an LC matrix, with surfactants at the interface that stabilize the structure. By varying the type of surfactant one can access almost an infinite variety of unusual LC composite microstructures. Due to the importance of the interface in these types of systems, we have also developed molecular simulation models for liquid crystals at interfaces, and made some of the first measurements of the interfacial tension between liquid crystals and water.

Magda, Jules J.↗
NASA NTRS1999

Testing of the Engineering Model Electrical Power Control Unit for the Fluids and Combustion Facility

The John H. Glenn Research Center at Lewis Field (GRC) in Cleveland, OH and the Sundstrand Corporation in Rockford, IL have designed and developed an Engineering Model (EM) Electrical Power Control Unit (EPCU) for the Fluids Combustion Facility, (FCF) experiments to be flown on the International Space Station (ISS). The EPCU will be used as the power interface to the ISS power distribution system for the FCF's space experiments'test and telemetry hardware. Furthermore. it is proposed to be the common power interface for all experiments. The EPCU is a three kilowatt 12OVdc-to-28Vdc converter utilizing three independent Power Converter Units (PCUs), each rated at 1kWe (36Adc @ 28Vdc) which are paralleled and synchronized. Each converter may be fed from one of two ISS power channels. The 28Vdc loads are connected to the EPCU output via 48 solid-state and current-limiting switches, rated at 4Adc each. These switches may be paralleled to supply any given load up to the 108Adc normal operational limit of the paralleled converters. The EPCU was designed in this manner to maximize allocated-power utilization. to shed loads autonomously, to provide fault tolerance. and to provide a flexible power converter and control module to meet various ISS load demands. Tests of the EPCU in the Power Systems Facility testbed at GRC reveal that the overall converted-power efficiency, is approximately 89% with a nominal-input voltage of 12OVdc and a total load in the range of 4O% to 110% rated 28Vdc load. (The PCUs alone have an efficiency of approximately 94.5%). Furthermore, the EM unit passed all flight-qualification level (and beyond) vibration tests, passed ISS EMI (conducted, radiated. and susceptibility) requirements. successfully operated for extended periods in a thermal/vacuum chamber, was integrated with a proto-flight experiment and passed all stability and functional requirements.

Kimnach, Greg L.↗
NASA NTRS1993

On-board closed-loop congestion control for satellite based packet switching networks

NASA LeRC is currently investigating a satellite architecture that incorporates on-board packet switching capability. Because of the statistical nature of packet switching, arrival traffic may fluctuate and thus it is necessary to integrate congestion control mechanism as part of the on-board processing unit. This study focuses on the closed-loop reactive control. We investigate the impact of the long propagation delay on the performance and propose a scheme to overcome the problem. The scheme uses a global feedback signal to regulate the packet arrival rate of ground stations. In this scheme, the satellite continuously broadcasts the status of its output buffer and the ground stations respond by selectively discarding packets or by tagging the excessive packets as low-priority. The two schemes are evaluated by theoretical queuing analysis and simulation. The former is used to analyze the simplified model and to determine the basic trends and bounds, and the later is used to assess the performance of a more realistic system and to evaluate the effectiveness of more sophisticated control schemes. The results show that the long propagation delay makes the closed-loop congestion control less responsive. The broadcasted information can only be used to extract statistical information. The discarding scheme needs carefully-chosen status information and reduction function, and normally requires a significant amount of ground discarding to reduce the on-board packet loss probability. The tagging scheme is more effective since it tolerates more uncertainties and allows a larger margin of error in status information. It can protect the high-priority packets from excessive loss and fully utilize the downlink bandwidth at the same time.

Chu, Pong P.↗
NASA NTRS2006

NASA Tech Briefs, March 2006

Topics covered include: Medical Signal-Conditioning and Data-Interface System; Instruments for Reading Direct-Marked Data-Matrix Symbols; Processing EOS MLS Level-2 Data; Ground Processing of Data From the Mars Exploration Rovers; Estimating Total Electron Content Using 1,000+ GPS Receivers; NASA Solar Array Demonstrates Commercial Potential; Improved Control of Charging Voltage for Li-Ion Battery; Programmable Pulse-Position-Modulation Encoder; Wavelength-Agile External-Cavity Diode Laser for DWDM; Pattern-Recognition Processor Using Holographic Photopolymer; Submicrosecond Power-Switching Test Circuit; Three-Function Logic Gate Controlled by Analog Voltage; Integrated System for Autonomous Science; Montage Version 3.0; Utilizing AI in Temporal, Spatial, and Resource Scheduling; Satellite Image Mosaic Engine; Architecture for Control of the K9 Rover; HFGMC Enhancement of MAC/GMC; Automated Activation and Deactivation of a System Under Test; Cleaning Carbon Nanotubes by Use of Mild Oxygen Plasmas; Generating Aromatics From CO2 on Mars or Natural Gas on Earth; Attaching Thermocouples by Peening or Crimping; Heat Treatment of Friction-Stir-Welded 7050 Aluminum Plates; Generating Breathable Air Through Dissociation of N2O; High-Performance Scanning Acousto-Ultrasonic System; Correction for Thermal EMFs in Thermocouple Feedthroughs; Using Quasiparticle Poisoning To Detect Photons; Estimating Resolution Lengths of Hybrid Turbulence Models; Education and Training Module in Alertness Management; Cargo-Positioning System for Next-Generation Spacecraft; Micro-Imagers for Spaceborne Cell-Growth Experiments; Holographic Solar Photon Thrusters; Plasma-Based Detector of Outer-Space Dust Particles; and Generation of Data-Rate Profiles of Ka-Band Deep-Space Links.

Source record↗
NASA NTRS2021

Predicting the Functional State of Protein Kinases Using Interpretable Graph Neural Networks

Kinases are a family of proteins that function as molecular switches, regulating several essential cellular activities such as cell proliferation. Dysfunctional kinases are implicated in several types of cancers and hence they are actively pursued as drug targets. Given the vast number of complex kinase structures that are available in the protein data bank (PDB), there is a necessity to develop methodologies that can identify structurally important moieties of the kinases in an automated fashion, for such techniques can be instrumental in identifying novel drug targets. In this work, we develop a graph neural network (GNN) based deep learning framework for classifying the functionally active and inactive states of a large set of eukaryotic protein kinases, making use of their 3D structure from the PDB. We show that GNN based machine learning models can classify protein states with an accuracy greater than 97%. We further use the GNN models to automatically identify regions of the kinases that are important for its function. For this purpose, Gradient-weighted Class Activation Mapping (Grad-CAM) was implemented on the protein graphs. Remarkably, Grad-CAM consistently identifies the highly conserved DFG motif as the most important part of the protein across the entire kinome, without any prior input. Other regions of the hydrophobic core such as the HRD motif were also identified by the interpretable GNN framework, consistent with the literature. We discuss the significance of each of these regions in detail.

Ashwin Ravichandran↗
NASA NTRS1987

Advanced Components for Spaceborne Infrared Astronomy

Basic improvements in the technology of low noise read-out systems for low background detectors were demonstrated. Using discrete JFET integrating amplifiers at their optimum temperature of 55 K, read noise less than 7.5 electrons in 128 seconds of integration was obtained. Two models of single channel integrators are now available, the JF-77 for use between 50 and 80 K and the JF-4 for lower temperatures. A 1 x 15 linear array of complete integrators on a single integrated circuit was developed and will be made available in the near future. The successful operation of a superconducting stepper motor was demonstrated. The motor shows a three fold increase in torque over conventional motors operating at room temperature. The success of the motor stems from the use of superconducting coils in conjunction with developments in bearings for cryogenic use, rare-earth rotors, and motor cooling techniques. The current state of development will allow the rapid development of motors optimized for specific applications. An electronic switch capable of resetting cooled JFET integrating amplifiers was developed. The JFET integrating amplifiers that use this switch have demonstrated read noise of less than 10 electrons. The JFET reset device exhibits an extremely high open impedance and low leakage current. Capacitance is sufficiently low so as not to impair amplifier sensitivity. The effects of transient switching charges are minimized by a compensation technique and variable transient current problems inherent to devices of this type are overcome by external circuity.

Davidson, Arnold W.↗
NASA NTRS2019

A Simple Control to Reduce the Voltage Stress of Non-Conducting Switches in Three-Level ANPC Converter

With the development of wide band-gap (WBG) technology, the switching speed of power semiconductor devices is increased, which makes circuits more sensitive to parasitics. For three-level active neutral point clamped (3L-ANPC) converters, the over-voltage of non-conducting switches can be an issue. This paper analyzes the multiple commutation loops in 3L-ANPC converter and summarizes the impact factors of the over-voltage for the non-conducting switch. It is found that the nonlinearity of the output capacitance of the device can significantly influence the over-voltage. A simple control without introducing any additional hardware circuit is proposed to attenuate the impact of the nonlinearity. With the proposed control, the peak over-voltage of the non-conducting switch can be reduced significantly. Multi-pulse test is conducted for a 3L- ANPC converter built with silicon carbide (SiC) MOSFETs. The testing results show that the peak over-voltage decreases from 892 V to 624 V with the proposed control. More detailed analysis and experimental results will be provided in the final paper.

SiC MOSFET↗
NASA NTRS1995

Advanced Propulsion Power Distribution System for Next Generation Electric/Hybrid Vehicle: Preliminary System Studies - Phase 1

The report essentially summarizes the work performed in order to satisfy the above project objective. In the beginning, different energy storage devices, such as battery, flywheel and ultra capacitor are reviewed and compared, establishing the superiority of the battery. Then, the possible power sources, such as IC engine, diesel engine, gas turbine and fuel cell are reviewed and compared, and the superiority of IC engine has been established. Different types of machines for drive motor/engine generator, such as induction machine, PM synchronous machine and switched reluctance machine are compared, and the induction machine is established as the superior candidate. Similar discussion was made for power converters and devices. The Insulated Gate Bipolar Transistor (IGBT) appears to be the most superior device although Mercury Cadmium Telluride (MCT) shows future promise. Different types of candidate distribution systems with the possible combinations of power and energy sources have been discussed and the most viable system consisting of battery, IC engine and induction machine has been identified. Then, HFAC system has been compared with the DC system establishing the superiority of the former. The detailed component sizing calculations of HFAC and DC systems reinforce the superiority of the former. A preliminary control strategy has been developed for the candidate HFAC system. Finally, modeling and simulation study have been made to validate the system performance. The study in the report demonstrates the superiority of HFAC distribution system for next generation electric/hybrid vehicle.

Bose, Bimal K.↗
NASA NTRS2001

Spatial Linear Instability of Confluent Wake/Boundary Layers

The spatial linear instability of incompressible confluent wake/boundary layers is analyzed. The flow model adopted is a superposition of the Blasius boundary layer and a wake located above the boundary layer. The Orr-Sommerfeld equation is solved using a global numerical method for the resulting eigenvalue problem. The numerical procedure is validated by comparing the present solutions for the instability of the Blasius boundary layer and for the instability of a wake with published results. For the confluent wake/boundary layers, modes associated with the boundary layer and the wake, respectively, are identified. The boundary layer mode is found amplified as the wake approaches the wall. On the other hand, the modes associated with the wake, including a symmetric mode and an antisymmetric mode, are stabilized by the reduced distance between the wall and the wake. An unstable mode switching at low frequency is observed where the antisymmetric mode becomes more unstable than the symmetric mode when the wake velocity defect is high.

Liou, William W.↗
NASA NTRS1991

Development of software to improve AC power quality on large spacecraft

To insure the reliability of a 20 kHz, alternating current (AC) power system on spacecraft, it is essential to analyze its behavior under many adverse operating conditions. Some of these conditions include overloads, short circuits, switching surges, and harmonic distortions. Harmonic distortions can become a serious problem. It can cause malfunctions in equipment that the power system is supplying, and, during distortions such as voltage resonance, it can cause equipment and insulation failures due to the extreme peak voltages. To address the harmonic distortion issue, work was begun under the 1990 NASA-ASEE Summer Faculty Fellowship Program. Software, originally developed by EPRI, called HARMFLO, a power flow program capable of analyzing harmonic conditions on three phase, balanced, 60 Hz AC power systems, was modified to analyze single phase, 20 kHz, AC power systems. Since almost all of the equipment used on spacecraft power systems is electrically different from equipment used on terrestrial power systems, it was also necessary to develop mathematical models for the equipment to be used on the spacecraft. The modelling was also started under the same fellowship work period. Details of the modifications and models completed during the 1990 NASA-ASEE Summer Faculty Fellowship Program can be found in a project report. As a continuation of the work to develop a complete package necessary for the full analysis of spacecraft AC power system behavior, deployment work has continued through NASA Grant NAG3-1254. This report details the work covered by the above mentioned grant.

Kraft, L. Alan↗
NASA NTRS1997

High Resolution Far-Infrared Studies

We have been obtained high-resolution data (20 ft at 50 microns and 30 ft at 100 microns) on the KAO using Paul Harvey's 2 x 10 element photometer in both scanning and nodding modes. The practical flux limit for scanning is about 100 Jy. For fainter sources, a nodding (beam-switching) mode, which spend more time on the source, is used. This technique has been used successfully on objects as faint as 10 Jy; the 1 sigma noise for a 1 hour integration is about 1 Jy. Although not as sensitive as space-based instruments, the higher spatial resolution afforded by the KAO is essential in studying the far-infrared emission associated with young stars; in several cases we have been able to distinguish emission from multiple sources which were blended in the IRAS beam. In addition, comparison of fluxes in the KAO beam to those in the much larger IRAS beam provides information on the extended low-level emission arising from the surrounding region. We have developed a number of codes for producing model intensity distributions.

Mundy, Lee G.↗
NASA NTRS1998

Generic Equations for Constructing Smooth Paths Along Circles and Tangent Lines With Application to Airport Ground Paths

The primary purpose of this publication is to develop a mathematical model to describe smooth paths along any combination of circles and tangent lines. Two consecutive circles in a path are either tangent (externally or internally) or they appear on the same (lateral) or opposite (transverse) sides of a connecting tangent line. A path may start or end on either a segment or circle. The approach is to use mathematics common to robotics to design the path as a multilink manipulator. This approach allows a hierarchical view of the problem and keeps the notation manageable. A user simply specifies a few parameters to configure a path. Necessary and sufficient conditions automatically ensure the consistency of the inputs for a smooth path. Two example runway exit paths are given, and an angle to go assists in knowing when to switch from one path element to the next.

Barker, L. Keith↗