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At least 883 records · Page 49
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Model verifies design of mobile data modem

It has been proposed to use differential minimum shift keying (DMSK) modems in spacecraft-based mobile communications systems. For an employment of these modems, it is necessary that the transmitted carrier frequency be known prior to signal detection. In addition, the time needed by the receiver to lock onto the carrier frequency must be minimized. The present article is concerned with a DMSK modem developed for the Mobile Satellite Service. This device demonstrated fast acquisition time and good performance in the presence of fading. However, certain problems arose in initial attempts to study the acquisition behavior of the AFC loop through breadboard techniques. The development of a software model of the AFC loop is discussed, taking into account two cases which were plotted using the model. Attention is given to a demonstration of the viability of the modem by an approach involving modeling and analysis of the frequency synchronizer.

Davarian, F.↗
NASA NTRS1998

Fast Transformation of Temporal Plans for Efficient Execution

Temporal plans permit significant flexibility in specifying the occurrence time of events. Plan execution can make good use of that flexibility. However, the advantage of execution flexibility is counterbalanced by the cost during execution of propagating the time of occurrence of events throughout the flexible plan. To minimize execution latency, this propagation needs to be very efficient. Previous work showed that every temporal plan can be reformulated as a dispatchable plan, i.e., one for which propagation to immediate neighbors is sufficient. A simple algorithm was given that finds a dispatchable plan with a minimum number of edges in cubic time and quadratic space. In this paper, we focus on the efficiency of the reformulation process, and improve on that result. A new algorithm is presented that uses linear space and has time complexity equivalent to Johnson s algorithm for all-pairs shortest-path problems. Experimental evidence confirms the practical effectiveness of the new algorithm. For example, on a large commercial application, the performance is improved by at least two orders of magnitude. We further show that the dispatchable plan, already minimal in the total number of edges, can also be made minimal in the maximum number of edges incoming or outgoing at any node.

Tsamardinos, Ioannis↗
NASA NTRS2016

Xeropreservation of Functionalized Lipid Biomarkers in Hyperarid Soils in the Atacama Desert

Our understanding of long-term organic matter preservation comes mostly from studies in aquatic systems. In contrast, taphonomic processes in extremely dry environments are relatively understudied and are poorly understood. We investigated the accumulation and preservation of lipid biomarkers in hyperarid soils in the Yungay region of the Atacama Desert. Lipids from seven soil horizons in a 2.5 m vertical profile were extracted and analyzed using GC-MS and LC-MS. Diagnostic functionalized lipids and geolipids were detected and increased in abundance and diversity with depth. Deeper clay units contain fossil organic matter (radiocarbon dead) that has been protected from rainwater since the onset of hyperaridity. We show that these clay units contain lipids in an excellent state of structural preservation with functional groups and unsaturated bonds in carbon chains. This indicates that minimal degradation of lipids has occurred in these soils since the time of their deposition between greater than 40,000 and 2 million years ago. The exceptional structural preservation of biomarkers is likely due to the long-term hyperaridity that has minimized microbial and enzymatic activity, a taphonomic process we term xeropreservation (i.e., preservation by drying). The degree of biomarker preservation allowed us to reconstruct major changes in ecology in the Yungay region that reflect a shift in hydrological regime from wet to dry since the early Quaternary. Our results suggest that hyperarid environments, which comprise 7.5 percent of the continental landmass, could represent a rich and relatively unexplored source of paleobiological informationon Earth.

Hyperarid↗
NASA NTRS1988

Research on output feedback control

A summary is presented of the main results obtained during the course of research on output feedback control. The term output feedback is used to denote a controller design approach which does not rely on an observer to estimate the states of the system. Thus, the order of the controller is fixed, and can even be zero order, which amounts to constant gain ouput feedback. The emphasis has been on optimal output feedback. That is, a fixed order controller is designed based on minimizing a suitably chosen quadratic performance index. A number of problem areas that arise in this context have been addressed. These include developing suitable methods for selecting an index of performance, both time domain and frequency domain methods for achieving robustness of the closed loop system, developing canonical forms to achieve a minimal parameterization for the controller, two time scale design formulations for ill-conditioned systems, and the development of convergent numerical algorithms for solving the output feedback problem.

Calise, Anthony J.↗
NASA NTRSDate not supplied

Aerial Vehicle Routing and Scheduling for UAS Traffic Management: A Monte Carlo Tree Search Approach

Numerous unmanned aircraft systems operating at low altitudes to deliver goods and services may one day become ubiquitous in our cities. In the Unmanned Aircraft Systems (UAS) Traffic Management (UTM) framework, such a concept is envisioned, where aerial vehicles operate beyond visual line of sight (BVLOS) within specifically reserved and time stamped “corridors” in the airspace. For example, these corridors or operational intent volumes can connect an aerial vehicle’s origin site to its destination site for package delivery operations. There may also be more than one corridor available for an aerial vehicle to choose from and often different corridors may intersect with one another. Thus, it is imperative to ensure flight trajectories belonging to different aerial vehicles are not in conflict. Per the UTM CONOPs, we assume that a vehicle almost always stays inside its corridor or operational volume. This work provides a framework for strategic deconfliction of UTM or package delivery drones, where we schedule the departure time of all vehicles subject to various temporal constraints (including the corridor deconfliction at the intersections). We present the “multi-route weighted package delivery problem” which serves as an exemplifying model for strategic deconfliction in UTM. In the multi-route weighted package delivery problem, a graph network is given which consists of a set of depots (source) and drop-off (destination) nodes, with multiple routes (defined as a sequence of waypoints) connecting the depots to drop-off nodes. In addition, routes are weighted by the associated ground risk and total travel distance for package delivery. The goal is for a known set of aerial vehicles to depart from the depots, choose a route and take off time, while avoiding conflicts with other aerial vehicles, and minimizing both risk and distance traveled. We provide a mixed integer linear programming (MILP) formulation of the problem, as well as a heuristic solution based on Monte Carlo Tree Search (MCTS) – a method used in game theory and artificial intelligence – to overcome limitations inherent to optimal solvers. Computational results show the advantages of using MCTS over the MILP formulation; the former can provide a sub-optimal solution quickly, and may sometimes even reach an optimal solution, whereas the latter may not even produce a solution in reasonable time. Furthermore, results from both the MILP formulation and MCTS methods were validated using a preliminary agent-based simulator implementing the UTM concept of operations. Thus, the MCTS method can be seen as a scalable solution to the complex multi-route weighted package delivery problem and may possibly be extended to similar complex optimization problems.

Kenny Chour↗
NASA NTRS2009

Spacecraft Station-Keeping Trajectory and Mission Design Tools

Two tools were developed for designing station-keeping trajectories and estimating delta-v requirements for designing missions to a small body such as a comet or asteroid. This innovation uses NPOPT, a non-sparse, general-purpose sequential quadratic programming (SQP) optimizer and the Two-Level Differential Corrector (T-LDC) in LTool (Libration point mission design Tool) to design three kinds of station-keeping scripts: vertical hovering, horizontal hovering, and orbiting. The T-LDC is used to differentially correct several trajectory legs that join hovering points. In a vertical hovering, the maximum and minimum range points must be connected smoothly while maintaining the spacecrafts range from a small body, all within the law of gravity and the solar radiation pressure. The same is true for a horizontal hover. A PatchPoint is an LTool class that denotes a space-time event with some extra information for differential correction, including a set of constraints to be satisfied by T-LDC. Given a set of PatchPoints, each with its own constraint, the T-LDC differentially corrects the entire trajectory by connecting each trajectory leg joined by PatchPoints while satisfying all specified constraints at the same time. Vertical and horizontal hover both are needed to minimize delta-v spent for station keeping. A Python I/F to NPOPT has been written to be used from an LTool script. In vertical hovering, the spacecraft stays along the line joining the Sun and a small body. An instantaneous delta-v toward the anti- Sun direction is applied at the closest approach to the small body for station keeping. For example, the spacecraft hovers between the minimum range (2 km) point and the maximum range (2.5 km) point from the asteroid 1989ML. Horizontal hovering buys more time for a spacecraft to recover if, for any reason, a planned thrust fails, by returning almost to the initial position after some time later via a near elliptical orbit around the small body. The mapping or staging orbit may be similarly generated using T-LDC with a set of constraints. Some delta-v tables are generated for several different asteroid masses.

Chung, Min-Kun J.↗
NASA NTRS2012

Real Time Space Weather Support for Chandra X-Ray Observatory Operations

NASA launched the Chandra X-ray Observatory in July 1999. Soon after first light in August 1999, however, degradation in the energy resolution and charge transfer efficiency of the Advanced CCD Imaging Spectrometer (ACIS) x-ray detectors was observed. The source of the degradation was quickly identified as radiation damage in the charge-transfer channel of the front-illuminated CCDs, by weakly penetrating ( soft , 100 500 keV) protons as Chandra passed through the Earth s radiation belts and ring currents. As soft protons were not considered a risk to spacecraft health before launch, the only on-board radiation monitoring system is the Electron, Proton, and Helium Instrument (EPHIN) which was included on Chandra with the primary purpose of monitoring energetic solar particle events. Further damage to the ACIS detector has been successfully mitigated through a combination of careful mission planning, autonomous on-board radiation protection, and manual intervention based upon real-time monitoring of the soft-proton environment. The AE-8 and AP-8 trapped radiation models and Chandra Radiation Models are used to schedule science operations in regions of low proton flux. EPHIN has been used as the primary autonomous in-situ radiation trigger; but, it is not sensitive to the soft protons that damage the front-illuminated CCDs. Monitoring of near-real-time space weather data sources provides critical information on the proton environment outside the Earth s magnetosphere due to solar proton events and other phenomena. The operations team uses data from the Geostationary Operational Environmental Satellites (GOES) to provide near-real-time monitoring of the proton environment; however, these data do not give a representative measure of the soft-proton (< 1 MeV) flux in Chandra s high elliptical orbit. The only source of relevant measurements of sub-MeV protons is the Electron, Proton, and Alpha Monitor (EPAM) aboard the Advanced Composition Explorer (ACE) satellite at L1, with real-time data provided by NOAA s Space Weather Prediction Center. This presentation describes the radiation mitigation strategies to minimize the proton damage in the ACIS CCD detectors and the importance of real-time data sources that are used to protect the ACIS detector system from space weather events.

O'Dell, Stephen L.↗
NASA NTRS2019

UAVSAR real-time embedded GPU processor

Synthetic aperture radar (SAR) can provide high-resolution imagery regardless of cloud cover or lighting conditions. These qualities make SAR potentially well-suited for informing response efforts to natural and man-made disasters, but such applications require data products with minimal latency. To meet this challenge, we implemented a real-time SAR processor capable of producing 10 m imagery using an NVIDIA Jetson TX2 embedded GPU module. With its low mass (87 g module) and power consumption under 8 W, the system also holds promise for spaceborne applications.

Tung, Wayne↗
NASA NTRS2016

Xeropreservation of Functionalized Lipid Biomarkers in Hyperarid Soils in the Atacama Desert

Our understanding of long-term organic matter preservation comes mostly from studies in aquatic systems. In contrast, taphonomic processes in extremely dry environments are relatively understudied and are poorly understood. We investigated the accumulation and preservation of lipid biomarkers in hyperarid soils in the Yungay region of the Atacama Desert. Lipids from seven soil horizons in a 2.5 meter vertical profile were extracted and analyzed using GC-MS ( Gas Chromatography-Mass Spectrometry) and LC-MS (Liquid Chromatography-Mass Spectrometry). Diagnostic functionalized lipids and geolipids were detected and increased in abundance and diversity with depth. Deeper clay units contain fossil organic matter (radiocarbon dead) that has been protected from rainwater since the onset of hyperaridity. We show that these clay units contain lipids in an excellent state of structural preservation with functional groups and unsaturated bonds in carbon chains. This indicates that minimal degradation of lipids has occurred in these soils since the time of their deposition between more than 40,000 and up to 2 million years ago. The exceptional structural preservation of biomarkers is likely due to the long-term hyperaridity that has minimized microbial and enzymatic activity, a taphonomic process we term xeropreservation (i.e. preservation by drying). The degree of biomarker preservation allowed us to reconstruct major changes in ecology in the Yungay region that reflect a shift in hydrological regime from wet to dry since the early Quaternary. Our results suggest that hyperarid environments, which comprise 7.5 percent of the continental landmass, could represent a rich and relatively unexplored source of paleobiological information on Earth.

Xeropreservation↗
NASA NTRS1962

An Investigation of the Effects of the Time Lag Due to Long Transmission Distance upon Remote Control. Phase II - Vehicle Experiments. Phase III - Conclusions

An experimental program is undertaken to define the effects upon remote control of long transmission delays. Investigation centers around remote control of a ground vehicle, which is considered to be a representative remote control task. A series of pursuit tracking tests is performed with transport lags ranging from 0 to 6 seconds between the control and the controlled quantity. Various target speeds are tracked with both velocity and acceleration controls. Two types of tracking are performed in an attempt to bracket the actual vehicle situation. In the first the operator attempts to follow the target with his controlled quantity in real time, using the delayed position and rates as feedback. In the second he attempts to follow the target with the delayed controlled quantity. In addition, tests are performed substituting simple electronic models for the human in an attempt to gain an understanding of human response with time delays in the control loop. A series of tests with an actual vehicle are performed with the intent of relating the tracking tests to the actual situation of interest. Time delays of from 0 to 3 seconds are included in the control loop. Performance is scored at various speeds over both continuous and obstacle courses. Both two and four-wheel steering are investigated. In the experiments the effects of all variables except delay magnitude and target complexity are minimized. Curves are obtained showing performance as a function of time delay and target complexity. These curves are discussed. Correlation of the tracking and vehicle experiments is discussed. Comments are made concerning the design of a minimum control system for a remotely controlled lunar roving vehicle.

REMOTE CONTROL↗
NASA NTRS2017

A New Non-Resonant Laser-Induced Fluorescence Instrument for the Airborne in Situ Measurement of Formaldehyde

A new in situ instrument for gas-phase formaldehyde (HCHO), COmpact Formaldehyde FluorescencE Experiment (COFFEE), is presented. COFFEE utilizes nonresonant laser-induced fluorescence (NR-LIF) to measure HCHO, with 300 mW of 40 kHz 355 nm laser output exciting multiple HCHO absorption features. The resulting HCHO fluorescence is collected at 5 ns resolution, and the fluorescence time profile is fit to yield the ambient HCHO mixing ratio. Typical 1 sigma precision at approximately 0 pptv HCHO is 150 pptv for 1 s data. The compact instrument was designed to operate with minimal in-flight operator interaction and infrequent maintenance (1-2 times per year). COFFEE fits in the wing pod of the Alpha Jet stationed at the NASA Ames Research Center and has successfully collected HCHO data on 27 flights through 2017 March. The frequent flights, combined with a potentially long-term data set, makes the Alpha Jet a promising platform for validation of satellite-based column HCHO.

Nonresonant laser-induced fluorescenc↗
NASA NTRS1997

Neural Generalized Predictive Control: A Newton-Raphson Implementation

An efficient implementation of Generalized Predictive Control using a multi-layer feedforward neural network as the plant's nonlinear model is presented. In using Newton-Raphson as the optimization algorithm, the number of iterations needed for convergence is significantly reduced from other techniques. The main cost of the Newton-Raphson algorithm is in the calculation of the Hessian, but even with this overhead the low iteration numbers make Newton-Raphson faster than other techniques and a viable algorithm for real-time control. This paper presents a detailed derivation of the Neural Generalized Predictive Control algorithm with Newton-Raphson as the minimization algorithm. Simulation results show convergence to a good solution within two iterations and timing data show that real-time control is possible. Comments about the algorithm's implementation are also included.

Soloway, Donald↗
NASA NTRS1995

Analysis of composite ablators using massively parallel computation

In this work, the feasibility of using massively parallel computation to study the response of ablative materials is investigated. Explicit and implicit finite difference methods are used on a massively parallel computer, the Thinking Machines CM-5. The governing equations are a set of nonlinear partial differential equations. The governing equations are developed for three sample problems: (1) transpiration cooling, (2) ablative composite plate, and (3) restrained thermal growth testing. The transpiration cooling problem is solved using a solution scheme based solely on the explicit finite difference method. The results are compared with available analytical steady-state through-thickness temperature and pressure distributions and good agreement between the numerical and analytical solutions is found. It is also found that a solution scheme based on the explicit finite difference method has the following advantages: incorporates complex physics easily, results in a simple algorithm, and is easily parallelizable. However, a solution scheme of this kind needs very small time steps to maintain stability. A solution scheme based on the implicit finite difference method has the advantage that it does not require very small times steps to maintain stability. However, this kind of solution scheme has the disadvantages that complex physics cannot be easily incorporated into the algorithm and that the solution scheme is difficult to parallelize. A hybrid solution scheme is then developed to combine the strengths of the explicit and implicit finite difference methods and minimize their weaknesses. This is achieved by identifying the critical time scale associated with the governing equations and applying the appropriate finite difference method according to this critical time scale. The hybrid solution scheme is then applied to the ablative composite plate and restrained thermal growth problems. The gas storage term is included in the explicit pressure calculation of both problems. Results from ablative composite plate problems are compared with previous numerical results which did not include the gas storage term. It is found that the through-thickness temperature distribution is not affected much by the gas storage term. However, the through-thickness pressure and stress distributions, and the extent of chemical reactions are different from the previous numerical results. Two types of chemical reaction models are used in the restrained thermal growth testing problem: (1) pressure-independent Arrhenius type rate equations and (2) pressure-dependent Arrhenius type rate equations. The numerical results are compared to experimental results and the pressure-dependent model is able to capture the trend better than the pressure-independent one. Finally, a performance study is done on the hybrid algorithm using the ablative composite plate problem. It is found that there is a good speedup of performance on the CM-5. For 32 CPU's, the speedup of performance is 20. The efficiency of the algorithm is found to be a function of the size and execution time of a given problem and the effective parallelization of the algorithm. It also seems that there is an optimum number of CPU's to use for a given problem.

Shia, David↗
NASA NTRS1990

Decomposition technique and optimal trajectories for the aeroassisted flight experiment

An actual geosynchronous Earth orbit-to-low Earth orbit (GEO-to-LEO) transfer is considered with reference to the aeroassisted flight experiment (AFE) spacecraft, and optimal trajectories are determined by minimizing the total characteristic velocity. The optimization is performed with respect to the time history of the controls (angle of attack and angle of bank), the entry path inclination and the flight time being free. Two transfer maneuvers are considered: direct ascent (DA) to LEO and indirect ascent (IA) to LEO via parking Earth orbit (PEO). By taking into account certain assumptions, the complete system can be decoupled into two subsystems: one describing the longitudinal motion and one describing the lateral motion. The angle of attack history, the entry path inclination, and the flight time are determined via the longitudinal motion subsystem. In this subsystem, the difference between the instantaneous bank angle and a constant bank angle is minimized in the least square sense subject to the specified orbital inclination requirement. Both the angles of attack and the angle of bank are shown to be constant. This result has considerable importance in the design of nominal trajectories to be used in the guidance of AFE and aeroassisted orbital transfer (AOT) vehicles.

Miele, A.↗
NASA NTRS1991

Decomposition technique and optimal trajectories for the aeroassisted flight experiment

An actual geosynchronous earth orbit-to-low earth orbit (GEO-to-LEO) transfer is considered with reference to the aeroassisted flight experiment (AFE) spacecraft, and optimal trajectories are determined by minimizing the total characteristic velocity. The optimization is performed with respect to the time history of the controls (angle of attack and angle of bank), the entry path inclination and the flight time being free. Two transfer maneuvers are considered: direct ascent (DA) to LEO and indirect ascent (IA) to LEO via parking earth orbit (PEO). By taking into account certain assumptions, the complete system can be decoupled into two subsystems: one describing the longitudinal motion and one describing the lateral motion. The angle of attack history, the entry path inclination, and the flight time are determined via the longitudinal motion subsystem. In this subsystem, the difference between the instantaneous bank angle and a constant bank angle is minimized in the least square sense subject to the specified orbital inclination requirement. Both the angles of attack and the angle of bank are shown to be constant. This result has considerable importance in the design of nominal trajectories to be used in the guidance of AFE and aeroassisted orbital transfer (AOT) vehicles.

Miele, A.↗
NASA NTRS1977

Development of a drift-correction procedure for a direct-reading spectrometer

A procedure which provides automatic correction for drifts in the radiometric sensitivity of each detector channel in a direct-reading emission spectrometer is described. Such drifts are customarily controlled by the regular analyses of standards, which provide corrections for changes in the excitational, optical, and electronic components of the instrument. This standardization procedure, however, corrects for the optical and electronic drifts. It is a step that must be taken if the time, effort, and cost of processing standards is to be minimized. This method of radiometric drift correction uses a 1,000-W tungsten-halogen reference lamp to illuminate each detector through the same optical path as that traversed during sample analysis. The responses of the detector channels to this reference light are regularly compared with channel response to the same light intensity at the time of analytical calibration in order to determine and correct for drift. Except for placing the lamp in position, the procedure is fully automated and compensates for changes in spectral intensity due to variations in lamp current. A discussion of the implementation of this drift-correction system is included.

Chapman, G. B., II↗
NASA NTRS2021

Compass Final Report: Nuclear Electric Propulsion (NEP)-Chemical Vehicle 1.2

Many previous studies have examined sending crews to and from Mars. The most economical involved a ‘conjunction’ class whereby the crew spends around 500 days on Mars waiting for a ‘cheap’ return. The total mission time results in over a 1000-day mission duration (about 3 years). Given the current experience level of only one year on the International Space Station (ISS), it of interest to reduce that time to only two years, thus reducing risk and minimizing required Mars surface infrastructure. The Phase 1.1 Study goal was stated as follows, “Determine the feasibility of a two-year roundtrip class Mars mission concept of operation that enables boots on Mars no later than 2036.” While the Phase1 study did show feasibility for the NEP-Chemical option, the 2036 Opposition opportunity was found to stress the schedule due to proposed technology development schedules. A 2039 Opposition (which requires even more energy than the 2036 case) was chosen as representative for Phase 1.2. Phase 1.2 also sought to further refine the concept, building on the feasibility, but addressing several challenges brought by the red team and habitat team. Given the date of 2039, nearer term technologies, primarily nuclear thermal and nuclear electric were deemed as the most viable for these missions. As will be shown, the energy required to perform such a mission in only two years (for the 2039 opportunity at least) is about three times that of the three-year conjunction mission. The rocket equation shows that this mission would then require several times the propellant of the three-year mission unless the specific impulse (ISP) of the propulsion system can be increased. Based on lunar needs, a limit of five Space Launch System (SLS) launchers with 8.4m fairings was imposed for the piloted transportation portion of the mission, limiting the size of the system. When using nuclear electric propulsion, the main limiting factor was packaging the required radiator area. The higher Isp nuclear electric propulsion (NEP) system option is described herein but with a twist: in order to keep the size of radiators packageable in one SLS and use proven reactor power system technology (~1200K reactor outlet temperature and superalloy-class Brayton) the NEP system had to be combined with a chemical propulsion system. This combination of electric propulsion and high thrust chemical was found to be useful in previous design studies combining solar electric propulsion (SEP) and chemical propulsion. Such a combination allowed the low-thrust system to provide significant change in velocity (∆V) during the interplanetary portions of the mission, thereby notably reducing the ∆V required by the high thrust system to capture and depart from the Mars gravity well. Here the high thrust ‘impulsive’ system is more efficient due to the Oberth Effect. A plethora of trades, both at the mission and system level, as well as the subsystem level were performed to develop these vehicle concepts. An entire family of NEP-Chemical transportation vehicles is described herein. The main driver and the primary focus was the piloted vehicle but additional concepts for cargo were performed using the same ‘building blocks’ in order to reduce costs and provide commonality.

Nuclear Power↗
NASA NTRS2011

Optimal Time Advance In Terminal Area Arrivals: Throughput vs. Fuel Savings

The current operational practice in scheduling air traffic arriving at an airport is to adjust flight schedules by delay, i.e. a postponement of an aircrafts arrival at a scheduled location, to manage safely the FAA-mandated separation constraints between aircraft. To meet the observed and forecast growth in traffic demand, however, the practice of time advance (speeding up an aircraft toward a scheduled location) is envisioned for future operations as a practice additional to delay. Time advance has two potential advantages. The first is the capability to minimize, or at least reduce, the excess separation (the distances between pairs of aircraft immediately in-trail) and thereby to increase the throughput of the arriving traffic. The second is to reduce the total traffic delay when the traffic sample is below saturation density. A cost associated with time advance is the fuel expenditure required by an aircraft to speed up. We present an optimal control model of air traffic arriving in a terminal area and solve it using the Pontryagin Maximum Principle. The admissible controls allow time advance, as well as delay, some of the way. The cost function reflects the trade-off between minimizing two competing objectives: excess separation (negatively correlated with throughput) and fuel burn. A number of instances are solved using three different methods, to demonstrate consistency of solutions.

Sadovsky, Alexander V .↗