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At least 739 records · Page 41

A weak Hamiltonian finite element method for optimal guidance of an advanced launch vehicle

A temporal finite-element method based on a mixed form of the Hamiltonian weak principle is presented for optimal control problems. The mixed form of this principle contains both states and costates as primary variables, which are expanded in terms of nodal values and simple shape functions. Time derivatives of the states and costates do not appear in the governing variational equation; the only quantities whose time derivatives appear therein are virtual states and virtual costates. Numerical results are presented for an elementary trajectory optimization problem; they show very good agreement with the exact solution along with excellent computational efficiency and self-starting capability. The feasibility of this approach for real-time guidance applications is evaluated. A simplified model for an advanced launch vehicle application that is suitable for finite-element solution is presented.

Hodges, Dewey H.↗

Solution of the minimum time-to-climb problem by matched asymptotic expansions

Application of singular perturbation techniques to trajectory optimization problems of flight mechanics is discussed. The method of matched asymptotic expansions is used to obtain an approximate solution to the aircraft minimum time-to-climb problem. Outer, boundary-layer, and composite solutions are obtained to zeroth and first orders. A stability criterion is derived for the zeroth-order boundary-layer solutions (the theory requires a form of boundary-layer stability). A numerical example is considered for which it is shown that the stability criterion is satisfied and a useful numerical solution is obtained. The zeroth-order solution proves to be a poor approximation, but the first-order solution gives a good approximation for both the trajectory and the minimum time-to-climb. The computational cost of the singular perturbation solution is considerably less than that of a steepest descent solution. Thus singular perturbation methods appear to be promising for the solution of optimal control problems.

Ardema, M. D.↗

A performance measure for evaluating aircraft landing trajectories

A general performance index is developed for evaluating aircraft landing trajectories. The primary term in the index is the effect of noise on people residing near the air terminal. Other terms included are passenger comfort, fuel consumed, and the time spent in the near-terminal area. Models are developed for aircraft engine noise, passenger comfort, the population distribution about a specific airport, and the aircraft flight behavior. While this performance index may be used in computing optimal trajectories, it is also useful for comparing nonoptimal trajectories which, for one reason or another, may be worthy of consideration. Some examples of such comparisons are included through simulations of landing. The aircraft considered is a Boeing 737.

Witt, R. M.↗

Preliminary design for a proposed Saturn mission with a second Galileo spacecraft

A study has been performed to assess the feasibility of using a second Galileo spacecraft for a Titan-probe/Saturn-orbiter mission that would be launched on a Shuttle/Centaur in the early 1990s. The interplanetary transfer is accomplished by means of a Delta-V earth-gravity-assist trajectory with a 3-year flight time from launch to earth flyby. Just prior to arrival at Saturn, the Titan probe is released, and the orbiter is used to relay data from the probe back to earth as it performs a close gravity-assist flyby of Titan. The orbiter then conducts a satellite tour containing multiple encounters with Saturn's satellites. Discussed in detail are the optimal trajectory design, Saturn approach trajectory design (Titan flyby, probe relay, and initial orbit selection), satellite tour design, and mission performance.

D'Amario, Louis A.↗

Optimization of interplanetary trajectories with unpowered planetary swingbys

A method is presented for calculating and optimizing unpowered planetary swingby trajectories using a patched conic trajectory generator. Examples of unpowered swingby trajectories are given to demonstrate the method. The method, which uses primer vector theory, is not highly accurate, but provides projections for preliminary mission definition studies. Advantages to using a patched conic trajectory simulation for preliminary studies which examine many different and complex missions include calculation speed and adaptability to changes or additions to the formulation.

Sauer, Carl G., Jr.↗

Annualized TASAR Benefits for Virgin America Operations

The Traffic Aware Strategic Aircrew Request (TASAR) concept offers onboard automation for the purpose of advising the pilot of traffic compatible trajectory changes that would be beneficial to the flight. A fast-time simulation study was conducted to assess the benefits of TASAR to Virgin America. The simulation compares historical trajectories without TASAR to trajectories developed with TASAR and evaluated by controllers against their objectives. It was estimated that about 25,000 gallons of fuel and about 2,500 minutes could be saved annually per aircraft. These savings were applied fleet-wide to produce an estimated annual cost savings to Virgin America in excess of $5 million due to fuel, maintenance, and depreciation cost savings. Switching to a more wind-optimal trajectory was found to be the use case that generated the highest benefits out of the three TASAR use cases analyzed. Virgin America TASAR requests peaked at two to four requests per hour per sector in high-altitude Oakland and Salt Lake City center sectors east of San Francisco.

Source record↗

Annualized TASAR Benefit Estimate for Virgin America Operations

The Traffic Aware Strategic Aircrew Request (TASAR) concept offers onboard automation for the purpose of advising the pilot of traffic compatible trajectory changes that would be beneficial to the flight. A fast-time simulation study was conducted to assess the benefits of TASAR to Virgin America. The simulation compares historical trajectories without TASAR to trajectories developed with TASAR and evaluated by controllers against their objectives. It was estimated that about 25,000 gallons of fuel and about 2,500 minutes could be saved annually per aircraft. These savings were applied fleet-wide to produce an estimated annual cost savings to Virgin America in excess of $5 million due to fuel, maintenance, and depreciation cost savings. Switching to a more wind-optimal trajectory was found to be the use case that generated the highest benefits out of the three TASAR use cases analyzed. Virgin America TASAR requests peaked at two to four requests per hour per sector in high-altitude Oakland and Salt Lake City center sectors east of San Francisco.

Henderson, Jeffrey↗

Stochastic multi-period optimal dispatch of energy storage in unbalanced distribution feeders

This report presents a convex, multi-period, AC-feasible Optimal Power Flow (OPF) framework that robustly dispatches flexible demand-side resources in unbalanced distribution feeders against uncertainty in very-short timescale solar Photo-Voltaic (PV) forecasts. This is valuable for power systems with significant behind-the-meter solar PV generation as their operation is affected by uncertainty from forecasts of demand and solar PV generation. The aim of this work is then to ensure the feasibility and reliability of distribution system operation under high solar PV penetration. We develop and present a novel, robust OPF formulation that accounts for both the nonlinear power flow constraints and the uncertainty in forecasts. This is achieved by linearizing an optimal trajectory and using first-order methods to systematically tighten voltage bounds. Case studies on a realistic distribution feeder shows the effectiveness of a receding-horizon implementation.

25 ENERGY STORAGE↗

Applications of fuzzy theories to multi-objective system optimization

Most of the computer aided design techniques developed so far deal with the optimization of a single objective function over the feasible design space. However, there often exist several engineering design problems which require a simultaneous consideration of several objective functions. This work presents several techniques of multiobjective optimization. In addition, a new formulation, based on fuzzy theories, is also introduced for the solution of multiobjective system optimization problems. The fuzzy formulation is useful in dealing with systems which are described imprecisely using fuzzy terms such as, 'sufficiently large', 'very strong', or 'satisfactory'. The proposed theory translates the imprecise linguistic statements and multiple objectives into equivalent crisp mathematical statements using fuzzy logic. The effectiveness of all the methodologies and theories presented is illustrated by formulating and solving two different engineering design problems. The first one involves the flight trajectory optimization and the main rotor design of helicopters. The second one is concerned with the integrated kinematic-dynamic synthesis of planar mechanisms. The use and effectiveness of nonlinear membership functions in fuzzy formulation is also demonstrated. The numerical results indicate that the fuzzy formulation could yield results which are qualitatively different from those provided by the crisp formulation. It is felt that the fuzzy formulation will handle real life design problems on a more rational basis.

Rao, S. S.↗

Finite element method for optimal guidance of an advanced launch vehicle

A temporal finite element based on a mixed form of Hamilton's weak principle is summarized for optimal control problems. The resulting weak Hamiltonian finite element method is extended to allow for discontinuities in the states and/or discontinuities in the system equations. An extension of the formulation to allow for control inequality constraints is also presented. The formulation does not require element quadrature, and it produces a sparse system of nonlinear algebraic equations. To evaluate its feasibility for real-time guidance applications, this approach is applied to the trajectory optimization of a four-state, two-stage model with inequality constraints for an advanced launch vehicle. Numerical results for this model are presented and compared to results from a multiple-shooting code. The results show the accuracy and computational efficiency of the finite element method.

Hodges, Dewey H.↗

Traffic Aware Strategic Aircrew Requests (TASAR)

The Traffic Aware Strategic Aircrew Request (TASAR) concept offers onboard automation for the purpose of advising the pilot of traffic compatible trajectory changes that would be beneficial to the flight. A fast-time simulation study was conducted to assess the benefits of TASAR to Alaska Airlines. The simulation compares historical trajectories without TASAR to trajectories developed with TASAR and evaluated by controllers against their objectives. It was estimated that between 8,000 and 12,000 gallons of fuel and 900 to 1,300 minutes could be saved annually per aircraft. These savings were applied fleet-wide to produce an estimated annual cost savings to Alaska Airlines in excess of $5 million due to fuel, maintenance, and depreciation cost savings. Switching to a more wind-optimal trajectory was found to be the use case that generated the highest benefits out of the three TASAR use cases analyzed. Alaska TASAR requests peaked at four to eight requests per hour in high-altitude Seattle center sectors south of Seattle-Tacoma airport..

Wing, David J.↗

Annualized TASAR Benefit Estimate for Alaska Airlines Operations

The Traffic Aware Strategic Aircrew Request (TASAR) concept offers onboard automation for the purpose of advising the pilot of traffic compatible trajectory changes that would be beneficial to the flight. A fast-time simulation study was conducted to assess the benefits of TASAR to Alaska Airlines. The simulation compares historical trajectories without TASAR to trajectories developed with TASAR and evaluated by controllers against their objectives. It was estimated that between 8,000 and 12,000 gallons of fuel and 900 to 1,300 minutes could be saved annually per aircraft. These savings were applied fleet-wide to produce an estimated annual cost savings to Alaska Airlines in excess of $5 million due to fuel, maintenance, and depreciation cost savings. Switching to a more wind-optimal trajectory was found to be the use case that generated the highest benefits out of the three TASAR use cases analyzed. Alaska TASAR requests peaked at four to eight requests per hour in high-altitude Seattle center sectors south of Seattle-Tacoma airport.

Henderson, Jeffrey↗

Integrated Framework to Enable Design Space Exploration of In-Space Transportation Architectures

Even with the recent shift in focus of NASA’s human spaceflight program towards the Moon, the long-term goal continues to be crewed missions to Mars. Regardless of the accepted architecture, in-space transportation systems are a critical portion to achieving this goal. An emphasis is placed on presenting decision makers with many options early on to make an informed down-selection. Although current processes are able to address any aspects of the challenging underlying multi-disciplinary analysis and optimization problem of these advanced concepts, they are unable to comprehensively perform design space exploration inexpensively,potentially leaving attractive alternatives on the table. A design framework is proposed that is capable of enabling the integrated mission analysis, vehicle sizing and synthesis problem for in-space transportation architectures. This framework is enabled through the use of the vehicle synthesis tool, Dynamic Rocket Equation Tool, various subsystem sizing models, and low-thrust trajectory optimization codes. As a case study to demonstrate the framework, two design points of a hybrid propulsion stage concept, studied by Georgia Tech’s 2018 Revolutionary Aerospace Systems Concepts-Academic Linkage team, is explored.

Akshay Prasad↗

Integrated Framework to Enable Design Space Exploration of In-Space Transportation Architectures

Even with the recent shift in focus of NASA’s human spaceflight program towards the Moon, the long-term goal continues to be crewed missions to Mars. Regardless of the accepted architecture, in-space transportation systems are a critical portion to achieving this goal. An emphasis is placed on presenting decision makers with many options early on to make an informed down-selection. Although current processes are able to address any aspects of the challenging underlying multi-disciplinary analysis and optimization problem of these advanced concepts, they are unable to comprehensively perform design space exploration inexpensively, potentially leaving attractive alternatives on the table. A design framework is proposed that is capable of enabling the integrated mission analysis, vehicle sizing and synthesis problem for in-space transportation architectures. This framework is enabled through the use of the vehicle synthesis tool, Dynamic Rocket Equation Tool, various subsystem sizing models, and low-thrust trajectory optimization codes. As a case study to demonstrate the framework, two design points of a hybrid propulsion stage concept, studied by Georgia Tech’s 2018 Revolutionary Aerospace Systems Concepts-Academic Linkage team, is explored.

Akshay Prasad↗

James Webb Space Telescope Navigation Optimization Challenges

This paper details the orbit determination, solar radiation pressure (SRP) modeling, and station-keeping maneuver planning for the NASA James Webb Space Telescope during the routine science phase of the mission. The complexities of SRP modeling driven by the vehicle’s large area, attitude profile, and attitude constraints for maneuver execution entail unique challenges for spaceflight navigation. The techniques utilized to combine predictive attitude and maneuver targeting modeling were refined using the experiences and data accumulated during and following the commissioning phase. The Navigation Team at NASA Goddard Space Flight Center’s Flight Dynamics Facility responded to these challenges and implemented methods for trajectory optimization and improving maneuver efficiency.

Flight Dynamics↗

James Webb Space Telescope Navigation Optimization Challenges

This paper details the orbit determination, solar radiation pressure (SRP) modeling, and station-keeping maneuver planning for the NASA James Webb Space Telescope during the routine science phase of the mission. The complexities of SRP modeling driven by the vehicle’s large area, attitude profile, and attitude constraints for maneuver execution entail unique challenges for spaceflight navigation. The techniques utilized to combine predictive attitude and maneuver targeting modeling were refined using the experiences and data accumulated during and following the commissioning phase. The Navigation Team at NASA Goddard Space Flight Center’s Flight Dynamics Facility responded to these challenges and implemented methods for trajectory optimization and improving maneuver efficiency.

Flight Dynamics↗

Simulated Trajectory Reconstruction of the Genesis Aeroballistic Testing for Dragonfly

Dragonfly is a NASA New Frontiers Program mission, led by Johns Hopkins Applied Physics Laboratory (APL), that will deliver a rotorcraft lander to Saturn’s moon, Titan, which uses a Genesis derived entry vehicle shape. During the Genesis mission, there were concerns with the dynamic stability of the configuration leading to testing at the Aeroballistic Research Facility at Eglin Air Force Base and Dragonfly shares these concerns given the similarity of the entry vehicle shapes. The focus of this paper is to compare the dynamics observed in the ballistic range shots from 1999 against the dynamics from simulation using the Program to Optimize Trajectories II (POST2). This analysis provides a confirmation that the aerodynamics developed during the Genesis mission, especially from ballistic range shots, is being used properly in the Dragonfly mission entry aerodynamics database.

Dragonfly↗

Preliminary Benefits Assessment of Traffic Aware Strategic Aircrew Requests (TASAR)

While en route, aircrews submit trajectory change requests to air traffic control (ATC) to better meet their objectives including reduced delays, reduced fuel burn, and passenger comfort. Aircrew requests are currently made with limited to no information on surrounding traffic. Consequently, these requests are uninformed about a key ATC objective, ensuring traffic separation, and therefore less likely to be accepted than requests informed by surrounding traffic and that avoids creating conflicts. This paper studies the benefits of providing aircrews with on-board decision support to generate optimized trajectory requests that are probed and cleared of known separation violations prior to issuing the request to ATC. These informed requests are referred to as traffic aware strategic aircrew requests (TASAR) and leverage traffic surveillance information available through Automatic Dependent Surveillance Broadcast (ADS-B) In capability. Preliminary fast-time simulation results show increased benefits with longer stage lengths since beneficial trajectory changes can be applied over a longer distance. Also, larger benefits were experienced between large hub airports as compared to other airport sizes. On average, an aircraft equipped with TASAR reduced its travel time by about one to four minutes per operation and fuel burn by about 50 to 550 lbs per operation depending on the objective of the aircrew (time, fuel, or weighted combination of time and fuel), class of airspace user, and aircraft type. These preliminary results are based on analysis of approximately one week of traffic in July 2012 and additional analysis is planned on a larger data set to confirm these initial findings.

Henderson, Jeff↗