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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS2018

PURE: Scalable Phase Unwrapping with Spatial Redundant Arcs

Phase unwrapping is a key problem in many coherent imaging systems, such as syntheticapertureradar(SAR)interferometry. Ageneralformulationforredundant integration of finite differences for phase unwrapping (Costantini et al., 2010) was shown to produce a more reliable solution by exploiting redundant differential estimates. However, this technique requires a commercial linear programming solver for large-scale problems. For a linear cost function, we propose a method based on Dual Decomposition that breaks the given problem defined over a nonplanar graph into tractable sub-problems over planar subgraphs. We also propose a decomposition technique that exploits the underlying graph structure for solving thesub-problemsefficientlyandguaranteesasymptoticconvergencetotheglobally optimal solution. The experimental results demonstrate that the proposed approach is comparable to the existing state-of-the-art methods in terms of the estimate with a better runtime and memory footprint.

Lanka, Ravi↗
NASA NTRS2009

Direct Multiple Shooting Optimization with Variable Problem Parameters

Taking advantage of a novel approach to the design of the orbital transfer optimization problem and advanced non-linear programming algorithms, several optimal transfer trajectories are found for problems with and without known analytic solutions. This method treats the fixed known gravitational constants as optimization variables in order to reduce the need for an advanced initial guess. Complex periodic orbits are targeted with very simple guesses and the ability to find optimal transfers in spite of these bad guesses is successfully demonstrated. Impulsive transfers are considered for orbits in both the 2-body frame as well as the circular restricted three-body problem (CRTBP). The results with this new approach demonstrate the potential for increasing robustness for all types of orbit transfer problems.

Whitley, Ryan J.↗
NASA NTRS1996

A Higher Harmonic Optimal Controller to Optimise Rotorcraft Aeromechanical Behaviour

Three methods to optimize rotorcraft aeromechanical behavior for those cases where the rotorcraft plant can be adequately represented by a linear model system matrix were identified and implemented in a stand-alone code. These methods determine the optimal control vector which minimizes the vibration metric subject to constraints at discrete time points, and differ from the commonly used non-optimal constraint penalty methods such as those employed by conventional controllers in that the constraints are handled as actual constraints to an optimization problem rather than as just additional terms in the performance index. The first method is to use a Non-linear Programming algorithm to solve the problem directly. The second method is to solve the full set of non-linear equations which define the necessary conditions for optimality. The third method is to solve each of the possible reduced sets of equations defining the necessary conditions for optimality when the constraints are pre-selected to be either active or inactive, and then to simply select the best solution. The effects of maneuvers and aeroelasticity on the systems matrix are modelled by using a pseudo-random pseudo-row-dependency scheme to define the systems matrix. Cases run to date indicate that the first method of solution is reliable, robust, and easiest to use, and that it was superior to the conventional controllers which were considered.

Leyland, Jane Anne↗
NASA NTRS2016

Use of the NLP10x10 Sequential Quadratic Programming Algorithm To Solve Rotorcraft Hub Loads Minimisation Problems

Previous research and experimentation on the use of a non-linear programming constrained optimisation technique to define an optimal control vector for rotorcraft applications indicated that use of this methodology was feasible and desirable in many cases. In particular, use of non-linear programming methods that solve a sequence of related quadratic-programming sub-problems were used successfully to solve these problems. Accordingly, a licence for one of the latest versions of Professor Klaus Schittkowskis very successful Sequential Quadratic Programming NLPQLP software was obtained and used to experiment with and analyse typical optimisation problems of the type encountered in various rotorcraft wind tunnel and flight tests. This research resulted in the development of the general NLPQLP Computation System that could be used to solve problems of the type encountered in various rotorcraft applications where there is a linear dependence of the measurement vector on the control vector, and where equality andor inequality constraints might be imposed. This development was accomplished on a mainframe computer not part of actual wind tunnel andor flight-test experiment, but in a format which was transferable to wind tunnel lap-top computers. Emphasis was directed toward obtaining efficiency, robustness and speed in computation.The System was developed in support of the five-bladed SMART Rotor Active Flap Rotor Hub Loads analytical minimisation research. The design and development of the Computation System was tailored to address the particular requirements of the problem to minimise a performance metric function of measured hub load harmonic angular couple components by optimising the control vector harmonic flap angular couple components subject to constraints on the amplitudes of these control vector harmonic flap angular couple components. In addition, to facilitate real time wind tunnel experimentation, the ability to rapidly selectchange the particular hub load harmonic angular couple components andor the particular control vector harmonic angular couple components to be considered in the optimisation procedure was provided in the System. This capability allows the singling out of particular hub load frequencies andor particular flap angle frequencies to be analysed during testing operations. The System was used very successfully for the SMART Active Flap Rotor Hub minimisation problems considered in the study, the results of which were presented at the American Helicopter Society Fifth Decennial Aeromechanics Specialist Conference in January 2014. Excellent agreement between cases initiated with best guess starting estimates for the control vector elements and cases initiated with zero control vector starting element estimates resulted, indicating the robustness of the NLP10x10 algorithm.

Rotorcraft Hub Loads↗
NASA NTRS1998

Robust Control Design via Linear Programming

This paper deals with the problem of synthesizing or designing a feedback controller of fixed dynamic order. The closed loop specifications considered here are given in terms of a target performance vector representing a desired set of closed loop transfer functions connecting various signals. In general these point targets are unattainable with a fixed order controller. By enlarging the target from a fixed point set to an interval set the solvability conditions with a fixed order controller are relaxed and a solution is more easily enabled. Results from the parametric robust control literature can be used to design the interval target family so that the performance deterioration is acceptable, even when plant uncertainty is present. It is shown that it is possible to devise a computationally simple linear programming approach that attempts to meet the desired closed loop specifications.

Keel, L. H.↗
NASA NTRS2001

Synthesizing Dynamic Programming Algorithms from Linear Temporal Logic Formulae

The problem of testing a linear temporal logic (LTL) formula on a finite execution trace of events, generated by an executing program, occurs naturally in runtime analysis of software. We present an algorithm which takes an LTL formula and generates an efficient dynamic programming algorithm. The generated algorithm tests whether the LTL formula is satisfied by a finite trace of events given as input. The generated algorithm runs in linear time, its constant depending on the size of the LTL formula. The memory needed is constant, also depending on the size of the formula.

Rosu, Grigore↗
NASA NTRS2019

On Expected Value Strong Controllability

The Probabilistic Simple Temporal Network (PSTN) generalizes Simple Temporal Networks with Uncertainty (STNUs) by introducing probability distributions over the timing of uncontrollable timepoints. PSTNs are controllable if there is a strategy to execute the controllable timepoints while bounding the risk of violating any constraint to a small value. If this risk bound can't be satisfied, PSTNs are not considered controllable. We introduce the Expected Value Probabilistic SimpleTemporal Network (EPSTN), which extends PSTNs by including a benefit to the satisfaction of temporal constraints. We study the problem of Expected Value Strong Controllability (EvSC) of EPSTNs, which seeks a schedule maximizing the expected value of satisfied constraints. We solve the EvSC problem by extending a previously developed linear program, combined with search over constraints to violate at execution time. We describe conditions under which the solution to this linear program is the maximum expected value schedule. We then show how to search for constraints to discard, using the linear program at the core of the search. While the general problem is shown to be exponential, we conclude by providing several methods to bound the complexity of search.

Planning↗
NASA NTRS1974

Neighboring optimal guidance theory and computer program

Developments of the linear quadratic optimal control problem are discussed. The theory is applicable to the development of neighboring optimal feedback guidance gains, and is useful as a tool for synthesizing feedback control laws. A computer program which requires only the pertinent matrices of the linear quadratic problem is described.

Powers, W. F.↗
NASA NTRS1990

An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices, part 2

It is shown how the look-ahead Lanczos process (combined with a quasi-minimal residual QMR) approach) can be used to develop a robust black box solver for large sparse non-Hermitian linear systems. Details of an implementation of the resulting QMR algorithm are presented. It is demonstrated that the QMR method is closely related to the biconjugate gradient (BCG) algorithm; however, unlike BCG, the QMR algorithm has smooth convergence curves and good numerical properties. We report numerical experiments with our implementation of the look-ahead Lanczos algorithm, both for eigenvalue problem and linear systems. Also, program listings of FORTRAN implementations of the look-ahead algorithm and the QMR method are included.

Freund, Roland W.↗
NASA NTRS2004

Autonomous Guidance of Agile Small-scale Rotorcraft

This report describes a guidance system for agile vehicles based on a hybrid closed-loop model of the vehicle dynamics. The hybrid model represents the vehicle dynamics through a combination of linear-time-invariant control modes and pre-programmed, finite-duration maneuvers. This particular hybrid structure can be realized through a control system that combines trim controllers and a maneuvering control logic. The former enable precise trajectory tracking, and the latter enables trajectories at the edge of the vehicle capabilities. The closed-loop model is much simpler than the full vehicle equations of motion, yet it can capture a broad range of dynamic behaviors. It also supports a consistent link between the physical layer and the decision-making layer. The trajectory generation was formulated as an optimization problem using mixed-integer-linear-programming. The optimization is solved in a receding horizon fashion. Several techniques to improve the computational tractability were investigate. Simulation experiments using NASA Ames 'R-50 model show that this approach fully exploits the vehicle's agility.

Mettler, Bernard↗
NASA NTRS1986

Optimizing a Linear Array of Radiating Elements

EOPS empirically optimizes linear array of radiating elements. Program directly addresses problem of minimizing maximum side-lobe level of fixed length, linear arrays of radiating elements under realistic "on-the-vehicle" conditions. Used for both electromagnetic and acoustic arrays.

Blank, S. J.↗
NASA NTRS2012

A Linear Programming Approach to the Development of Contrail Reduction Strategies Satisfying Operationally Feasible Constraints

A class of strategies has been proposed to reduce contrail formation in the United States airspace. A 3D grid based on weather data and the cruising altitude level of aircraft is adjusted to avoid the persistent contrail potential area with the consideration to fuel-efficiency. In this paper, the authors introduce a contrail avoidance strategy on 3D grid by considering additional operationally feasible constraints from an air traffic controller's aspect. First, shifting too many aircraft to the same cruising level will make the miles-in-trail at this level smaller than the safety separation threshold. Furthermore, the high density of aircraft at one cruising level may exceed the workload for the traffic controller. Therefore, in our new model we restrict the number of total aircraft at each level. Second, the aircraft count variation for successive intervals cannot be too drastic since the workload to manage climbing/descending aircraft is much larger than managing cruising aircraft. The contrail reduction is formulated as an integer-programming problem and the problem is shown to have the property of total unimodularity. Solving the corresponding relaxed linear programming with the simplex method provides an optimal and integral solution to the problem. Simulation results are provided to illustrate the methodology.

Wei, Peng↗
NASA NTRS2022

SatNet: A Benchmark for Satellite Scheduling Optimization

Satellites provide essential services such as networking and weather tracking, and the number of near-earth and deep space satellites are expected to grow rapidly in the coming years. Communications with terrestrial ground stations is one of the critical functionalities of any space mission. Satellite scheduling is a problem that has been scientifically investigated since the 1970s. A central aspect of this problem is the need to consider resource contention and satellite visibility constraints as they require line of sight. Due to the combinatorial nature of the problem, prior solutions such as linear programs and evolutionary algorithms require extensive compute capabilities to output a feasible schedule for each scenario. Machine learning based scheduling can provide an alternative solution by training a model with historical data and generating a schedule quickly with model inference. We present SatNet, a benchmark for satellite scheduling optimization based on historical data from the NASA Deep Space Network. We propose formulation of the satellite scheduling problem as a Markov Decision Process and use reinforcement learning (RL) policies to generate schedules. The nature of constraints imposed by SatNet differ from other combinatorial optimization problems such as vehicle routing studied in prior literature. Our initial results indicate that RL is an alternative optimization approach that can generate candidate solutions of comparable quality to existing state-of-the-practice results. However, we also find that RL policies overfit to the training dataset and do not generalize well to new data, thereby necessitating continued research on reusable and generalizable agents.

Wilson, Brian↗
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 NTRS1986

On orbital allotments for geostationary satellites

The following satellite synthesis problem is addressed: communication satellites are to be allotted positions on the geostationary arc so that interference does not exceed a given acceptable level by enforcing conservative pairwise satellite separation. A desired location is specified for each satellite, and the objective is to minimize the sum of the deviations between the satellites' prescribed and desired locations. Two mixed integer programming models for the satellite synthesis problem are presented. Four solution strategies, branch-and-bound, Benders' decomposition, linear programming with restricted basis entry, and a switching heuristic, are used to find solutions to example synthesis problems. Computational results indicate the switching algorithm yields solutions of good quality in reasonable execution times when compared to the other solution methods. It is demonstrated that the switching algorithm can be applied to synthesis problems with the objective of minimizing the largest deviation between a prescribed location and the corresponding desired location. Furthermore, it is shown that the switching heuristic can use no conservative, location-dependent satellite separations in order to satisfy interference criteria.

Gonsalvez, David J. A.↗
NASA NTRSDate not supplied

Mixed Integer Linear Programming in Planning

This project, Activity Planning with Resources for the Exploration of Space (APRES), uses a mixed-integer linear program (MILP) to solve planning problems. This work enables APRES to interpret a model file and output a solution with improved human readability. A plan model is optimized using a MILP solver and the best solution is taken. Once a plan is generated, it is parsed allowing it to retain only desired information and modified for swift human readability.

Christina Erwin↗
NASA NTRS1984

Applying optimization software libraries to engineering problems

Nonlinear programming, preliminary design problems, performance simulation problems trajectory optimization, flight computer optimization, and linear least squares problems are among the topics covered. The nonlinear programming applications encountered in a large aerospace company are a real challenge to those who provide mathematical software libraries and consultation services. Typical applications include preliminary design studies, data fitting and filtering, jet engine simulations, control system analysis, and trajectory optimization and optimal control. Problem sizes range from single-variable unconstrained minimization to constrained problems with highly nonlinear functions and hundreds of variables. Most of the applications can be posed as nonlinearly constrained minimization problems. Highly complex optimization problems with many variables were formulated in the early days of computing. At the time, many problems had to be reformulated or bypassed entirely, and solution methods often relied on problem-specific strategies. Problems with more than ten variables usually went unsolved.

Healy, M. J.↗