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At least 181 records · Page 10

Preliminary Optimal Orbit Design for the Laser Interferometer Space Antenna (LISA)

In this paper we present a preliminary optimal orbit analysis for the Laser Interferometer Space Antenna (LISA). LISA is a NASA/ESA mission to study gravitational waves and test predictions of general relativity. The nominal formation consists of three spacecraft in heliocentric orbits at 1 AU and trailing the Earth by twenty degrees. This configuration was chosen as a trade off to reduce the noise sources that will affect the instrument and to reduce the fuel to achieve the final orbit. We present equations for the nominal orbit design and discuss several different measures of performance for the LISA formation. All of the measures directly relate the formation dynamics to science performance. Also, constraints on the formation dynamics due to spacecraft and instrument limitations are discussed. Using the nominal solution as an initial guess, the formation is optimized using Sequential Quadratic Programming to maximize the performance while satisfying a set of nonlinear constraints. Results are presented for each of the performance measures.

Hughes, Steven P.↗

Kalman Filtering with Inequality Constraints for Turbofan Engine Health Estimation

Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This paper develops two analytic methods of incorporating state variable inequality constraints in the Kalman filter. The first method is a general technique of using hard constraints to enforce inequalities on the state variable estimates. The resultant filter is a combination of a standard Kalman filter and a quadratic programming problem. The second method uses soft constraints to estimate state variables that are known to vary slowly with time. (Soft constraints are constraints that are required to be approximately satisfied rather than exactly satisfied.) The incorporation of state variable constraints increases the computational effort of the filter but significantly improves its estimation accuracy. The improvement is proven theoretically and shown via simulation results. The use of the algorithm is demonstrated on a linearized simulation of a turbofan engine to estimate health parameters. The turbofan engine model contains 16 state variables, 12 measurements, and 8 component health parameters. It is shown that the new algorithms provide improved performance in this example over unconstrained Kalman filtering.

Simon, Dan↗

A Comparison of Trajectory Optimization Methods for the Impulsive Minimum Fuel Rendezvous Problem

In this paper we present a comparison of optimization approaches to the minimum fuel rendezvous problem. Both indirect and direct methods are compared for a variety of test cases. The indirect approach is based on primer vector theory. The direct approaches are implemented numerically and include Sequential Quadratic Programming (SQP), Quasi-Newton, Simplex, Genetic Algorithms, and Simulated Annealing. Each method is applied to a variety of test cases including, circular to circular coplanar orbits, LEO to GEO, and orbit phasing in highly elliptic orbits. We also compare different constrained optimization routines on complex orbit rendezvous problems with complicated, highly nonlinear constraints.

Hughes, Steven P.↗

A Comparison of Trajectory Optimization Methods for the Impulsive Minimum Fuel Rendezvous Problem

In this paper we present, a comparison of trajectory optimization approaches for the minimum fuel rendezvous problem. Both indirect and direct methods are compared for a variety of test cases. The indirect approach is based on primer vector theory. The direct approaches are implemented numerically and include Sequential Quadratic Programming (SQP). Quasi- Newton and Nelder-Meade Simplex. Several cost function parameterizations are considered for the direct approach. We choose one direct approach that appears to be the most flexible. Both the direct and indirect methods are applied to a variety of test cases which are chosen to demonstrate the performance of each method in different flight regimes. The first test case is a simple circular-to-circular coplanar rendezvous. The second test case is an elliptic-to-elliptic line of apsides rotation. The final test case is an orbit phasing maneuver sequence in a highly elliptic orbit. For each test case we present a comparison of the performance of all methods we consider in this paper.

Hughes, Steven P.↗

Aircraft Turbofan Engine Health Estimation Using Constrained Kalman Filtering

Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This paper develops an analytic method of incorporating state variable inequality constraints in the Kalman filter. The resultant filter is a combination of a standard Kalman filter and a quadratic programming problem. The incorporation of state variable constraints increases the computational effort of the filter but significantly improves its estimation accuracy. The improvement is proven theoretically and shown via simulation results obtained from application to a turbofan engine model. This model contains 16 state variables, 12 measurements, and 8 component health parameters. It is shown that the new algorithms provide improved performance in this example over unconstrained Kalman filtering.

Simon, Dan↗

Orbit Design for Phase I and II of the Magnetospheric Multiscale Mission (MMS)

The Magnetospheric Multiscale Mission (MMS) is a NASA mission intended to make fundamental advancements in our understanding of the Earth's Magnetosphere. There are three processes that MMS is intended to study including magnetic recon- nection, charged particle acceleration, and turbulence. There are four phases of the MMS mission and each phase is designed to study a particular region of the Earth's magnetosphere. The mission is composed of a formation of four spacecraft that are nominally in a regular tetrahedron formation. In this work, we present optimal orbit designs for Phase I and II. This entails designing optimal reference orbits so that the spacecraft dwell-time in the region of interest is a maximum. This is non-trivial because the Earth's magnetosphere is dynamic and its shape and position are not constant in inertial space. Optimal orbit design for MMS also entails designing the formation so that the relative motion of the four spacecraft yields the greatest science return. We develop performance metrics that are related to the science return, and use Sequential Quadratic Programming (SQP) to determine optimal relative motion solutions. We also ensure that practical constraints such as maximum eclipse time and minimum inter-spacecraft separation distances are not violated.

Hughes, Steve P.↗

Formation Tetrahedron Design for Phase I of the Magnetospheric Multiscale Mission

The Magnetospheric Multiscale Mission (MMS) is a NASA mission intended to make fundamental advancements in our understanding of the Earth's Magnetosphere. There are three processes that MMS will study including magnetic reconnection, charged particle acceleration, and turbulence. There are four phases in the nominal mission and this work addresses some of the outstanding issues in phase I. The nominal phase I orbit is 1.2 x 12 R(sub e) highly elliptic orbit with four spacecraft nominally forming a regular tetrahedron. In this paper we investigate the relative dynamics of the four MMS spacecraft about an assumed reference orbit. There are several tetrahedron dimensions required in Phase I of the mission and in this work we design optimal tetrahedrons for the 10 km baseline. The performance metric used in the optimization process is directly related to the science return, and is based on an extension of previous work performed by Glassmeier. The optimizer we use is a commercially available Sequential Quadratic Programming (SQP) routine. Multiple optimal solutions are found, and we characterize how the performance of the formation varies between different regions of the reference orbit.

Hughes, Steven P.↗

Orbit Design for Phase I and II of the Magnetospheric Multiscale Mission

The Magnetospheric Multiscale Mission (MMS) is a NASA mission intended to make fundamental advancements in our understanding of the Earth s magnetosphere. There are three processes that MMS is intended to study including magnetic reconnection, charged particle acceleration, and turbulence. There are four phases of the MMS mission and each phase is designed to study a particular region of the Earth's magnetosphere. The mission is composed of a formation of four spacecraft that are nominally in a regular tetrahedron formation. In this work, we present optimal orbit designs for Phase I and II. This entails designing reference orbits such that the spacecraft dwell-time in the region of interest is a maximum. This is non-trivial because the Earth's magnetosphere is dynamic and its shape and position are not constant in inertial space. Optimal orbit design for MMS also entails designing the formation so that the relative motion of the four spacecraft yields the greatest science return. We develop performance metrics that are directly related to the science return, and use Sequential Quadratic Programming (SQP) to determine optimal relative motion solutions. While designing for optimal science return, we also consider practical constraints such as maximum eclipse time and minimum inter-spacecraft separation distances. Data are presented that illustrates how long we can ensure that the formation remains in the relevant region of the Earth's magnetosphere. We also draw general conclusions about where in the orbit acceptable tetrahedron configurations can be provided and for how long.

Hughes, Steve P.↗

Modeling of polychromatic attenuation using computed tomography reconstructed images

This paper presents a procedure for estimating an accurate model of the CT imaging process including spectral effects. As raw projection data are typically unavailable to the end-user, we adopt a post-processing approach that utilizes the reconstructed images themselves. This approach includes errors from x-ray scatter and the nonidealities of the built-in soft tissue correction into the beam characteristics, which is crucial to beam hardening correction algorithms that are designed to be applied directly to CT reconstructed images. We formulate this approach as a quadratic programming problem and propose two different methods, dimension reduction and regularization, to overcome ill conditioning in the model. For the regularization method we use a statistical procedure, Cross Validation, to select the regularization parameter. We have constructed step-wedge phantoms to estimate the effective beam spectrum of a GE CT-I scanner. Using the derived spectrum, we computed the attenuation ratios for the wedge phantoms and found that the worst case modeling error is less than 3% of the corresponding attenuation ratio. We have also built two test (hybrid) phantoms to evaluate the effective spectrum. Based on these test phantoms, we have shown that the effective beam spectrum provides an accurate model for the CT imaging process. Last, we used a simple beam hardening correction experiment to demonstrate the effectiveness of the estimated beam profile for removing beam hardening artifacts. We hope that this estimation procedure will encourage more independent research on beam hardening corrections and will lead to the development of application-specific beam hardening correction algorithms.

NASA Discipline Musculoskeletal↗

Multiplexed Predictive Control of a Large Commercial Turbofan Engine

Model predictive control is a strategy well-suited to handle the highly complex, nonlinear, uncertain, and constrained dynamics involved in aircraft engine control problems. However, it has thus far been infeasible to implement model predictive control in engine control applications, because of the combination of model complexity and the time allotted for the control update calculation. In this paper, a multiplexed implementation is proposed that dramatically reduces the computational burden of the quadratic programming optimization that must be solved online as part of the model-predictive-control algorithm. Actuator updates are calculated sequentially and cyclically in a multiplexed implementation, as opposed to the simultaneous optimization taking place in conventional model predictive control. Theoretical aspects are discussed based on a nominal model, and actual computational savings are demonstrated using a realistic commercial engine model.

Richter, hanz↗

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 Tech Briefs, August 2005

Topics include: Hidden Identification on Parts: Magnetic Machine-Readable Matrix Symbols; System for Processing Coded OFDM Under Doppler and Fading; Multipurpose Hyperspectral Imaging System; Magnetic-Flux-Compensated Voltage Divider; High-Performance Satellite/Terrestrial-Network Gateway; Internet-Based System for Voice Communication With the ISS; Stripline/Microstrip Transition in Multilayer Circuit Board; Dual-Band Feed for a Microwave Reflector Antenna; Quadratic Programming for Allocating Control Effort; Range Process Simulation Tool; Simulator of Space Communication Networks; Computing Q-D Relationships for Storage of Rocket Fuels; Contour Error Map Algorithm; Portfolio Analysis Tool; Glass Frit Filters for Collecting Metal Oxide Nanoparticles; Anhydrous Proton-Conducting Membranes for Fuel Cells; Portable Electron-Beam Free-Form Fabrication System; Miniature Laboratory for Detecting Sparse Biomolecules; Multicompartment Liquid-Cooling/Warming Protective Garments; Laser Metrology for an Optical-Path-Length Modulator; PCM Passive Cooling System Containing Active Subsystems; Automated Electrostatics Environmental Chamber; Estimating Aeroheating of a 3D Body Using a 2D Flow Solver; Artificial Immune System for Recognizing Patterns; Computing the Thermodynamic State of a Cryogenic Fluid; Safety and Mission Assurance Performance Metric; Magnetic Control of Concentration Gradient in Microgravity; Avionics for a Small Robotic Inspection Spacecraft; and Simulation of Dynamics of a Flexible Miniature Airplane.

Source record↗

Active Mirror Predictive and Requirements Verification Software (AMP-ReVS)

This software is designed to predict large active mirror performance at various stages in the fabrication lifecycle of the mirror. It was developed for 1-meter class powered mirrors for astronomical purposes, but is extensible to other geometries. The package accepts finite element model (FEM) inputs and laboratory measured data for large optical-quality mirrors with active figure control. It computes phenomenological contributions to the surface figure error using several built-in optimization techniques. These phenomena include stresses induced in the mirror by the manufacturing process and the support structure, the test procedure, high spatial frequency errors introduced by the polishing process, and other process-dependent deleterious effects due to light-weighting of the mirror. Then, depending on the maturity of the mirror, it either predicts the best surface figure error that the mirror will attain, or it verifies that the requirements for the error sources have been met once the best surface figure error has been measured. The unique feature of this software is that it ties together physical phenomenology with wavefront sensing and control techniques and various optimization methods including convex optimization, Kalman filtering, and quadratic programming to both generate predictive models and to do requirements verification. This software combines three distinct disciplines: wavefront control, predictive models based on FEM, and requirements verification using measured data in a robust, reusable code that is applicable to any large optics for ground and space telescopes. The software also includes state-of-the-art wavefront control algorithms that allow closed-loop performance to be computed. It allows for quantitative trade studies to be performed for optical systems engineering, including computing the best surface figure error under various testing and operating conditions. After the mirror manufacturing process and testing have been completed, the software package can be used to verify that the underlying requirements have been met.

Basinger, Scott A.↗

Minimum deltaV Burn Planning for the International Space Station Using a Hybrid Optimization Technique, Level 1

The International Space Station's (ISS) trajectory is coordinated and executed by the Trajectory Operations and Planning (TOPO) group at NASA's Johnson Space Center. TOPO group personnel routinely generate look-ahead trajectories for the ISS that incorporate translation burns needed to maintain its orbit over the next three to twelve months. The burns are modeled as in-plane, horizontal burns, and must meet operational trajectory constraints imposed by both NASA and the Russian Space Agency. In generating these trajectories, TOPO personnel must determine the number of burns to model, each burn's Time of Ignition (TIG), and magnitude (i.e. deltaV) that meet these constraints. The current process for targeting these burns is manually intensive, and does not take advantage of more modern techniques that can reduce the workload needed to find feasible burn solutions, i.e. solutions that simply meet the constraints, or provide optimal burn solutions that minimize the total DeltaV while simultaneously meeting the constraints. A two-level, hybrid optimization technique is proposed to find both feasible and globally optimal burn solutions for ISS trajectory planning. For optimal solutions, the technique breaks the optimization problem into two distinct sub-problems, one for choosing the optimal number of burns and each burn's optimal TIG, and the other for computing the minimum total deltaV burn solution that satisfies the trajectory constraints. Each of the two aforementioned levels uses a different optimization algorithm to solve one of the sub-problems, giving rise to a hybrid technique. Level 2, or the outer level, uses a genetic algorithm to select the number of burns and each burn's TIG. Level 1, or the inner level, uses the burn TIGs from Level 2 in a sequential quadratic programming (SQP) algorithm to compute a minimum total deltaV burn solution subject to the trajectory constraints. The total deltaV from Level 1 is then used as a fitness function by the genetic algorithm in Level 2 to select the number of burns and their TIGs for the next generation. In this manner, the two levels solve their respective sub-problems separately but collaboratively until a burn solution is found that globally minimizes the deltaV across the entire trajectory. Feasible solutions can also be found by simply using the SQP algorithm in Level 1 with a zero cost function. This paper discusses the formulation of the Level 1 sub-problem and the development of a prototype software tool to solve it. The Level 2 sub-problem will be discussed in a future work. Following the Level 1 formulation and solution, several look-ahead trajectory examples for the ISS are explored. In each case, the burn targeting results using the current process are compared against a feasible solution found using Level 1 in the proposed technique. Level 1 is then used to find a minimum deltaV solution given the fixed number of burns and burn TIGs. The optimal solution is compared with the previously found feasible solution to determine the deltaV (and therefore propellant) savings. The proposed technique seeks to both improve the current process for targeting ISS burns, and to add the capability to optimize ISS burns in a novel fashion. The optimal solutions found using this technique can potentially save hundreds of kilograms of propellant over the course of the ISS mission compared to feasible solutions alone. While the software tool being developed to implement this technique is specific to ISS, the concept is extensible to other long-duration, central-body orbiting missions that must perform orbit maintenance burns to meet operational trajectory constraints.

Brown, Aaron J.↗

Multibody Simulation of REMORA CubeSat Docking to and Pushing a Spent Rocket Booster

This paper details the multibody simulation of three phases of critical importance to the feasibility of the REMORA CubeSat space debris mitigation concept: the final approach of the CubeSat to a spent rocket booster; the grappling of the spent rocket booster using a robotic arm; and the pushing of the spent rocket booster to divert its course from another on-orbit asset. The extension of a robotic mobility and manipulation modeling toolkit (M3TK) from multibody dynamics simulation of manipulators and ground vehicles to simulation of orbital robotics is outlined. This includes the identification of the appropriate parameters required to concisely and generically describe thruster loads, thruster mixing, spacecraft control, and spacecraft navigation for the purpose of on-orbit robotics simulation. A high-level spacecraft navigator commands maneuvers to target spacecraft states. A PID spacecraft controller takes the target states and calculates desired forces and torques. A thruster mixer solves a quadratic program to determine the optimal thruster firing times for the propulsion system. Pulse width modulated actuation of eight canted cold gas thrusters is used in the simulated approach to a rocket nozzle from a distance of 200 m. A five degree of freedom robotic arm is controlled to position a pair of pincers to grasp the rocket nozzle. Contact dynamics are used to accurately simulate the grasping of the rocket nozzle by the pincers. A similar, but separate simulation is performed to assess the ability of the REMORA CubeSat to push the large spent rocket booster. This diversion maneuver makes use of an additional, larger thruster, and pushes the rocket booster in excess of 400 m. Appropriate motor control gains on the robotic arm are found to be higher during the pushing phase than those which are appropriate during free motion; this increase promotes rigidity of the arm and allows it to properly direct the pushing force. Challenges encountered in time step selection for numerical stability of the simulation are also discussed.

Mukherjee, Rudranarayan↗

Chance-Constrained System Identification of Nonlinear Discrete Systems with Safety and Stability Guarantees

This paper presents a discrete-time nonlinear system identification method while satisfying the stability and safety properties of the system with high probability. An Extreme Learning Machine (ELM) is used with a Gaussian assumption on the function reconstruction error. A quadratically constrained quadratic program (QCQP) is developed with probabilistic safety and stability constraints that are only required to be satisfied at sampled points inside the invariant region. The proposed method is validated using two simulation examples: a two degrees-of-freedom (DoF) robot manipulator with constraints on joint angles whose trajectories are guaranteed to remain inside a safe set and on motion trajectories data of a hand-drawn shape.

Iman Salehi↗

Optimization Based Data Mining Approah for Forecasting Real-Time Energy Demand

The worldwide concern over environmental degradation, increasing pressure on electric utility companies to meet peak energy demand, and the requirement to avoid purchasing power from the real-time energy market are motivating the utility companies to explore new approaches for forecasting energy demand. Until now, most approaches for forecasting energy demand rely on monthly electrical consumption data. The emergence of smart meters data is changing the data space for electric utility companies, and creating opportunities for utility companies to collect and analyze energy consumption data at a much finer temporal resolution of at least 15-minutes interval. While the data granularity provided by smart meters is important, there are still other challenges in forecasting energy demand; these challenges include lack of information about appliances usage and occupants behavior. Consequently, in this paper, we develop an optimization based data mining approach for forecasting real-time energy demand using smart meters data. The objective of our approach is to develop a robust estimation of energy demand without access to these other building and behavior data. Specifically, the forecasting problem is formulated as a quadratic programming problem and solved using the so-called support vector machine (SVM) technique in an online setting. The parameters of the SVM technique are optimized using simulated annealing approach. The proposed approach is applied to hourly smart meters data for several residential customers over several days.

data mining↗

Optimal Voltage Regulation for Unbalanced Distribution Networks Considering Distributed Energy Resources

With increasing penetration of distributed generation in the distribution networks (DN), the secure and optimal operation of DN has become an important concern. In this paper, an iterative quadratic constrained quadratic programming model to minimize voltage deviations and maximize distributed energy resource (DER) active power output in a three phase unbalanced distribution system is developed. The optimization model is based on the linearized sensitivity coefficients between controlled variables (e.g., node voltages) and control variables (e.g., real and reactive power injections of DERs). To avoid the oscillation of solution when it is close to the optimum, a golden search method is introduced to control the step size. Numerical simulations on modified IEEE 13 nodes test feeders show the efficiency of the proposed model. Compared to the results solved by heuristic search (harmony algorithm), the proposed model converges quickly to the global optimum.

distributed energy resources↗