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All sourcesNASA NTRSDOE OSTI
NASA NTRS2007

Solar Sail Model Validation from Echo Trajectories

The NASA In-Space Propulsion program has been engaged in a project to increase the technology readiness of solar sails. Recently, these efforts came to fruition in the form of several software tools to model solar sail guidance, navigation and control. Furthermore, solar sails are one of five technologies competing for the New Millennium Program Space Technology 9 flight demonstration mission. The historic Echo 1 and Echo 2 balloons were comprised of aluminized Mylar, which is the near-term material of choice for solar sails. Both spacecraft, but particularly Echo 2, were in low Earth orbits with characteristics similar to the proposed Space Technology 9 orbit. Therefore, the Echo balloons are excellent test cases for solar sail model validation. We present the results of studies of Echo trajectories that validate solar sail models of optics, solar radiation pressure, shape and low-thrust orbital dynamics.

Heaton, Andrew F.↗
NASA NTRS1993

Minimum Hamiltonian Ascent Trajectory Evaluation (MASTRE) program (update to automatic flight trajectory design, performance prediction, and vehicle sizing for support of Shuttle and Shuttle derived vehicles) engineering manual

The Minimum Hamiltonian Ascent Trajectory Evaluation (MASTRE) program and its predecessors, the ROBOT and the RAGMOP programs, have had a long history of supporting MSFC in the simulation of space boosters for the purpose of performance evaluation. The ROBOT program was used in the simulation of the Saturn 1B and Saturn 5 vehicles in the 1960's and provided the first utilization of the minimum Hamiltonian (or min-H) methodology and the steepest ascent technique to solve the optimum trajectory problem. The advent of the Space Shuttle in the 1970's and its complex airplane design required a redesign of the trajectory simulation code since aerodynamic flight and controllability were required for proper simulation. The RAGMOP program was the first attempt to incorporate the complex equations of the Space Shuttle into an optimization tool by using an optimization method based on steepest ascent techniques (but without the min-H methodology). Development of the complex partial derivatives associated with the Space Shuttle configuration and using techniques from the RAGMOP program, the ROBOT program was redesigned to incorporate these additional complexities. This redesign created the MASTRE program, which was referred to as the Minimum Hamiltonian Ascent Shuttle TRajectory Evaluation program at that time. Unique to this program were first-stage (or booster) nonlinear aerodynamics, upper-stage linear aerodynamics, engine control via moment balance, liquid and solid thrust forces, variable liquid throttling to maintain constant acceleration limits, and a total upgrade of the equations used in the forward and backward integration segments of the program. This modification of the MASTRE code has been used to simulate the new space vehicles associated with the National Launch Systems (NLS). Although not as complicated as the Space Shuttle, the simulation and analysis of the NLS vehicles required additional modifications to the MASTRE program in the areas of providing additional flexibility in the use of the program, allowing additional optimization options, and providing special options for the NLS configuration.

Lyons, J. T.↗
NASA NTRS1974

Prediction and verification of creep behavior in metallic materials and components, for the space shuttle thermal protection system. Volume 1, phase 1: Cyclic materials creep predictions

Cyclic creep response was investigated and design methods applicable to thermal protection system structures were developed. The steady-state (constant temperature and load) and cyclic creep response characteristics of four alloys were studied. Steady-state creep data were gathered through a literature survey to establish reference data bases. These data bases were used to develop empirical equations describing creep as a function of time, temperature, and stress and as a basis of comparison for test data. Steady-state creep tests and tensile cyclic tests were conducted. The following factors were investigated: material thickness and rolling direction; material cyclic creep response under varying loads and temperatures; constant stress and temperature cycles representing flight conditions; changing stresses present in a creeping beam as a result of stress redistribution; and complex stress and temperature profiles representative of space shuttle orbiter trajectories. A computer program was written, applying creep hardening theories and empirical equations for creep, to aid in analysis of test data. Results are considered applicable to a variety of structures which are cyclicly exposed to creep producing thermal environments.

Davis, J. W.↗
NASA NTRS1983

Monte Carlo Investigation of Trajectories

Monte Carlo Investigation of Trajectory Operations and Requirements (MONITOR) program performs spacecraft mission maneuver simulations for craft mission maneuver simulations for geosynchronous single-maneuver, and cometencounter trajectories. Used primarily to study geosynchronous missions and model trajectories of satellites deployed by Space Shuttle. Program written in FORTRAN IV.

Glass, A. B.↗
NASA NTRS1999

The Lunar Prospector Mission: Final Results of Trajectory Design, Quasi-Frozen Orbits, Extended Mission Targeting, and Lunar Topography and Potential Models

The National Aeronautics and Space Administration (NASA) selected Lunar Prospector (LP) as one of the discovery missions to conduct solar system exploration science investigations. The mission was NASA's first lunar voyage to investigate key science objectives since Apollo and was launched in January 1998. In keeping with discovery program requirements to reduce total mission cost and utilize new technology, Lunar Prospector's mission design and control will focus on the use of innovative and proven trajectory analysis programs. As part of this effort, the Goddard Space Flight Center and the Ames Research Center became partners in the Lunar Prospector trajectory team to provide the trajectory analysis and orbit determination support. At the end of 1998, Lunar Prospector completed its one-year primary mission at 100-km altitude above the lunar surface. On December 19, 1998, Lunar Prospector entered its extended mission phase. The mission orbit was lowered from 100 km to a mean altitude of 40 km. Due to lunar potential effects, the altitude of Lunar Prospector varied from 25 to 55 km above the mean lunar geoid. After one month at 40 km, the lunar potential model was updated based upon the new tracking data at 40 km. On January 15, 1999, the altitude was lowered again to a mean altitude of 30 km. The spherical altitude varied between 15 km and 45 km above the mean lunar geoid while the topographical altitude varied between 10 km and 50 km. Various means were employed to get accurate lunar surface elevation including Clementine altimetry and LOS analysis. Based upon the best available terrain maps, Lunar Prospector reached actual altitudes of 8 km above lunar mountains in the southern polar region. This extended mission phase of six months will enable LP to obtain science data up to 3 orders of magnitude better than at the mission orbit. At the end of the operations mission, LP was targeted for impact at a chosen location that allowed optical observation of the lunar ejecta as LP ended its mission at 1.6 km/sec. This paper details the trajectory design and orbit determination planning and actual results of the Lunar Prospector nominal and extended mission including maneuver design, eccentricity vs. argument of perigee evolution, topographical altitude estimation, and lunar potential modeling. This paper provides understanding of the quasi-frozen orbit design of the LP mission, the optimization process of lunar orbit targets, the impacts that the selected lunar potential models play, and discusses the feasibility of meeting the mission goals. Observed evolution of the Keplerian orbit elements are compared to the theoretical predictions using the latest lunar potential model available which incorporates the Lunar Prospector Doppler data. Mapping orbit maintenance maneuver design along with results of the actual maneuvers to maintain the orbital requirements are also presented.

Folta, David↗
NASA NTRS1975

Dispersion analysis and linear error analysis capabilities of the space vehicle dynamics simulation program

Previous error analyses conducted by the Guidance and Dynamics Branch of NASA have used the Guidance Analysis Program (GAP) as the trajectory simulation tool. Plans are made to conduct all future error analyses using the Space Vehicle Dynamics Simulation (SVDS) program. A study was conducted to compare the inertial measurement unit (IMU) error simulations of the two programs. Results of the GAP/SVDS comparison are presented and problem areas encountered while attempting to simulate IMU errors, vehicle performance uncertainties and environmental uncertainties using SVDS are defined. An evaluation of the SVDS linear error analysis capability is also included.

Snow, L. S.↗
NASA NTRS1987

Kinematically redundant robot manipulators

Research on control, design and programming of kinematically redundant robot manipulators (KRRM) is discussed. These are devices in which there are more joint space degrees of freedom than are required to achieve every position and orientation of the end-effector necessary for a given task in a given workspace. The technological developments described here deal with: kinematic programming techniques for automatically generating joint-space trajectories to execute prescribed tasks; control of redundant manipulators to optimize dynamic criteria (e.g., applications of forces and moments at the end-effector that optimally distribute the loading of actuators); and design of KRRMs to optimize functionality in congested work environments or to achieve other goals unattainable with non-redundant manipulators. Kinematic programming techniques are discussed, which show that some pseudo-inverse techniques that have been proposed for redundant manipulator control fail to achieve the goals of avoiding kinematic singularities and also generating closed joint-space paths corresponding to close paths of the end effector in the workspace. The extended Jacobian is proposed as an alternative to pseudo-inverse techniques.

Baillieul, J.↗
NASA NTRS2017

Automation of POST Cases via External Optimizer and "Artificial p2" Calculation

During early conceptual design of complex systems, speed and accuracy are often at odds with one another. While many characteristics of the design are fluctuating rapidly during this phase there is nonetheless a need to acquire accurate data from which to down-select designs as these decisions will have a large impact upon program life-cycle cost. Therefore enabling the conceptual designer to produce accurate data in a timely manner is tantamount to program viability. For conceptual design of launch vehicles, trajectory analysis and optimization is a large hurdle. Tools such as the industry standard Program to Optimize Simulated Trajectories (POST) have traditionally required an expert in the loop for setting up inputs, running the program, and analyzing the output. The solution space for trajectory analysis is in general non-linear and multi-modal requiring an experienced analyst to weed out sub-optimal designs in pursuit of the global optimum. While an experienced analyst presented with a vehicle similar to one which they have already worked on can likely produce optimal performance figures in a timely manner, as soon as the "experienced" or "similar" adjectives are invalid the process can become lengthy. In addition, an experienced analyst working on a similar vehicle may go into the analysis with preconceived ideas about what the vehicle's trajectory should look like which can result in sub-optimal performance being recorded. Thus, in any case but the ideal either time or accuracy can be sacrificed. In the authors' previous work a tool called multiPOST was created which captures the heuristics of a human analyst over the process of executing trajectory analysis with POST. However without the instincts of a human in the loop, this method relied upon Monte Carlo simulation to find successful trajectories. Overall the method has mixed results, and in the context of optimizing multiple vehicles it is inefficient in comparison to the method presented POST's internal optimizer functions like any other gradient-based optimizer. It has a specified variable to optimize whose value is represented as optval, a set of dependent constraints to meet with associated forms and tolerances whose value is represented as p2, and a set of independent variables known as the u-vector to modify in pursuit of optimality. Each of these quantities are calculated or manipulated at a certain phase within the trajectory. The optimizer is further constrained by the requirement that the input u-vector must result in a trajectory which proceeds through each of the prescribed events in the input file. For example, if the input u-vector causes the vehicle to crash before it can achieve the orbital parameters required for a parking orbit, then the run will fail without engaging the optimizer, and a p2 value of exactly zero is returned. This poses a problem, as this "non-connecting" region of the u-vector space is far larger than the "connecting" region which returns a non-zero value of p2 and can be worked on by the internal optimizer. Finding this connecting region and more specifically the global optimum within this region has traditionally required the use of an expert analyst.

Dees, Patrick D.↗
NASA NTRS2019

Methods of Performing Large Scale, Multidimensional Parametric Studies for Space Launch System Mission Analysis

Optimizing a large number of trajectories over a wide range of parameters is a difficult and computationally intensive, particularly when the parametric space has a large number of dimensions. Solving parametric studies like these require good initial conditions for each optimization case, which results in a significant amount of manual interaction and human judgment and can be time consuming. The Space Launch System (SLS) uses POST2 (Program to Optimize Simulated Trajectories II) to simulate different ascent trajectories and perform mission analysis. SLS mission analysis currently uses two types of large scale, multidimensional parameter spaces. The qualifying factor between these spaces is the grid density, which determines the set of applicable solution methodologies. One type has a relatively low number of dimensions (2-3), but a large number of grid coordinates (2000- 4000), whereas the second type has a relatively low number of grid coordinates (150-350), but a higher number of dimensions (7-10).

Stein, W. B.↗
NASA NTRS1977

An explicit solution to the exoatmospheric powered flight guidance and trajectory optimization problem for rocket propelled vehicles

A derivation of an explicit solution to the two point boundary-value problem of exoatmospheric guidance and trajectory optimization is presented. Fixed initial conditions and continuous burn, multistage thrusting are assumed. Any number of end conditions from one to six (throttling is required in the case of six) can be satisfied in an explicit and practically optimal manner. The explicit equations converge for off nominal conditions such as engine failure, abort, target switch, etc. The self starting, predictor/corrector solution involves no Newton-Rhapson iterations, numerical integration, or first guess values, and converges rapidly if physically possible. A form of this algorithm has been chosen for onboard guidance, as well as real time and preflight ground targeting and trajectory shaping for the NASA Space Shuttle Program.

Jaggers, R. F.↗
NASA NTRS1972

Performance Analysis and Design Synthesis (PADS) computer program. Volume 1: Formulation

The program formulation for PADS computer program is presented. It can size launch vehicles in conjunction with calculus-of-variations optimal trajectories and can also be used as a general-purpose branched trajectory optimization program. In the former use, it has the Space Shuttle Synthesis Program as well as a simplified stage weight module for optimally sizing manned recoverable launch vehicles. For trajectory optimization alone or with sizing, PADS has two trajectory modules. The first trajectory module uses the method of steepest descent; the second employs the method of quasilinearization, which requires a starting solution from the first trajectory module.

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