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NASA NTRS2000

Real-Time Trajectory Assessment and Abort Management for the X-33 Vehicle

The X-33 is a flying testbed to evaluate technologies and designs for a reusable Single Stage To Orbit (SSTO) production vehicle. Although it is sub-orbital, it is trans-atmospheric. This paper will discuss the abort capabilities, both commanded and autonomous, available to the X-33. The cornerstone of the abort capabilities is the Performance Monitor (PM) and it's supporting software. PM is an on-board 3-DOF simulation, which evaluates the vehicle ability to execute the current trajectory. The Abort Manager evaluates the results from PM, and, when indicated, computes and implements an abort trajectory.

Moise, M. C.↗

NASA NTRS2001

Trajectory Design Strategies for the NGST L2 Libration Point Mission

The Origins' Next Generation Space Telescope (NGST) trajectory design is addressed in light of improved methods for attaining constrained orbit parameters and their control at the exterior collinear libration point, L2. The use of a dynamical systems approach, state-space equations for initial libration orbit control, and optimization to achieve constrained orbit parameters are emphasized. The NGST trajectory design encompasses a direct transfer and orbit maintenance under a constant acceleration. A dynamical systems approach can be used to provide a biased orbit and stationkeeping maintenance method that incorporates the constraint of a single axis correction scheme.

Folta, David↗

NASA NTRS2001

Comparison of ER-2 Aircraft and POAM-III, MLS, and SAGE-II Satellite Measurements During SOLVE Using Traditional Correlative Analysis and Trajectory Hunting Technique

We compared the version 5 Microwave Limb Sounder (MLS) aboard the Upper Atmosphere Research Satellite (UARS), version 3 Polar Ozone and Aerosol Measurement-III (POAM-111) aboard the French satellite SPOT-IV, version 6.0 Stratospheric Aerosol and Gas Experiment 11 (SAGE-II) aboard the Earth Radiation Budget Satellite, and NASA ER-2 aircraft measurements made in the northern hemisphere in January-February 2000 during the SAGE III Ozone Loss and Validation Experiment (SOLVE). This study addresses one of the key scientific objectives of the SOLVE campaign, namely, to validate multi-platform satellite measurements made in the polar stratosphere during winter. This intercomparison was performed using a traditional correlative analysis (TCA) and a trajectory hunting technique (THT). Launching backward and forward trajectories from the points of measurement, the THT identifies air parcels sampled at least twice within a prescribed match criterion during the course of 5 days. We found that the ozone measurements made by these four instruments agree most of the time within 110% in the stratosphere up to 1400 K (approximately 35 km). The water vapor measurements from POAM-III and the ER-2 Harvard Lyman-alpha hygrometer and JPL laser hygrometer agree to within 10.5 ppmv (or about +/-10%) in the lower stratosphere above 380 K. The MLS and ER-2 ClO measurements agree within their error bars for the TCA. The MLS and ER-2 nitric acid measurements near 17-20 km altitude agree within their uncertainties most of the time with a hint of a positive offset by MLS according to the TCA. We also applied the AER box model constrained by the ER-2 measurements for analysis of the ClO and HN03 measurements using the THT. We found that: (1) the model values of ClO are smaller by about 0.3-0.4 (0.2) ppbv below (above) 400 K than those by MLS and (2) the HN03 comparison shows a positive offset of MLS values by approximately 1 and 1-2 ppbv below 400 K and near 450 K, respectively. It is hard to quantify the HN03 offset in the 400-440 K range because of the high sensitivity of nitric acid to the PSC schemes. Our study shows that, with some limitations (like HN03 comparison under PSC conditions), the THT is a more powerful tool for validation studies than the TCA, making conclusions of the comparison statistically more robust.

Danilin, M. Y.↗

NASA NTRS2001

Uncertainty Optimization Applied to the Monte Carlo Analysis of Planetary Entry Trajectories

Recently, strong evidence of liquid water under the surface of Mars and a meteorite that might contain ancient microbes have renewed interest in Mars exploration. With this renewed interest, NASA plans to send spacecraft to Mars approx. every 26 months. These future spacecraft will return higher-resolution images, make precision landings, engage in longer-ranging surface maneuvers, and even return Martian soil and rock samples to Earth. Future robotic missions and any human missions to Mars will require precise entries to ensure safe landings near science objective and pre-employed assets. Potential sources of water and other interesting geographic features are often located near hazards, such as within craters or along canyon walls. In order for more accurate landings to be made, spacecraft entering the Martian atmosphere need to use lift to actively control the entry. This active guidance results in much smaller landing footprints. Planning for these missions will depend heavily on Monte Carlo analysis. Monte Carlo trajectory simulations have been used with a high degree of success in recent planetary exploration missions. These analyses ascertain the impact of off-nominal conditions during a flight and account for uncertainty. Uncertainties generally stem from limitations in manufacturing tolerances, measurement capabilities, analysis accuracies, and environmental unknowns. Thousands of off-nominal trajectories are simulated by randomly dispersing uncertainty variables and collecting statistics on forecast variables. The dependability of Monte Carlo forecasts, however, is limited by the accuracy and completeness of the assumed uncertainties. This is because Monte Carlo analysis is a forward driven problem; beginning with the input uncertainties and proceeding to the forecasts outputs. It lacks a mechanism to affect or alter the uncertainties based on the forecast results. If the results are unacceptable, the current practice is to use an iterative, trial-and-error approach to reconcile discrepancies. Therefore, an improvement to the Monte Carlo analysis is needed that will allow the problem to be worked in reverse. In this way, the largest allowable dispersions that achieve the required mission objectives can be determined quantitatively.

Olds, John↗

NASA NTRS1996

Tracking Virtual Trajectories

Current models of smooth pursuit eye movements assume that it is largely driven by retinal image motion. We tested this hypothesis by measuring pursuit of elliptical motion (3.2s, 0.9 Hz, 1.4 deg x 1.6 deg, 4 randomly interleaved phases) of either a small spot ("real" motion) or of a line-figure diamond viewed through apertures such that only the motion of four isolated oblique line segments was visible ("virtual" motion). Each segment moved sinusoidally along a linear trajectory yet subjects perceived a diamond moving along an elliptical path behind the aperture. We found, as expected, that real motion produced accurate tracking (N = 2) with mean gain (over horizontal and vertical) of 0.9, mean phase of -6 deg (lag), mean relative phase (H vs V) of 90 +/- 8 deg (RMS error). Virtual motion behind an X-shaped aperture (N= 4 with one naive) yielded a mean gain of 0.7, mean phase of -11 deg, mean relative phase of 87 +/- 15 deg. We also measured pursuit with the X-shaped aperture using a higher segment luminance which prevents the segments from being grouped into a coherently moving diamond while keeping the motion otherwise identical. In this incoherent case, the same four subjects no longer showed consistent elliptical tracking (RMS error in relative phase rose to 60 deg) suggesting that perceptual coherence is critical. Furthermore, to rule out tracking of the centroid, we also used vertical apertures so that all segment motion was vertical (N = 3). This stimulus still produced elliptical tracking (mean relative phase of 84 +/- 19 deg), albeit with a lower gain (0.6). These data show that humans can track moving objects reasonably accurately even when the trajectory can only be derived by spatial integration of motion signals. Models that merely seek to minimize retinal or local stimulus motion cannot explain these results.

Stone, Leland S.↗

NASA NTRS2002

The Solar-Sail Launched Interstellar Probe: Pre-Perihelion Trajectories and Application of Holography

Design of missions beyond our solar system presents many challenges. Here, we consider certain aspects of the solar-sail launched interstellar probe (ISP), a spacecraft slated for launch in the 2010 time period that is planned to reach the heliopause, at 200 Astronomical Units (AU) from the Sun after a flight of about 20-years duration. The baseline mission under consideration by NASA / JPL has a sail radius of 200 m, a science payload of 25 kg, a spacecraft areal mass thickness of about two grams per square meter and is accelerated out of the solar system at about 14 AU per year after performing a perihelion pass of about 0.25 AU. In current plans, the sail is to be dropped near Jupiter's orbit (5.2 AU from the Sun) on the outbound trajectory leg. One aspect of this study is application of a realistic model of sail thermo-optics to sail kinematics that includes diffuse / specular reflectance and sail roughness. The effects of solar-wind degradation of sail material, based on recent measurements at the NASA MSFC (Marshall Space Flight Center) Space Environment Facility were incorporated in the kinematical model. After setting initial and final conditions for the spacecraft, trajectory was optimized using the provision of variable sail aspect angle. The second phase of the study included consideration of rainbow holography as a medium for a message plaque that would be carried aboard the ISP in the spirit of the message plaques aboard Pioneer 10 /11 and Voyager 1 /2. A prototype holographic message plaque was designed and created by artist C. Bangs with the assistance of Ana Maria Nicholson and Dan Schweitzer of the Center for Holographic Arts in Long Island City, NY. The piece was framed by Simon Liu Inc. of Brooklyn, NY. Concurrent to the creation of the prototype message plaque, we explored the potential of this medium to transmit large amounts of visual information to any extraterrestrial civilization that might detect and intercept ISP. It was also necessary to investigate possible degradation of holograms by the space environment. We developed a new way of characterizing the optical quality of holograms.

Gregory L. Matloff↗

NASA NTRS2002

An Overview of Trajectory Design Operations for the Microwave Anisotropy Probe Mission

The purpose of this paper is to document the results of the pre-launch trajectory design and the real-time operations for the Microwave Anisotropy Probe (MAP) mission, launched on June 30, 2001. Once MAP was successfully inserted into a highly elliptical phasing orbit, three perigee maneuvers and a final perigee correction maneuver were performed to tailor a lunar encounter on July 30, 2001. MAP achieved its final Lissajous orbit (0.5 deg. by 10.5 deg.) about the Sun-Earth/Moon L2 libration point via this lunar encounter. This paper will show the maneuvers that were designed to arrive at the mission orbit. A further discussion of how the MAP trajectory analysts altered the pre-launch phasing loop maneuvers as well as the lunar encounter to meet all mission constraints, including the constraint of zero lunar shadows is also included.

Mesarch, Michael A.↗

NASA NTRS2002

On-Board Generation of Three-Dimensional Constrained Entry Trajectories

A methodology for very fast design of 3DOF entry trajectories subject to all common inequality and equality constraints is developed. The approach make novel use of the well known quasi-equilibrium glide phenomenon in lifting entry as a center piece for conveniently enforcing the inequality constraints which are otherwise difficulty to handle. The algorithm is able to generate a complete feasible 3DOF entry trajectory, given the entry conditions, values of constraint parameters, and final conditions in about 2 seconds on a PC. Numerical simulations with the X-33 vehicle model for various entry missions to land at Kennedy Space Center will be presented.

Shen, Zuojun↗

NASA NTRS2002

Trajectories for High Specific Impulse High Specific Power Deep Space Exploration

Preliminary results are presented for two methods to approximate the mission performance of high specific impulse high specific power vehicles. The first method is based on an analytical approximation derived by Williams and Shepherd and can be used to approximate mission performance to outer planets and interstellar space. The second method is based on a parametric analysis of trajectories created using the well known trajectory optimization code, VARITOP. This parametric analysis allows the reader to approximate payload ratios and optimal power requirements for both one-way and round-trip missions. While this second method only addresses missions to and from Jupiter, future work will encompass all of the outer planet destinations and some interstellar precursor missions.

Polsgrove, T.↗

NASA NTRS2002

Machine Learning for Biological Trajectory Classification Applications

Machine-learning techniques, including clustering algorithms, support vector machines and hidden Markov models, are applied to the task of classifying trajectories of moving keratocyte cells. The different algorithms axe compared to each other as well as to expert and non-expert test persons, using concepts from signal-detection theory. The algorithms performed very well as compared to humans, suggesting a robust tool for trajectory classification in biological applications.

Sbalzarini, Ivo F.↗

NASA NTRS2003

Mars Exploration Rover Six-Degree-Of-Freedom Entry Trajectory Analysis

The Mars Exploration Rover mission will be the next opportunity for surface exploration of Mars in January 2004. Two rovers will be delivered to the surface of Mars using the same entry, descent, and landing scenario that was developed and successfully implemented by Mars Pathfinder. This investigation describes the trajectory analysis that was performed for the hypersonic portion of the MER entry. In this analysis, a six-degree-of-freedom trajectory simulation of the entry is performed to determine the entry characteristics of the capsules. In addition, a Monte Carlo analysis is also performed to statistically assess the robustness of the entry design to off-nominal conditions to assure that all entry requirements are satisfied. The results show that the attitude at peak heating and parachute deployment are well within entry limits. In addition, the parachute deployment dynamics pressure and Mach number are also well within the design requirements.

Desai, Prasun N.↗

NASA NTRS2003

Genetic Algorithm Tuned Fuzzy Logic for Gliding Return Trajectories

The problem of designing and flying a trajectory for successful recovery of a reusable launch vehicle is tackled using fuzzy logic control with genetic algorithm optimization. The plant is approximated by a simplified three degree of freedom non-linear model. A baseline trajectory design and guidance algorithm consisting of several Mamdani type fuzzy controllers is tuned using a simple genetic algorithm. Preliminary results show that the performance of the overall system is shown to improve with genetic algorithm tuning.

Burchett, Bradley T.↗

NASA NTRS1961

Trajectory Control in Rendezvous Problems Using Proportional Navigation

The rendezvous problem is defined by the end conditions that the position and velocity of a vehicle and its target are to be matched. In its present form proportional navigation theory allows the interception of a target by the vehicle, that is , the matching of positions. This report extends the theory to include the full rendezvous end conditions. Trajectory constraint equations are derived and the method of computing the required thrust program in idealized problems is outlined. The thrust program obtained results entirely from the trajectory and does not consider the dynamics of the vehicles or errors inherent in a real system. The properties of the thrust program, such as its variation both in magnitude and direction, are examined. An acceleration forcing function is also derived and its properties examined. The theory is applied to the satellite rendezvous problem as an example and some computations are presented.

Cicolani, Luigi S.↗

NASA NTRS2003

Optimum Climb to Cruise Noise Trajectories for the High Speed Civil Transport

By entraining large quantities of ambient air into advanced ejector nozzles, the jet noise of the proposed High Speed Civil Transport (HSCT) is expected to be reduced to levels acceptable for airport-vicinity noise certification. Away from the airport, however, this entrained air is shut off and the engines are powered up from their cutback levels to provide better thrust for the climb to cruise altitude. Unsuppressed jet noise levels propagating to the ground far from the airport are expected to be high. Complicating this problem is the HSCT's relative noise level with respect to the subsonic commercial fleet of 2010, which is expected to be much quieter than it is today after the retirement of older, louder, domestic stage II aircraft by the year 2000. In this study, the classic energy state approximation theory is extended to calculate trajectories that minimize the climb to cruise noise of the HSCT. The optimizer dynamically chooses the optimal altitude velocity trajectory, the engine power setting, and whether the ejector should be stowed or deployed with respect to practical aircraft climb constraints and noise limits.

Berton, Jeffrey J.↗

NASA NTRS2003

Trajectory-Based Performance Assessment for Aviation Weather Information

Based on an analysis of aviation decision-makers' time-related weather information needs, an abstraction of the aviation weather decision task was developed, that involves 4-D intersection testing between aircraft trajectory hypertubes and hazardous weather hypervolumes. The framework builds on the hypothesis that hazardous meteorological fields can be simplified using discrete boundaries of surrogate threat attributes. The abstractions developed in the framework may be useful in studying how to improve the performance of weather forecasts from the trajectory-centric perspective, as well as for developing useful visualization techniques of weather information.

Vigeant-Langlois, Laurence↗

NASA NTRS2004

Mars Exploration Rovers Entry, Descent, and Landing Trajectory Analysis

The Mars Exploration Rover mission successfully landed two rovers "Spirit" and "Opportunity" on Mars on January 4th and 25th of 2004, respectively. The trajectory analysis performed to define the entry, descent, and landing (EDL) scenario is described. The entry requirements and constraints are presented, as well as uncertainties used in a Monte Carlo dispersion analysis to statistically assess the robustness of the entry design to off-nominal conditions. In the analysis, six-degree-of-freedom and three-degree-of-freedom trajectory results are compared to assess the entry characteristics of the capsule. Comparison of the preentry results to preliminary post-landing reconstruction data shows that all EDL parameters were within the requirements. In addition, the final landing position for both "Spirit" and "Opportunity" were within 15 km of the predicted landing location.

Desai, Prasun N.↗

NASA NTRS1995

Motor adaptation to Coriolis force perturbations of reaching movements: endpoint but not trajectory adaptation transfers to the nonexposed arm

1. Reaching movements made in a rotating room generate Coriolis forces that are directly proportional to the cross product of the room's angular velocity and the arm's linear velocity. Such Coriolis forces are inertial forces not involving mechanical contact with the arm. 2. We measured the trajectories of arm movements made in darkness to a visual target that was extinguished at the onset of each reach. Prerotation subjects pointed with both the right and left arms in alternating sets of eight movements. During rotation at 10 rpm, the subjects reached only with the right arm. Postrotation, the subjects pointed with the left and right arms, starting with the left, in alternating sets of eight movements. 3. The initial perrotary reaching movements of the right arm were highly deviated both in movement path and endpoint relative to the prerotation reaches of the right arm. With additional movements, subjects rapidly regained straight movement paths and accurate endpoints despite the absence of visual or tactile feedback about reaching accuracy. The initial postrotation reaches of the left arm followed straight paths to the wrong endpoint. The initial postrotation reaches of the right arm had paths with mirror image curvature to the initial perrotation reaches of the right arm but went to the correct endpoint. 4. These observations are inconsistent with current equilibrium point models of movement control. Such theories predict accurate reaches under our experimental conditions. Our observations further show independent implementation of movement and posture, as evidenced by transfer of endpoint adaptation to the nonexposed arm without transfer of path adaptation. Endpoint control may occur at a relatively central stage that represents general constraints such as gravitoinertial force background or egocentric direction relative to both arms, and control of path may occur at a more peripheral stage that represents moments of inertia and muscle dynamics unique to each limb. 5. Endpoint and path adaptation occur despite the absence both of mechanical contact cues about the perturbing force and visual or tactile cues about movement accuracy. These findings point to the importance of muscle spindle signals, monitoring of motor commands, and possibly joint and tendon receptors in a detailed trajectory monitoring process. Muscle spindle primary and secondary afferent signals may differentially influence adaptation of movement shape and endpoint, respectively.

Non-NASA Center↗

NASA NTRS2005

Planetary Gravity Fields and Their Impact on a Spacecraft Trajectory

The present work touches an interdisciplinary aspect of space exploration: the improvement of spacecraft navigation by means of enhanced planetary interior model derivation. The better the bodies in our solar system are known and modelled, the more accurately (and safely) a spacecraft can be navigated. In addition, the information about the internal structure of a planet, moon or any other planetary body can be used in arguments for different theories of solar system evolution. The focus of the work lies in a new approach for modelling the gravity field of small planetary bodies: the implementation of complex ellipsoidal coordinates (figure 1, [4]) for irregularly shaped bodies that cannot be represented well by a straightforward spheroidal approach. In order to carry out the required calculations the computer programme GRASP (Gravity Field of a Planetary Body and its Influence on a Spacecraft Trajectory) has been developed [5]. The programme furthermore allows deriving the impact of the body s gravity field on a spacecraft trajectory and thus permits predictions for future space mission flybys.

Weinwurm, G.↗