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NASA NTRS1992

Interplanetary program to optimize simulated trajectories (IPOST). Volume 4: Sample cases

The Interplanetary Program to Optimize Simulated Trajectories (IPOST) is intended to support many analysis phases, from early interplanetary feasibility studies through spacecraft development and operations. The IPOST output provides information for sizing and understanding mission impacts related to propulsion, guidance, communications, sensor/actuators, payload, and other dynamic and geometric environments. IPOST models three degree of freedom trajectory events, such as launch/ascent, orbital coast, propulsive maneuvering (impulsive and finite burn), gravity assist, and atmospheric entry. Trajectory propagation is performed using a choice of Cowell, Encke, Multiconic, Onestep, or Conic methods. The user identifies a desired sequence of trajectory events, and selects which parameters are independent (controls) and dependent (targets), as well as other constraints and the cost function. Targeting and optimization are performed using the Standard NPSOL algorithm. The IPOST structure allows sub-problems within a master optimization problem to aid in the general constrained parameter optimization solution. An alternate optimization method uses implicit simulation and collocation techniques.

Hong, P. E.↗
NASA NTRS1992

Interplanetary Program to Optimize Simulated Trajectories (IPOST). Volume 2: Analytic manual

The Interplanetary Program to Optimize Space Trajectories (IPOST) is intended to support many analysis phases, from early interplanetary feasibility studies through spacecraft development and operations. The IPOST output provides information for sizing and understanding mission impacts related to propulsion, guidance, communications, sensor/actuators, payload, and other dynamic and geometric environments. IPOST models three degree of freedom trajectory events, such as launch/ascent, orbital coast, propulsive maneuvering (impulsive and finite burn), gravity assist, and atmospheric entry. Trajectory propagation is performed using a choice of Cowell, Encke, Multiconic, Onestep, or Conic methods. The user identifies a desired sequence of trajectory events, and selects which parameters are independent (controls) and dependent (targets), as well as other constraints and the cost function. Targeting and optimization is performed using the Stanford NPSOL algorithm. IPOST structure allows subproblems within a master optimization problem to aid in the general constrained parameter optimization solution. An alternate optimization method uses implicit simulation and collocation techniques.

Hong, P. E.↗
NASA NTRS1993

Trajectory optimization for the National aerospace plane

While continuing the application of the inverse dynamics approach in obtaining the optimal numerical solutions, the research during the past six months has been focused on the formulation and derivation of closed-form solutions for constrained hypersonic flight trajectories. Since it was found in the research of the first year that a dominant portion of the optimal ascent trajectory of the aerospace plane is constrained by dynamic pressure and heating constraints, the application of the analytical solutions significantly enhances the efficiency in trajectory optimization, provides a better insight to understanding of the trajectory and conceivably has great potential in guidance of the vehicle. Work of this period has been reported in four technical papers. Two of the papers were presented in the AIAA Guidance, Navigation, and Control Conference (Hilton Head, SC, August, 1992) and Fourth International Aerospace Planes Conference (Orlando, FL, December, 1992). The other two papers have been accepted for publication by Journal of Guidance, Control, and Dynamics, and will appear in 1993. This report briefly summarizes the work done in the past six months and work currently underway.

Lu, Ping↗
NASA NTRS1993

Trajectory-based heating analysis for the ESA/Rosetta earth return vehicle

A coupled, trajectory based flowfield and material thermal response analysis is presented for the European Space Agency (ESA) proposed Rosetta comet nucleus sample return vehicle. The probe returns to Earth along a hyperbolic trajectory with an entry velocity of 16.5 km/sec and requires an ablative heat shield on the forebody. Combined radiative and convective, ablating flowfield analyses were performed for the significant heating portion of the shallow ballistic entry trajectory. Both quasi-steady ablation and fully transient analyses were performed for a heat shield composed of carbon-phenolic ablative material. Quasi-steady analysis was performed using the two-dimensional, axisymmetric codes RASLE and BLIMPK. Transient computational results were obtained from the one-dimensional ablation/conduction code, CMA. Results are presented for heating, temperature and ablation rate distributions over the probe forebody for various trajectory points. Comparison of transient and quasi-steady results indicates that, for the heating pulse encountered by this probe, the quasi-static approach is conservative from the standpoint of predicted surface recession.

Henline, William D.↗
NASA NTRS1993

Optimal return-to-launchsite abort trajectories for an HL-20 Personnel Launch System vehicle

The Personnel Launch System (PLS) being studied by NASA is a system to complement the Space Shuttle and provide alternative access to space. The PLS consists of a manned spacecraft launched by an expendable launch vehicle (ELV). A candidate for the manned spacecraft is the HL-20 lifting body. In the event of an ELV malfunction during the initial portion of the ascent trajectory, the HL-20 will separate from the rocket and perform an unpowered return-to-launchsite (RTLS) abort. This paper describes an investigation of the RTLS abort scenario using optimal control theory. The objective of the abort trajectory is to maximize final altitude at a point near the runway. The assumption is then made that there exists a control history to steer the vehicle to any final altitude lower than the final optimal altitude. With this selection of cost function, and with this assumption, the feasibility of an RTLS abort at different times along the ascent trajectory can be determined. The method of differential inclusions, which allows the determination of optimal states and eliminates the need for determining the optimal controls, is used to determine the optimal trajectories.

Dutton, Kevin E.↗
NASA NTRS1993

Path planning by querying persistent stores of trajectory segments

We introduce an algorithm for path planning (long duration) paths of dynamical systems, given a persistent object store containing suitable collections of short duration trajectory segments. We also describe experimental results from a proof-of-concept implementation of the algorithm. The basic idea is to interpret a path planning algorithm as a suitable query on a persistent object store consisting of short duration trajectory segments. The query returns a concatenation of short duration trajectory segments which is close to the desired path. The needed short duration segments are computed by using a divide and conquer algorithm to break up the original path into shorter paths; each shorter path is then matched to a nearby trajectory segment which is part of the persistent object store by using a suitable index function.

Grossman, Robert L.↗
NASA NTRS1994

Innovative design of composite structures: Design, manufacturing, and testing of plates utilizing curvilinear fiber trajectories

As a means of improving structural design, the concept of fabricating flat plates containing holes by incorporating curvilinear fiber trajectories to transmit loads around the hole is studied. In the present discussion this concept is viewed from a structural level, where access holes, windows, doors, and other openings are of significant size. This is opposed to holes sized for mechanical fasteners. Instead of cutting the important load-bearing fibers at the hole edge, as a conventional straightline design does, the curvilinear design preserves the load-bearing fibers by orienting them in smooth trajectories around the holes, their loading not ending abruptly at the hole edge. Though the concept of curvilinear fiber trajectories has been studied before, attempts to manufacture and test such plates have been limited. This report describes a cooperative effort between Cincinnati Milacron Inc., NASA Langley Research Center, and Virginia Polytechnic Institute and State University to design, manufacture, and test plates using the curvilinear fiber trajectory concept. The paper discusses details of the plate design, details of the manufacturing, and a summary of results from testing the plates with inplane compressive buckling loads and tensile loads. Comparisons between the curvilinear and conventional straightline fiber designs based on measurements and observation are made. Failure modes, failure loads, strains, deflections, and other key responses are compared.

Hyer, M. W.↗
NASA NTRS1993

Trajectory design for a lunar mapping and near-Earth-asteroid flyby mission

In August, 1994, the unusual asteroid (1620) Geographos will pass very close to the Earth. This provides one of the best opportunities for a low-cost asteroid flyby mission that can be achieved with the help of a gravity assist from the Moon during the years 1994 and 1995. A Geographos flyby mission, including a lunar orbiting phase, was recommended to the Startegic Defense Initiative (SDI) Office when they were searching for ideas for a deep-space mission to test small imaging systems and other lightweight technologies. The goals for this mission, called Clementine, were defined to consist of a comprehensive lunar mapping phase before leaving the Earth-Moon system to encounter Geographos. This paper describes how the authors calculated a trajectory that met the mission goals within a reasonable total Delta-V budget. The paper also describes some refinements of the initially computed trajectory and alternative trajectories were investigated. The paper concludes with a list of trajectories to fly by other near-Earth asteroids during the two years following the Geographos opportunity. Some of these could be used if the Geographos schedule can not be met. If the 140 deg phase angle of the Geographos encounter turns out to be too risky, a flyby of (2120) Tantalus in January, 1995, has a much more favorable approach illumination. Tantalus apparently can be reached from the same lunar orbit needed to get to Geographos. However, both the flyby speed and distance from the Earth are much larger for Tantalus than for Geographos.

Dunham, David W.↗
NASA NTRS1994

Effect of Aeropropulsive Interactions and Design Sensitivities on Optimal Hypersonic Ascent Trajectories

In this paper, trajectory optimization is used as a tool to better understand the performance characteristics of hypersonic Single-Stage-To-Orbit(SSTO) vehicle exhibiting significant aeropropulsive interactions. The energy state approximation is used to determine a straightforward method of determining the scramjet-powered phase of the mission. The energy state method is then used to generate fuel-optimal trajectory results over this portion of the mission for a vehicle configuration of this class. The fuel-optimal unconstrained trajectory is marked by low-altitude acceleration, while a dynamic pressure-constrained trajectory is seen to ride the dynamic pressure constraint for the entire scramjet mission phase. The significance of aeropropulsive interactions in affecting vehicle performance is also investigated.

Lovell, T. Alan↗
NASA NTRS1996

Minimum Heating Re-Entry Trajectories for Advanced Hypersonic Launch Vehicles

Optimal re-entry trajectories are generated for reusable launch vehicles which minimize: (1) the heat absorbed at the vehicle surface, (2) the lower surface temperature, and (3) the heat absorbed by the internal structure. The approach uses the energy state approximation technique and a finite control volume heat transfer code coupled to a flight path integration code. These trajectories are compared to the optimal re-entry trajectory minimizing the integrated convective heat rate to determine which trajectory produces the minimum internal structural temperatures for a given thermal protection system. Three different thermal protection systems are considered: tile, blanket, and metallic.

Robert Windhorst↗
NASA NTRS1997

Near-Optimal Re-Entry Trajectories for Reusable Launch Vehicles

A near-optimal guidance law for the descent trajectory for earth orbit re-entry of a fully reusable single-stage-to-orbit pure rocket launch vehicle is derived. A methodology is developed to investigate using both bank angle and altitude as control variables and selecting parameters that maximize various performance functions. The method is based on the energy-state model of the aircraft equations of motion. The major task of this paper is to obtain optimal re-entry trajectories under a variety of performance goals: minimum time, minimum surface temperature, minimum heating, and maximum heading change; four classes of trajectories were investigated: no banking, optimal left turn banking, optimal right turn banking, and optimal bank chattering. The cost function is in general a weighted sum of all performance goals. In particular, the trade-off between minimizing heat load into the vehicle and maximizing cross range distance is investigated. The results show that the optimization methodology can be used to derive a wide variety of near-optimal trajectories.

Chou, H.-C.↗
NASA NTRS1999

Autolanding Trajectory Design for the X-34

An Autolanding I-load Program (ALIP) is developed to design unpowered autolanding trajectories for the X-34 Mach 8 vehicle. The trajectory is comprised of geometric flight segments that are based on the shuttle approach and landing design (steep glideslope, circular flare, exponential flare to shallow glideslope). Enforcing physical constraints such as loads, vertical descent rate, continuity and smoothness reduces the design problem to a two point boundary value problem with conditions on the initial and final dynamic pressure. Finding a solution required the development of trajectory simulation techniques that constrained the flight profile to a prescribed geometry. The design methodology can be extended beyond the autolanding flight regime by repeating the series of geometric segments and solving multiple two-point boundary values problems (one for each series). The techniques described in this paper facilitate rapid design of reference trajectories.

Barton, Gregg H.↗
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 NTRS1995

Freezing Behavior of Stratospheric Sulfate Aerosols Inferred from Trajectory Studies

Temperature histories based on 10-day back growth trajectories for six ER-2 flights during AASE I (1989) and AAOE (1987) are presented. These trajectories along with the properties of the observed PSC (polar stratospheric cloud) particles are used here to infer the physical state of the pre-existing sulfuric acid aerosols. Of all the ER-2 flights described here, only the PSCs observed on the flights of January 24 and 25, 1989 are consistent with the thermodynamics of liquid ternary solutions of H2SO4/HNO3/H2O Ib PSCs). For these two days, back trajectories indicate that the air mass was exposed to SAT (sulfuric acid tetrahydrate) melting temperatures about 24 hours prior to being sampled by the ER-2. For the remaining ER-2 flights (January, 16, 19, and 20 for the AASE I campaign and August 17 for the AAOE campaign), the observed PSCs were probably composed of amorphous solid solutions of HNO3 and H2O (Type Ic PSCs). Formation of such Type Ic PSCs requires the presence of solid H2SO4 aerosols since liquid aerosols yield ternary solutions. The 10-day back trajectories of these flights indicate that the air mass was not exposed to SAT melting temperatures during the past week and had experienced cooling/warming cycles prior to being sampled by the ER-2. These temperature histories, recent laboratory measurements and the properties of glassy solids suggest that stratospheric H2SO4 aerosols may undergo a phase transition to SAT upon warming at approximately 198 K after going through a cooling cycle to about 194 K or lower.

Tabazadeh, A.↗
NASA NTRS1999

Near Earth Asteroid Rendezvous (NEAR) Revised Eros Orbit Phase Trajectory Design

Trajectory design of the orbit phase of the NEAR mission involves a new process that departs significantly from those procedures used in previous missions. In most cases, a precise spacecraft ephemeris is designed well in advance of arrival at the target body. For NEAR, the uncertainty in the dynamic environment around Eros does not allow the luxury of a precise spacecraft trajectory to be defined in advance. The principal cause of this uncertainty is the limited knowledge oi' the gravity field a,-id rotational state of Eros. As a result, the concept for the NEAR trajectory design is to define a number of rules for satisfying spacecraft, mission, and science constraints, and then apply these rules to various assumptions for the model of Eros. Nominal, high, and low Eros mass models are used for testing the trajectory design strategy and to bracket the ranges of parameter variations that are expected upon arrival at the asteroid. The final design is completed after arrival at Eros and determination of the actual gravity field and rotational state. As a result of the unplanned termination of the deep space rendezvous maneuver on December 20, 1998, the NEAR spacecraft passed within 3830 km of Eros on December 23, 1998. This flyby provided a brief glimpse of Eros, and allowed for a more accurate model of the rotational parameters and gravity field uncertainty. Furthermore, after the termination of the deep space rendezvous burn, contact with the spacecraft was lost and the NEAR spacecraft lost attitude control. During the subsequent gyrations of the spacecraft, hydrazine thruster firings were used to regain attitude control. This unplanned thruster activity used Much of the fuel margin allocated for the orbit phase. Consequently, minimizing fuel consumption is now even more important.

Helfrich, J↗
NASA NTRS2001

A Non-Linear Approach to Spacecraft Trajectory Control in the Vicinity of a Libration Point

An expanding interest in mission design strategies that exploit libration point regions demands the continued development of enhanced, efficient, control algorithms for station-keeping and formation maintenance. This paper discusses the development of a non-linear, station-keeping, control algorithm for trajectories in the vicinity of a libration point. The control law guarantees exponential convergence, based on a Lyaponov analysis. Controller performance is evaluated using FreeFlyer(R) and MATLAB(R) for a spacecraft stationed near the L2 libration point in the Earth-Moon system, tracking a pre-defined reference trajectory. Evaluation metrics are fuel usage and tracking accuracy. Simulation results are compared with a linear-based controller for a spacecraft tracking the same reference trajectory. Although the analysis is framed in the context of station-keeping, the control algorithm is equally applicable to a formation flying problem with an appropriate definition of the reference trajectory.

Luquette, Richard J.↗
NASA NTRS2001

Trajectory Design for the Microwave Anisotropy Probe (MAP)

The Microwave Anisotropy, Probe (MAP) is a Medium Class Explorers (MIDEX) Mission produced in partnership between Goddard Space Flight Center (GSFC) and Princeton University. The goal of the MAP mission is to produce an accurate fill-sky, map of the cosmic microwave background temperature fluctuations (anisotropy). The mission orbit is a Lissajous orbit about the L(sub 2) Sun-Earth Lagrange point. The trajectory design for MAP is complex, having many requirements that must be met including shadow avoidance, sun angle constraints, Lissqjous size and shape characteristics, and limited Delta-V budget. In order to find a trajectory that met the design requirements for the entire 4-year mission lifetime goal, GSFC Flight Dynamics engineers performed many analyses, the results of which are presented herein. The paper discusses the preliminary trade-offs to establish a baseline trajectory, analysis to establish the nominal daily trajectory, and the launch window determination to widen the opportunity from instantaneous to several minutes for each launch date.

Newman, Lauri Kraft↗
NASA NTRS1995

Optimal Trajectories and Control Strategies for the Helicopter in One-Engine-Inoperative Terminal-Area Operations

Engine failure represents a major safety concern to helicopter operations, especially in the critical flight phases of takeoff and landing from/to small, confined areas. As a result, the JAA and FAA both certificate a transport helicopter as either Category-A or Category-B according to the ability to continue its operations following engine failures. A Category-B helicopter must be able to land safely in the event of one or all engine failures. There is no requirement, however, for continued flight capability. In contrast, Category-A certification, which applies to multi-engine transport helicopters with independent engine systems, requires that they continue the flight with one engine inoperative (OEI). These stringent requirements, while permitting its operations from rooftops and oil rigs and flight to areas where no emergency landing sites are available, restrict the payload of a Category-A transport helicopter to a value safe for continued flight as well as for landing with one engine inoperative. The current certification process involves extensive flight tests, which are potentially dangerous, costly, and time consuming. These tests require the pilot to simulate engine failures at increasingly critical conditions, Flight manuals based on these tests tend to provide very conservative recommendations with regard to maximum takeoff weight or required runway length. There are very few theoretical studies on this subject to identify the fundamental parameters and tradeoff factors involved. Furthermore, a capability for real-time generation of OEI optimal trajectories is very desirable for providing timely cockpit display guidance to assist the pilot in reducing his workload and to increase safety in a consistent and reliable manner. A joint research program involving NASA Ames Research Center, the FAA, and the University of Minnesota is being conducted to determine OEI optimal control strategies and the associated optimal,trajectories for continued takeoff (CTO), rejected takeoff (RTO), balked landing (BL), and continued landing (CL) for a twin engine helicopter in both VTOL and STOL terminal-area operations. This proposed paper will present the problem formulation, the optimal control solution methods, and the key results of the trajectory optimization studies for both STOL and VTOL OEI operations. In addition, new results concerning the recently developed methodology, which enable a real-time generation of optimal OEI trajectories, will be presented in the paper. This new real-time capability was developed to support the second piloted simulator investigation on cockpit displays for Category-A operations being scheduled for the NASA Ames Vertical Motion Simulator in June-August of 1995. The first VMS simulation was conducted in 1994 and reported.

Chen, Robert T. N.↗