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All sourcesNASA NTRSDOE OSTI
NASA NTRS2009

Robust Landing Using Time-to-Collision Measurement with Actuator Saturation

This paper considers a landing problem for an MAV that uses only a monocular camera for guidance. Although this sensor cannot measure the absolute distance to the target, by using optical flow algorithms, time-to-collision to the target is obtained. Existing work has applied a simple proportional feedback control to simple dynamics and demonstrated its potential. However, due to the singularity in the time-to-collision measurement around the target, this feedback could require an infinite control action. This paper extends the approach into nonlinear dynamics. In particular, we explicitly consider the saturation of the actuator and include the effect of the aerial drag. It is shown that the convergence to the target is guaranteed from a set of initial conditions, and the boundaries of such initial conditions in the state space are numerically obtained. The paper then introduces parametric uncertainties in the vehicle model and in the time-to-collision measurements. Using an argument similar to the nominal case, the robust convergence to the target is proven, but the region of attraction is shown to shrink due to the existence of uncertainties. The numerical simulation validates these theoretical results.

parametric uncertainty↗
NASA NTRS2012

Generation After Next Propulsor Research: Robust Design for Embedded Engine Systems

The National Aeronautics and Space Administration, United Technologies Research Center and Virginia Polytechnic and State University have contracted to pursue multi-disciplinary research into boundary layer ingesting (BLI) propulsors for generation after next environmentally responsible subsonic fixed wing aircraft. This Robust Design for Embedded Engine Systems project first conducted a high-level vehicle system study based on a large commercial transport class hybrid wing body aircraft, which determined that a 3 to 5 percent reduction in fuel burn could be achieved over a 7,500 nanometer mission. Both pylon-mounted baseline and BLI propulsion systems were based on a low-pressure-ratio fan (1.35) in an ultra-high-bypass ratio engine (16), consistent with the next generation of advanced commercial turbofans. An optimized, coupled BLI inlet and fan system was subsequently designed to achieve performance targets identified in the system study. The resulting system possesses an inlet with total pressure losses less than 0.5%, and a fan stage with an efficiency debit of less than 1.5 percent relative to the pylon-mounted, clean-inflow baseline. The subject research project has identified tools and methodologies necessary for the design of next-generation, highly-airframe-integrated propulsion systems. These tools will be validated in future large-scale testing of the BLI inlet / fan system in NASA's 8 foot x 6 foot transonic wind tunnel. In addition, fan unsteady response to screen-generated total pressure distortion is being characterized experimentally in a JT15D engine test rig. These data will document engine sensitivities to distortion magnitude and spatial distribution, providing early insight into key physical processes that will control BLI propulsor design.

Arend, David J.↗
NASA NTRS2012

A Brief Review of the Need for Robust Smart Wireless Sensor Systems for Future Propulsion Systems, Distributed Engine Controls, and Propulsion Health Management

Smart Sensor Systems with wireless capability operational in high temperature, harsh environments are a significant component in enabling future propulsion systems to meet a range of increasingly demanding requirements. These propulsion systems must incorporate technology that will monitor engine component conditions, analyze the incoming data, and modify operating parameters to optimize propulsion system operations. This paper discusses the motivation towards the development of high temperature, smart wireless sensor systems that include sensors, electronics, wireless communication, and power. The challenges associated with the use of traditional wired sensor systems will be reviewed and potential advantages of Smart Sensor Systems will be discussed. A brief review of potential applications for wireless smart sensor networks and their potential impact on propulsion system operation, with emphasis on Distributed Engine Control and Propulsion Health Management, will be given. A specific example related to the development of high temperature Smart Sensor Systems based on silicon carbide electronics will be discussed. It is concluded that the development of a range of robust smart wireless sensor systems are a foundation for future development of intelligent propulsion systems with enhanced capabilities.

Hunter, Gary W.↗
NASA NTRS2015

Recent Space PV Concentrator Advances: More Robust, Lighter, and Easier to Track

Over the past three years, the authors have collaborated on several significant advances in space photovoltaic concentrator technology, including a far more robust Fresnel lens for sunlight concentration, improved color-mixing features for the lens to minimize chromatic aberration losses for next-generation 4-junction and 6-junction IMM cells, a new approach to suntracking requiring only one axis of rotation even in the presence of large beta angles (e.g., +/- 50 deg), a new waste heat radiator made of graphene, with 80-90% reduction in mass, and a new platform for deployment and support on orbit (SOLAROSA). These patent-pending advances are described in this paper.

concentrators↗
NASA NTRS2015

Who's Got the Bridge? - Towards Safe, Robust Autonomous Operations at NASA Langley's Autonomy Incubator

NASA aeronautics research has made decades of contributions to aviation. Both aircraft and air traffic management (ATM) systems in use today contain NASA-developed and NASA sponsored technologies that improve safety and efficiency. Recent innovations in robotics and autonomy for automobiles and unmanned systems point to a future with increased personal mobility and access to transportation, including aviation. Automation and autonomous operations will transform the way we move people and goods. Achieving this mobility will require safe, robust, reliable operations for both the vehicle and the airspace and challenges to this inevitable future are being addressed now in government labs, universities, and industry. These challenges are the focus of NASA Langley Research Center's Autonomy Incubator whose R&D portfolio includes mission planning, trajectory and path planning, object detection and avoidance, object classification, sensor fusion, controls, machine learning, computer vision, human-machine teaming, geo-containment, open architecture design and development, as well as the test and evaluation environment that will be critical to prove system reliability and support certification. Safe autonomous operations will be enabled via onboard sensing and perception systems in both data-rich and data-deprived environments. Applied autonomy will enable safety, efficiency and unprecedented mobility as people and goods take to the skies tomorrow just as we do on the road today.

Allen, B. Danette↗
NASA NTRS2017

Designing for Reliability and Robustness

Long duration spaceflight has a negative effect on the human body, and exercise countermeasures are used on-board the International Space Station (ISS) to minimize bone and muscle loss, combatting these effects. Given the importance of these hardware systems to the health of the crew, this equipment must continue to be readily available. Designing spaceflight exercise hardware to meet high reliability and availability standards has proven to be challenging throughout the time the crewmembers have been living on ISS beginning in 2000. Furthermore, restoring operational capability after a failure is clearly time-critical, but can be problematic given the challenges of troubleshooting the problem from 220 miles away. Several best-practices have been leveraged in seeking to maximize availability of these exercise systems, including designing for robustness, implementing diagnostic instrumentation, relying on user feedback, and providing ample maintenance and sparing. These factors have enhanced the reliability of hardware systems, and therefore have contributed to keeping the crewmembers healthy upon return to Earth. This paper will review the failure history for three spaceflight exercise countermeasure systems identifying lessons learned that can help improve future systems. Specifically, the Treadmill with Vibration Isolation and Stabilization System (TVIS), Cycle Ergometer with Vibration Isolation and Stabilization System (CEVIS), and the Advanced Resistive Exercise Device (ARED) will be reviewed, analyzed, and conclusions identified so as to provide guidance for improving future exercise hardware designs. These lessons learned, paired with thorough testing, offer a path towards reduced system down-time.

Svetlik, Randall G.↗
NASA NTRS2016

A Robust Method to Integrate End-to-End Mission Architecture Optimization Tools

End-to-end mission simulations include multiple phases of flight. For example, an end-to-end Mars mission simulation may include launch from Earth, interplanetary transit to Mars and entry, descent and landing. Each phase of flight is optimized to meet specified constraints and often depend on and impact subsequent phases. The design and optimization tools and methodologies used to combine different aspects of end-to-end framework and their impact on mission planning are presented. This work focuses on a robust implementation of a Multidisciplinary Design Analysis and Optimization (MDAO) method that offers the flexibility to quickly adapt to changing mission design requirements. Different simulations tailored to the liftoff, ascent, and atmospheric entry phases of a trajectory are integrated and optimized in the MDAO program Isight, which provides the user a graphical interface to link simulation inputs and outputs. This approach provides many advantages to mission planners, as it is easily adapted to different mission scenarios and can improve the understanding of the integrated system performance within a particular mission configuration. A Mars direct entry mission using the Space Launch System (SLS) is presented as a generic end-to-end case study. For the given launch period, the SLS launch performance is traded for improved orbit geometry alignment, resulting in an optimized a net payload that is comparable to that in the SLS Mission Planner's Guide.

Lugo, Rafael↗
NASA NTRS2016

Space Photovoltaic Concentrator Using Robust Fresnel Lenses, 4-Junction Cells, Graphene Radiators, and Articulating Receivers

At the 42nd PVSC, our team presented recent advances in our space photovoltaic concentrator technology. These advances include more robust Fresnel lenses for optical concentration, more thermally conductive graphene radiators for waste heat rejection, improved color-mixing lens technology to minimize chromatic aberration losses with 4-junction solar cells, and an articulating photovoltaic receiver enabling single-axis sun-tracking, while maintaining a sharp focal line despite large beta angles of incidence. In the past year, under a NASA Phase II SBIR program, our team has made much additional progress in the development of this new space photovoltaic concentrator technology, as described in this paper.

photovoltaic↗
NASA NTRS2017

Advection of Potential Temperature in the Atmosphere of Irradiated Exoplanets: A Robust Mechanism to Explain Radius Inflation

The anomalously large radii of strongly irradiated exoplanets have remained a major puzzle in astronomy. Based on a two-dimensional steady-state atmospheric circulation model, the validity of which is assessed by comparison to three-dimensional calculations, we reveal a new mechanism, namely the advection of the potential temperature due to mass and longitudinal momentum conservation, a process occurring in the Earth's atmosphere or oceans. In the deep atmosphere, the vanishing heating flux forces the atmospheric structure to converge to a hotter adiabat than the one obtained with 1D calculations, implying a larger radius for the planet. Not only do the calculations reproduce the observed radius of HD 209458b, but also reproduce the observed correlation between radius inflation and irradiation for transiting planets. Vertical advection of potential temperature induced by non-uniform atmospheric heating thus provides a robust mechanism to explain the inflated radii of irradiated hot Jupiters.

tmospheric effects; methods: numerical; planets an↗
NASA NTRS2017

Robust Exploration and Commercial Missions to the Moon Using LANTR Propulsion and Lunar Liquid Oxygen Derived from FeO-Rich Pyroclastic Deposits

The nuclear thermal rocket (NTR) has frequently been identified as a key space asset required for the human exploration of Mars. This proven technology can also provide the affordable access through cislunar space necessary for commercial development and sustained human presence on the Moon. It is a demonstrated technology capable of generating both high thrust and high specific impulse (Isp approx.900 s) twice that of todays best chemical rockets. Nuclear lunar transfer vehicles consisting of a propulsion stage using three approx.16.5 klbf Small Nuclear Rocket Engines (SNREs), an in-line propellant tank, plus the payload can enable a variety of reusable lunar missions. These include cargo delivery and crewed lunar landing missions. Even weeklong tourism missions carrying passengers into lunar orbit for a day of sightseeing and picture taking are possible. The NTR can play an important role in the next phase of lunar exploration and development by providing a robust in-space lunar transportation system (LTS) that can allow initial outposts to evolve into settlements supported by a variety of commercial activities such as in-situ propellant production used to supply strategically located propellant depots and transportation nodes. The use of lunar liquid oxygen (LLO2) derived from iron oxide (FeO)-rich volcanic glass beads, found in numerous pyroclastic deposits on the Moon, can significantly reduce the launch mass requirements from Earth by enabling reusable, surface-based lunar landing vehicles (LLVs) using liquid oxygen/hydrogen (LO2/H2) chemical rocket engines. Afterwards, a LO2/H2 propellant depot can be established in lunar equatorial orbit to supply the LTS. At this point a modified version of the conventional NTR called the LOX-augmented NTR, or LANTR is introduced into the LTS allowing bipropellant operation and leveraging the mission benefits of refueling with lunar-derived propellants for Earth return. The bipropellant LANTR engine utilizes the large divergent section of its nozzle as an afterburner into which oxygen is injected and supersonically combusted with nuclear preheated hydrogen emerging from the engines choked sonic throat - essentially scramjet propulsion in reverse. By varying the oxygen-to-hydrogen mixture ratio, LANTR engines can operate over a range of thrust and Isp values while the reactor core power level remains relatively constant. A LANTR-based LTS offers unique mission capabilities including short transit time crewed cargo transports. Even a commuter shuttle service may be possible allowing one-way trip times to and from the Moon on the order of 36 hours or less. If only 1 of the extracted LLO2 propellant from identified resource sites were available for use in lunar orbit, such a supply could support daily commuter flights to the Moon for many thousands of years! The proposed paper outlines an evolutionary architecture and examines a variety of mission types and transfer vehicle designs, along with the increasing demands on LLO2 production as mission complexity and (Delta)V requirements increase. A comparison of vehicle features and engine operating characteristics, for both NTR and LANTR engines, is also provided along with a discussion of the propellant production and mining requirements associated with using FeO-rich volcanic glass as source material.

Nuclear rocket engines↗
NASA NTRS2017

Robust Exploration and Commercial Missions to the Moon Using LANTR Propulsion and In-Situ Propellants Derived From Lunar Polar Ice (LPI) Deposits

Since the 1960s, scientists have conjectured that water icecould survive in the cold, permanently shadowed craters located at the Moons poles Clementine (1994), Lunar Prospector (1998),Chandrayaan-1 (2008), and Lunar Reconnaissance Orbiter (LRO) and Lunar CRater Observation and Sensing Satellite(LCROSS) (2009) lunar probes have provided data indicating the existence of large quantities of water ice at the lunar poles The Mini-SAR onboard Chandrayaan-1discovered more than 40 permanently shadowed craters near the lunar north pole that are thought to contain 600 million metric tons of water ice. Using neutron spectrometer data, the Lunar Prospector science team estimated a water ice content (1.5 +-0.8 wt in the regolith) found in the Moons polar cold trap sand estimated the total amount of water at both poles at 2 billion metric tons Using Mini-RF and spectrometry data, the LRO LCROSS science team estimated the water ice content in the regolith in the south polar region to be 5.6 +-2.9 wt. On the basis of the above scientific data, it appears that the water ice content can vary from 1-10 wt and the total quantity of LPI at both poles can range from 600 million to 2 billion metric tons NTP offers significant benefits for lunar missions and can take advantage of the leverage provided from using LDPs when they become available by transitioning to LANTR propulsion. LANTR provides a variablethrust and Isp capability, shortens burn times and extends engine life, and allows bipropellant operation The combination of LANTR and LDP has performance capability equivalent to that of a hypothetical gaseousfuel core NTR (effective Isp 1575 s) and can lead to a robust LTS with unique mission capabilities that include short transit time crewed cargo transports and routine commuter flights to the Moon The biggest challenge to making this vision a reality will be the production of increasing amounts of LDP andthe development of propellant depots in LEO, LLO and LPO. An industry-operated, privately financed venture, with NASA as its initial customer, might provide a possible blueprint for future development and operation With industry interested in developing cislunar space and commerce, and competitive forces at work, the timeline for developing this capability could well be accelerated, quicker than any of us can imagine, and just the beginning of things to come.

Nuclear Thermal Propulsion↗
NASA NTRS2017

Robust Exploration and Commercial Missions to the Moon Using LANTR Propulsion and In-Situ Propellants Derived from Lunar Polar Ice (LPI) Deposits

The nuclear thermal rocket (NTR) has frequently been identified as a key space asset required for the human exploration of Mars. This proven technology can also provide the affordable access through cislunar space necessary for commercial development and sustained human presence on the Moon. It is a demonstrated technology capable of generating both high thrust and high specific impulse (Isp 900 s) twice that of todays best chemical rockets. Nuclear lunar transfer vehicles consisting of a propulsion stage using three approx.16.5 klbf "Small Nuclear Rocket Engines (SNREs)", an in-line propellant tank, plus the payload can enable a variety of reusable lunar missions. These include cargo delivery and crewed lunar landing missions. Even weeklong "tourism" missions carrying passengers into lunar orbit for a day of sightseeing and picture taking are possible. The NTR can play an important role in the next phase of lunar exploration and development by providing a robust in-space lunar transportation system (LTS) that can allow initial outposts to evolve into settlements supported by a variety of commercial activities such as in-situ propellant production used to supply strategically located propellant depots and transportation nodes. The processing of LPI deposits (estimated to be approx. 2 billion metric tons) for propellant production - specifically liquid oxygen (LO2) and hydrogen (LH2) can significantly reduce the launch mass requirements from Earth and can enable reusable, surface-based lunar landing vehicles (LLVs) using LO2/LH2 chemical rocket engines. Afterwards, LO2/LH2 propellant depots can be established in lunar polar and equatorial orbits to supply the LTS. At this point a modified version of the conventional NTR called the LO2-augmented NTR, or LANTR would be introduced into the LTS allowing bipropellant operation and leveraging the mission benefits of refueling with lunar-derived propellants (LDPs) for Earth return. The bipropellant LANTR engine utilizes the large divergent section of its nozzle as an afterburner into which oxygen is injected and supersonically combusted with nuclear preheated hydrogen emerging from the engines choked sonic throat essentially scramjet propulsion in reverse. By varying the oxygen-to-hydrogen mixture ratio, LANTR engines can operate over a range of thrust and Isp values while the reactor core power level remains relatively constant. A LANTR-based LTS offers unique mission capabilities including short transit time crewed cargo transports. Even a commuter shuttle service may be possible allowing one-way trip times to and from the Moon on the order of 36 hours or less. If only 1 of the postulated water ice trapped in deep shadowed craters at the lunar poles were available for use in lunar orbit, such a supply could support daily commuter flights to the Moon for many thousands of years! The proposed paper outlines an evolutionary mission architecture and examines a variety of mission types and transfer vehicle designs, along with the increasing demands on LDP production as mission complexity and delta V requirements increase. A comparison of vehicle features and engine operating characteristics are also provided together with a discussion of the propellant production and mining requirements, and issues, associated with using LPI as the source material.

Nuclear Thermal Propulsion↗
NASA NTRS2018

Robust Exploration and Commercial Missions to the Moon Using Nuclear Thermal Rocket Propulsion and Lunar Liquid Oxygen Derived from FeO-Rich Pyroclasitc Deposits

The nuclear thermal rocket (NTR) has frequently been identified as a key space asset required for the human exploration of Mars. This proven technology can also provide the affordable access through cislunar space necessary for commercial development and sustained human presence on the Moon. It is a demonstrated technology capable of generating both high thrust and high specific impulse (I(sub sp) approx. 900 s) twice that of today's best chemical rockets. Nuclear lunar transfer vehicles-consisting of a propulsion stage using three approx. 16.5-klb(sub f) small nuclear rocket engines (SNREs), an in-line propellant tank, plus the payload-are reusable, enabling a variety of lunar missions. These include cargo delivery and crewed lunar landing missions. Even weeklong ''tourism'' missions carrying passengers into lunar orbit for a day of sightseeing and picture taking are possible. The NTR can play an important role in the next phase of lunar exploration and development by providing a robust in-space lunar transportation system (LTS) that can allow initial outposts to evolve into settlements supported by a variety of commercial activities such as in-situ propellant production used to supply strategically located propellant depots and transportation nodes. The use of lunar liquid oxygen (LLO2) derived from iron oxide (FeO)-rich volcanic glass beads, found in numerous pyroclastic deposits on the Moon, can significantly reduce the launch mass requirements from Earth by enabling reusable, surface-based lunar landing vehicles (LLVs)that use liquid oxygen and hydrogen (LO2/LH2) chemical rocket engines. Afterwards, a LO2/LH2 propellant depot can be established in lunar equatorial orbit to supply the LTS. At this point a modified version of the conventional NTR-called the LO2-augmented NTR, or LANTR-is introduced into the LTS allowing bipropellant operation and leveraging the mission benefits of refueling with lunar-derived propellants for Earth return. The bipropellant LANTR engine utilizes the large divergent section of its nozzle as an ''afterburner'' into which oxygen is injected and supersonically combusted with nuclear preheated hydrogen emerging from the engine's choked sonic throat-essentially ''scramjet propulsion in reverse.'' By varying the oxygen-to-hydrogen mixture ratio, LANTR engines can operate over a range of thrust and I(sub sp) values while the reactor core power level remains relatively constant. A LANTR-based LTS offers unique mission capabilities including short-transit-time crewed cargo transports. Even a ''commuter'' shuttle service may be possible allowing ''one-way'' trip times to and from the Moon on the order of 36 hours or less. If only 1% of the extracted LLO2 propellant from identified resource sites were available for use in lunar orbit, such a supply could support daily commuter flights to the Moon for many thousands of years! This report outlines an evolutionary architecture and examines a variety of mission types and transfer vehicle designs, along with the increasing demands on LLO2 production as mission complexity and velocity change delta V requirements increase. A comparison of vehicle features and engine operating characteristics, for both NTR and LANTR engines, is also provided along with a discussion of the propellant production and mining requirements associated with using FeO-rich volcanic glass as source material.

rocket↗
NASA NTRS2018

Advanced Development of Space Photovoltaic Concentrators Using Robust Lenses, Multi-Junction Cells, and Graphene Radiators

At the past three PVSCs, our team has presented recent advances in our space photovoltaic concentrator technology. In the past year, under multiple NASA-funded research and technology development programs, our team has made much additional progress in the advanced development of space photovoltaic concentrators. New robust Fresnel lenses, new high-efficiency multi-junction cells, and new graphene radiators have been developed. The paper will present the latest advances in this technology.

O'Neill, Mark↗
NASA NTRS2018

Robust Exploration and Commercial Missions to the Moon Using Nuclear Thermal Rocket Propulsion and In Situ Propellants Derived from Lunar Polar Ice Deposits

The nuclear thermal rocket (NTR) has frequently been identified as a key space asset required for the human exploration of Mars. This proven technology can also provide the affordable “access through cislunar space” necessary for commercial development and sustained human presence on the Moon. It is a demonstrated technology capable of generating both high thrust and high specific impulse (I(sub sp) ~900 s)— twice that of today’s best chemical rockets. Nuclear lunar transfer vehicles—consisting of a propulsion stage using three ~16.5-klb(sub f) small nuclear rocket engines (SNREs), an in-line propellant tank, plus the payload—can enable a variety of reusable lunar missions. These include cargo delivery and crewed lunar landing missions. Even weeklong “tourism” missions carrying passengers into lunar orbit for a day of sightseeing and picture taking are possible. The NTR can play an important role in the next phase of lunar exploration and development by providing a robust in-space lunar transportation system (LTS) that can allow initial outposts to evolve into settlements supported by a variety of commercial activities such as in situ propellant production used to supply strategically located propellant depots and transportation nodes. The processing of lunar polar ice (LPI) deposits (estimated to be ~2 billion metric tons) for propellant production—specifically liquid oxygen (LO(sub 2)) and hydrogen (LH(sub 2))—can significantly reduce the launch mass requirements from Earth and can enable reusable, surface-based lunar landing vehicles (LLVs) using LO(sub 2)/LH(sub 2) chemical rocket engines. Afterwards, LO(sub 2)/LH(sub 2) propellant depots can be established in lunar polar and equatorial orbits to supply the LTS. At this point a modified version of the conventional NTR called the LO(sub 2)-augmented NTR, or LANTR, would be introduced into the LTS, allowing bipropellant operation and leveraging the mission benefits of refueling with lunar-derived propellants (LDPs) for Earth return. The bipropellant LANTR engine utilizes the large divergent section of its nozzle as an “afterburner” into which oxygen is injected and supersonically combusted with nuclear preheated hydrogen emerging from the engine’s choked sonic throat—essentially “scramjet propulsion in reverse.” By varying the oxygen-to-hydrogen mixture ratio, LANTR engines can operate over a range of thrust and I(sub sp) values while the reactor core power level remains relatively constant. A LANTR-based LTS offers unique mission capabilities including short transit time crewed cargo transports. Even a “commuter” shuttle service may be possible, allowing “one-way” trip times to and from the Moon on the order of 36 hr or less. If only 1% of the postulated trapped water ice were available for use in lunar orbit, such a supply could support routine commuter flights to the Moon for many thousands of years. This report outlines an evolving LTS architecture that uses propellants derived from LPI and examines a variety of mission types and transfer vehicle designs along with their operating characteristics and increasing demands on LDP production as mission complexity and velocity change ΔV requirements increase. A comparison of the LDP production and mining requirements using LPI and volcanic glass to produce lunar-derived liquid oxygen (LUNOX) via the hydrogen reduction process is included, and the synergy with an evolving helium-3 mining industry is also discussed.

Borowski, Stanley K.↗
NASA NTRS2019

Modeling, Simulation, and Robust Design of the TSIS Pointing Controller for ISS Deployment

To ensure high quality TSIS science measurements, stringent requirements were levied on the pointing system performance. Several factors complicated the design of the pointing system controller including uncertainty in knowledge of the ISS base motion jitter, the use of direct drive brushless DC motors for the gimbal system, and the presence of TSIS structure low frequency modes. This paper will describe the modeling, simulation, analysis, and robust design techniques employed to reduce risk resulting in a pointing system that met requirements on-orbit.

Engelmann, Andrew↗
NASA NTRS2012

A Robust Initialization Scheme for a Lateral Trajectory Optimization Problem with Time of Arrival Windows

We present a robust initialization scheme that estimates parameter values for the numerical solution of a two-point boundary value problem. The two-point boundary value problem formulation stems from the optimization of a cost functional subject to the dynamics of a simplified lateral aircraft model and other constraints. Leveraging regular perturbation methods, initial parameter estimates are analytically determined and used to initialize a gradient descent optimization routine which is shown to rapidly converge over a range of initial aircraft positions and heading angles. Additionally, the velocity of the aircraft is optimized to ensure the trajectory of the aircraft terminates within a desired region in both time and space.

lateral trajectory optimization↗