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Lessons Learned With Risk Management: A Systems Engineer's Perspective

Risk management is a communications device that, when executed as an essential task, enables systems engineering to effectively balance risk across the project. Developing and baselining risks is an essential continuous task to ensure top project concerns both from bottom up and top down are being mitigated. Risk management provides the opportunity to avoid the consequence of the risk when mitigation steps start early enough. Just discussing risk with all the project flight elements during development, even if no risks are open, provides an excellent communication opportunity between systems engineering and those elements, ensuring concerns and worries have a platform for discussion. A well-managed risk identification process will identify concerns that are serious but not being clearly communicated, and it will enable mitigation of those potential problems before they cause a failure. Effective risk management requires considerable time and effort, but that effort will save time and money across the development. Risk management must be frequent enough to be useful and in depth enough to bring out emerging issues. It also requires a trusting relationship between the lead systems engineer and element and/or subsystem leads. The discussions need to be with the right number of individuals (typically a handful) and the right duration in time (typically an hour a month). Outside of these risk working groups, there is a formal management process to input, status, and disposition risks, and a monthly Risk Management Board meeting where key project stakeholders are informed. This paper provides good guidance on effective risk management from a systems engineering perspective and provides project lessons learned from the NASA spaceflight missions NICER, Landsat 9, LRO, and OSIRIS-REx to demonstrate the effectiveness of risk management.

Lessons Learned↗

Real-time simulation model of the HL-20 lifting body

A proposed manned spacecraft design, designated the HL-20, has been under investigation at Langley Research Center. Included in that investigation are flight control design and flying qualities studies utilizing a man-in-the-loop real-time simulator. This report documents the current real-time simulation model of the HL-20 lifting body vehicle, known as version 2.0, presently in use at NASA Langley Research Center. Included are data on vehicle aerodynamics, inertias, geometries, guidance and control laws, and cockpit displays and controllers. In addition, trim case and dynamic check case data is provided. The intent of this document is to provide the reader with sufficient information to develop and validate an equivalent simulation of the HL-20 for use in real-time or analytical studies.

Jackson, E. Bruce↗

An Overview of the Formation and Attitude Control System for the Terrestrial Planet Finder Formation Flying Interferometer

The Terrestrial Planet Finder formation flying Interferometer (TPF-I) will be a five-spacecraft, precision formation operating near a Sun-Earth Lagrange point. As part of technology development for TPF-I, a formation and attitude control system (FACS) is being developed that achieves the precision and functionality associated with the TPF-I formation. This FACS will be demonstrated in a distributed, real-time simulation environment. In this paper we present an overview of the FACS and discuss in detail its constituent formation estimation, guidance and control architectures and algorithms. Since the FACS is currently being integrated into a high-fidelity simulation environment, component simulations demonstrating algorithm performance are presented.

Terrestrial Planet Finder (TPF)↗

Gimbal Control Algorithms for the Global Precipitation Measurement Core Observatory

There are two gimbaled systems on the Global Precipitation Measurement Core Observatory: two single-degree-of-freedom solar arrays (SAs) and one two-degree-of-freedom high gain antenna (HGA). The guidance, navigation, and control analysis team was presented with the following challenges regarding SA orientation control during periods of normal mission science: (1) maximize solar flux on the SAs during orbit day, subject to battery charging limits, (2) minimize atmospheric drag during orbit night to reduce frequency of orbit maintenance thruster usage, (3) minimize atmospheric drag during orbits for which solar flux is nearly independent of SA orientation, and (4) keep array-induced spacecraft attitude disturbances within allocated tolerances. The team was presented with the following challenges regarding HGA control during mission science periods: (1) while tracking a ground-selected Tracking Data and Relay Satellite (TDRS), keep HGA control error below about 4', (2) keep array-induced spacecraft attitude disturbances small, and (3) minimize transition time between TDRSs subject to constraints imposed by item 2. This paper describes the control algorithms developed to achieve these goals and certain analysis done as part of that work.

Welter, Gary L.↗

Human Landing System Lunar Thermal Analysis Guidebook

The purpose of the Human Landing System (HLS) Lunar Thermal Analysis Guidebook (L-TAG) is to provide guidance to experienced thermal engineering personnel on how to conduct worst-case hot and cold lunar thermal analyses for the design of HLS hardware in both lunar orbit and lunar surface environments. The HLS L-TAG will include pointers to the Cross-Program Design Specification for Natural Environments (DSNE), SLS-SPEC-159, and best practices/approaches for interpreting and complying with the DSNE lunar thermal environments in the analysis of HLS spacecraft, vehicles and systems. The HLS L-TAG is a reference document that is available to all HLS thermal analysts. In the event of a conflict with the descriptions provided herein, the DSNE takes precedence. This document represents the best available information at the time of publication and will undergo updates as the HLS program evolves. Feedback from the user community is encouraged to support further refinement of the Guidebook.

Thermal Analysis↗

Lunar Thermal Analysis Guidebook (L-TAG): Thermo-physical and Optical Properties of Lunar Regolith

The purpose of the Human Landing System (HLS) Lunar Thermal Analysis Guidebook (L-TAG) is to provide guidance to experienced thermal engineering personnel on how to conduct worst-case hot and cold lunar thermal analyses for the design of HLS hardware in both lunar orbit and lunar surface environments. The HLS L-TAG will include pointers to the Cross-Program Design Specification for Natural Environments (DSNE), SLS-SPEC-159, and best practices/approaches for interpreting and complying with the DSNE lunar thermal environments in the analysis of HLS spacecraft, vehicles and systems. The HLS L-TAG is a reference document that is available to all HLS thermal analysts. In the event of a conflict with the descriptions provided herein, the DSNE takes precedence. This document represents the best available information at the time of publication and will undergo updates as the HLS program evolves. Feedback from the user community is encouraged to support further refinement of the Guidebook.

Thermal Analysis↗

Lunar Thermal Analysis Guidebook (L-TAG)

The purpose of the Human Landing System (HLS) Lunar Thermal Analysis Guidebook (L-TAG) is to provide guidance to experienced thermal engineering personnel on how to conduct worst-case hot and cold lunar thermal analyses for the design of HLS hardware in both lunar orbit and lunar surface environments. The HLS L-TAG will include pointers to the Cross-Program Design Specification for Natural Environments (DSNE), SLS-SPEC-159, and best practices/approaches for interpreting and complying with the DSNE lunar thermal environments in the analysis of HLS spacecraft, vehicles and systems. The HLS L-TAG is a reference document that is available to all HLS thermal analysts. In the event of a conflict with the descriptions provided herein, the DSNE takes precedence. This document represents the best available information at the time of publication and will undergo updates as the HLS program evolves. Feedback from the user community is encouraged to support further refinement of the Guidebook.

Thermal Analysis↗

Lunar Thermal Analysis Guidebook (L-TAG)

The purpose of the Human Landing System (HLS) Lunar Thermal Analysis Guidebook (L-TAG) is to provide guidance to experienced thermal engineering personnel on how to conduct worst-case hot and cold lunar thermal analyses for the design of HLS hardware in both lunar orbit and lunar surface environments. The HLS L-TAG will include pointers to the Cross-Program Design Specification for Natural Environments (DSNE), SLS-SPEC-159, and best practices/approaches for interpreting and complying with the DSNE lunar thermal environments in the analysis of HLS spacecraft, vehicles and systems. The HLS L-TAG is a reference document that is available to all HLS thermal analysts. In the event of a conflict with the descriptions provided herein, the DSNE takes precedence. This document represents the best available information at the time of publication and will undergo updates as the HLS program evolves. Feedback from the user community is encouraged to support further refinement of the Guidebook.

Thermal Analysis↗

Relative Navigation of Formation Flying Satellites

The Guidance, Navigation, and Control Center (GNCC) at Goddard Space Flight Center (GSFC) has successfully developed high-accuracy autonomous satellite navigation systems using the National Aeronautics and Space Administration's (NASA's) space and ground communications systems and the Global Positioning System (GPS). In addition, an autonomous navigation system that uses celestial object sensor measurements is currently under development and has been successfully tested using real Sun and Earth horizon measurements.The GNCC has developed advanced spacecraft systems that provide autonomous navigation and control of formation flyers in near-Earth, high-Earth, and libration point orbits. To support this effort, the GNCC is assessing the relative navigation accuracy achievable for proposed formations using GPS, intersatellite crosslink, ground-to-satellite Doppler, and celestial object sensor measurements. This paper evaluates the performance of these relative navigation approaches for three proposed missions with two or more vehicles maintaining relatively tight formations. High-fidelity simulations were performed to quantify the absolute and relative navigation accuracy as a function of navigation algorithm and measurement type. Realistically-simulated measurements were processed using the extended Kalman filter implemented in the GPS Enhanced Inboard Navigation System (GEONS) flight software developed by GSFC GNCC. Solutions obtained by simultaneously estimating all satellites in the formation were compared with the results obtained using a simpler approach based on differencing independently estimated state vectors.

Long, Anne↗

Empire. a study of early manned interplanetary missions final report, may 26 - nov. 25, 1962

This report summarizes the investigations and results of the EMPIRE Study Program undertaken by Aeronutronic Division of Ford Motor Company for the Future Projects Office, Marshall Space Flight Center, under Contract NAS8-5025. The dual planet flyby missions of the Crocco and Symmetric trajectory classes are discussed. The Crocco mission with an August 1971 launch window requires an interplanetary injection velocity increment of i0.i km/sec, has a return velocity of 13.5 km/sec, and takes approximately 400 days. The Symmetric mission with a July 1970 launch window has an injection velocity increment of 5.3 km/sec, a return velocity of 15.8 km/sec, and takes approximately 630 days. Additional results of the trajectory studies and abort trajectories are reported. The guidance and navigation subsystem, midcourse corrections, and planetary approach corrections are discussed. A detailed analysis of the reentry phase of EMPIRE includes consideration of an Apollo-type, a Drag Brake, and a lifting-type reentry vehicle to return the six-man crew at mission completion or in an aborted condition. The High L/D reentry vehicle is used in the missions considered. The various technological areas required for design criteria are developed and several spacecraft designs are considered. The all chemical propulsion Crocco system is discarded due to weight, complexity, and cost. The nuclear injected Crocco is treated in a similar manner. The lower energy injection for the Symmetric Mission leads to the feasibility of a nuclear injected vehicle with an Earth orbit weight of about 180,000 kilograms (400,000 pounds) before interplanetary transit. In addition, two chemical symmetric vehicles are treated. Conservative radiation exposures are derived, for the 630 day mission, of less than 200 REM and a polyethelene radiation shelter is designed. Scientific aspects of the missions are discussed. Mission Success Probabilities are presented for the various missions considered and for Saturn C-5, Nova, and Super-Nova Earth launch vehicles in light of possible development. The need for acceleration of nuclear rocket engine developments and auxiliary power developments is indicated. Definition of a larger nuclear engine of the order of 200,000 pounds thrust and about 800 seconds burning time or 50,000 pound thrust and 3600 seconds burning time is indicated for the Symmetric Mission in 1970 (energy requirements are higher in 1972 and for later launch due to the less favorable position of Mars)_ Immediate development of this advanced nuclear propulsion capability is recommended. A Development Plan and Funding Schedule is given for the 1970 launch window pinpointing the critical development areas and indicating a total program cost of $12.6 billion independent of other programmed R&D costs. In conclusion, technological feasibility for an early manned dual planet Mars-Venus flyby is believed to be demonstrated in this study. Several areas of accelerated development and experimental confirmation of theory are pinpointed. The necessary funding and development of Nova or orbital operations capability with Saturn C-5's is required. The 1970 launch window appears to offer the least expensive Symmetric Mission for several years into the 1980's.

F. P. Dixon↗

An investigation into the milliarcsecond attitude control errors of Hubble Space Telescope

An analysis of the fine pointing errors of the Hubble Space Telescope (HST), in the range from 1 to 15 milliarcsecs, is reported on. The emphasis is on the study of the performance characteristics of the pointing control system, fine guidance sensors and the optical telescope assembly, which produce relative attitude and astrometric measurement errors. Since the first servicing mission in December 1993, the HST relative short term position stability is of the order of 3 milliarcsecs RMS when averaged over 1 min intervals. At this level of accuracy, longer term systematic attitude errors in this range can have a noticeable impact on the telescope's observations. The various error sources are described, including: internal temperature effects; spacecraft structure temperature effects; calibration procedures, and computational inaccuracies.

Bradley, A. J.↗

Demonstration of Autonomous Rendezvous Technology (DART) Project Summary

Since the 1960's, NASA has performed numerous rendezvous and docking missions. The common element of all US rendezvous and docking is that the spacecraft has always been piloted by astronauts. Only the Russian Space Program has developed and demonstrated an autonomous capability. The Demonstration of Autonomous Rendezvous Technology (DART) project currently funded under NASA's Space Launch Initiative (SLI) Cycle I, provides a key step in establishing an autonomous rendezvous capability for the United States. DART's objective is to demonstrate, in space, the hardware and software necessary for autonomous rendezvous. Orbital Sciences Corporation intends to integrate an Advanced Video Guidance Sensor and Autonomous Rendezvous and Proximity Operations algorithms into a Pegasus upper stage in order to demonstrate the capability to autonomously rendezvous with a target currently in orbit. The DART mission will occur in April 2004. The launch site will be Vandenburg AFB and the launch vehicle will be a Pegasus XL equipped with a Hydrazine Auxiliary Propulsion System 4th stage. All mission objectives will be completed within a 24 hour period. The paper provides a summary of mission objectives, mission overview and a discussion on the design features of the chase and target vehicles.

TImothy E Rumford↗

Advanced Pioneer guidance and navigation requirements for outer planet missions

Three advanced Pioneer missions to the outer planets are analyzed to assess midcourse velocity and navigation requirements. Selecting the results of the Saturn/Uranus mission as representative values for the three missions, the Earth-Saturn midcourse mean plus 3-sigma velocity correction is 80 m/sec. Earth-based radio-only tracking results in a navigational error of 2000 km at Saturn which in turn requires a mean plus 3-sigma velocity correction of 140 m/sec on the Saturn-Uranus leg to nullify this error mapped to Uranus. In contrast to these figures, if a proposed optical V-slit sensor is incorporated into the spacecraft navigational system, a Saturn B-plane error of only 350 km results with a corresponding required mean plus 3-sigma post-Saturn velocity correction of 23.2 m/sec. An 8000 km miss at Uranus results from radio-only tracking at Saturn which can be considerably reduced to 1400 km by utilizing the optical sensor during the Saturn flyby.

Paul, C. K.↗

Thermal Protection System Design of Aerocapture Systems for Uranus Orbiters

The National Academies Planetary Science and Astrobiology Decadal Survey recently identified Uranus and Neptune - called Ice Giants - as the priority destinations for science[1]. The survey assessed both a mission to Uranus through the Uranus Orbiter and Probe (UOP) concept, and Neptune through the Neptune-Triton Odyssey concept and determined that Uranus is the highest priority for a Flagship class mission. The UOP mission will deliver an in situ probe and conduct a multi-year orbital tour of the system to meet the science objectives. While the Uranus mission is currently viable with launch windows starting in 2031 using existing launch vehicles, the mission has a long cruise time to destination (between 12 and 15 years) and would require more than half of its weight in fuel propellant to achieve the change in velocity necessary for orbital insertion. Aerocapture is a method of orbital control that uses aerodynamic forces generated on a vehicle by the planet’s atmosphere to modulate a spacecraft’s trajectory, allowing mission designers to target the final orbital state. For the Uranus mission, using aerocapture for orbital insertion can decrease not only the cruise time to the destination by 2 - 3 years, but the propellant required to achieve orbital insertion (by more than 40%) which would, in turn, increase the available science payload and reduce the timeline for retrieving data vital to the mission’s science objectives[2]. Achieving orbital insertion via aerocapture requires novel algorithms for Guidance, Navigation and Control[3], and mass-efficient Thermal Protection Systems (TPS) performing in a new atmosphere. This paper will focus on the selection and tailoring of the Thermal Protection Systems for the forebody and aftbody heatshields of an aerocapture mission to Uranus. While preliminary results indicate that multiple systems in NASA’s repertoire are capable of performing in the predicted aerothermal environment there are unique aspects like the inert environment that affect ablation efficiency, and the heatload for aerocapture trajectories to the outer planets are among the highest of any mission to-date[4]. These two factors may impose operational requirements to heatshield separation in order to minimize thermal soak to the payload, and may demand TPS thickness and configurations that have not yet been demonstrated. This paper will discuss the updated maturity, manufacturing, and performance capabilities of candidate thermal protection systems, with specific areas of need highlighted to make thermal protection systems viable for use in the recommended Uranus Orbiter and Probe mission.

Uranus↗

Funding and Strategic Alignment Guidance for Infusing Small Business Innovation Research Technology Into Science Mission Directorate Projects at Glenn Research Center for 2015

This report is intended to help NASA program and project managers incorporate Glenn ResearchCenter Small Business Innovation Research/Small Business Technology Transfer (SBIR)/(STTR)technologies into NASA Science Mission Directorate (SMD) programs/projects. Other Government and commercial project managers can also find this useful.

Spacecraft and Platform Subsystems↗

Solar Dynamics Observatory Guidance, Navigation, and Control System Overview

The Solar Dynamics Observatory (SDO) was designed and built at the Goddard Space Flight Center, launched from Cape Canaveral on February 11, 2010, and reached its final geosynchronous science orbit on March 16, 2010. The purpose of SDO is to observe the Sun and continuously relay data to a dedicated ground station. SDO remains Sun-pointing throughout most of its mission for the instruments to take measurements of the Sun. The SDO attitude control system (ACS) is a single-fault tolerant design. Its fully redundant attitude sensor complement includes sixteen coarse Sun sensors (CSSs), a digital Sun sensor (DSS), three two-axis inertial reference units (IRUs), and two star trackers (STs). The ACS also makes use of the four guide telescopes included as a part of one of the science instruments. Attitude actuation is performed using four reaction wheels assemblies (RWAs) and eight thrusters, with a single main engine used to provide velocity-change thrust for orbit raising. The attitude control software has five nominal control modes, three wheel-based modes and two thruster-based modes. A wheel-based Safehold running in the attitude control electronics box improves the robustness of the system as a whole. All six modes are designed on the same basic proportional-integral-derivative attitude error structure, with more robust modes setting their integral gains to zero. This paper details the final overall design of the SDO guidance, navigation, and control (GN&C) system and how it was used in practice during SDO launch, commissioning, and nominal operations. This overview will include the ACS control modes, attitude determination and sensor calibration, the high gain antenna (HGA) calibration, and jitter mitigation operation. The Solar Dynamics Observatory mission is part of the NASA Living With a Star program, which seeks to understand the changing Sun and its effects on the Solar System, life, and society. To this end, the SDO spacecraft carries three Sun-observing instruments: Helioseismic and Magnetic Imager (HMI), led by Stanford University; Atmospheric Imaging Assembly (AIA), led by Lockheed Martin Space and Astrophysics Laboratory; and Extreme Ultraviolet Variability Experiment (EVE), led by the University of Colorado. The basic mission is to observe the Sun for a very high percentage of the 5-year mission (10-year goal) with long stretches of uninterrupted observations and with constant, high-data-rate transmission to a dedicated ground station to be located in White Sands, New Mexico. These goals guided the design of the spacecraft bus that will carry and service the three-instrument payload. Overarching design goals for the bus are geosynchronous orbit, near-constant Sun observations with the ability to fly through eclipses, and constant HGA contact with the dedicated ground station. A three-axis stabilized ACS is needed both to point at the Sun accurately and to keep the roll about the Sun vector correctly positioned with respect to the solar north pole. This roll control is especially important for the magnetic field imaging of HM I. The mission requirements have several general impacts on the ACS design. Both the AIA and HMI instruments are very sensitive to the blurring caused by jitter. Each has an image stabilization system (ISS) with some ability to filter out high frequency motion, but below the bandwidth of the ISS the control system must compensate for disturbances within the ACS bandwidth or avoid exciting jitter at higher frequencies. Within the ACS bandwidth, the control requirement imposed by AIA is to place the center of the solar disk no more than 2 arc sec, 3 , from a body-defined target based on one of the GTs that accompany the instrument. This body-defined target, called the science reference boresight (SRB), was determined from the postlaunch orientation of the GTs by averaging the bounding telescope boresights for pitch to get a pitch SRB coordinate, and by averaging the bounding boresights for yaw toet the yaw SRB coordinate. The location of this SRB in the 0.5-deg field-of-view for each GT then becomes the central target for each telescope; one GT is selected for use as the ACS controlling guide telescope (CGT) at any given time. Fine Sun-pointing is effected based on this SRB for all three instruments when the Sun is within the linear range of the CGT. In addition to limiting jitter, HMI science requires averaging several observations, making the instrument sensitive to low frequency motion that induces differential motion between each observation. This requires the spacecraft attitude to be stable about the roll axis to approximately 10 arcsec over a ten-minute period. Instrument calibrations require that the spacecraft point the SRB up to 2.5 degrees in pitch and yaw away from the center of the Sun, placing the Sun outside the field-of-view of the guide telescopes. In such instances, when the GTs cannot provide the definitive target for the ACS, on-board attitude determination combined with ephemeris prediction of the Sun direction must provide the definitive target. EVE is capable of observing the Sun with less dependence on attitude control. However, the ground data processing needs for calibrations result in the most strict attitude knowledge requirements for the mission: [35,70,70] arcsec, 3 , of knowledge with respect to the center of the solar disk. In addition to driving the ACS sensor selection, the knowledge requirements, which have their effect primarily during Inertial mode calibrations, drive the accuracy requirements for the solar ephemeris. The need to achieve and maintain geosynchronous orbit (GEO) drove the need for high-efficiency propulsive systems and appropriate attitude control. The main engine provided high specific impulse for the maneuvers to attain GEO, while the smaller ACS thrusters managed the disturbance torques of the larger engine and provided the capability for much smaller adjustment burns on orbit. SDO s large solar profile means that solar radiation pressure is a large torque disturbance, and the momentum buildup from this disturbance and the GEO altitude drives the ACS to use thrusters to manage vehicle momentum. The demanding data capture budget for the mission, however, requires SDO to avoid frequent thruster maneuvers, while concerns about on-orbit jitter restrict the maximum desired wheel speeds desired from the RWAs. The plan for on-orbit wheel speed and momentum management will be discussed as well as what is now being done in operation after the jitter environment was characterized. The SDO ACS hardware complement is single-fault tolerant. Two main processors carry virtually identical copies of the command and data handling and ACS software, and two identical attitude control electronics (ACE) boxes carry Coldfire processors with contingency ACS software and other hardware interface cards; the ACE structure allows reaction wheels to be commanded by the Sun-pointing Safehold independent of the Mil Std 1553 data bus. The sixteen Adcole CSSs are grouped into primary and backup sets of eight sensors, each set providing the ability to calculate a sun vector. Each set of eight eyes provides full 4 -steradian coverage. The Adcole DSS comprises an optics head and a separate electronics box providing a 1553 data interface. The electronics box is mounted inside the Faraday cage created by the spacecraft bus module. The DSS head with its 32- deg square FOV is mounted on the instrument module with its boresight along the spacecraft X axis, nearly aligned with the Sun during observations. Adcole has designed the DSS calibration parameters so that the accuracy is 0.24 arcminutes within 10 deg of the boresight, and diminishes to 3 arcminutes as the Sun moves towards the edges of its FOV . This DSS calibration scheme provides higher accuracy attitude determination over the range of the instrument calibration maneuvers.

Morgenstern, Wendy M.↗

Rapid Generation of Optimal Asteroid Powered Descent Trajectories Via Convex Optimization

Mission proposals that land on asteroids are becoming popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site. The problem under investigation is how to design a fuel-optimal powered descent trajectory that can be quickly computed on-board the spacecraft, without interaction from ground control. An optimal trajectory designed immediately prior to the descent burn has many advantages. These advantages include the ability to use the actual vehicle starting state as the initial condition in the trajectory design and the ease of updating the landing target site if the original landing site is no longer viable. For long trajectories, the trajectory can be updated periodically by a redesign of the optimal trajectory based on current vehicle conditions to improve the guidance performance. One of the key drivers for being completely autonomous is the infrequent and delayed communication between ground control and the vehicle. Challenges that arise from designing an asteroid powered descent trajectory include complicated nonlinear gravity fields, small rotating bodies and low thrust vehicles.

Pinson, Robin↗

Trajectory Design Employing Convex Optimization for Landing on Irregularly Shaped Asteroids

Mission proposals that land on asteroids are becoming popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site. The problem under investigation is how to design a fuel-optimal powered descent trajectory that can be quickly computed on- board the spacecraft, without interaction from ground control. An optimal trajectory designed immediately prior to the descent burn has many advantages. These advantages include the ability to use the actual vehicle starting state as the initial condition in the trajectory design and the ease of updating the landing target site if the original landing site is no longer viable. For long trajectories, the trajectory can be updated periodically by a redesign of the optimal trajectory based on current vehicle conditions to improve the guidance performance. One of the key drivers for being completely autonomous is the infrequent and delayed communication between ground control and the vehicle. Challenges that arise from designing an asteroid powered descent trajectory include complicated nonlinear gravity fields, small rotating bodies and low thrust vehicles. There are two previous studies that form the background to the current investigation. The first set looked in-depth at applying convex optimization to a powered descent trajectory on Mars with promising results.1, 2 This showed that the powered descent equations of motion can be relaxed and formed into a convex optimization problem and that the optimal solution of the relaxed problem is indeed a feasible solution to the original problem. This analysis used a constant gravity field. The second area applied a successive solution process to formulate a second order cone program that designs rendezvous and proximity operations trajectories.3, 4 These trajectories included a Newtonian gravity model. The equivalence of the solutions between the relaxed and the original problem is theoretically established. The proposed solution for designing the asteroid powered descent trajectory is to use convex optimization, a gravity model with higher fidelity than Newtonian, and an iterative solution process to design the fuel optimal trajectory. The solution to the convex optimization problem is the thrust profile, magnitude and direction, that will yield the minimum fuel trajectory for a soft landing at the target site, subject to various mission and operational constraints. The equations of motion are formulated in a rotating coordinate system and includes a high fidelity gravity model. The vehicle's thrust magnitude can vary between maximum and minimum bounds during the burn. Also, constraints are included to ensure that the vehicle does not run out of propellant, or go below the asteroid's surface, and any vehicle pointing requirements. The equations of motion are discretized and propagated with the trapezoidal rule in order to produce equality constraints for the optimization problem. These equality constraints allow the optimization algorithm to solve the entire problem, without including a propagator inside the optimization algorithm.

Pinson, Robin M.↗