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NASA NTRS2014

Doppler Lidar System Design via Interdisciplinary Design Concept at NASA Langley Research Center - Part III

Optimized designs of the Navigation Doppler Lidar (NDL) instrument for Autonomous Landing Hazard Avoidance Technology (ALHAT) were accomplished via Interdisciplinary Design Concept (IDEC) at NASA Langley Research Center during the summer of 2013. Three branches in the Engineering Directorate and three students were involved in this joint task through the NASA Langley Aerospace Research Summer Scholars (LARSS) Program. The Laser Remote Sensing Branch (LRSB), Mechanical Systems Branch (MSB), and Structural and Thermal Systems Branch (STSB) were engaged to achieve optimal designs through iterative and interactive collaborative design processes. A preliminary design iteration was able to reduce the power consumption, mass, and footprint by removing redundant components and replacing inefficient components with more efficient ones. A second design iteration reduced volume and mass by replacing bulky components with excessive performance with smaller components custom-designed for the power system. The existing power system was analyzed to rank components in terms of inefficiency, power dissipation, footprint and mass. Design considerations and priorities are compared along with the results of each design iteration. Overall power system improvements are summarized for design implementations.

Barnes, Bruce W.↗

NASA NTRS2014

Doppler Lidar System Design via Interdisciplinary Design Concept at NASA Langley Research Center - Part II

Optimized designs of the Navigation Doppler Lidar (NDL) instrument for Autonomous Landing Hazard Avoidance Technology (ALHAT) were accomplished via Interdisciplinary Design Concept (IDEC) at NASA Langley Research Center during the summer of 2013. Three branches in the Engineering Directorate and three students were involved in this joint task through the NASA Langley Aerospace Research Summer Scholars (LARSS) Program. The Laser Remote Sensing Branch (LRSB), Mechanical Systems Branch (MSB), and Structural and Thermal Systems Branch (STSB) were engaged to achieve optimal designs through iterative and interactive collaborative design processes. A preliminary design iteration was able to reduce the power consumption, mass, and footprint by removing redundant components and replacing inefficient components with more efficient ones. A second design iteration reduced volume and mass by replacing bulky components with excessive performance with smaller components custom-designed for the power system. Thermal modeling software was used to run steady state thermal analyses, which were used to both validate the designs and recommend further changes. Analyses were run on each redesign, as well as the original system. Thermal Desktop was used to run trade studies to account for uncertainty and assumptions about fan performance and boundary conditions. The studies suggested that, even if the assumptions were significantly wrong, the redesigned systems would remain within operating temperature limits.

Crasner, Aaron I.↗

NASA NTRS2013

Doppler Lidar System Design via Interdisciplinary Design Concept at NASA Langley Research Center - Part I

Optimized designs of the Navigation Doppler Lidar (NDL) instrument for Autonomous Landing Hazard Avoidance Technology (ALHAT) were accomplished via Interdisciplinary Design Concept (IDEC) at NASA Langley Research Center during the summer of 2013. Three branches in the Engineering Directorate and three students were involved in this joint task through the NASA Langley Aerospace Research Summer Scholars (LARSS) Program. The Laser Remote Sensing Branch (LRSB), Mechanical Systems Branch (MSB), and Structural and Thermal Systems Branch (STSB) were engaged to achieve optimal designs through iterative and interactive collaborative design processes. A preliminary design iteration was able to reduce the power consumption, mass, and footprint by removing redundant components and replacing inefficient components with more efficient ones. A second design iteration reduced volume and mass by replacing bulky components with excessive performance with smaller components custom-designed for the power system. Mechanical placement collaboration reduced potential electromagnetic interference (EMI). Through application of newly selected electrical components and thermal analysis data, a total electronic chassis redesign was accomplished. Use of an innovative forced convection tunnel heat sink was employed to meet and exceed project requirements for cooling, mass reduction, and volume reduction. Functionality was a key concern to make efficient use of airflow, and accessibility was also imperative to allow for servicing of chassis internals. The collaborative process provided for accelerated design maturation with substantiated function.

Boyer, Charles M.↗

NASA NTRS2014

Mars Sample Return Using Commercial Capabilities: Propulsive Entry, Descent, and Landing of a Capsule Form Vehicle

This paper describes a critical portion of the work that has been done at NASA, Ames Research Center regarding the use of the commercially developed Dragon capsule as a delivery vehicle for the elements of a high priority Mars Sample Return mission. The objective of the investigation was to determine entry and landed mass capabilities that cover anticipated mission conditions. The "Red Dragon", Mars configuration, uses supersonic retro-propulsion, with no required parachute system, to perform Entry, Descent, and Landing (EDL) maneuvers. The propulsive system proposed for use is the same system that will perform an abort, if necessary, for a human rated version of the Dragon capsule. Standard trajectory analysis tools are applied to publically available information about Dragon and other legacy capsule forms in order to perform the investigation. Trajectory simulation parameters include entry velocity, flight path angle, lift to drag Ratio (L/D), landing site elevation, atmosphere density, and total entry mass, in addition engineering assumptions for the performance of the propulsion system are stated. Mass estimates for major elements of the overall proposed architecture are coupled to this EDL analysis to close the overall architecture. Three synodic launch opportunities, beginning with the 2022 opportunity, define the arrival conditions. Results state the relations between the analysis parameters as well as sensitivities to those parameters. The EDL performance envelope includes landing altitudes between 0 and -4 km referenced to the Mars Orbiter Laser Altimeter datum as well as minimum and maximum atmosphere density. Total entry masses between 7 and 10 mt are considered with architecture closure occurring between 9.0 and 10 mt. Propellant mass fractions for each major phase of the EDL - Entry, Terminal Descent, and Hazard Avoidance - have been derived. An assessment of the effect of the entry conditions on the Thermal Protection System (TPS) currently in use for Dragon missions shows no significant stressors. A useful payload mass of 2.0 mt is provided and includes mass and grow allowance for a Mars Ascent Vehicle (MAV), Earth Return Vehicle (ERV), and mission unique equipment. The useful payload supports an architecture that receives a sample from another surface asset and sends it directly back to Earth for recovery in a high Earth orbit. The work shows that emerging commercial capabilities as well as previously studied EDL methodologies can be used to efficiently support an important planetary science objective. The work also has applications for human exploration missions that will also use propulsive EDL techniques

EDL↗

NASA NTRS2014

Mars Sample Return Using Commercial Capabilities: Mission Architecture Overview

Mars Sample Return (MSR) is the highest priority science mission for the next decade as recommended by the recent Decadal Survey of Planetary Science. This paper presents an overview of a feasibility study for an MSR mission. The objective of the study was to determine whether emerging commercial capabilities can be used to reduce the number of mission systems and launches required to return the samples, with the goal of reducing mission cost. We report the feasibility of a complete and closed MSR mission design using the following scenario that covers three synodic launch opportunities, beginning with the 2022 opportunity: A Falcon Heavy injects a SpaceX Red Dragon capsule and trunk onto a Trans Mars Injection (TMI) trajectory. The capsule is modified to carry all the hardware needed to return samples collected on Mars including a Mars Ascent Vehicle (MAV), an Earth Return Vehicle (ERV), and hardware to transfer a sample collected in a previously landed rover mission to the ERV. The Red Dragon descends to land on the surface of Mars using Super Sonic Retro Propulsion (SSRP). After previously collected samples are transferred to the ERV, the single-stage MAV launches the ERV from the surface of Mars. The MAV uses a storable liquid bi-propellant propulsion system to deliver the ERV to a Mars phasing orbit. After a brief phasing period, the ERV, which also uses a storable bi-propellant system, performs a Trans Earth Injection (TEI) burn. Upon arrival at Earth, the ERV performs Earth and lunar swing-bys and is placed into a lunar trailing circular orbit - an Earth orbit, at lunar distance. A later mission, using Dragon and launched by a Falcon Heavy, performs a rendezvous with the ERV in the lunar trailing orbit, retrieves the sample container and breaks the chain of contact with Mars by transferring the sample into a sterile and secure container. With the sample contained, the retrieving spacecraft makes a controlled Earth re-entry preventing any unintended release of pristine martian materials into the Earth's biosphere. The analysis methods employed standard and specialized aerospace engineering tools. Mission system elements were analyzed with either direct techniques or by using parametric mass estimating relationships (MERs). The architecture was iterated until overall mission convergence was achieved on at least one path. Subsystems analyzed in this study include support structures, power system, nose fairing, thermal insulation, actuation devices, MAV exhaust venting, and GN&C. Best practice application of loads, mass growth contingencies, and resource margins were used. For Falcon Heavy capabilities and Dragon subsystems we utilized publically available data from SpaceX, published analyses from other sources, as well as our own engineering and aerodynamic estimates. Earth Launch mass is under 11 mt, which is within the estimated capability of a Falcon Heavy, with margin. Total entry masses between 7 and 10 mt were considered with closure occurring between 9 and 10 mt. Propellant mass fractions for each major phase of the EDL - Entry, Terminal Descent, and Hazard Avoidance - have been derived. An assessment of the effect of the entry conditions on the thermal protection system (TPS), currently in use for Dragon missions, shows no significant stressors. A useful payload mass of 2.0 mt is provided and includes mass growth allowances for the MAV, the ERV, and mission unique equipment. We also report options for the MAV and ERV, including propulsion systems, crewed versus robotic retrieval mission, as well as direct Earth entry. International planetary protection policies as well as verifiable means of compliance will have a large impact on any MSR mission design. We identify areas within our architecture where such impacts occur. We also describe preliminary compliance measures that will be the subject of future work. This work shows that emerging commercial capabilities as well as new methodologies can be used to efficiently support an important planetary science objective. The work also has applications for human exploration missions that use propulsive EDL techniques

Red Dragon↗

NASA NTRS2013

Mars Sample Return Using Commercial Capabilities: Mission Architecture Overview

Mars Sample Return (MSR) is the highest priority science mission for the next decade as recommended by the recent Decadal Survey of Planetary Science. This paper presents an overview of a feasibility study for a MSR mission. The objective of the study was to determine whether emerging commercial capabilities can be used to reduce the number of mission systems and launches required to return the samples, with the goal of reducing mission cost. The major element required for the MSR mission are described and include an integration of the emerging commercial capabilities with small spacecraft design techniques; new utilizations of traditional aerospace technologies; and recent technological developments. We report the feasibility of a complete and closed MSR mission design using the following scenario that covers three synodic launch opportunities, beginning with the 2022 opportunity: A Falcon Heavy injects a SpaceX Red Dragon capsule and trunk onto a Trans Mars Injection (TMI) trajectory. The capsule is modified to carry all the hardware needed to return samples collected on Mars including a Mars Ascent Vehicle (MAV); an Earth Return Vehicle (ERV); and hardware to transfer a sample collected in a previously landed rover mission to the ERV. The Red Dragon descends to land on the surface of Mars using Supersonic Retro Propulsion (SRP). After previously collected samples are transferred to the ERV, the single-stage MAV launches the ERV from the surface of Mars to a Mars phasing orbit. The MAV uses a storable liquid, pump fed bi-propellant propulsion system. After a brief phasing period, the ERV, which also uses a storable bi-propellant system, performs a Trans Earth Injection (TEI) burn. Once near Earth the ERV performs Earth and lunar swing-bys and is placed into a Lunar Trailing Orbit (LTO0 - an Earth orbit, at lunar distance. A later mission, using a Dragon and launched by a Falcon Heavy, performs a rendezvous with the ERV in the lunar trailing orbit, retrieves the sample container and breaks the chain of contact with Mars by transferring the sample into a sterile and secure container. With the sample contained, the retrieving spacecraft, makes a controlled Earth re-entry preventing any unintended release of pristine Martian materials into the Earth's biosphere. Other capsule type vehicles and associated launchers may be applicable. The analysis methods employed standard and specialized aerospace engineering tools. Mission system elements were analyzed with either direct techniques or by using parametric mass estimating relationships (MERs). The architecture was iterated until overall mission convergence was achieved on at least one path. Subsystems analyzed in this study include support structures, power system, nose fairing, thermal insulation, actuation devices, MAV exhaust venting, and GN&C. Best practice application of loads, mass growth contingencies, and resource margins were used. For Falcon Heavy capabilities and Dragon subsystems we utilized publically available data from SpaceX; published analyses from other sources; as well as our own engineering and aerodynamic estimates. Earth Launch mass is under 11 mt, which is within the estimated capability of a Falcon Heavy, with margin. Total entry masses between 7 and 10 mt were considered with closure occurring between 9 and 10 mt. Propellant mass fractions for each major phase of the EDL - Entry, Terminal Descent, and Hazard Avoidance - have been derived. An assessment of the entry conditions on the thermal protection system (TPS), currently in use for Dragon missions, has been made. And shows no significant stressors. A useful mass of 2.0 mt is provided and includes mass growth allowances for the MAV, the ERV, and mission unique equipment. We also report on alternate propellant options for the MAV and options for the ERV, including propulsion systems; crewed versus robotic retrieval mission; as well as direct Earth entry. International Planetary Protection Policies as well as verifiable means of compliance will have a large impact on any MSR mission design. We identify areas within our architecture where such impacts occur. This work shows that emerging commercial capabilities can be used to effectively integrated into a mission to achieve an important planetary science objective.

Mars Sample Return↗

NASA NTRS2014

Design and Analysis of Morpheus Lander Flight Control System

The Morpheus Lander is a vertical takeoff and landing test bed vehicle developed to demonstrate the system performance of the Guidance, Navigation and Control (GN&C) system capability for the integrated autonomous landing and hazard avoidance system hardware and software. The Morpheus flight control system design must be robust to various mission profiles. This paper presents a design methodology for employing numerical optimization to develop the Morpheus flight control system. The design objectives include attitude tracking accuracy and robust stability with respect to rigid body dynamics and propellant slosh. Under the assumption that the Morpheus time-varying dynamics and control system can be frozen over a short period of time, the flight controllers are designed to stabilize all selected frozen-time control systems in the presence of parametric uncertainty. Both control gains in the inner attitude control loop and guidance gains in the outer position control loop are designed to maximize the vehicle performance while ensuring robustness. The flight control system designs provided herein have been demonstrated to provide stable control systems in both Draper Ares Stability Analysis Tool (ASAT) and the NASA/JSC Trick-based Morpheus time domain simulation.

Jang, Jiann-Woei↗

NASA NTRS2014

Morpheus Lander Roll Control System and Wind Modeling

The Morpheus prototype lander is a testbed capable of vertical takeoff and landing developed by NASA Johnson Space Center to assess advanced space technologies. Morpheus completed a series of flight tests at Kennedy Space Center to demonstrate autonomous landing and hazard avoidance for future exploration missions. As a prototype vehicle being tested in Earth's atmosphere, Morpheus requires a robust roll control system to counteract aerodynamic forces. This paper describes the control algorithm designed that commands jet firing and delay times based on roll orientation. Design, analysis, and testing are supported using a high fidelity, 6 degree-of-freedom simulation of vehicle dynamics. This paper also details the wind profiles generated using historical wind data, which are necessary to validate the roll control system in the simulation environment. In preparation for Morpheus testing, the wind model was expanded to create day-of-flight wind profiles based on data delivered by Kennedy Space Center. After the test campaign, a comparison of flight and simulation performance was completed to provide additional model validation.

Gambone, Elisabeth A.↗

NASA NTRS2015

Interfacing and Verifying ALHAT Safe Precision Landing Systems with the Morpheus Vehicle

The NASA Autonomous precision Landing and Hazard Avoidance Technology (ALHAT) project developed a suite of prototype sensors to enable autonomous and safe precision landing of robotic or crewed vehicles under any terrain lighting conditions. Development of the ALHAT sensor suite was a cross-NASA effort, culminating in integration and testing on-board a variety of terrestrial vehicles toward infusion into future spaceflight applications. Terrestrial tests were conducted on specialized test gantries, moving trucks, helicopter flights, and a flight test onboard the NASA Morpheus free-flying, rocket-propulsive flight-test vehicle. To accomplish these tests, a tedious integration process was developed and followed, which included both command and telemetry interfacing, as well as sensor alignment and calibration verification to ensure valid test data to analyze ALHAT and Guidance, Navigation and Control (GNC) performance. This was especially true for the flight test campaign of ALHAT onboard Morpheus. For interfacing of ALHAT sensors to the Morpheus flight system, an adaptable command and telemetry architecture was developed to allow for the evolution of per-sensor Interface Control Design/Documents (ICDs). Additionally, individual-sensor and on-vehicle verification testing was developed to ensure functional operation of the ALHAT sensors onboard the vehicle, as well as precision-measurement validity for each ALHAT sensor when integrated within the Morpheus GNC system. This paper provides some insight into the interface development and the integrated-systems verification that were a part of the build-up toward success of the ALHAT and Morpheus flight test campaigns in 2014. These campaigns provided valuable performance data that is refining the path toward spaceflight infusion of the ALHAT sensor suite.

Carson, John M., III↗

NASA NTRS2015

Flight Testing of Guidance, Navigation and Control Systems on the Mighty Eagle Robotic Lander Testbed

During 2011 a series of progressively more challenging flight tests of the Mighty Eagle autonomous terrestrial lander testbed were conducted primarily to validate the GNC system for a proposed lunar lander. With the successful completion of this GNC validation objective the opportunity existed to utilize the Mighty Eagle as a flying testbed for a variety of technologies. In 2012 an Autonomous Rendezvous and Capture (AR&C) algorithm was implemented in flight software and demonstrated in a series of flight tests. In 2012 a hazard avoidance system was developed and flight tested on the Mighty Eagle. Additionally, GNC algorithms from Moon Express and a MEMs IMU were tested in 2012. All of the testing described herein was above and beyond the original charter for the Mighty Eagle. In addition to being an excellent testbed for a wide variety of systems the Mighty Eagle also provided a great learning opportunity for many engineers and technicians to work a flight program.

Hannan, Mike↗

NASA NTRS2011

Intelligent Autonomy for Unmanned Surface and Underwater Vehicles

As the Autonomous Underwater Vehicle (AUV) and Autonomous Surface Vehicle (ASV) platforms mature in endurance and reliability, a natural evolution will occur towards longer, more remote autonomous missions. This evolution will require the development of key capabilities that allow these robotic systems to perform a high level of on-board decisionmaking, which would otherwise be performed by humanoperators. With more decision making capabilities, less a priori knowledge of the area of operations would be required, as these systems would be able to sense and adapt to changing environmental conditions, such as unknown topography, currents, obstructions, bays, harbors, islands, and river channels. Existing vehicle sensors would be dual-use; that is they would be utilized for the primary mission, which may be mapping or hydrographic reconnaissance; as well as for autonomous hazard avoidance, route planning, and bathymetric-based navigation. This paper describes a tightly integrated instantiation of an autonomous agent called CARACaS (Control Architecture for Robotic Agent Command and Sensing) developed at JPL (Jet Propulsion Laboratory) that was designed to address many of the issues for survivable ASV/AUV control and to provide adaptive mission capabilities. The results of some on-water tests with US Navy technology test platforms are also presented.

environmental sensing↗

NASA NTRS2015

Real-time Terrain Relative Navigation Test Results from a Relevant Environment for Mars Landing

Terrain Relative Navigation (TRN) is an on-board GN&C function that generates a position estimate of a spacecraft relative to a map of a planetary surface. When coupled with a divert, the position estimate enables access to more challenging landing sites through pin-point landing or large hazard avoidance. The Lander Vision System (LVS) is a smart sensor system that performs terrain relative navigation by matching descent camera imagery to a map of the landing site and then fusing this with inertial measurements to obtain high rate map relative position, velocity and attitude estimates. A prototype of the LVS was recently tested in a helicopter field test over Mars analog terrain at altitudes representative of Mars Entry Descent and Landing conditions. TRN ran in real-time on the LVS during the flights without human intervention or tuning. The system was able to compute estimates accurate to 40m (3 sigma) in 10 seconds on a flight like processing system. This paper describes the Mars operational test space definition, how the field test was designed to cover that operational envelope, the resulting TRN performance across the envelope and an assessment of test space coverage.

Pin-point Landing↗

NASA NTRS2016

COBALT CoOperative Blending of Autonomous Landing Technology

COBALT is a terrestrial test platform for development and maturation of GN&C (Guidance, Navigation and Control) technologies for PL&HA (Precision Landing and Hazard Avoidance). The project is developing a third generation, Langley Navigation Doppler Lidar (NDL) for ultra-precise velocity and range measurements, which will be integrated and tested with the JPL Lander Vision System (LVS) for Terrain Relative Navigation (TRN) position estimates. These technologies together provide navigation that enables controlled precision landing. The COBALT hardware will be integrated in 2017 into the GN&C subsystem of the Xodiac rocket-propulsive Vertical Test Bed (VTB) developed by Masten Space Systems (MSS), and two terrestrial flight campaigns will be conducted: one open-loop (i.e., passive) and one closed-loop (i.e., active).

Carson, John M. III↗

NASA NTRS2016

The "Deep Blue" Aerosol Project at NASA GSFC

Atmospheric aerosols such as mineral dust, wildfire smoke, sea spray, and volcanic ash are of interest for a variety of reasons including public health, climate change, hazard avoidance, and more. Deep Blue is a project which uses satellite observations of the Earth from sensors such as SeaWiFS, MODIS, and VIIRS to monitor the global aerosol burden. This talk will cover some basics about aerosols and the principles of aerosol remote sensing, as well as discussing specific results and future directions for the Deep Blue project.

Deep Blue↗

NASA NTRS2017

Boulder Distributions at Legacy Landing Sites: Assessing Regolith Production Rates and Landing Site Hazards

Understanding how the distribution of boulders on the lunar surface changes over time is key to understanding small-scale erosion processes and the rate at which rocks become regolith. Boulders degrade over time, primarily as a result of micrometeorite bombardment so their residence time at the surface can inform the rate at which rocks become regolith or become buried within regolith. Because of the gradual degradation of exposed boulders, we expect that the boulder population around an impact crater will decrease as crater age increases. Boulder distributions around craters of varying ages are needed to understand regolith production rates, and Lunar Reconnaissance Orbiter Camera (LROC) Narrow Angle Camera (NAC) images provide one of the best tools for conducting these studies. Using NAC images to assess how the distribution of boulders varies as a function of crater age provides key constraints for boulder erosion processes. Boulders also represent a potential hazard that must be addressed in the planning of future lunar landings. A boulder under a landing leg can contribute to deck tilt, and boulders can damage spacecraft during landing. Using orbital data to characterize boulder populations at locations where landers have safely touched down (Apollo, Luna, Surveyor, Chang'e-3) provides validation for landed mission hazard avoidance planning. Additionally, counting boulders at legacy landing sites is useful because: 1) LROC has extensive coverage of these sites at high resolutions (approximately 0.5 meters per pixel). 2) Returned samples from craters at these sites have been radiometrically dated, allowing assessment of how boulder distributions vary as a function of crater age. 3) Surface photos at these sites can be used to correlate with remote sensing measurements.

Watkins, R. N.↗

NASA NTRS2015

ALHAT COBALT: CoOperative Blending of Autonomous Landing Technology

The COBALT project is a flight demonstration of two NASA ALHAT (Autonomous precision Landing and Hazard Avoidance Technology) capabilities that are key for future robotic or human landing GN&C (Guidance, Navigation and Control) systems. The COBALT payload integrates the Navigation Doppler Lidar (NDL) for ultraprecise velocity and range measurements with the Lander Vision System (LVS) for Terrain Relative Navigation (TRN) position estimates. Terrestrial flight tests of the COBALT payload in an open-loop and closed-loop GN&C configuration will be conducted onboard a commercial, rocket-propulsive Vertical Test Bed (VTB) at a test range in Mojave, CA.

Carson, John M.↗

NASA NTRS2016

COBALT: A GN&C Payload for Testing ALHAT Capabilities in Closed-Loop Terrestrial Rocket Flights

The COBALT (CoOperative Blending of Autonomous Landing Technology) payload is being developed within NASA as a risk reduction activity to mature, integrate and test ALHAT (Autonomous precision Landing and Hazard Avoidance Technology) systems targeted for infusion into near-term robotic and future human space flight missions. The initial COBALT payload instantiation is integrating the third-generation ALHAT Navigation Doppler Lidar (NDL) sensor, for ultra high-precision velocity plus range measurements, with the passive-optical Lander Vision System (LVS) that provides Terrain Relative Navigation (TRN) global-position estimates. The COBALT payload will be integrated onboard a rocket-propulsive terrestrial testbed and will provide precise navigation estimates and guidance planning during two flight test campaigns in 2017 (one open-loop and closed- loop). The NDL is targeting performance capabilities desired for future Mars and Moon Entry, Descent and Landing (EDL). The LVS is already baselined for TRN on the Mars 2020 robotic lander mission. The COBALT platform will provide NASA with a new risk-reduction capability to test integrated EDL Guidance, Navigation and Control (GN&C) components in closed-loop flight demonstrations prior to the actual mission EDL.

Carson, John M., III↗

NASA NTRS2018

Modeling Principles Using the Relation Between Lagrange Multipliers and Bond Graphs

Final document is attached. Modeling dynamic systems by bond graphs has become state of the art technology since hundreds of researchers around the world have incorporated the technology in many fields of engineering and science. The legacy of its invertor Prof. Henry Paynter at MIT in 1959 is now a fundamental and practical technique to understand reality by building computer models. This paper addresses a particular aspect of this technology when modeling of mechanical systems require relaxation of constraints by means of Lagrange principles. Lagrange's equations are a useful means of describing and solving systems with kinematic constraints. Lagrange multipliers are variables used in equations to find the extremes of multivariate functions. Here we explore the relation of Lagrange multipliers to solve modeling difficulties of a space vehicle with equations with dependent derivatives. Lagrange multipliers were used in conjunction with bond graphs to simulate a system where joints of kinematic linkages produce dependent derivatives. NASA's Morpheus Project lunar lander was used as a case study. The Morpheus Project is a terrestrial test vehicle designed to fly the terminal descent trajectory of a lunar lander to advance the Autonomous Landing Hazard Avoidance Technology (ALHAT). An objective of this study is to apply the modeling approach herein to capture the dynamic movement of the lander as the propellant is sloshed and consumed. This paper expands further the analysis presented by (Granda, J J. Nguyen, L, Carlson, T, Sahragard-Monfared, G., Fornalski, E., Brocker 2016). Using an automated approach bond graph models of state space equations were generated using the Computer Aided Modeling Program (CAMPG). Integral causality models and derivative causality models were considered in order to find the simpler solution for the mathematical dependencies produced in modeling this vehicle.

Granda, Jose J.↗