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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.↗

NASA NTRS2018

Air Traffic Management Technology Demostration-1 (ATD-1) Avionics Phase 2 Flight Test and Results

NASA’s first Air Traffic Management Technology Demonstration (ATD-1) subproject successfully completed 19 days of flight test validation in January and February 2017 of an Interval Management (IM) avionics prototype and the procedures used to conduct IM arrival and approach operations. IM is one of the three elements integrated into NASA’s ATD-1 concept of operations with the subproject goal of improving aircraft efficiency and airport throughput during high-density arrival operations. The ATD-1 concept of operations combines advanced arrival scheduling, controller decision support tools, and interval management (IM) avionics to enable merging of multiple, time-based, efficient arrival streams. IM contributes to the operation by calculating speeds that enable an aircraft to precisely achieve a specific time or distance behind another aircraft. When precise spacing intervals can be calculated, achieved, and then maintained during high-density operations, aircraft efficiency should be improved by enabling the aircraft to remain closer to the optimum descent trajectory instead of using vectors and step-down altitudes, and airport throughput should be maintained or improved by each aircraft arriving at the runway threshold closer to the assigned spacing interval. This avionics development and flight test was conducted under a NASA contract by Boeing Research and Technology, with Boeing Commercial Aircraft, Honeywell, United Airlines, and Jeppesen as sub-contractors. The Honeywell built IM avionics were the first ever prototype built based on NASA requirements as well as developing and non-flight tested international IM standards, integrated into two test aircraft, and then flown in real-world conditions at the Grant County International Airport (KMWH). The IM prototype flown in the flight test used data from the Ownship and the assigned lead, or Target, aircraft to calculate the airspeed necessary for the Ownship to achieve the desired spacing. The flight test demonstrated that the IM avionics prototype generally met the IM requirement for spacing accuracy. However, the control laws implemented require further development to reduce the high IM speed command rate and the number of speed reversals observed during the test. Pilots assessed the IM procedure as acceptable, and issues requiring further attention were identified. In summary, the IM avionics prototype showed significant promise in contributing to the goals of improving aircraft efficiency and airport throughput. The flight test results also provided important data to the FAA and the working group developing the follow-on version of the international IM standards.

Baxley, Brian T.↗

NASA NTRSDate not supplied

Path-Adaptive Guidance Algorithm Trades for a Two-Stage Lunar Descent Vehicle

For the next generation of NASA’s missions, explicit, path-adaptive descent guidance algorithms must provide the stability and customizability required for a safe and efficient descent to the lunar surface, while also meeting program and vehicle constraints. Several descent algorithms have been flown and tested for single-stage landers through the Apollo and Altair programs, but thus far little analysis has been conducted involving the application of these algorithms to a two-stage descent vehicle. Due to payload mass and fairing constraints of the existing fleet of launch vehicles, multi-stage descent architectures are a unique option for achieving the greatest possible mass to lunar surface. This paper seeks to compare the performance of guidance configurations of a lunar lander system consisting of two stages, one of which separates partway through descent. Through development of this paper, an optimization suite has been written that is specifically designed for optimizing planetary non-atmospheric two-stage descent trajectories, and is used as a baseline to compare the guidance algorithms tested. Time-to-go computational methods and ignition logic routines that may be employed in a lunar environment are also discussed. Preliminary results are presented that show relative performance metrics for a range of different guidance algorithm configurations.

Jason M Everett↗

NASA NTRSDate not supplied

Application of a Detached Eddy Simulation Approach with Finite-Rate Chemistry to Mars-Relevant Retropropulsion Operating Environments

Human-scale Mars vehicles will require retropropulsion for descent and landing, replacing heritage supersonic parachute systems with an extended phase of powered flight. Due to the limitations of terrestrial testing in Mars-relevant conditions, design and analysis will increasingly rely on computational modeling and simulation. This paper provides an overview of a computational campaign investigating the aerodynamics of a Mars lander concept along various points on a powered descent trajectory including supersonic, transonic, and subsonic conditions using finite-rate chemistry. Simulations using unstructured grids containing billions of elements are performed at scale using thousands of Graphics Processing Units, enabling run-times of a few days for each simulation presented. At each freestream condition, significant minor species concentrations are observed external to the nozzles in the large mixing region upstream of the vehicle. While the flowfields are highly non-stationary in all cases, the mean integrated forces and moments on the vehicle remain small in comparison to the deceleration provided through retropropulsion.

Ashley Korzun↗

NASA NTRSDate not supplied

Feasibility Study of a Multi Tilt-rotor Aircraft as the Artemis Lunar Training Vehicle

The Lunar Landing Research Vehicles (LLRVs) and the Lunar Landing Training Vehicles (LLTVs) provided astronaut candidates for the Apollo program with essential experience and confidence required to complete the missions, and contributed to six successful manned landings on the moon. The primary challenge in terrestrial training was being able to replicate the ratio of bank angle to linear acceleration that a pilot would experience in lunar gravity. Presently, as the Artemis program seeks to return humans to the Moon by 2025, engineers are evaluating suitable platforms to serve as an In-Flight Trainer (IFT) or Artemis Lunar Training Vehicle (ALTV) for astronauts training in the task of manual landing. The program is investigating the viability of current technology in the field of electric vertical takeoff and landing (eVTOL) vehicles and is evaluating using a multi tilt-rotor aircraft platform as a candidate platform for a preliminary ALTV. The tilt-rotor capability enables the vehicle attitude to be decoupled from its flight path, which is a crucial requirement in realistically simulating lunar gravity on Earth. Other key considerations include compensating for a lack of aerodynamic forces while flying through the atmosphere of Earth, as well as the ability to simulate the dynamics of multiple different lander designs for the Human Landing System (HLS) program. This paper details the feasibility study and presents a preliminary flight control architecture for an IFT based on a notional multi tilt-rotor platform. The modeling-following control law, based on nonlinear dynamic inversion (NDI), removes the need for gain scheduling because the vehicle operates across a wide range of flight conditions. The inner-loop dynamic control allocation strategy consists of a static portion that is optimized offline for trim while compensating for the difference in gravity and a dynamic portion that is computed in real time. The reference model consists of the full closed-loop dynamics of a generic HLS design. The modularity of the flight control architecture enables evaluation of multiple HLS concepts with minimal modifications to the control law. Simulation results of the multi tilt-rotor configuration following the final portion of the Apollo 11 descent trajectory are shown.

Jing Pei↗

NASA NTRSDate not supplied

Feasibility Study of a Multi-Tilt-Rotor Aircraft as the Artemis Lunar Training Vehicle

The Lunar Landing Research Vehicles (LLRVs) and the Lunar Landing Training Vehicles (LLTVs) provided astronauts of the Apollo program with essential experience and confidence required to complete the missions, and contributed to six successful manned landings on the moon. The primary challenge in terrestrial training was being able to replicate the ratio of tilt angle to linear acceleration that a pilot would experience in lunar gravity. Presently, as the Artemis program seeks to return humans to the Moon by 2025, engineers are evaluating suitable platforms to serve as an In-Flight Trainer (IFT) or Artemis Lunar Training Vehicle (ALTV) for astronauts training in the task of manual landing. The program is investigating the viability of current technology in the field of electric vertical takeoff and landing (eVTOL) vehicles and is evaluating using a multi-tilt-rotor aircraft platform as a candidate for a preliminary ALTV. The tilt-rotor capability enables the vehicle attitude to be decoupled from its flight path, which is a crucial requirement in realistically simulating lunar gravity on Earth. Other key considerations include compensating for a lack of aerodynamic forces while flying through the atmosphere of Earth, as well as the ability to simulate the dynamics of multiple different lander designs for the Human Landing System (HLS) program. This paper details the feasibility study and presents a preliminary flight control architecture for an IFT based on a notional multi-tilt-rotor platform. The model-following control law, based on nonlinear dynamic inversion (NDI), removes the need for gain scheduling. The inner-loop dynamic control allocation strategy consists of a static portion that is optimized offline for trim while compensating for the difference in gravity and a dynamic portion that is computed in real time. The reference model consists of the full closed-loop dynamics of a generic HLS design. The modularity of the flight control architecture enables evaluation of multiple HLS concepts with minimal modifications to the control law. Simulation results of the multi-tilt-rotor configuration following the final portion of the Apollo 11 descent trajectory are shown.

Jing Pei↗

NASA NTRS2020

Path-Adaptive Guidance Algorithm Trades for a Two-Stage Lunar Descent Vehicle

For the next generation of NASA’s missions, the necessity for path-adaptive guidance algorithms has become clear in order to provide the stability and customizability required for a safe and efficient descent to the lunar surface, while meeting specified program and vehicle constraints. Several descent algorithms have been tested and flown for single-stage landers through the Apollo and Altair programs, but thus far little analysis has been conducted involving the application of these algorithms for a two-stage descent vehicle. Due to the limited payload mass constraints of the existing fleet of launch vehicles, multi-stage descent architectures have become a viable course of action. This paper seeks to compare the performance of guidance configurations for a lunar lander system consisting of two stages, one of which separates partway through descent. Through development of this paper, an optimization suite has been written that is specifically designed for optimizing planetary non-atmospheric two-stage descent trajectories, and is used as a comparison baseline for the guidance algorithms tested. Time-to -go computational methods and ignition logic routines that may be employed in a lunar environment are also discussed. Further work is to be completed on trajectory design trades as well as the effects of modifying guidance targets in simulation based on trajectories that are optimized for different performance indices.

Jason M Everett↗

NASA NTRSDate not supplied

AERACEPT (Aerosol Rapid Analysis Combined Entry Probe/sonde Technology): Enabling Technology for Missions to the Venus Clouds

AERACEPT (AErosol Rapid Analysis Combined Entry Probe/sonde Technology) is an early-stage technology allowing a single aeroshell body to act as both an entry vehicle and aerosol-sampling passive descent sonde. AERACEPT does not require heat shield separation, deployable parachutes, or descent control, thus reducing the mass, volume, and complexity of planetary aerosol sampling. AERACEPT is particularly well suited for a Venus mission, where the particles of greatest interest are within the subsonic descent regime. AERACEPT uses the aeroshell’s own velocity to drive aerosol capture and separation through a series of embedded inlets. It takes advantage of recently developed thermal protection materials (3D-CC and HEEET) in combination with heritage aerosol sampling technologies from both planetary and airborne science (high-speed inlets and particle separation). The trade space for a given descent trajectory includes the particle capture efficiency for a given size, the bias introduced in the sampled particle size and concentration distributions, and the thermal alteration experienced by the particles during their brief exposure to the internal flow environment. AERACEPT is included in the Nephele mission concept study for a small spacecraft targeting the Venus middle and lower cloud layers. Nephele complements larger missions targeting Venus atmospheric gas analysis, such as DAVINCI and Venera-D, by specifically targeting cloud and haze particles. Because of the short lifetime of the probe in the lower atmosphere, Nephele requires a fast cadence of analysis of the captured particles, and includes the VOLTR dual optical spectrometer (SERS/LIBS) as part of its notional payload. Preliminary modeling based on the Nephele trajectory at 63 km to 39 km indicates AERACEPT can limit sample heating to 30-60 K above ambient. A modified particle tracking model has been implemented to estimate capture efficiency of particles larger than 0.1 µm and total sample volume as part of an inlet and interal flow path geometry trade study. Further modeling and empirical testing is underway to improve these estimates.

AERACEPT↗

NASA NTRS2024

DAVINCI: Venus Atmospheric Model Comparisons

The Deep Atmosphere Venus Investigation of Noble gases, Chemistry, and Imaging(DAVINCI) mission aims to answer long-standing questions regarding Venus’ origin using Zephyr, an atmospheric descent probe. Zephyr will be the first probe to take high-resolution aerial photographs of a mountainous tesserae surface as it descends over the Alpha Regio highlands region, which has the oldest surfaces of Venus. The Zephyr’s descent trajectory that determines the touchdown in the Alpha Regio, which is crucial for the DAVINCI mission, depends on Venus’ atmospheric properties and winds. Unfortunately, the atmospheric data for Venus from previous missions is sparse. Therefore, it is essential to consider various atmospheric models and scenarios from past flight data to predict Zephyr’s flight performance, specifically landing ellipse. To this end, this work compares three atmospheric models: the Venus Global Reference Atmospheric Model (Venus-GRAM), the Venus Climate Database(VCD), and an empirical wind model developed by Ralph Lorenz for the DAVINCI trajectory simulation and modeling. This paper compares the mean and variations of different atmospheric properties and winds from these atmospheric models. In addition, this work combines the atmospheric properties and the wind variability from the Venus-GRAM with the winds from the Lorenz-based model to have more stressing Venus wind dispersions that allow for more conservative trajectory analysis. Furthermore, this work relies on the DAVINCI landing ellipse size as a metric to measure how robust the trajectory analysis will be to the change in the atmospheric properties and winds of the Venus atmosphere.

Pardha Sai Chadalavada↗

NASA NTRSDate not supplied

AERACEPT (AErosol Rapid Analysis Combined Entry Probe/sonde Technology) for the Nephele Venus Cloud Mission Concept

Nephele is a small atmospheric probe mission concept to determine whether the Venus clouds contain organic matter. Nephele complements larger missions that seek to conduct Venus atmospheric analyses, such as DAVINCI, Venera-D, and the Morning Star missions, by directly sampling and analyzing cloud and haze particles. AERACEPT is an aerosol sampling technology designed to minimize the mass, volume, and complexity required for in situ planetary atmosphere characterization. A single aeroshell functions as a combined entry vehicle, descent probe, and instrumented sonde, combining recent advances in thermal protection materials with heritage technology from planetary and airborne science. The velocity of descent drives aerosol through inlets embedded in the aeroshell’s thermal protection material; inertial separation isolates the particles from the gas stream; and the particle capture surface doubles as the analysis substrate. This method can work without heat shield separation, descent control, or active sample handling; these advantages trade against a smaller sample volume, higher risk of sample heating, and shorter time for analysis and data return. AERACEPT further benefits from modeling of the internal and external flow to understand the particle capture efficiency and bias for size and concentration distributions. AERACEPT is well suited for a Venus mission such as Nephele, where a passive descent trajectory is both subsonic over the altitudes of interest and provides sufficient velocity and pressure differential for the particle sizes of interest. A thermal and flow toolchain developed in-house (Traj→ DPLR→ PATO→ openFOAM) was used to model an 80-cm aeroshell with science operations 63–39 km. These models indicate that AERACEPT will provide ~24 µL accumulated sample of particles ≥ 0.2 µm, substantially above the 2 µL threshold requirement. The worst-case particle heating will be ~14 K above ambient, for the smallest particles at the lowest altitude; most particles will experience ≤ 1 K rise, at which almost all analytes of interest will be unaffected. Plasma jet testing of a small-scale aeroshell-material inlet was recently conducted to validate the thermal model parameters; wind tunnel testing to validate the flow model parameters is underway.

AERACEPT↗

NASA NTRS2006

Titan Explorer Entry, Descent and Landing Trajectory Design

The Titan Explorer mission concept includes an orbiter, entry probe and inflatable airship designed to take remote and in-situ measurements of Titan's atmosphere. A modified entry, descent and landing trajectory at Titan that incorporates mid-air airship inflation (under a parachute) and separation is developed and examined for Titan Explorer. The feasibility of mid-air inflation and deployment of an airship under a parachute is determined by implementing and validating an airship buoyancy and inflation model in the trajectory simulation program, Program to Optimize Simulated Trajectories II (POST2). A nominal POST2 trajectory simulation case study is generated which examines different descent scenarios by varying airship inflation duration, orientation, and separation. The buoyancy model incorporation into POST2 is new to the software and may be used in future trajectory simulations. Each case from the nominal POST2 trajectory case study simulates a successful separation between the parachute and airship systems with sufficient velocity change as to alter their paths to avoid collision throughout their descent. The airship and heatshield also separate acceptably with a minimum distance of separation from the parachute system of 1.5 km. This analysis shows the feasibility of airship inflation on a parachute for different orientations, airship separation at various inflation times, and preparation for level-flight at Titan.

Fisher, Jody L.↗

NASA NTRS1996

Capture Conditions for Merging Trajectory Segments to Model Realistic Aircraft Descents

A typical commercial aircraft trajectory consists of a series of flight segments. An aircraft switches from one segment to another when certain specified variables reach their desired values. Trajectory synthesis for air traffic control automation must be consistent with practical pilot procedures. We examine capture conditions for merging trajectory segments to model commercial aircraft descent in trajectory synthesis. These conditions translate into bounds on measurements of atmospheric wind, pressure, and temperature. They also define ranges of thrust and drag feasible for a descent trajectory. Capture conditions are derived for the Center-TRACON Automation System developed at NASA Ames Research Center for automated air traffic control. Various uses of capture conditions are discussed. A Boeing 727-200 aircraft is used to provide numerical examples of capture conditions.

Zhao, Yiyuan↗

NASA NTRS2002

Using inertial measurements for the reconstruction of 6-DOF entry, descent, and landing trajectory and attitude profiles

Understanding MER-A's entry, descent, and landing (EDL) is critical to the success of its twin's EDL twenty-one days later.

EDL↗

NASA NTRS2004

Mars Exploration Rovers Entry, Descent, and Landing Trajectory Analysis

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

Desai, Prasun N.↗

NASA NTRS2013

Mars Science Laboratory Entry, Descent, and Landing Trajectory and Atmosphere Reconstruction

On August 5th 2012, The Mars Science Laboratory entry vehicle successfully entered Mars atmosphere and landed the Curiosity rover on its surface. A Kalman filter approach has been implemented to reconstruct the entry, descent, and landing trajectory based on all available data. The data sources considered in the Kalman filtering approach include the inertial measurement unit accelerations and angular rates, the terrain descent sensor, the measured landing site, orbit determination solutions for the initial conditions, and a new set of instrumentation for planetary entry reconstruction consisting of forebody pressure sensors, known as the Mars Entry Atmospheric Data System. These pressure measurements are unique for planetary entry, descent, and landing reconstruction as they enable a reconstruction of the freestream atmospheric conditions without any prior assumptions being made on the vehicle aerodynamics. Moreover, the processing of these pressure measurements in the Kalman filter approach enables the identification of atmospheric winds, which has not been accomplished in past planetary entry reconstructions. This separation of atmosphere and aerodynamics allows for aerodynamic model reconciliation and uncertainty quantification, which directly impacts future missions. This paper describes the mathematical formulation of the Kalman filtering approach, a summary of data sources and preprocessing activities, and results of the reconstruction.

Karlgaard, Christopher D.↗

NASA NTRS1970

Lunar descent and ascent trajectories

Apollo 11 premission planning, real time situation and postflight analysis for lunar descent and ascent phases, providing navigation correction capability for Apollo 12

Bennett, F. V.↗

NASA NTRSDate not supplied

Mars InSight Entry, Descent, and Landing Trajectory and Atmosphere Reconstruction

The InSight mission landed on the surface of Mars on November 26th, 2018. The InSight system performance met all design requirements, although several performance metrics fell near the boundaries of the predictions. The peak deceleration was high, the overall timeline was short, and the landing site was uprange and crossrange from the target. This paper describes the reconstruction of the entry, descent, and landing trajectory and atmosphere. The approach utilizes a Kalman filter to blend sensor data to obtain the vehicle trajectory. The aerodynamic database is used in combination with the sensed accelerations to obtain estimates of the atmosphere-relative state, which in turn is used to derive the free-stream atmospheric conditions during entry, until the time of parachute deployment. The results indicate that the reconstructed atmosphere was approximately 1σbelow the preflight atmosphere. Analysis of the reconstructed vehicle attitude angles indicate that the aerodynamic lift was oriented downward at entry. The vehicle developed a roll rate during entry, which directed a component of the lift to the north. The low density and aerodynamic lift direction are determined to be the primary causes of the high deceleration, short timeline, and location of the landing site relative to the target.

Christopher D Karlgaard↗

NASA NTRS2020

Mars InSight Entry, Descent, and Landing Trajectory and Atmosphere Reconstruction

Christopher D Karlgaard↗