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Traction Control Design and Integration Onboard the Mars Science Laboratory Curiosity Rover

The Mars Science Laboratory (MSL) Curiosity rover experienced increasing wheel damage beginning in October 2013. While the wheels were designed to operate with considerable damage, the rate at which damage was occurring was unexpected and raised concerns regarding wheel lifetime. The Jet Propulsion Laboratory (JPL) has now developed and deployed new software on Curiosity that reduces the forces acting on the wheels. Our new Traction Control algorithm adapts each wheel’s speed to fit the terrain it drives over. It does not rely on any a priori knowledge of the terrain, and instead leverages the rover’s measured attitude rates and suspension angles, together with a rigid-body kinematics model, to estimate the real-time wheel-terrain contact angles and ideal, no-slip wheel angular rates. In addition, free-floating “wheelies” are detected and autonomously corrected. In this paper, we describe the algorithm, its ground testing campaign and associated challenges, and finally its validation and performance in flight. Ground test data demonstrates reductions in the forces acting on the wheels and validates the wheelie-damping capability. Secondary benefits in some terrains include a reduction in heading deviations while climbing rocks, with a reduction in slip in certain sandy terrains. Preliminary validation from flight data confirms these findings.

Maimone, Mark↗

End-to-End Mission Design & Trajectory Optimization

The ability to compute end-to-end mission optimized trajectories is a critical component needed for the next generation of complex human spaceflight design and operations (Orion, HLS, Gateway, Mars). This project created a new interface for two of NASA’s trajectory tools: Copernicus and Genesis, enabling them to be used together for end-to-end mission design and optimization of all flight phases, including Earth ascent, lunar ascent, rendezvous, and lunar descent. This capability can also serve as a pathfinder for developing a future autonomous, onboard trajectory optimizer.

Software↗

End-to-End Mission Design & Trajectory Optimization

The ability to compute end-to-end mission optimized trajectories is a critical component needed for the next generation of complex human spaceflight design and operations (Orion, HLS, Gateway, Mars). This project created a new interface for two of NASA’s trajectory tools: Copernicus and Genesis, enabling them to be used together for end-to-end mission design and optimization of all flight phases, including Earth ascent, lunar ascent, rendezvous, and lunar descent. This capability can also serve as a pathfinder for developing a future autonomous, onboard trajectory optimizer.

Software↗

Autonomy Operating System for UAVs: Pilot-in-a-Box

The Autonomy Operating System (AOS) is an open flight software platform with Artificial Intelligence for smart UAVs. It is built to be extendable with new apps, similar to smartphones, to enable an expanding set of missions and capabilities. AOS has as its foundations NASAs core flight executive and core flight software (cFEcFS). Pilot-in-a-Box (PIB) is an expanding collection of interacting AOS apps that provide the knowledge and intelligence onboard a UAV to safely and autonomously fly in the National Air Space, eventually without a remote human ground crew. Longer-term, the goal of PIB is to provide the capability for pilotless air vehicles such as air taxis that will be key for new transportation concepts such as mobility-on-demand. PIB provides the procedural knowledge, situational awareness, and anticipatory planning (thinking ahead of the plane) that comprises pilot competencies. These competencies together with a natural language interface will enable Pilot-in-a-Box to dialogue directly with Air Traffic Management from takeoff through landing. This paper describes the overall AOS architecture, Artificial Intelligence reasoning engines, Pilot-in-a-box competencies, and selected experimental flight tests to date.

Lowry, Michael↗

Fault Detection and Diagnosis in Spacecraft Electrical Power Systems

The ability to accurately identify and isolate failures in the electrical power system (EPS) is critical to ensure the reliability of spacecraft. This paper proposes a novel solution to the problem of fault detection and diagnosis in direct current (DC) electric power systems for spacecraft. Autonomous operation becomes essential during deep space missions that lack the ability to monitor and control the spacecraft from ground locations. The current state of EPS fault supervision is insufficient to guarantee highly reliable operation. To solve this issue, a combination of model-based and knowledge-based techniques are used in a hierarchical framework to improve the diagnostic performance of the system. Noise, disturbances, and modeling errors are considered in the design of the fault detection system. Practical considerations related to spacecraft flight hardware and software are accounted for in the system design for flight applications. To assess the functionality of the design, a wide array of failures are simulated in a series of experiments. The experiments showed that the technique improved the capability of the autonomous system by increasing the number of fault types diagnosed. The significance of this study is to provide a framework capable of advanced diagnostics of an EPS with little to no interaction from human operators.

Autonomous Power Systems↗

Science Benefits of Onboard Spacecraft Navigation

Primitive bodies (asteroids and comets), which have remained relatively unaltered since their formation, are important targets for scientific missions that seek to understand the evolution of the solar system. Often the first step is to fly by these bodies with robotic spacecraft. The key to maximizing data returns from these flybys is to determine the spacecraft trajectory relative to the target body-in short, navigate the spacecraft- with sufficient accuracy so that the target is guaranteed to be in the instruments' field of view. The most powerful navigation data in these scenarios are images taken by the spacecraft of the target against a known star field (onboard astrometry). Traditionally, the relative trajectory of the spacecraft must be estimated hours to days in advance using images collected by the spacecraft. This is because of (1)!the long round-trip light times between the spacecraft and the Earth and (2)!the time needed to downlink and process navigation data on the ground, make decisions based on the result, and build and uplink instrument pointing sequences from the results. The light time and processing time compromise navigation accuracy considerably, because there is not enough time to use more accurate data collected closer to the target-such data are more accurate because the angular capability of the onboard astrometry is essentially constant as the distance to the target decreases, resulting in better "plane-of- sky" knowledge of the target. Excellent examples of these timing limitations are high-speed comet encounters. Comets are difficult to observe up close; their orbits often limit scientists to brief, rapid flybys, and their coma further restricts viewers from seeing the nucleus in any detail, unless they can view the nucleus at close range. Comet nuclei details are typically discernable for much shorter durations than the roundtrip light time to Earth, so robotic spacecraft must be able to perform onboard navigation. This onboard navigation can be accomplished through a self- contained system that by eliminating light time restrictions dramatically improves the relative trajectory knowledge and control and subsequently increases the amount of quality data collected. Flybys are one-time events, so the system's underlying algorithms and software must be extremely robust. The autonomous software must also be able to cope with the unknown size, shape, and orientation of the previously unseen comet nucleus. Furthermore, algorithms must be reliable in the presence of imperfections and/or damage to onboard cameras accrued after many years of deep-space operations. The AutoNav operational flight software packages, developed by scientists at the Jet Propulsion Laboratory (JPL) under contract with NASA, meet all these requirements. They have been directly responsible for the successful encounters on all of NASA's close-up comet-imaging missions (see Figure !1). AutoNav is the only system to date that has autonomously tracked comet nuclei during encounters and performed autonomous interplanetary navigation. AutoNav has enabled five cometary flyby missions (Table!1) residing on four NASA spacecraft provided by three different spacecraft builders. Using this software, missions were able to process a combined total of nearly 1000 images previously unseen by humans. By eliminating the need to navigate spacecraft from Earth, the accuracy gained by AutoNav during flybys compared to ground-based navigation is about 1!order of magnitude in targeting and 2!orders of magnitude in time of flight. These benefits ensure that pointing errors do not compromise data gathered during flybys. In addition, these benefits can be applied to flybys of other solar system objects, flybys at much slower relative velocities, mosaic imaging campaigns, and other proximity activities (e.g., orbiting, hovering, and descent/ascent).

Autonomy↗

Assessment of M2020 Terrain Relative Landing Accuracy: Flight Performance vs Predicts

Terrain Relative Navigation (TRN) was a critical enabling Entry, Descent, and Landing (EDL) technology that enabled Mars 2020 mission Perseverance rover to land at Jezero crater. TRN pro-vides real-time, autonomous, map-relative position determination and generates a landing target based on a priori knowledge of hazards. The required performance for TRN was to land within 60m of the selected target. The required 60m was sub-allocated to various error sources in three major categories: targeting error, knowledge error, and control error. The targeting error is the error in selecting an appropriate landing target and the knowledge of the target on the surface. It includes the Lander Vision System (LVS) position localization with respect the ground, the synchronization between the Lander Vision System measurement and the main Navigation filter, and errors associated with the LVS Reference Map and Safe Target Selec-tion (STS). The knowledge error is the contribution of knowledge growth from the synchronization with LVS to touchdown. The control error encompasses how accurately the system could stay on the desired reference trajectory. The TRN error budget uses a combination of analysis, simulation, and hardware test-ing results to bound the various error contributions obtained during the verification and validation process. This paper first presents a description the TRN system, focusing on the architecture of LVS and STS. The paper then gives detailed overview of the TRN error budget, with a description of the major error contribu-tions in each of the three categories. Next, the paper gives the results for three versions of the error budget, pre-launch, in-flight pre-landing, and post-landing. The paper compares the pre-flight analysis, the pre-landing analysis using in-flight data during cruise, to the post-landing analysis of the TRN performance. Pre-landing analysis best estimate of the landing performance was 33m, compared to the 60m require-ment. Post-landing analysis estimated a landing accuracy of 8.53m or better, much better than the 33m pre-landing estimate. The actual post-landing imagery calculated the distance of the rover to the targeted location to be 5m. The post-landing analysis closely bounds the image-based assessment of landing accu-racy, indicating the success of the error budget architecture in bounding the landing accuracy, as well as the fidelity of the simulations used to model and predict performance.

Chen, Allen↗

VFR Trajectory Forecasting using Deep Generative Model for Autonomous Airspace Operations

To enable the airspace integration of autonomous operations, such as uncrewed aircraft conducting cargo deliveries, there is a need to forecast the positions of the surrounding traffic with which they may interact. This paper focuses on forecasting Visual Flight Rules traffic, a significant source of uncertainty and risk in the airspace, especially around small regional airports, due to the unplanned and often untracked nature of such flights. A deep generative model is developed, trained on historical traffic data at example towered and non-towered airports, and used to predict flight trajectories. Experimental results are presented comparing the performance of variational autoencoder and classical machine learning forecasting when applied to both the towered and non-towered airports over varying time horizons. The results show the advantages of the variational autoencoder in producing accurate probabilistic forecasts over varying time horizons.

uncrewed aircraft↗

X-43C Plans and Status

X-43C Project is a hypersonic flight demonstration being executed as a collaboration between the National Aeronautics and Space Administration (NASA) and the United States Air Force (USAF). X-43C will expand the hypersonic flight envelope for air breathing engines beyond the history making efforts of the Hyper-X Program (X-43A). X-43C will demonstrate sustained accelerating flight during three flight tests of expendable X-43C Demonstrator Vehicles (DVs). The approximately 16-foot long X-43C DV will be boosted to the starting test conditions, separate from the booster, and accelerate from Mach 5 to Mach 7 under its own power and autonomous control. The DVs are to be powered by a liquid hydrocarbon-fueled, fuel-cooled, dual-mode, airframe integrated scramjet engine system developed under the USAF HyTech Program. The Project is managed by NASA Langley Research Center as part of NASA s Next Generation Launch Technology Program. Flight tests will be conducted by NASA Dryden Flight Research Center over water off the coast of California in the Pacific Test Range. The NASA/USAF/industry project is a natural extension of the Hyper-X Program (X-43A), which will demonstrate short duration (~ 10 seconds) gaseous hydrogen-fueled scramjet powered flight at Mach 7 and Mach 10 using a heavyweight, largely heat sink construction, experimental engine. The X-43C Project will demonstrate sustained accelerating flight from Mach 5 to Mach 7 (~ 4 minutes) using a flight-weight, fuel-cooled, scramjet engine powered by much denser liquid hydrocarbon fuel. The X-43C DV design flows from integrating USAF HyTech developed engine technologies with a NASA Air Breathing Launch Vehicle accelerator-class configuration and Hyper-X heritage vehicle systems designs. This paper describes the X-43C Project and provides background for NASA s current hypersonic flight demonstration efforts.

Moses, Paul L.↗

VFR Trajectory Forecasting using Deep Generative Model for Autonomous Airspace Operations

To enable the airspace integration of autonomous operations, such as uncrewed aircraft conducting cargo deliveries, there is a need to forecast the positions of the surrounding traffic with which they may interact. This paper focuses on forecasting Visual Flight Rules traffic, a significant source of uncertainty and risk in the airspace, especially around small regional airports, due to the unplanned and often untracked nature of such flights. A deep generative model is developed, trained on historical traffic data at example towered and non-towered airports, and used to predict flight trajectories. Experimental results are presented comparing the performance of variational autoencoder and classical machine learning forecasting when applied to both the towered and non-towered airports over varying time horizons. The results show the advantages of the variational autoencoder in producing accurate probabilistic forecasts over varying time horizons.

uncrewed aircraft↗

Autonomous Mission Operations Roadmap

As light time delays increase, the number of such situations in which crew autonomy is the best way to conduct the mission is expected to increase. However, there are significant open questions regarding which functions to allocate to ground and crew as the time delays increase. In situations where the ideal solution is to allocate responsibility to the crew and the vehicle, a second question arises: should the activity be the responsibility of the crew or an automated vehicle function? More specifically, we must answer the following questions: What aspects of mission operation responsibilities (Plan, Train, Fly) should be allocated to ground based or vehicle based planning, monitoring, and control in the presence of significant light-time delay between the vehicle and the Earth?How should the allocated ground based planning, monitoring, and control be distributed across the flight control team and ground system automation? How should the allocated vehicle based planning, monitoring, and control be distributed between the flight crew and onboard system automation?When during the mission should responsibility shift from flight control team to crew or from crew to vehicle, and what should the process of shifting responsibility be as the mission progresses? NASA is developing a roadmap of capabilities for Autonomous Mission Operations for human spaceflight. This presentation will describe the current state of development of this roadmap, with specific attention to in-space inspection tasks that crews might perform with minimum assistance from the ground.

Mission Operations↗

Results of the Magnetometer Navigation (MAGNAV)lnflight Experiment

The Magnetometer Navigation (MAGNAV) algorithm is currently running as a flight experiment as part of the Wide Field Infrared Explorer (WIRE) Post-Science Engineering Testbed. Initialization of MAGNAV occurred on September 4, 2003. MAGNAV is designed to autonomously estimate the spacecraft orbit, attitude, and rate using magnetometer and sun sensor data. Since the Earth's magnetic field is a function of time and position, and since time is known quite precisely, the differences between the computed magnetic field and measured magnetic field components, as measured by the magnetometer throughout the entire spacecraft orbit, are a function of the spacecraft trajectory and attitude errors. Therefore, these errors are used to estimate both trajectory and attitude. In addition, the time rate of change of the magnetic field vector is used to estimate the spacecraft rotation rate. The estimation of the attitude and trajectory is augmented with the rate estimation into an Extended Kalman filter blended with a pseudo-linear Kalman filter. Sun sensor data is also used to improve the accuracy and observability of the attitude and rate estimates. This test serves to validate MAGNAV as a single low cost navigation system which utilizes reliable, flight qualified sensors. MAGNAV is intended as a backup algorithm, an initialization algorithm, or possibly a prime navigation algorithm for a mission with coarse requirements. Results from the first six months of operation are presented.

Thienel, Julie K.↗

Multi-Sensor Testing for Automated Rendezvous and Docking Sensor Testing at the Flight Robotics Laboratory

The Exploration Systems Architecture defines missions that require rendezvous, proximity operations, and docking (RPOD) of two spacecraft both in Low Earth Orbit (LEO) and in Low Lunar Orbit (LLO). Uncrewed spacecraft must perform automated and/or autonomous rendezvous, proximity operations and docking operations (commonly known as AR&D). The crewed missions may also perform rendezvous and docking operations and may require different levels of automation and/or autonomy, and must provide the crew with relative navigation information for manual piloting. The capabilities of the RPOD sensors are critical to the success of the Exploration Program. NASA has the responsibility to determine whether the Crew Exploration Vehicle (CEV) contractor proposed relative navigation sensor suite will meet the requirements. The relatively low technology readiness level of AR&D relative navigation sensors has been carried as one of the CEV Project's top risks. The AR&D Sensor Technology Project seeks to reduce the risk by the testing and analysis of selected relative navigation sensor technologies through hardware-in-the-loop testing and simulation. These activities will provide the CEV Project information to assess the relative navigation sensors maturity as well as demonstrate test methods and capabilities. The first year of this project focused on a series of"pathfinder" testing tasks to develop the test plans, test facility requirements, trajectories, math model architecture, simulation platform, and processes that will be used to evaluate the Contractor-proposed sensors. Four candidate sensors were used in the first phase of the testing. The second phase of testing used four sensors simultaneously: two Marshall Space Flight Center (MSFC) Advanced Video Guidance Sensors (AVGS), a laser-based video sensor that uses retroreflectors attached to the target vehicle, and two commercial laser range finders. The multi-sensor testing was conducted at MSFC's Flight Robotics Laboratory (FRL) using the FRL's 6-DOF gantry system, called the Dynamic Overhead Target System (DOTS). The target vehicle for "docking" in the laboratory was a mockup that was representative of the proposed CEV docking system, with added retroreflectors for the AVGS. The multi-sensor test configuration used 35 open-loop test trajectories covering three major objectives: (1) sensor characterization trajectories designed to test a wide range of performance parameters; (2) CEV-specific trajectories designed to test performance during CEV-like approach and departure profiles; and (3) sensor characterization tests designed for evaluating sensor performance under more extreme conditions as might be induced during a spacecraft failure or during contingency situations. This paper describes the test development, test facility, test preparations, test execution, and test results of the multi-sensor series of trajectories.

Brewster, L.↗

Multi-Sensor Testing for Automated Rendezvous and Docking Sensor Testing at the Flight Robotics Lab

The Exploration Systems Architecture defines missions that require rendezvous, proximity operations, and docking (RPOD) of two spacecraft both in Low Earth Orbit (LEO) and in Low Lunar Orbit (LLO). Uncrewed spacecraft must perform automated and/or autonomous rendezvous, proximity operations and docking operations (commonly known as AR&D). The crewed missions may also perform rendezvous and docking operations and may require different levels of automation and/or autonomy, and must provide the crew with relative navigation information for manual piloting. The capabilities of the RPOD sensors are critical to the success ofthe Exploration Program. NASA has the responsibility to determine whether the Crew Exploration Vehicle (CEV) contractor-proposed relative navigation sensor suite will meet the requirements. The relatively low technology readiness level of AR&D relative navigation sensors has been carried as one of the CEV Project's top risks. The AR&D Sensor Technology Project seeks to reduce the risk by the testing and analysis of selected relative navigation sensor technologies through hardware-in-the-Ioop testing and simulation. These activities will provide the CEV Project information to assess the relative navigation sensors maturity as well as demonstrate test methods and capabilities. The first year of this project focused on a series of "pathfinder" testing tasks to develop the test plans, test facility requirements, trajectories, math model architecture, simulation platform, and processes that will be used to evaluate the Contractor-proposed sensors. Four candidate sensors were used in the first phase of the testing. The second phase of testing used four sensors simultaneously: two Marshall Space Flight Center (MSFC) Advanced Video Guidance Sensors (AVGS), a laser-based video sensor that uses retroreflectors attached to the target vehicle, and two commercial laser range finders. The multi-sensor testing was conducted at MSFC's Flight Robotics Laboratory (FRL) using the FRL's 6-DOF gantry system, called the Dynamic Overhead Target System (DOTS). The target vehicle for "docking" in the laboratory was a mockup that was representative of the proposed CEV docking system, with added retroreflectors for the AVGS.' The multi-sensor test configuration used 35 open-loop test trajectories covering three major objectives: (l) sensor characterization trajectories designed to test a wide range of performance parameters; (2) CEV-specific trajectories designed to test performance during CEV-like approach and departure profiles; and (3) sensor characterization tests designed for evaluating sensor performance under more extreme conditions as might be induced during a spacecraft failure or during contingency situations. This paper describes the test development, test facility, test preparations, test execution, and test results of the multisensor series oftrajectories

Brewster, Linda L.↗

Grasping objects autonomously in simulated KC-135 zero-g

The KC-135 aircraft was chosen for simulated zero gravity testing of the Extravehicular Activity Helper/retriever (EVAHR). A software simulation of the EVAHR hardware, KC-135 flight dynamics, collision detection and grasp inpact dynamics has been developed to integrate and test the EVAHR software prior to flight testing on the KC-135. The EVAHR software will perform target pose estimation, tracking, and motion estimation for rigid, freely rotating, polyhedral objects. Manipulator grasp planning and trajectory control software has also been developed to grasp targets while avoiding collisions.

Norsworthy, Robert S.↗

Results of the Magnetometer Navigation (MAGNAV) Inflight Experiment

The Magnetometer Navigation (MAGNAV) algorithm is currently running as a flight experiment as part of the Wide Field Infrarad Explorer Post-Science Engineer- ing Testbed. Initialization of MAGNAV occured on September 4, 2004. MAGNAV is designed to autonomously estimate the spacecraft orbit, attitude, and rate using magnetometer and sun sensor data. Since the earth s magnetic field is a function of time and position, and since time is known quite precisely, the differences between the computed magnetic field and measured magnetic field components, as measured by the magnetometer throughout the entire spacecraft orbit, are a function of the spacecraft trajectory and attitude errors. Therefore, these errors are used to estimate both trajec- tory and attitude. In addition, the time rate of change of the magnetic field vector is used to estimate the spacecraft rotation rate. The estimation of the attitude and tra- jectory is augmented with the rate estimation into an Extended Kalman filter blended with a pseudc-linear Kalman filter. Sun sensor data is also used to improve the accu- racy and observability of the attitude and rate estimates. This test serves to validate MAGNAV as a single low cost navigation system which utilizes reliable, flight qualified sensors. MAGNAV is intended as a backup algorithm, an initialization algorithm, or possibly a prime navigation algorithm for a mission with coarse constraints.

Thienel, Julie↗

A ROS-based Simulator for Testing the Enhanced Autonomous Navigation of the Mars 2020 Rover

In order to achieve the ambitious objectives of the Mars 2020 (M2020) mission, in particular the ability to autonomously traverse more challenging terrains more efficiently, new surface mobility software was developed for Enhanced Navigation (ENav). That decision was made early in the project, before most of the new surface flight software (FSW) existed, which created a need for a separate framework where the new navigation algorithms could be quickly prototyped and tested, before more realistic FSW-based testbeds became available. The JPL robotics team chose the Robot Operating System [1] (ROS) as the environment in which to test the new ENav algorithms. This made it possible to write the algorithms in the C language required by the FSW, so they could be directly ported over to the flight module later on, while leveraging all the C++ libraries and tools provided by ROS for simulation and testing. The ENav algorithms were developed as a separate C library, and stubs were used to replace any FSW-specific code, such as Event Reporting (EVRs) and data products (DPs). A ROS simulator was developed to generate a rich set of varied 3D terrains representative of the candidate Mars landing sites and simulate the physics of the rover motion, the point cloud perceived by the rover’s stereo vision system, and the new thinking-while-driving (TWD) navigation logic which directs the rover to drive autonomously to user-specified waypoints. To simulate the rover motion and perception, a ROS node was developed that uses a software library called HyperDrive Sim (HDSim), which is a wrapper for the Rover Sequencing and Visualization Program [2] (RSVP). That library provides roverterrain settling, realistic slip modelling, and camera rendering capability based on the rover’s NavCam machine vision models. To simulate the navigation logic, a ROS node was created that initializes and runs the ENav algorithms in a way that mimics the FSW execution, while also providing the capability to load and replay data products, including re-running the recorded inputs through the ENav algorithms for testing. An engineering Graphical User Interface (GUI) was also developed to visualize various elements, such as the rover pose during the drive, the simulated and perceived terrain, the selected local and global paths to the goal, the evaluated candidate paths and the reasons why they were rejected, the keep-in and keep-out zones (KIOZs), etc. Finally, an advanced Monte Carlo (MC) framework that can run many simulations in parallel on the Cloud and automatically generate reports that capture the key ENav performance metrics was developed to evaluate the system in a statisticallymeaningful way. This paper provides an overview of the ROSbased simulator used for testing the M2020 ENav algorithms.

Toupet, Olivier↗

Simulation models for autonomous rendezvous and capture

Autonomous rendezvous and capture (AR&C) is a critical space technology with significant application to a variety of missions. Martin Marietta Astronautics Group (MMAG) has been developing AR&C technical capability in support of several recent NASA contracts. The use of AR&C for the Mars Rover/Sample Return (MRSR) mission was studied through a contract with JSC. Incorporation of AR&C in the Space Transportation Vehicle (STV) lunar mission was studied through a contract with MSFC. The MMAG has also been developing AR&C simulation capability under independent research and development studies. Simulation development was driven by two goals: comprehensive software simulation of the autonomous rendezvous and capture mission from launch to final capture; and integration of the overall software and hardware simulation to support an AR&C flight demonstration. This presentation will highlight the AR&C software simulation tools and analyze results from their application to the STV lunar mission. Plans for an integrated software and hardware simulation will also be summarized.

Smith, Nick G.↗