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Mathematical models, diagrams, and computer programs involving an unmanned mission to the planet Venus are presented. This work was done in support of the proposed project called Ninevah. The specific subjects covered are trajectory analysis, propulsion analysis, and structural analysis.
The term trajectory planning has been used to refer to the process of determining the time history of joint trajectory of each joint variable corresponding to a specified trajectory of the end effector. The trajectory planning problem was solved as a purely kinematic problem. The drawback is that there is no guarantee that the actuators can deliver the effort necessary to track the planned trajectory. To overcome this limitation, a motion planning approach which addresses the kinematics, dynamics, and feedback control of a manipulator in a unified framework was developed. Actuator constraints are taken into account explicitly and a priori in the synthesis of the feedback control law. Therefore the result of applying the motion planning approach described is not only the determination of the entire set of joint trajectories but also a complete specification of the feedback control strategy which would yield these joint trajectories without violating actuator constraints. The effectiveness of the unified motion planning approach is demonstrated on two problems which are of practical interest in manipulator robotics.
A computational procedure and data base are developed for manned space exploration missions for which estimates are made for the energetic particle fluences encountered and the resulting dose equivalent incurred. The data base includes the following options: statistical or continuum model for ordinary solar proton events, selection of up to six large proton flare spectra, and galactic cosmic ray fluxes for elemental nuclei of charge numbers 1 through 92. The program requires an input trajectory definition information and specifications of optional parameters, which include desired spectral data and nominal shield thickness. The procedure may be implemented as an independent program or as a subroutine in trajectory codes. This code should be most useful in mission optimization and selection studies for which radiation exposure is of special importance.
A performance analysis of a Discovery Class Venus Exploration Mission in which aerocapture is used to capture a spacecraft into a 300km polar orbit for a two year science mission has been conducted to quantify its performance. A preliminary performance assessment determined that a high heritage 70 sphere-cone rigid aeroshell with a 0.25 lift to drag ratio has adequate control authority to provide an entry flight path angle corridor large enough for the mission s aerocapture maneuver. A 114 kilograms per square meter ballistic coefficient reference vehicle was developed from the science requirements and the preliminary assessment s heating indicators and deceleration loads. Performance analyses were conducted for the reference vehicle and for sensitivity studies on vehicle ballistic coefficient and maximum bank rate. The performance analyses used a high fidelity flight simulation within a Monte Carlo executive to define the aerocapture heating environment and deceleration loads and to determine mission success statistics. The simulation utilized the Program to Optimize Simulated Trajectories (POST) that was modified to include Venus specific atmospheric and planet models, aerodynamic characteristics, and interplanetary trajectory models. In addition to Venus specific models, an autonomous guidance system, HYPAS, and a pseudo flight controller were incorporated in the simulation. The Monte Carlo analyses incorporated a reference set of approach trajectory delivery errors, aerodynamic uncertainties, and atmospheric density variations. The reference performance analysis determined the reference vehicle achieves 100% successful capture and has a 99.87% probability of attaining the science orbit with a 90 meters per second delta V budget for post aerocapture orbital adjustments. A ballistic coefficient trade study conducted with reference uncertainties determined that the 0.25 L/D vehicle can achieve 100% successful capture with a ballistic coefficient of 228 kilograms per square meter and that the increased ballistic coefficient increases post aerocapture V budget to 134 meters per second for a 99.87% probability of attaining the science orbit. A trade study on vehicle bank rate determined that the 0.25 L/D vehicle can achieve 100% successful capture when the maximum bank rate is decreased from 30 deg/s to 20 deg/s. The decreased bank rate increases post aerocapture delta V budget to 102 meters per second for a 99.87% probability of attaining the science orbit.
Unmanned aerial systems (UASs) in urban areas can pose significant safety risks to dynamic ground objects (DGOs) such as people, pets, and bikes; especially for off-nominal emergency traverses and landings. This paper will examine a framework for evaluating the UAS safety benefits which can be achieved by classifying DGO hazards, modeling their behavior, and assigning collision costs. DGOs are assumed to be any ground objects which are either moving or capable of moving. Safety benefits will be assessed by analyzing metrics computed from UAS and DGO trajectories which take into account intent and uncertainties. This paper will establish the theoretical relationships mapping these trajectories and DGO classifications to safety levels. Sensor capabilities will be mapped to DGO trajectory uncertainties, so that safety can be directly estimated from the sensor specifications for a given UAS trajectory.
This paper describes the basic characteristics of circulating (cyclical) orbit design as applied to round-trip transportation of crew and materials between earth and Mars in support of a sustained manned Mars Surface Base. The two main types of nonstopover circulating trajectories are the socalled VISIT orbits and the Up/Down Escalator orbits. Access to the large transportation facilities placed in these orbits is by way of taxi vehicles using hyperbolic rendezvous techniques during the successive encounters with earth and Mars. Specific examples of real trajectory data are presented in explanation of flight times, encounter frequency, hyperbolic velocities, closest approach distances, and Delta V maneuver requirements in both interplanetary and planetocentric space.
Passive drag devices provide opportunities to return payloads from low Earth orbits quickly without using onboard propulsive systems to de-orbit the spacecraft. However, one potential disadvantage of such systems has been the lack of landing accuracy. Drag modulation or changing the shape of the drag device during flight offer a way to control the de-orbit trajectory and target a specific landing location. This paper discusses a candidate passive drag based system, called Exo-brake, as well as efforts to model the dynamics of the vehicle as it de-orbits and guidance schemes used to control the trajectory. Such systems can enable quick return of payloads from low Earth orbit assets like the International Space Station without the use of large re-entry cargo capsules or propulsive systems.
Multi-model Monte Carlo methods have been demonstrated to be an efficient and accurate alternative to standard Monte Carlo (MC) in the model-based propagation of uncertainty in entry, descent, and landing (EDL) applications. These multi-model MC methods fuse predictions from low-fidelity models with the high-fidelity EDL model of interest to produce unbiased statistics with a fraction of the computational cost. The accuracy and efficiency of the multi-model MC methods are dependent upon the magnitude of correlations of the low-fidelity models with the high-fidelity model, but also upon the correlation amongst the low-fidelity models, and their relative computational cost. Because of this layer of complexity, the question of how to optimally select the set of low-fidelity models has remained open. In this work, methods for optimal model construction and tuning are investigated as a means to increase the speed and precision of trajectory simulation for EDL. Specifically, the focus is on the inclusion of low-fidelity model tuning within the sample allocation optimization that accompanies multi-model MC methods. Preliminary results indicate that low-fidelity model tuning can significantly improve efficiency and precision of trajectory simulations and provide an increased edge to multi-model MC methods when compared to standard MC. The challenges and potential benefits to exploring a fully iterative and comprehensive optimization strategy in future work are highlighted.
Multi-model Monte Carlo methods have been demonstrated to be an efficient and accurate alternative to standard Monte Carlo (MC) in the model-based propagation of uncertainty in entry, descent, and landing (EDL) applications. These multi-model MC methods fuse predictions from low-fidelity models with the high-fidelity EDL model of interest to produce unbiased statistics with a fraction of the computational cost. The accuracy and efficiency of the multi-model MC methods are dependent upon the magnitude of correlations of the low-fidelity models with the high-fidelity model, but also upon the correlation among the low-fidelity models, and their relative computational cost. Because of this layer of complexity, the question of how to optimally select the set of low-fidelity models has remained open. In this work, methods for optimal model construction and tuning are investigated as a means to increase the speed and precision of trajectory simulation for EDL. Specifically, the focus is on the inclusion of low-fidelity model tuning within the sample allocation optimization that accompanies multi-model MC methods. Preliminary results indicate that low-fidelity model tuning can significantly improve efficiency and precision of trajectory simulations and provide an increased edge to multi-model MC methods when compared to standard MC. The challenges and potential benefits to exploring a fully iterative and comprehensive optimization strategy in future work are highlighted.
Modern rocket nozzles are designed to operate over a wide range of altitudes, and are also built with large aspect ratios to enable high efficiencies. Nozzles designed to operate over specific regions of a trajectory are being replaced in modern launch vehicles by those that are designed to operate from earth to orbit. This is happening in parallel with modern manufacturing and wall cooling techniques allowing for larger aspect ratio nozzles to be produced. Such nozzles, though operating over a large range of altitudes and ambient pressures, are typically designed for one specific altitude. Above that altitude the nozzle flow is 'underexpanded' and below that altitude, the nozzle flow is 'overexpanded'. In both conditions the nozzle produces less than the maximum possible thrust at that altitude. Usually the nozzle design altitude is well above sea level, leaving the nozzle flow in an overexpanded state for its start up as well as for its ground testing where, if it is a reusable nozzle such as the Space Shuttle Main Engine (SSME), the nozzle will operate for the majority of its life. Overexpansion in a rocket nozzle presents the critical, and sometimes design driving, problem of flow separation induced side loads. To increase their understanding of nozzle side loads, engineers at MSFC began an investigation in 2000 into the phenomenon through a task entitled "Characterization and Accurate Modeling of Rocket Engine Nozzle Side Loads", led by A. Brown. The stated objective of this study was to develop a methodology to accurately predict the character and magnitude of nozzle side loads. The study included further hot-fire testing of the MC-l engine, cold flow testing of subscale nozzles, CFD analyses of both hot-fire and cold flow nozzle testing, and finite element (fe.) analysis of the MC-1 engine and cold flow tested nozzles. A follow on task included an effort to formulate a simplified methodology for modeling a side load during a two nodal diameter fluid/structure interaction for a single moment in time.
A systems analysis has been conducted for a Neptune-Triton Exploration Mission in which aerocapture is used to capture a spacecraft at Neptune. Aerocapture uses aerodynamic drag instead of propulsion to decelerate from the interplanetary approach trajectory to a captured orbit during a single pass through the atmosphere. After capture, propulsion is used to move the spacecraft from the initial captured orbit to the desired science orbit. A preliminary assessment identified that a spacecraft with a lift to drag ratio of 0.8 was required for aerocapture. Performance analyses of the 0.8 L/D vehicle were performed using a high fidelity flight simulation within a Monte Carlo executive to determine mission success statistics. The simulation was the Program to Optimize Simulated Trajectories (POST) modified to include Neptune specific atmospheric and planet models, spacecraft aerodynamic characteristics, and interplanetary trajectory models. To these were added autonomous guidance and pseudo flight controller models. The Monte Carlo analyses incorporated approach trajectory delivery errors, aerodynamic characteristics uncertainties, and atmospheric density variations. Monte Carlo analyses were performed for a reference set of uncertainties and sets of uncertainties modified to produce increased and reduced atmospheric variability. For the reference uncertainties, the 0.8 L/D flatbottom ellipsled vehicle achieves 100% successful capture and has a 99.87 probability of attaining the science orbit with a 360 m/s V budget for apoapsis and periapsis adjustment. Monte Carlo analyses were also performed for a guidance system that modulates both bank angle and angle of attack with the reference set of uncertainties. An alpha and bank modulation guidance system reduces the 99.87 percentile DELTA V 173 m/s (48%) to 187 m/s for the reference set of uncertainties.
Computing approximate trajectories returning from moon to earth specific landing site
The National Aeronautics and Space Administration (NASA) solicited proposals in 2006 for an opportunity to include a small secondary payload with the launch of the Lunar Reconnaissance Orbiter (LRO) scheduled for October 2008. The cost cap of the proposal was between $50 and $80M, and the mass cap was 1,000 kilograms. JPL proposed a Lunar Impactor (LI) concept for this solicitation. The mission objective of LI was to impact the permanently shadowed region of a South polar crater ultimately to detect the presence of water. The detection of water ice would prove to be an important factor on future lunar exploration. NASA Ames Research Center also proposed a similar concept, the Lunar Crater observation and Sensing Satellite (LCROSS), which was selected by NASA for the mission. However, in this paper, the trajectory design of the LI proposed by JPL is considered. Since the LI spacecraft was to be launched on the LRO launch vehicle as a secondary payload, its initial trajectory must be diverted at some later time from the LRO trans-lunar trajectory for the subsequent impact. Several such trajectories have been considered, where each trajectory option fields some specific values for the mission parameters. The mission parameters include the availability of LRO instruments at the time of impact for the observation by LRO, the mission duration, the impact velocity, the impact angle, etc. It is possible for the LI to be deflected with a relatively low delta-V to impact a South polar crater at a reasonable impact velocity and impact angle directly with no delay. However, the instruments on-board LRO may not be ready for observation. Thus, several delayed trajectory options have been considered further. The lunar phase at the time of impact may also play an important factor for observation, especially from Earth. Several lunar flyby trajectory maneuvers have been identified to arrive at the Moon for impact at the desired lunar phase. By using a combination of these successive lunar flyby maneuvers, the impact lunar phase may be adjusted to the desired location. A few such trajectories have been suggested. Also, some attempts have been made to maximize the impact velocity by converting the impact trajectory into a retrograde orbit with respect to Earth. Since these types of trajectories take advantage of the Sun-Earth three-body region to minimize the delta-V, the mission duration is relatively long. A few such trajectories are suggested. Also, an attempt has been made to adjust the lunar impact within a desired time period for the optimum Earth observation for the above trajectories. The mission parameters resulting from each trajectory option above are considered and weighed against the cost and robustness of the mission in a brief summary.
Reports submitted to the conference encompass: administration and law relating to inhabited space facilities and colonies; space manufacturing and processing; organization and construction of space habitats and management of space colony farms; winning and acquisition of lunar and asteroidal materials for sustaining autonomous space colonies. Attention is given to trajectories between earth, low earth orbit, earth-moon libration points (specifically L5), circumlunar parking orbits, and trajectories in translunar space; effects of low gravity and zero gravity on human physiology and on materials processing; architecture and landscaping for space colonies; closed ecosystems of space colonies. Varieties of human cultures and value hierarchies around the earth are examined for broader perspectives on the social organization of space colonies.
For compressible three-dimensional flow, the method of multiple scales to formulate the three-dimensional stability problem and determine the partial-differential equations governing variations of the amplitude and complex wavenumbers is used. A method for following one specific wave along its trajectory to ascertain the characteristics of the most unstable disturbance is proposed. Numerical results using the flow over the X-21 wing as calculated from the Kaups-Cebeci code will be presented.
Optimal control theory is used to examine a specific class of spacecraft trajectory problems where high- and low-thrust propulsion systems are utilized. These problems assume a spacecraft is in an established orbit about a planet. It is desired to execute an intercept of a pre-determined position in space in a specified amount of time using an optimal high-thrust program. The spacecraft then returns to the original orbit station using the low-thrust propulsion system in an optimal fashion. A minimum fuel solution is sought using the linearized equations of motion, known as the CW equations, which simplify the necessary computations. Solutions are obtained for problems with a fixed final time. However, for the time-open case, the optimal solution is for the final time to be infinite. With a weighted function of the final time in the performance index, a limited range of optimal single impulse solutions for the time -open case can also be found.
The identification of unmanned aircraft systems (UAS) using trajectory data is considered. Specifically, a number of smoothness metrics are proposed, which can be used to distinguish UAS from other aerial objects even when they are engaged in accelerative maneuvers (non-constant-velocity flight). The metrics are evaluated on a data set from a UAS sense-and-avoid field test, which contains track data of aerial objects recorded by a vehicle-board radar system during a flight test. The metrics are found to effectively differentiate UAS from other objects such as birds for this data set. In addition, an initial statistical performance analysis of one of the smoothness metrics is undertaken, using 15 data sets deriving from multiple flight tests. The smoothness metric is shown to identify the target UAS with 95% accuracy (95% true positive rate), while achieving a false positive rate of less than 9%.
The supersonic and transonic dynamic stability of blunt-body reentry vehicles currently poses large risks in all of NASA’s ongoing entry missions (MSR SRL, MSR EES, and Dragonfly). These projects have allocated millions of dollars to testing and modeling efforts to buy down risk by using the current state-of-the-art (SoA) facilities at NASA’s disposal. While these facilities have heritage in supplying dynamics data to reentry missions, their availability is severely limited – particularly with the high number of concur-rent projects requesting simultaneous testing– and are costly when considering the science density per dollar. None of the current SoA facility methodologies allow the test model to have the dynamics fully develop through a flight relevant free-stream profile and as such require extrapolations with resultant high uncertainties in order to relate the test dynamics to flight expectations. SPEED is a NASA Ames Center Innovation Fund (CIF) project that is developing a highly tailorable and cost-effective test methodology to better assess the dynamic stability of blunt-body reentry vehicles via a stratospheric balloon flight. This is accomplished by dropping a suite of instrumented capsules from a stratospheric balloon to gain a statistically relevant dataset of scaled reentry vehicles in mission relevant free-flight conditions. This presentation will walk through how the test methodology is being implemented specifically for the Mars Sample Return (MSR) Earth Entry System (EES) geometry in an awarded Flight Opportunities Program (FOP) test flight in early CY24. SPEED Application to MSR: SPEED consists of three main mechanical systems: the Drop Platform, the Projectile, and the test Capsule. SPEED is being developed as a set of guidelines and recommendations for how to test with the proposed Concept of Operations (Conops) since the specific design parameters will vary depending on the specific project’s reference trajectory and entry vehicle design. As such, this presentation will walk through the development time-line as shown in Fig. 2. This is meant to serve as a blueprint for further missions as desired. Mechanical and Avionics Design. The SPEED test platform designed for the MSR-EES capsule geometry with nominal entry parameters has the ability to carry 10 Capsules to altitude instrumented with: 1. 3-Axis Accelerometer 2. IMU 3. Gyroscope 4. Magnetometer 5. Pressure Transducer cruciform 6. Uplook and Horizon Cameras To package the avionics/instrumentation suite, the capsule is approximately 1’ in diameter with the Outer Mold Line (OML) centroid-scaled from the full EES design. The internal volume is gutted and custom-shaped to fit the desired instrumentation suite, as well as to allow for the positioning of ballast mass such that the Center of Gravity is analogous to the flight vehicle. All structural components in the Capsule and Projectile are 3D printed, which significantly reduces the cost of each flight unit to around $1500 including all instrumentation, avionics, and structural components. Flight Conops. The test Capsule is accelerated to the desired altitude and Mach number while stowed in the Projectile, a missile-like vehicle consisting of steel ballast in the nose, a low-drag OML, and an Ejection Mechanism to reliably release the Capsule into the free-flow supersonic conditions. For the MSR-EES design, the capsule employs ~3kg of ballast mass at the nose to accelerate the 1.25kg test Capsule to ~Mach 1.7 at 23km altitude. This requires an initial release altitude of 40km, the quoted limit of a 80kg payload by the FOP-contracted balloon provider. Once the Ejection Mechanism avionics detect the proper conditions, the spring-loaded Ejection Mechanism will release and – guided by the sabot – expose the test Capsule to the desired test conditions for ~5 seconds of free-flight in the supersonic/transonic regimes. Dynamics in the subsonic regime will also be captured with the instrumentation suite with post-flight recovery operations aimed at recovering the high-G-load capable SD cards after the planned hard impact landings. Testing and Development: In the few months the SPEED project has worked the development of MSR-EES flight test, the team has performed lab and drone based testing which this presentation will overview. After the first design phase, the team fabricated Engineering Demonstration Units (EDUs) of all subsystems to perform validation testing shown in Fig. 5. After validation was completed on the subsystem level, a drone-drop test was performed at the recreational flight ceiling of 400ft altitude to assess the SPEED systems in a flight environment. Parameters such as in-flight stability, hard impact landing performance, and avionics performance were quantified and qualified. The FY23 CIF will culminate in a helicopter drop test aboard an Air National Guard Blackhawk. This will prepare the team for the CY24 FOP stratospheric balloon flight that should provide the final verification to begin offering the test platform for mission support. Focus of Presentation: This presentation will outline the technology maturation path of the SPEED implementation to the MSR-EES capsule baseline as well as the details regarding the mechanical system, avionics and instrumentation, and flight operations. Note that a complementary presentation is being submitted for a methodology overview of the SPEED test platform, introducing the testing technique and benefits as well as the full application space of the technology.