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At least 91 records · Page 5

Insights into Regolith Dynamics from the Irradiation Record Preserved in Hayabusa Samples

The rates of space weathering processes are poorly constrained for asteroid surfaces, with recent estimates ranging over 5 orders of magnitude. The return of the first surface samples from a space-weathered asteroid by the Hayabusa mission and their laboratory analysis provides "ground truth" to anchor the timescales for space weathering. We determine the rates of space weathering on Itokawa by measuring solar flare track densities and the widths of solar wind damaged rims on grains. These measurements are made possible through novel focused ion beam (FIB) sample preparation methods.

Keller, Lindsay P.↗

Ideal Integrating Bolometer

We describe a new 'ideal integrator' bolometer as a prototype for a new generation of sensitive, flexible far-IR detectors suitable for use in large arrays. The combination of a non-dissipative sensor coupled with a fast heat switch provides breakthrough capabilities in both sensitivity and operation. The bolometer temperature varies linearly with the integrated infrared power incident on the detector, and may be sampled intermittently without loss of information between samples. The sample speed and consequent dynamic range depend only on the heat switch reset cycle and can be selected in software. Between samples, the device acts as an ideal integrator with noise significantly lower than resistive bolometers. Since there is no loss of information between samples, the device is well-suited for large arrays. A single SQUID readout could process an entire column of detectors, greatly reducing the complexity, power requirements, and cost of readout electronics for large pixel arrays.

Kogut, Alan↗

Ideal Integrating Bolometer

We describe a new "ideal integrator" bolometer as a prototype for a new generation of sensitive, flexible far-IR detectors suitable for use in large arrays. The combination of a non-dissipative sensor coupled with a fast heat switch provides breakthrough capabilities in both sensitivity and operation. The bolometer temperature varies linearly with the integrated infrared power incident on the detector, and may be sampled intermittently without loss of information between samples. The sample speed and consequent dynamic range depend only on the heat switch reset cycle and can be selected in software. Between samples, the device acts as an ideal integrator with noise significantly lower than resistive bolometers. Since there is no loss of information between samples, the device is well-suited for large arrays. A single SQUID readout could process an entire column of detectors, greatly reducing the complexity, power requirements, and cost of readout electronics for large pixel arrays.

Kogut, A.↗

Manual control models of industrial management

The industrial engineer is often required to design and implement control systems and organization for manufacturing and service facilities, to optimize quality, delivery, and yield, and minimize cost. Despite progress in computer science most such systems still employ human operators and managers as real-time control elements. Manual control theory should therefore be applicable to at least some aspects of industrial system design and operations. Formulation of adequate model structures is an essential prerequisite to progress in this area; since real-world production systems invariably include multilevel and multiloop control, and are implemented by timeshared human effort. A modular structure incorporating certain new types of functional element, has been developed. This forms the basis for analysis of an industrial process operation. In this case it appears that managerial controllers operate in a discrete predictive mode based on fast time modelling, with sampling interval related to plant dynamics. Successive aggregation causes reduced response bandwidth and hence increased sampling interval as a function of level.

Crossman, E. R. F. W.↗

Dynamics and Control of a Disordered System in Space

In this paper, we present some ideas regarding the modeling, dynamics and control aspects of granular spacecraft. Granular spacecraft are complex multibody systems composed of a spatially disordered distribution of a large number of elements, for instance a cloud of N grains in orbit, with N greater than 10(exp 3). These grains can be large (Cubesat-size) or small (mm-size), and can be active, i.e., a fully equipped vehicle capable sensing their own position and attitude, and enabled with propulsion means, or entirely passive. The ultimate objective would be to study the behavior of the single grains and of large ensembles of grains in orbit and to identify ways to guide and control the shape of a cloud composed of these grains so that it can perform a useful function in space, for instance, as an element of an optical imaging system for astrophysical applications. This concept, in which the aperture does not need to be continuous and monolithic, would increase the aperture size several times compared to large NASA observatories such as ATLAST, allowing for a true Terrestrial Planet Imager that would be able to resolve exo-planet details and do meaningful spectroscopy on distant world. In the paper, we address the modeling and autonomous operation of a distributed assembly (the cloud) of large numbers of highly miniaturized space-borne elements (the grains). A multi-scale, multi-physics model is proposed of the dynamics of the cloud in orbit, as well as a control law for cloud shape maintenance, and preliminary simulation studies yield an estimate of the computational effort, indicating a scale factor of approximately N(exp 1.4) as a function of the number of grains. A granular spacecraft can be defined as a collection of a large number of space-borne elements (in the 1000s) designed and controlled such that a desirable collective behavior emerges, either from the interactions among neighboring grains, and/or between the grains and the environment. In this paper, each grain is considered to be a highly miniaturized spacecraft which has limited size and mass, hence it has limited actuation, limited propulsive capability, limited power, limited sensing, limited communication, limited computational resources, limited range of motion, limited lifetime, and may be expendable. The modeling and dynamics of clouds of vehicles is more challenging than with conventional vehicles because we are faced with a probabilistic vehicle composed of a large number of physically disconnected vehicles. First, different scales of motion occur simultaneously in a cloud: translations and rotations of the cloud as a whole (macro-dynamics), relative rotation and translation of one cloud member with respect to another (meso-dynamics), and individual cloud member dynamics (micro-dynamics). Second, the control design needs to be tolerant of the system complexity, of the system architecture (centralized vs. decentralized large scale system control) as well as robust to un-modeled dynamics and noise sources. Figure 1, top left, shows the kinematic parameters of a 1000 element cloud in orbit. The motion of the system is described with respect to a local vertical-local horizontal (LV-LH) orbiting reference frame (x,y,z)=F(sub ORF) of origin O(sub ORF) which rotates with mean motion omega and orbital semi-major axis R(sub 0). The orbital geometry at the initial time is defined in terms of its six orbital elements, and the orbital dynamics equation for point O(sub ORF) is propagated forward in time under the influence of the gravitational field of the primary and other external perturbations, described below. The origin of this frame coincides with the initial position of the center of mass of the system, and the coordinate axes are z along the local vertical, x toward the flight direction, and y in the orbit normal direction. The assumptions we used to model the dynamics are as follows: 1) The inertial frame is fixed at Earth's center. 2) The orbiting Frame ORF follows Keplerian orbit. 3) the cloud system dynamics is referred to ORF. 4) the attitude of each grain uses the principal body frame as body fixed frame. 5) the atmosphere is assumed to be rigidly rotating with the Earth. Regarding the grains forming the cloud: 1) each grain is modeled as a rigid body; 2) a simple attitude estimator provides attitude estimates, 3) a simple guidance logic commands the position and attitude of each grain, 4) a simple local feedback controller based on PD control of local states is used to stabilize the attitude of the vehicle. Regarding the cloud: 1) the cloud as a whole is modeled as an equivalent rigid body in orbit, and 2) an associated graph establishes agent connectivity and enables coupling between modes of motion at the micro and macro scales; 3) a simple guidance and estimation logic is modeled to estimate and command the attitude of this equivalent rigid body; 4) a cloud shape maintenance controller is based on the dynamics of a stable virtual truss in the orbiting frame. Regarding the environmental perturbations acting on the cloud: 1) a non-spherical gravity field including JO (Earth's spherical field) zonal component, J2 (Earth's oblateness) and J3 zonal components is implemented; 2) atmospheric drag is modeled with an exponential model; 3) solar pressure is modeled assuming the Sun is inertially fixed; and 4) the Earth's magnetic field is model using an equivalent dipole model. The equations of motion are written in a referential system with respect to the origin of the orbiting frame and the state is propagated forward in time using an incremental predictor-corrector scheme. A representative cloud with varying number of grains is simulated to identify the limitations in computation time as the number of grains grows. We derive a control law to track a desired surface in the ORF (equivalently to maintain a reference cloud shape) by defining an error from a desired surface shape, and designing a control law that is exponentially stable and reduces the tracking error to zero. Figure 1 (top right) shows a comparison of various requirements for simulation of single spacecraft vs. granular spacecraft, indicating the high degree of complexity that needs to be taken into consideration. The ORF components of control force required by one of the grains is, for this particular case, in the micro-Newton range. However, no attempt has been made yet to reconfigure (or re-orient) the cloud configuration internally, for which forces in the milli-Newton level are expected, depending on the time required to do the reconfiguration. Figure 1, bottom, shows the computation time as a function of the number of grains, indicating an order N(exp 1.43) scaling on a 8 Gb, 1067 MHz RAM MacOSX computer with a 3.06 GHz Intel Core 2 Duo processor. With this metric, the same simulation for a system of N=1000 grains would take 5.4 hours, and 146 hours (i.e., 6 days) for a system with N=10,000 grains. Therefore, efficient ways to simulate this complex system, where not only the time scales of natural system dynamics, but also the sampling times of the Guidance, Navigation, and Control are included, remain to be explored. Additional details on the cloud modeling, dynamics, and control will be described in the paper.

simulation↗

Space-to-Ground Interactions While Conducting Scientific Fieldwork Under Mars Mission Constraints

The Biologic Analog Science Associated with Lava Terrains (BASALT) project is a 4-year program dedicated to iteratively designing, implementing, and evaluating concepts of operations (ConOps) and supporting capabilities to enable and enhance scientific exploration for future human Mars missions. BASALT incorporates three field deployments during which real (non-simulated) biological and geochemical field science is conducted at two high-fidelity Mars analog locations under simulated Mars mission conditions, including communication de-lays and data transmission limitations. BASALT’s primary science objective is to investigate how the redox conditions of altered basaltic environments affect the development of microbial communities in these Mars-relevant settings. Field sites include the active East Rift Zone on the Big Island of Hawaii, reminiscent of early Mars when basaltic volcanism and interaction with water were widespread, and the dormant eastern Snake River Plain in Idaho, similar to present-day Mars where basaltic volcanism is rare and most evidence for volcano-driven hydrothermal activity is relict. BASALT’s primary science operations objective is to investigate exploration ConOps and capabilities that facilitate scientific return during human-robotic exploration under Mars mission constraints. Each field deployment consists of ten extravehicular activities (EVAs) on the volcanic flows in which two extravehicular and two intravehicular (IV) crew-members conduct the science while communicating across time delay and under bandwidth constraints with an Earth-based Mission Support Center (MSC) comprised of expert scientists and operators. Communication latencies of 5 and 15-minute one-way light time and low (0.512 Mb/s uplink, 1.54 Mb/s down-link) and high (5.0 Mb/s uplink, 10.0 Mb/s downlink) bandwidth conditions are being evaluated. EVA crewmembers communicate with the MSC via voice and text messaging and provide scientific instrument data, still imagery, video streams, and GPS tracking information. The MSC reviews this data across delay and provides recommendations for presampling and sampling tasks. The scientists used dynamic leaderboards (priority rank-ing lists), to track and rank candidate samples relative to one another and against the science objectives for the current EVA and the overall mission. Updates to the dynamic leaderboards are relayed regularly to the IV crewmembers to provide scientific feedback from Earth and to help minimize crew idle time (time spent waiting for Earth input during which no productive tasks are performed). EVA timelines are strategically designed to enable continuous (delayed) feedback from an Earth-based science team while simultaneously minimizing crew idle time. Such timelines are operationally advantageous, reducing transport costs by eliminating the need for crews to return to the same locations on multiple EVAs while still providing opportunities for recommendations from science experts on Earth, and scientifically advantageous by minimizing the potential for cross-contamination across sites. This paper will highlight the space-to-ground interaction results from the three BASALT field deployments, including planned versus actual EVA time-line data, ground assimilation times (the amount of time available to the MSC to provide input to the crew), and idle time. Furthermore, we describe how these results vary under the different communication latency and bandwidth conditions. Together, these data will provide a basis for guiding and prioritizing capability development for future human exploration missions.

Beaton, Kara H.↗

Characterizing Detailed Grain Shape and Size Distribution Properties of Lunar Regolith

Introduction: As the nation prepares to return to the Moon, there is an increasing need for testing tools, instruments, and equipment in simulated environments on Earth to ensure successful operations during lunar missions. Regolith will affect all aspects of future lunar missions, from plume interactions during landing to space suit and tool design [1]. Because of this, it is important to understand the grain shape and size properties of lunar regolith and how those influence regolith behavior in order to prepare for these missions. This knowledge is also vital to create more accurate lunar regolith simulants for testing equipment in a lunar environment. While particle size analyses have been performed on most Apollo soils using simple sieving, shape has only been crudely addressed [2]. This work analyzes 4 lunar regolith samples to provide a better understanding of these size and shape parameters and will provide a more accurate baseline of data to create high-fidelity lunar regolith simulants. Methods: New technologies exist today that are capable of measuring size and shape simultaneously for hundreds of thousands of particles in a single measurement. We conducted a rigorous analysis of the particle size distribution (PSD) as well as the size-dependent 2D and 3D shape parameters of lunar regolith samples of different compositions and maturity levels. This analysis was done using a Microtrac SYNC which provides a unique combination of tri-laser diffraction and Dynamic Image Analysis (DIA). Sample Selection. Four regolith samples were selected for analysis based on maturity level and lunar terrain type: • 10084 – Mature high-Ti mare regolith • 15601 – Immature low-Ti mare regolith • 64501 – Mature highland regolith • 67461 – Immature highland regolith Sample Analysis. After receiving the samples, each sample was imaged with an optical microscope (Figure 1). To obtain 2D and 3D particle size and shape, 0.1 g of each sample was then added to the SYNC for analysis, which outputs more than 30 size and shape parameters for each individual grain as well as the complete size distribution from 0.01-2000 μm by blending laser diffraction and DIA together. For the 0.1 g sample masses requested, ~100,000 grains per sample were captured by DIA. Results: From the PSD analysis, it can be seen that the average particle size of 10084 is ~24.5 µm which is much smaller than the average particle size of the Apollo sample collection (~72 µm) [3], while the average particle size of samples 15601, 64501, and 67461 are larger than the Apollo sample average at ~106 µm, ~103 µm, and ~118.5 µm respectively. The size and shape measurements for the samples output ~30 parameters, four of which were focused on for this study: sphericity, aspect ratio, roundness, and concavity (Figure 3). However, after analyzing the plots it was found that only sphericity and aspect ratio showed differences between the samples. These two parameters are measured on a scale from 0 to 1, with 1 being a perfect sphere with equal dimensions. The results show that the sphericity values are slightly high-er for the mature samples 10084 and 64501 (~0.96) than they are for samples 15601 and 67461 (~0.95) (Figure 4). The aspect ratio values are slightly lower for samples 64501 (~0.7) and 67461 (~0.74) than they are for samples 10084 (~0.76) and 15601 (~0.8) (Figure 5). Discussion: Mature regoliths are those that have been exposed to micrometeorite and solar wind bombardment for long periods of time, breaking up particles and causing them to become more rounded [4]. Therefore, the smaller particle sizes and higher sphericity values for samples 10084 and 64501 are expected due to their higher maturity level compared to 15601 and 67461. However, the aspect ratio values are not dependent on maturity and are instead dependent on terrain type. The lower aspect ratio values for the high-land samples is potentially due to the higher plagioclase content, which occurs in elongated particles and does not break down as easily as the pyroxenes or olivines that are present in the mare. Conclusion and Future Work: The results of this work provide a baseline of high-quality data that will contribute to the creation of high-fidelity lunar simulants and will greatly benefit NASA’s efforts of establishing a human presence on the Moon. Future work includes performing unsupervised image classification on the ~105 particle images per sample in order to identify different classes of grains. These grain classes can then be linked to detailed shape properties, and the relative abundance of each class in the samples can be compared. Acknowledgments: We would like to thank the Extraterrestrial Materials Analysis Group (ExMAG) and the Astromaterials Allocation Review Board (AARB) for allocating lunar regolith samples 10084,9010, 15601,365, 64501,249, and 67461,171 for this work. References: [1] Taylor, L. A. et al. (2005) AIAA #2510. [2] Katagiri et al. (2015) ASCE. [3] Carrier III, W. D. (2005) Lunar Geotech Institute Tech Report. [4] McKay, D. S. et al. (1991) The Lunar Sourcebook, Chapter 7.

S R Deitrick↗

Lunar core 15010/11 - Grain size, petrology, and implications for regolith dynamics

Petrographic observations of six samples from various depths show that core 15010/11 is relatively homogeneous and consists mostly of basalt fragments and minerals derived from basalts. However, it also contains an appreciable highland component nearly equally distributed among the fine-grained fraction, dark matrix breccia and identifiable highland grains, and agglutinates. Grain size data and agglutinates show that this core is not mature and does not contain a well developed reworking profile. The unusual properties of the core are thought to be a direct result of its close proximity to the rim of Hadley Rille. This location favors relatively rapid regolith erosion into the rille, produces a thin regolith, and provides an abundant supply of bedrock-derived ejecta.

Mckay, D. S.↗

The Space Shuttle, fluid dynamics, and computer graphics

Several samples are presented of CFD-generated flow ribbon images of fuel flow in the SSME. The images result from simulations of H2 flow through a design iteration of the main injector, the hot gas manifold and the fuel bowl section. The color-coded ribbons provide three-dimensional perspectives which indicate the direction and orientation of the flow and the velocity magnitude in intervals along the flow path.

Belie, R. G.↗

Mars Science Laboratory Sample Acquisition, Sample Processing and Handling: Subsystem Design and Test Challenges

The Sample Acquisition/Sample Processing and Handling subsystem for the Mars Science Laboratory is a highly-mechanized, Rover-based sampling system that acquires powdered rock and regolith samples from the Martian surface, sorts the samples into fine particles through sieving, and delivers small portions of the powder into two science instruments inside the Rover. SA/SPaH utilizes 17 actuated degrees-of-freedom to perform the functions needed to produce 5 sample pathways in support of the scientific investigation on Mars. Both hardware redundancy and functional redundancy are employed in configuring this sampling system so some functionality is retained even with the loss of a degree-of-freedom. Intentional dynamic environments are created to move sample while vibration isolators attenuate this environment at the sensitive instruments located near the dynamic sources. In addition to the typical flight hardware qualification test program, two additional types of testing are essential for this kind of sampling system: characterization of the intentionally-created dynamic environment and testing of the sample acquisition and processing hardware functions using Mars analog materials in a low pressure environment. The overall subsystem design and configuration are discussed along with some of the challenges, tradeoffs, and lessons learned in the areas of fault tolerance, intentional dynamic environments, and special testing

Jandura, Louise↗

Acoustic levitation methods for density measurements

The capability of ultrasonic levitators operating in air to perform density measurements has been demonstrated. The remote determination of the density of ordinary liquids as well as low density solid metals can be carried out using levitated samples with size on the order of a few millimeters and at a frequency of 20 kHz. Two basic methods may be used. The first one is derived from a previously known technique developed for acoustic levitation in liquid media, and is based on the static equilibrium position of levitated samples in the earth's gravitational field. The second approach relies on the dynamic interaction between a levitated sample and the acoustic field. The first technique appears more accurate (1 percent uncertainty), but the latter method is directly applicable to a near gravity-free environment such as that found in space.

Trinh, E. H.↗

Modeling and Simulation of a Tethered Harpoon for Comet Sampling

This paper describes the development of a dynamic model and simulation results of a tethered harpoon for comet sampling. This model and simulation was done in order to carry out an initial sensitivity analysis for key design parameters of the tethered system. The harpoon would contain a canister which would collect a sample of soil from a cometary surface. Both a spring ejected canister and a tethered canister are considered. To arrive in close proximity of the spacecraft at the end of its trajectory so it could be captured, the free-flying canister would need to be ejected at the right time and with the proper impulse, while the tethered canister must be recovered by properly retrieving the tether at a rate that would avoid an excessive amplitude of oscillatory behavior during the retrieval. The paper describes the model of the tether dynamics and harpoon penetration physics. The simulations indicate that, without the tether, the canister would still reach the spacecraft for collection, that the tether retrieval of the canister would be achievable with reasonable fuel consumption, and that the canister amplitude upon retrieval would be insensitive to variations in vertical velocity dispersion.

small body↗

Analytical Simulations of Energy-Absorbing Impact Spheres for a Mars Sample Return Earth Entry Vehicle

Nonlinear dynamic finite element simulations were performed to aid in the design of an energy-absorbing impact sphere for a passive Earth Entry Vehicle (EEV) that is a possible architecture for the Mars Sample Return (MSR) mission. The MSR EEV concept uses an entry capsule and energy-absorbing impact sphere designed to contain and limit the acceleration of collected samples during Earth impact without a parachute. The spherical shaped impact sphere is composed of solid hexagonal and pentagonal foam-filled cells with hybrid composite, graphite-epoxy/Kevlar cell walls. Collected Martian samples will fit inside a smaller spherical sample container at the center of the EEV's cellular structure. Comparisons were made of analytical results obtained using MSC.Dytran with test results obtained from impact tests performed at NASA Langley Research Center for impact velocities from 30 to 40 m/s. Acceleration, velocity, and deformation results compared well with the test results. The correlated finite element model was then used for simulations of various off-nominal impact scenarios. Off-nominal simulations at an impact velocity of 40 m/s included a rotated cellular structure impact onto a flat surface, a cellular structure impact onto an angled surface, and a cellular structure impact onto the corner of a step.

Billings, Marcus Dwight↗

A new method for simulating atmospheric turbulence for rotorcraft applications

Simulation of atmospheric turbulence as seen by a rotating blade element involves treatment of cyclostationary processes. Conventional filtering techniques do not lend themselves well to the generation of such turbulence sample functions as are required in rotorcraft flight dynamics simulation codes. A method to generate sample functions containing second order statistics of mean and covariance is presented. Compared to ensemble averaging involving excessive computer time, the novelty is to exploit cycloergodicity and thereby, replace ensemble averaging by averaging over a single path sample function of long duration. The method is validated by comparing its covariance results with the analytical and ensemble averaged results for a widely used 1-D turbulence approximation.

J. Riaz↗

A new method for simulating atmospheric turbulence for rotorcraft applications

Simulation of atmospheric turbulence as seen by a rotating blade element involves treatment of cyclostationary processes. Conventional filtering techniques do not lend themselves well to the generation of such turbulence sample functions as are required in rotorcraft flight dynamics simulation codes. A method to generate sample functions containing second-order statistics of mean and covariance is presented. Compared to ensemble averaging involving excessive computer time, the novelty is to exploit cycloergodicity and thereby, replace ensemble averaging by averaging over a single-path sample function of long duration. The method is validated by comparing its covariance results with the analytical and ensemble-averaged results for a widely used one-dimensional turbulence approximation.

Prasad, J. V. R.↗

Sample Return Systems for Extreme Environments (SaRSEE)

Sample return missions offer a greater science yield when compared to missions that only employ in situ experiments or remote sensing observations, since they allow the application of more complex technological and analytical methodologies in controlled terrestrial laboratories,that are both repeatable and can be independently verified. The successful return of extraterrestrial materials over the last four decades has contributed to our understanding of the solar system, but retrieval techniques have largely depended on the use of either soft-landing, or touch-and-go procedures that result in high V requirements, larger spacecraft mass ratios, and return yields typically limited to a few grams of surface materials that have experienced varying degrees of alteration from space weathering. Hard-landing methods using planetary penetrators offer an alternative for sample return that significantly reduce a mission's V and mass ratios,increase sample yields, and allow for the collection of subsurface materials, and lessons can be drawn from previous sample return missions. The following details progress in the design,development, and testing of penetrator/sampler technology capable of surviving subsonic and low, supersonic impact velocities (<700 m/s) that would enable the collection of geologic materials using tether technology to return the sample to a passing spacecraft. The testing of energy absorbing material for protecting the sample, design evolution and field testing of the penetrator, and dynamic modeling of tether behavior during sampling are discussed. It is shown through both modeling and field testing that penetrators at speeds between 300-600 m/s (~Mach 1-2) can penetrator into the ground to depths of 1-2 m with overall structural integrity attained.The first flight tests demonstrated the potential for survivability at these speeds. The second flight series demonstrated core sample collection with partial ejection of the sample return canister. The 3rd flight series demonstrated self-ejection of the sample return system fully intact and with the core retaining the full stratigraphy of the rock bed. The tether analysis shows that the forces on the tether during release and return of the sample to the main spacecraft are all at levels that can easily be handled by existing tether materials. The mass analysis of the requirements indicates that sample return form the asteroids could be handled with Discovery or New Frontier range of missions dependent on the number of samples to be returned to the Earth.

Winglee, R. M.↗

Fast, Safe, Propellant-Efficient Spacecraft Motion Planning Under Clohessy-Wiltshire-Hill Dynamics

This paper presents a sampling-based motion planning algorithm for real-time and propellant-optimized autonomous spacecraft trajectory generation in near-circular orbits. Specifically, this paper leverages recent algorithmic advances in the field of robot motion planning to the problem of impulsively actuated, propellant- optimized rendezvous and proximity operations under the Clohessy-Wiltshire-Hill dynamics model. The approach calls upon a modified version of the FMT* algorithm to grow a set of feasible trajectories over a deterministic, low-dispersion set of sample points covering the free state space. To enforce safety, the tree is only grown over the subset of actively safe samples, from which there exists a feasible one-burn collision-avoidance maneuver that can safely circularize the spacecraft orbit along its coasting arc under a given set of potential thruster failures. Key features of the proposed algorithm include 1) theoretical guarantees in terms of trajectory safety and performance, 2) amenability to real-time implementation, and 3) generality, in the sense that a large class of constraints can be handled directly. As a result, the proposed algorithm offers the potential for widespread application, ranging from on-orbit satellite servicing to orbital debris removal and autonomous inspection missions.

spacecraft relative motio↗