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NASA NTRS2022

The Turning Point of the Aerosol Era

Over the CMIP6 historical period (1850–2014), aerosols provided the largest negative forcing compared to all other climate forcings via their ability to absorb or scatter solar radiation and alter clouds. Aerosols played an important role in counterbalancing warming by greenhouse gases (GHGs). Here we study aerosol forcing trends in the CMIP6 simulations of the NASA Goddard Institute for Space Studies (GISS) ocean-atmosphere ModelE version 2.1 (GISS-E2.1-G) using a fully coupled atmospheric composition configuration, including interactive gas-phase chemistry, and either an aerosol microphysical (MATRIX) or a mass-based aerosol (OMA) module. Simulations of the CMIP6 historical period are analyzed as well as four Shared Socioeconomic Pathway (SSP) future scenarios for 2015–2100: SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5. The main conclusion of this study is that aerosol forcing in the GISS model has reached its turning point, switching from globally increasing to a decreasing trend in the first decade of the 21st century. This result is robust, independent of which aerosol module or SSP scenario is used. Non-linear aerosol-cloud interactions dominate as a forcing agent over aerosol-radiation interactions. Aerosols' ability to counterbalance GHG forcing on the global scale is today at a level comparable to that at the beginning of the last century. In the 1980s, the decade of largest global aerosol loads, aerosols balanced up to 80% of GHG forcing. As a consequence, global warming of the last decades, which is primarily driven by greenhouse gases, has been augmented by the effect of decreasing aerosol cooling in our model. By the end of this century, following the SSP scenarios, aerosols will only counterbalance 0%–20% of GHG forcing, depending on model and on scenario.

Aerosol forcing↗

NASA NTRS2001

Human Centered Autonomous and Assistant Systems Testbed for Exploration Operations

The Engineering and Mission Operations Directorates at NASA Johnson Space Center are combining laboratories and expertise to establish the Human Centered Autonomous and Assistant Systems Testbed for Exploration Operations. This is a testbed for human centered design, development and evaluation of intelligent autonomous and assistant systems that will be needed for human exploration and development of space. This project will improve human-centered analysis, design and evaluation methods for developing intelligent software. This software will support human-machine cognitive and collaborative activities in future interplanetary work environments where distributed computer and human agents cooperate. We are developing and evaluating prototype intelligent systems for distributed multi-agent mixed-initiative operations. The primary target domain is control of life support systems in a planetary base. Technical approaches will be evaluated for use during extended manned tests in the target domain, the Bioregenerative Advanced Life Support Systems Test Complex (BIO-Plex). A spinoff target domain is the International Space Station (ISS) Mission Control Center (MCC). Prodl}cts of this project include human-centered intelligent software technology, innovative human interface designs, and human-centered software development processes, methods and products. The testbed uses adjustable autonomy software and life support systems simulation models from the Adjustable Autonomy Testbed, to represent operations on the remote planet. Ground operations prototypes and concepts will be evaluated in the Exploration Planning and Operations Center (ExPOC) and Jupiter Facility.

Malin, Jane T.↗

NASA NTRS2012

Evaluation of the Absolute Regional Temperature Potential

The Absolute Regional Temperature Potential (ARTP) is one of the few climate metrics that provides estimates of impacts at a sub-global scale. The ARTP presented here gives the time-dependent temperature response in four latitude bands (90-28degS, 28degS-28degN, 28-60degN and 60-90degN) as a function of emissions based on the forcing in those bands caused by the emissions. It is based on a large set of simulations performed with a single atmosphere-ocean climate model to derive regional forcing/response relationships. Here I evaluate the robustness of those relationships using the forcing/response portion of the ARTP to estimate regional temperature responses to the historic aerosol forcing in three independent climate models. These ARTP results are in good accord with the actual responses in those models. Nearly all ARTP estimates fall within +/-20%of the actual responses, though there are some exceptions for 90-28degS and the Arctic, and in the latter the ARTP may vary with forcing agent. However, for the tropics and the Northern Hemisphere mid-latitudes in particular, the +/-20% range appears to be roughly consistent with the 95% confidence interval. Land areas within these two bands respond 39-45% and 9-39% more than the latitude band as a whole. The ARTP, presented here in a slightly revised form, thus appears to provide a relatively robust estimate for the responses of large-scale latitude bands and land areas within those bands to inhomogeneous radiative forcing and thus potentially to emissions as well. Hence this metric could allow rapid evaluation of the effects of emissions policies at a finer scale than global metrics without requiring use of a full climate model.

Shindell, D. T.↗

NASA NTRS1998

A Cognitive-System Model for En Route Air Traffic Management

NASA Ames Research Center has been engaged in the development of advanced air traffic management technologies whose basic form is cognitive aiding systems for air traffic controller and flight deck operations. In the design and evaluation of such systems the dynamic interaction between the airborne aiding system and the ground-based aiding systems forms a critical coupling for control. The human operator is an integral control element in the system and the optimal integration of human decision and performance parameters with those of the automation aiding systems offers a significant challenge to cognitive engineering. This paper presents a study in full mission simulation and the development of a predictive computational model of human performance. We have found that this combination of methodologies provide a powerful design-aiding process. We have extended the computational model Man Machine Integrated Design and Analysis System (N13DAS) to include representation of multiple cognitive agents (both human operators and intelligent aiding systems), operating aircraft airline operations centers and air traffic control centers in the evolving airspace. The demands of this application require the representation of many intelligent agents sharing world-models, and coordinating action/intention with cooperative scheduling of goals and actions in a potentially unpredictable world of operations. The operator's activity structures have been developed to include prioritization and interruption of multiple parallel activities among multiple operators, to provide for anticipation (knowledge of the intention and action of remote operators), and to respond to failures of the system and other operators in the system in situation-specific paradigms. We have exercised this model in a multi-air traffic sector scenario with potential conflict among aircraft at and across sector boundaries. We have modeled the control situation as a multiple closed loop system. The inner and outer loop alerting structure of air traffic management has many implications that need to be investigated to assure adequate design. First, there are control and stability factors implicit in the design. As the inner loop response time approaches that of the outer loop, system stability may be compromised in that controllers may be solving a problem the nature of which has already been changed by pilot action. Second, information exchange and information presentation for both air and ground must be designed to complement as opposed to compete with each other. Third, the level of individual and shared awareness in trajectory modification and flight conformance needs to be defined. Fourth, the level of required awareness and performance impact of mixed fleet operations and failed-mode recovery must be explored.

Corker, Kevin M.↗

NASA NTRS2004

Distributed network scheduling

Distributed Network Scheduling is the scheduling of future communications of a network by nodes in the network. This report details software for doing this onboard spacecraft in a remote network. While prior work on distributed scheduling has been applied to remote spacecraft networks, the software reported here focuses on modeling communication activities in greater detail and including quality of service constraints. Our main results are based on a Mars network of spacecraft and include identifying a maximum opportunity of improving traverse exploration rate a factor of three; a simulation showing reduction in one-way delivery times from a rover to Earth from as much as 5 to 1.5 hours; simulated response to unexpected events averaging under an hour onboard; and ground schedule generation ranging from seconds to 50 minutes for 15 to 100 communication goals.

planning↗

NASA NTRS2004

Applications of Intelligent Tutoring Systems to Human-Robotic Exploration of Mars

Space missions with small crews extending over several years with time-delay preventing normal conversations with people on earth will raise many challenges for training. Of special interest are possible three-year missions to Mars, requiring refresher instruction and learning new skills based on unexpected problems with machines and environmental conditions. For example, the crew will be required to monitor and repair more complex life support systems for air and water recycling than we even know how to build today. Highly educated astronauts, often with several doctorate degrees, require a very different mode of interaction than we have developed for school children or even typical college students. Explanation methods may need to differ-using analogies and techniques from different domains-depending on whether the astronaut is an astrophysicist, a pilot, or a geologist.Virtual reality (e.g., for Hubble repair missions) and "integrated" simulations (involving role-playing and emphasizing failure scenarios) are the most common advanced forms of instruction used in space flight today. The emphasis is on collaborative, embodied interaction with the same workstations and tools used in practice (e.g., a cockpit simulator). Otherwise, computerized instructional technology used by NASA is not model-based or tutorial in nature. This discussion will review some of the key instructional methods used at NASA over the past two decades and consider why ITS methods have not been exploited. Some of the problems and opportunities for training for Mars missions are examined, including how using robots in exploration activities will help but raise new training problems. These ideas will be illustrated with examples from the BrahmsVE system in which a browser- based virtual reality display with avatars allows interacting with a distributed multiagent system, in which agents can be people, robots, or software programs. Using BrahmsVE may provide a way for astronauts to interact with proxies of people who serve as instructional coaches on Mars.

Clancey, William J.↗

NASA NTRS2018

Design and Development of a Laboratory-Scale Ice Adhesion Testing Device

When an aircraft traverses through clouds containing supercooled water droplets, in-flight icing can occur that negatively affects vehicle performance by increasing weight and drag leading to loss of lift. Super-cooled water droplets present in clouds that impact vehicle surfaces can lead to inflight icing any time during the year.1 Most events occur at temperatures ranging from 0 to -20degC. Ice generated on the aircraft can vary between clear/glaze, rime, and mixed (Fig. 1) depending on air temperature (-5 to -20degC), liquid water content (0.3-0.6 g/m3), and droplet size (median volumetric diameter of 15-40 μm). Current strategies to remove ice are based on active technologies such as pneumatic boots, heated surfaces, and deicing agents (i.e., ethylene- and propylene-based glycols). The latter have potential environmental concerns. A passive approach to mitigate accreting ice that is actively being investigated are protective coatings. An ice mitigating coating could potentially be used as a stand-alone material, but more likely in combination with an active approach. In the latter scenario, potential reduction in power consumption by the active approach may be realized. To determine the ice adhesion strength of impact ice that is representative of the aircraft environment is not a trivial matter. Test methods utilizing slowly formed ice (i.e., freezer ice) do not accurately simulate this environment. Likewise, some testing methodologies involve sample relocation from the icing environment to the test chamber that can result in thermal shock to the sample, thus affecting the results. The Adverse Environment Rotor Test Stand (AERTS) located at Pennsylvania State University (PSU) has been demonstrated to simulate impact icing conditions within the icing envelope for the determination of ice adhesion shear strength (IASS) without removal/relocation of the sample.2 Due to the confidence in results obtained from AERTS, this instrument is in high demand and requires a significant amount of lead time and capital investment to obtain IASS results. As a solution for quickly and economically screening coatings in a controlled manner under impact icing conditions, a laboratory-scale ice adhesion test and dead blades were then removed from the rotor/blade assembly to obtain the final mass. The IASS of the live blade was determined from the difference in mass (before and after testing) of the live and dead blades, the ice shed area, and the rpm of the shed event. The same live blade sample was tested in triplicate at all three test temperatures. Surface roughness was determined using a Bruker Dektak XT Stylus Profilometer. Measurements were conducted using a 12.5 μm tip at a vertical range of 65.5 μm with an applied force of 3 mg. Data were collected over a 1.0 mm length at a resolution of 0.056 μm/point. Five single line scans at different locations were collected and processed using a two-point leveling subtraction. The resultant Ra (arithmetic roughness) and Rq (root mean square roughness) average values were calculated.

Smith, Joseph G., Jr.↗

NASA NTRSDate not supplied

Modeling Distributed Situation Awareness in Resilience-based Design of Complex Systems

Human operators play a major role in the resilience of complex systems–while human error is one of the biggest contributors to hazardous events, operators additionally play a critical role in mitigating hazardous events. A key factor underlying this operator resilience is situation awareness–the ability of operators to understand their environment and each other to achieve desired system functions. In contrast to situation awareness-related accident models in the literature, which are largely conceptual in nature, this work proposes the use of a dynamic simulation framework to concretely model both the effects of situation awareness-related human errors and situation awareness-related hazard-mitigating properties using the distributed situation awareness theory. This work then presents specialized model constructs to enable agents’ individual perceptions of the system state and transactions with other agents (and thus distributed situation awareness) to be represented in simulation. To demonstrate this framework, it is then adapted to an aircraft taxiway case study, where it is used to model aircraft conflicts due to lack of vision and poor communications from the air traffic controller. This demonstration shows the potential of using simulation models to rigorously understand situation awareness-related human errors and thus inform the design of resilience.

Resilience Modeling↗

NASA NTRS1990

Dual redundant arm system operational quality measures and their applications - Dynamic measures

Dual-arm dynamic operation quality measures are presented which quantify the efficiency and capability of generating Cartesian accelerations by two cooperative arms based on the analysis of dual-arm dynamic interactions. Dual-arm dynamic manipulability is defined as the efficiency of generating Cartesian accelerations under the dynamic and kinematic interactions between individual arms and an object under manipulation. The analysis of dual-arm dynamic interactions is based on the so-called Cartesian space agent model of an arm, which represents an individual arm as a force source acting upon a point mass with the effective Cartesian space arm dynamics and an environment or an object under manipulation. The Cartesian space agent model of an arm makes it possible to derive the dynamic and kinematic constraints involved in the transport, assembly and grasping modes of dual-arm cooperation. A task-oriented operational quality measure, (TOQd) is defined by evaluating dual-arm dynamic manipulability in terms of given task requirements. TOQd is used in dual-arm joint configuration optimization. Simulation results are shown. A complete set of forward dynamic equations for a dual-arm system is derived, and dual-arm dynamic operational quality measures for various modes of dual-arm cooperation allowing sliding contacts are established.

Lee, Sukhan↗

NASA NTRS2020

Optimal Multi-Agent Search and Rescue Using Potential Field Theory

This paper presents an algorithm for efficient search and rescue using a multi-agent system of vehicles. The algorithm uses an artificial potential field combined with a time-varying reward function for visiting various points within the search area. The reward function is used to weight the attractiveness of these points in the potential field, and collision avoidance terms are used to repel vehicles from each other, which has the additional effect of reducing duplication of searching efforts. The algorithm generates velocity commands in real-time based on communication with the other vehicles. This framework allows vehicles to react in a dynamic environment, which is a significant advantage to simply following a-priori defined trajectories. Simulation results are presented to demonstrate the ability of the algorithm to cover the search area effectively. The algorithm is also compared to an exhaustive lawn-mower search pattern. This comparison is done via a Monte Carlo simulation with randomized target initial conditions and trajectories. The time to find the target improved by 16 and 30% in the mean and median, respectively. Additionally, this paper presents a method for analyzing the upper bound for time to find a target under the potential field guidance algorithm assuming a radially expanding search area.

John R Cooper↗

NASA NTRSDate not supplied

Modeling Distributed Situation Awareness in Resilience-Based Design of Complex Engineered Systems

Resilience Modeling↗

NASA NTRS2000

Adaptivity in Agent-Based Routing for Data Networks

Adaptivity, both of the individual agents and of the interaction structure among the agents, seems indispensable for scaling up multi-agent systems (MAS s) in noisy environments. One important consideration in designing adaptive agents is choosing their action spaces to be as amenable as possible to machine learning techniques, especially to reinforcement learning (RL) techniques. One important way to have the interaction structure connecting agents itself be adaptive is to have the intentions and/or actions of the agents be in the input spaces of the other agents, much as in Stackelberg games. We consider both kinds of adaptivity in the design of a MAS to control network packet routing. We demonstrate on the OPNET event-driven network simulator the perhaps surprising fact that simply changing the action space of the agents to be better suited to RL can result in very large improvements in their potential performance: at their best settings, our learning-amenable router agents achieve throughputs up to three and one half times better than that of the standard Bellman-Ford routing algorithm, even when the Bellman-Ford protocol traffic is maintained. We then demonstrate that much of that potential improvement can be realized by having the agents learn their settings when the agent interaction structure is itself adaptive.

Wolpert, David H.↗

NASA NTRS2017

Distributed Fast Motion Planning for Spacecraft Swarms in Cluttered Environments using Spherical Expansions and Sequence of Convex Optimization Problems

This paper presents a novel guidance algorithm for spacecraft swarms in an environment cluttered with many obstacles like a debris field or the asteroid belt. The objective of this algorithm is to reconfigure the swarm to a desired formation in a distributed manner while minimizing fuel and avoiding collisions among themselves and with the obstacles. The agents first use a spherical-expansion-based sampling algorithm to cooperatively explore the workspace and find paths to the desired terminal positions. Using a distributed assignment algorithm, the agents converge on an optimal assignment of the target locations in the desired formation. Then each agent generates a locally optimal trajectory from its current location to its terminal position by solving a sequence of convex optimization problems. As the agent moves along this trajectory, it receives the position of other agents and updates its trajectory to avoid collisions with other agents and the obstacles. Thus the swarm achieves the desired formation in a distributed manner while avoiding collisions. Moreover, this algorithm is computationally efficient, therefore it can be implemented onboard resource-constrained spacecraft. Simulations results show that the proposed distributed algorithm can be used by a spacecraft swarm to reconfigure a desired formation around an asteroid in a collision-free manner.

Bandyopadhyay, Saptarshi↗

NASA NTRS1996

A dual-input nonlinear system analysis of autonomic modulation of heart rate

Linear analyses of fluctuations in heart rate and other hemodynamic variables have been used to elucidate cardiovascular regulatory mechanisms. The role of nonlinear contributions to fluctuations in hemodynamic variables has not been fully explored. This paper presents a nonlinear system analysis of the effect of fluctuations in instantaneous lung volume (ILV) and arterial blood pressure (ABP) on heart rate (HR) fluctuations. To successfully employ a nonlinear analysis based on the Laguerre expansion technique (LET), we introduce an efficient procedure for broadening the spectral content of the ILV and ABP inputs to the model by adding white noise. Results from computer simulations demonstrate the effectiveness of broadening the spectral band of input signals to obtain consistent and stable kernel estimates with the use of the LET. Without broadening the band of the ILV and ABP inputs, the LET did not provide stable kernel estimates. Moreover, we extend the LET to the case of multiple inputs in order to accommodate the analysis of the combined effect of ILV and ABP effect on heart rate. Analyzes of data based on the second-order Volterra-Wiener model reveal an important contribution of the second-order kernels to the description of the effect of lung volume and arterial blood pressure on heart rate. Furthermore, physiological effects of the autonomic blocking agents propranolol and atropine on changes in the first- and second-order kernels are also discussed.

NASA Discipline Regulatory Physiology↗

NASA NTRS2003

A Real-Time Rover Executive based On Model-Based Reactive Planning

This paper reports on the experimental verification of the ability of IDEA (Intelligent Distributed Execution Architecture) effectively operate at multiple levels of abstraction in an autonomous control system. The basic hypothesis of IDEA is that a large control system can be structured as a collection of interacting control agents, each organized around the same fundamental structure. Two IDEA agents, a system-level agent and a mission-level agent, are designed and implemented to autonomously control the K9 rover in real-time. The system is evaluated in the scenario where the rover must acquire images from a specified set of locations. The IDEA agents are responsible for enabling the rover to achieve its goals while monitoring the execution and safety of the rover and recovering from dangerous states when necessary. Experiments carried out both in simulation and on the physical rover, produced highly promising results.

Bias, M. Bernardine↗

NASA NTRS1992

Human-like agents with posture planning ability

Human body models are geometric structures which may be ultimately controlled by kinematically manipulating their joints, but for animation, it is desirable to control them in terms of task-level goals. We address a fundamental problem in achieving task-level postural goals: controlling massively redundant degrees of freedom. We reduce the degrees of freedom by introducing significant control points and vectors, e.g., pelvis forward vector, palm up vector, and torso up vector, etc. This reduced set of parameters are used to enumerate primitive motions and motion dependencies among them, and thus to select from a small set of alternative postures (e.g., bend vs. squat to lower shoulder height). A plan for a given goal is found by incrementally constructing a goal/constraint set based on the given goal, motion dependencies, collision avoidance requirements, and discovered failures. Global postures satisfying a given goal/constraint set are determined with the help of incremental mental simulation which uses a robust inverse kinematics algorithm. The contributions of the present work are: (1) There is no need to specify beforehand the final goal configuration, which is unrealistic for the human body, and (2) the degrees of freedom problem becomes easier by representing body configurations in terms of 'lumped' control parameters, that is, control points and vectors.

Jung, Moon R.↗

NASA NTRS2001

Architectures and Evaluation for Adjustable Control Autonomy for Space-Based Life Support Systems

In the past five years, a number of automation applications for control of crew life support systems have been developed and evaluated in the Adjustable Autonomy Testbed at NASA's Johnson Space Center. This paper surveys progress on an adjustable autonomous control architecture for situations where software and human operators work together to manage anomalies and other system problems. When problems occur, the level of control autonomy can be adjusted, so that operators and software agents can work together on diagnosis and recovery. In 1997 adjustable autonomy software was developed to manage gas transfer and storage in a closed life support test. Four crewmembers lived and worked in a chamber for 91 days, with both air and water recycling. CO2 was converted to O2 by gas processing systems and wheat crops. With the automation software, significantly fewer hours were spent monitoring operations. System-level validation testing of the software by interactive hybrid simulation revealed problems both in software requirements and implementation. Since that time, we have been developing multi-agent approaches for automation software and human operators, to cooperatively control systems and manage problems. Each new capability has been tested and demonstrated in realistic dynamic anomaly scenarios, using the hybrid simulation tool.

Malin, Jane T.↗

NASA NTRS2013

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↗