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The development of optimal control laws for orbiting tethered platform systems

A mathematical model of the open and closed loop in orbit plane dynamics of a space platform-tethered-subsatellite system is developed. The system consists of a rigid platform from which an (assumed massless) tether is deploying (retrieving) a subsatellite from an attachment point which is, in general, offset from the platform's mass center. A Langrangian formulation yields equations describing platform pitch, subsatellite tetherline swing, and varying tether length motions. These equations are linearized about the nominal station keeping motion. Control can be provided by both modulation of the tether tension level and by a momentum type platform-mounted device; system controllability depends on the presence of both control inputs. Stability criteria are developed in terms of the control law gains, the platform inertia ratio, and tether offset parameter. Control law gains are obtained based on linear quadratic regulator techniques. Typical transient responses of both the state and required control effort are presented.

Bainum, P. M.

The development of optimal control laws for orbiting tethered platform systems

A mathematical model of the open and closed loop in-orbit plane dynamics of a space platform-tethered-subsatellite system is developed. The system consists of a rigid platform from which an (assumed massless) tether is deploying (retrieving) a subsatellite from an attachment point which is, in general, offset from the platform's mass center. A Lagrangian formulation yields equations describing platform pitch, subsatellite tether-line swing, and varying tether length motions. These equations are linearized about the nominal station keeping motion. Control can be provided by both modulation of the tether tension level and by a momentum type platform-mounted device; system controllability depends on the presence of both control inputs. Stability criteria are developed in terms of the control law gains, the platform inertia ratio, and tether offset parameter. Control law gains are obtained based on linear quadratic regulator techniques. Typical transient responses of both the state and required control effort are presented.

Bainum, P. M.

Mechanism synthesis and 2-D control designs of an active three cable crane

A Lunar Crane with a suspension system based on a three cable mechanism is investigated to provide a stable end-effector for hoisting, positioning, and assembling large components during construction and servicing of a Lunar Base. The three cable suspension mechanism consists of a structural framework of three cables pointing to a common point that closely coincides with the suspended payload's center of gravity. The vibrational characteristics of this three cable suspension system are investigated by comparing a simple 2-D symmetric suspension model and a swinging pendulum in terms of their analytical natural frequency equations. A study is also made of actively controlling the dynamics of the crane using two different actuator concepts. Also, Lyapunov-based control algorithms are developed to determine two regulator-type control laws performing the system vibrational suppression for both system dynamics. Simulations including initial-valued dynamic responses as well as control performances for two different system dynamics are also presented.

Yang, Li-Farn

Automation of a Versatile Crane (the LSMS) for Lunar Outpost Construction, Maintenance and Inspection

Devices for lifting, translating and precisely placing payloads are critical for efficient Earth-based construction operations. Both recent and past studies have demonstrated that devices with similar functionality will be needed to support lunar outpost operations. Although several designs have been developed for Earth based applications, these devices lack unique design characteristics necessary for transport to and use on the harsh lunar surface. These design characteristics include: a) lightweight components, b) compact packaging for launch, c) automated deployment, d) simple in-field reconfiguration and repair, and e) support for tele-operated or automated operations. Also, because the cost to transport mass to the lunar surface is very high, the number of devices that can be dedicated to surface operations will be limited. Thus, in contrast to Earth-based construction, where many single-purpose devices dominate a construction site, a lunar outpost will require a limited number of versatile devices that provide operational benefit from initial construction through sustained operations. The first generation test-bed of a new high performance device, the Lunar Surface Manipulation System (LSMS) has been designed, built and field tested. The LSMS has many unique features resulting in a mass efficient solution to payload handling on the lunar surface. Typically, the LSMS device mass is estimated at approximately 3% of the mass of the heaviest payload lifted at the tip, or 1.8 % of the mass of the heaviest mass lifted at the elbow or mid-span of the boom for a high performance variant incorporating advanced structural components. Initial operational capabilities of the LSMS were successfully demonstrated during field tests at Moses Lake, Washington using a tele-operated approach. Joint angle sensors have been developed for the LSMS to improve operator situational awareness. These same sensors provide the necessary information to support fully automated operations, greatly expanding the operational versatility of the LSMS. This paper develops the equations describing the forward and inverse relation between LSMS joint angles and Cartesian coordinates of the LSMS tip. These equations allow a variety of schemes to be used to maneuver the LSMS to optimize the maneuver. One such scheme will be described in detail that eliminates undesirable swinging of the payload at the conclusion of a maneuver, even when the payload is suspended from a passive rigid link. The swinging is undesirable when performing precision maneuvers, such as aligning an object for mating or positioning a camera. Use of the equations described here enables automated control of the LSMS greatly improving its operational versatility.

Doggett, William R.

Thermal investigation of a large lunar telescope

Recent interest in construction of a large telescope on the lunar surface (Nein and Davis, 1991; Bely, Burrows, and Illingworth, 1989) has prompted this feasibility study of a thermal control system for a 16 meter diameter telescope located near the lunar equator. In addition to detailed analyses for a telescope located in a flat area near the equator, the thermal effect of locating the telescope in a crater, on a hill, and at higher latitude sites is discussed. Because an unprotected telescope experiences a wide range of temperature swings, several thermal protection schemes have been examined, including domes, sunshades, and ground shields to limit the temperature excursions of the primary mirror. Results of these analyses indicate that mirror temperature excursions can be limited to less than 100 Kelvin (K) per lunar cycle with an appropriate passive thermal protection system (dome), and that the telescope primary mirror can be maintained at less than 100 K for at least 7 days of each lunar cycle. However, such a dome precludes observations during the lunar day. Mirror temperature excursions can be reduced by incorporating thermal enclosures or shades in the design or by placing the telescope at a higher latitude.

Walker, Sherry T.

Integrated Bosch Process System Models for In-Situ Oxygen and Carbon Production

In-Situ Resource Utilization (ISRU) technology is a vital component to NASA’s mission of a sustainable presence on the Moon and Mars. Local resources can be leveraged to reduce resupply frequency and mass. Elements of the Bosch process, combined with the carbothermal reduction process, can produce oxygen on the lunar surface with minimal consumables. The Bosch process can also produce oxygen on the Martian surface by using the CO 2 -rich environment. Between both systems, adsorption pump, solar thermal energy, carbon formation reactor, and water recovery subsystems are modeled and integrated to create a functional model in MATLAB software. The model is used to simulate performance of the system and reduce mass, power, and volume requirements. This integrated system model provides a tool to scale ISRU technologies for oxygen and carbon production. The MATLAB model is created by developing a system of independent subsystem models that are solved for their quasi-steady state values which can be integrated with respect to time to determine the change in current states. A flexible time stepping method is used to ensure a high level of accuracy during periods of rapid change while still making use of a simple explicit integration method. The flexible time step is calculated for each independent subsystem and the minimum value from those is used as the overall time step. A flexible time step is calculated by dividing a resolution value, or the maximum change per time step, by the variables current rate of change. The maximum value from all points in space is used for subsystem models that contain multiple values. The process is done for every variable that is being monitored in each subsystem and the global minimum is used as that iteration’s timestep. Several assumptions used in the MATLAB model for fluid flow dynamics, such as 1-D gas flow through the sorption pump, are supported by modeling in Ansys Fluent software. The Lunar oxygen production system is outlined in Fig. 1. The carbothermal reduction subsystem uses solar energy to heat a mixture of lunar regolith and carbon powder to produce carbon monoxide. To begin, the carbon monoxide feeds to the modified Bosch subsystem along with hydrogen gas. The reactants then enter the carbon formation reactor where water and carbon powder are produced. Solar thermal energy is used to add energy to the reactor, but waste heat from the carbothermal process is another potential heat source. The water is collected and electrolyzed to produce hydrogen which reenters the Bosch subsystem, and the oxygen is stored for downstream use. The carbon powder is collected and feeds back into the carbothermal subsystem. The Martian oxygen production system uses the full Bosch process and is outlined in Fig 2. A CO 2 adsorption pump thermally cycles to scrub and pressurize CO 2 from the environment. Along with an initial supply of hydrogen, the reactants enter the Reverse Water Gas Shift Reactor (RWGSR) which produces carbon monoxide and water. Carbon monoxide and unreacted hydrogen enter the carbon formation reactor to produce water and carbon powder. The water is collected from both reactors and electrolyzed to reintroduce hydrogen and store oxygen for propellant production or life support. Carbon is removed from the carbon formation reactor and stored. The adsorption pump utilizes rapid cycle temperature swings within a stack of zeolite coated surfaces. The subsystem model solves 1-D quasi-steady conservation laws of the quasi-steady form, shown in Eq. 1, for the gas stream and heat exchange liquid to predict performance parameters such as breakthrough capacity and optimum cycle time. The source term S is used to capture interactions between the fluid flows and the sorbent. A quasi-steady-state scheme is used where no time derivatives appear in the governing equations, except for those in the source terms. This results in an autonomous system, where ∂F/∂x = ƒ(F). The fluxes F are provided at the inlet, and an explicit method is used to solve for the spatial distribution of F. The heat and mass flows to the sorbent are then extracted from the source terms. These flows are numerically integrated to produce a 1-D solution for the system’s state as a function of both time and space. The body of the adsorption pump is separated into two semi-independent models: the heat exchanger fluid flow and gas flow through the zeolite coated surfaces. Both models are solved using the above-described method to find a 1-D solution as a function of space and interact only once a timestep is taken. The interaction point is the sorbent through which all heat transfer between the two models must occur. Sorbent mass adsorption is calculated using the Lagergren model, shown in Eq. 2, where the transfer coefficient, λ D , is found by solving a system of nondimensionalized equations derived by using the heat and mass transfer analogy for transport phenomena. Using Grade 544 Type 13X zeolite as the sorbent material, the equilibrium concentration, θ eq , is calculated using the k-site Langmuir isotherm and fit parameters. Additionally, the enthalpy of adsorption used in the model is computed by interpolation of available data [1]. The subsystem model was validated using the Rapid Cycle Temperature Swing Adsorption (RC-TSA) pump. The solar thermal energy subsystem focuses on a solar concentrator concept with a heat exchanger to heat the reactants before entering the carbon formation reactor. The subsystem model assumes a fixed solar flux and reflector efficiency to calculate the reactant temperature given the incoming temperature, pressure, and exchanger geometry. The receiver is a custom manufactured series of copper blocks with serpentine channels to increase its surface area and the residence time of the reactants to heat up to 550 °C. The subsystem model was validated using a heat exchanger developed at NASA Glenn Research Center (GRC). The solar thermal energy subsystem focuses on a solar concentrator concept with a heat exchanger to heat the reactants before entering the carbon formation reactor. The subsystem model assumes a fixed solar flux and reflector efficiency to calculate the reactant temperature given the incoming temperature, pressure, and exchanger geometry. The receiver is a custom manufactured series of copper blocks with serpentine channels to increase its surface area and the residence time of the reactants to heat up to 550 °C. The subsystem model was validated using a heat exchanger developed at NASA Glenn Research Center (GRC).

In situ Resource Utilization

Orion Crew Module Landing System Simulation and Verification

NASA Langley Research Center (LaRC) has developed a comprehensive test and analysis program to evaluate the ability of LS-DYNA to model the materials and the phenomena involved in soil and water landing impacts of the Orion crew module. Elemental, scale boilerplate, and full-scale prototype testing is being conducted in support of the simulation verification and validation approach. Aspects of the simulations evaluated against test data include soil constitutive properties, water equations of state, and contact algorithms. Subsystems tested include airbags, crushable energy absorbing honeycomb materials, and energy absorbing seat support struts. The procedures, instrumentation, and general observations from each test series are presented. Plans for a series of swing tests of a full-scale boilerplate into a purpose-built water basin are described. Further plans for swing tests of flight-like prototypes into the water basin are noted.

Vassilakos, Gregory J.

A revised analysis of micron-sized particles detected near Saturn by the Voyager 2 plasma wave instrument

The impulsive noise that the plasma wave and radio astronomy instruments detected during the Voyager 2 swing by Saturn was attributed to dust grains striking the spacecraft. This report presents a reanalysis of the dust impacts recorded by the plasma wave instrument using an improved model for the response of the electric antenna to dust impacts. The fundamental assumption used in this analysis is that the voltage induced on the antenna is proportional to the mass of the impacting grain. Using the above assumption and the antenna response constants used at Uranus and Neptune, the following conclusions can be reached. The primary dust distribution consists of a 'disk' of particles that coincides with the equator plane and has a north-south thickness of 2-Delta zeta = 962 km. A less dense 'halo' with a north-south thickness of 2-Delta zeta = 3376 km surrounds the primary distribution. The dust particle sizes are of the order of 10 microns, assuming a mass density of 1 g/cu cm. The corresponding particle masses are of the order of 10(exp -9) g, and maximum number densities are of the order of 10(exp -2)/cu m. Most likely, the G ring is the dominate source since the particles were observed very close to that ring, namely at 2.86 R(sub S). Other sources, like nearby moons, are not ruled out especially when perturbations due to electromagnetic forces are included. The calculated optical depth differs by about a factor of 2 from photometric studies. The current particle masses, radii, and the effective north-south thickness of the particle distribution are larger than what Gurnett et al. (1983) reported by about 2, 1, and 1 orders of magnitude, respectively. This is attributed to the fact that the collection coefficient used in this study is smaller than what was used in Gurnett et al.'s earlier publication.

Tsintikidis, D.

Interannual and Decadal Variability of Summer Rainfall over South America

Using the CPC (Climate Prediction Center) Merged Analysis of Precipitation product along with the Goddard Earth Observing System reanalysis and the Climate Analysis Center sea surface temperature (SST) data, we conduct a diagnostic study of the interannual and decadal scale variability of summer rainfall over South America. Results show three leading modes of rainfall variation identified with interannual, decadal, and long-term trend variability. Together, these modes explain more than half the total variance. The first mode is highly correlated with El Nino/southern oscillation (ENSO), showing severe drought over Northeast Brazil and copious rainfall over the Ecuador coast and the area of Uruguay-Southern Brazil in El Nino years. This pattern is attributed to the large scale zonal shift of the Walker circulation and local Hadley cell anomaly induced by positive (negative) SST anomaly over the eastern (western) equatorial Pacific. In El Nino years, two convective belts indicated by upper tropospheric velocity potential trough and mid-tropospheric rising motion, which are somewhat symmetric about the equator, extend toward the northeast and the southeast into the tropical North and South Atlantic respectively. Sandwiched between the ascent is a region of descending motion over Northeast Brazil. The southern branch of the anomalous Hadley cell is dynamically linked to the increase of rainfall over Uruguay-Southern Brazil. The regional response of anomalous circulation shows a stronger South American summer monsoon and an enhanced (weakened) subtropical high over the South Atlantic (South Pacific) Ocean. The decadal variation displays a meridional shift of the Intertropical Convergence Zone (ITCZ), which is tie to the anomalous cross-equatorial SST gradient over the Atlantic and the eastern Pacific. In conjunction with this mode is a large scale mass swing between the polar regions and midlatitudes in both hemispheres. Over the South Atlantic and the South Pacific, the changes of the strength of the subtropical high and the associated surface wind are dynamically consistent with the distribution of local SST anomalies, suggesting the importance of the atmospheric forcing in the decadal time scale. The decadal mode also presents a weak summer monsoon in its positive phase, which reduces the moisture supply from the equatorial Atlantic and the Amazon Basin and results in negative rainfall anomalies over the central Andes and Gran Chaco. The long-term trend shows decrease of rainfall from the northwest coast to the southeast subtropical region and a southward shift of Atlantic ITCZ that leads to increased rainfall over northern and eastern Brazil. Our result shows a close link of this mode to the observed SST warming trend over the subtropical South Atlantic and a remote connection to the interdecadal SST variation over the extratropical North Atlantic found in previous studies.

Zhou, Jiayu

Modal Analysis of the Orion Capsule Two Parachute System

As discussed in Ref [1], it is apparent from flight tests that the system made up of two main parachutes and a capsule can undergo several distinct dynamical behaviors. The most significant and problematic of these is the pendulum mode in which the system develops a pronounced swinging motion with an amplitude of up to 24 deg. Large excursions away from vertical by the capsule could cause it to strike the ground at a large horizontal or vertical speed and jeopardize the safety of the astronauts during a crewed mission. In reference [1], Ali et al. summarized a series of efforts taken by the Capsule Parachute Assembly System (CPAS) Program to understand and mitigate the pendulum issue. The period of oscillation and location of the system's pivot point are determined from post-flight analysis. Other noticeable but benign modes include: 1) flyout (scissors) mode, where the parachutes move back and forth symmetrically with respect to the vertical axis similar to the motion of a pair of scissors; 2) maypole mode, where the two parachutes circle around the vertical axis at a nearly constant radius and period; and 3) breathing mode, in which deformation of the non-rigid canopies affects the axial acceleration of the system in an oscillatory manner. Because these modes are relatively harm- less, little effort has been devoted to analyzing them in comparison with the pendulum motion. Motions of the actual system made up of two parachutes and a capsule are extremely complicated due to nonlinearities and flexibility effects. Often it is difficult to obtain insight into the fundamental dynamics of the system by examining results from a multi-body simulation based on nonlinear equations of motion (EOMs). As a part of this study, the dynamics of each mode observed during flight is derived from first principles on an individual basis by making numerous simplifications along the way. The intent is to gain a better understanding into the behavior of the complex multi-body system by studying the reduced set of differential equations associated with each mode. This approach is analogous to the traditional modal analysis technique used to study airplane flight dynamics, in which the full nonlinear behavior of the airframe is decomposed into the phugoid and short period modes for the longitudinal dynamics and the spiral, roll-subsidence, and dutch-roll modes for the lateral dynamics. It is important to note that the study does not address the mechanisms that cause the system to transition from one mode to another, nor does it discuss motions during which two or more modes occur simultaneously.

Pei, J.