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Control of nonlinear systems with applications to constrained robots and spacecraft attitude stabilization

This thesis is organized in two parts. In Part 1, control systems described by a class of nonlinear differential and algebraic equations are introduced. A procedure for local stabilization based on a local state realization is developed. An alternative approach to local stabilization is developed based on a classical linearization of the nonlinear differential-algebraic equations. A theoretical framework is established for solving a tracking problem associated with the differential-algebraic system. First, a simple procedure is developed for the design of a feedback control law which ensures, at least locally, that the tracking error in the closed loop system lies within any given bound if the reference inputs are sufficiently slowly varying. Next, by imposing additional assumptions, a procedure is developed for the design of a feedback control law which ensures that the tracking error in the closed loop system approaches zero exponentially for reference inputs which are not necessarily slowly varying. The control design methodologies are used for simultaneous force and position control in constrained robot systems. The differential-algebraic equations are shown to characterize the slow dynamics of a certain nonlinear control system in nonstandard singularly perturbed form. In Part 2, the attitude stabilization (reorientation) of a rigid spacecraft using only two control torques is considered. First, the case of momentum wheel actuators is considered. The complete spacecraft dynamics are not controllable. However, the spacecraft dynamics are small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized using continuous feedback, but a discontinuous feedback control strategy is constructed. Next, the case of gas jet actuators is considered. If the uncontrolled principal axis is not an axis of symmetry, the complete spacecraft dynamics are small time locally controllable. However, the spacecraft attitude cannot be asymptotically stabilized using continuous feedback, but a discontinuous stabilizing feedback control strategy is constructed. If the uncontrolled principal axis is an axis of symmetry, the complete spacecraft dynamics cannot be stabilized. However, the spacecraft dynamics are small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized using continuous feedback, but again a discontinuous feedback control strategy is constructed.

Krishnan, Hariharan↗

Human and Robotic Exploration of Near-Earth Objects

A study in late 2006 was sponsored by the Advanced Projects Office within NASA's Constellation Program to examine the feasibility of sending the Orion Crew Exploration Vehicle to a near-Earth object (NEO). The ideal mission profile would involve two or three astronauts on a 90 to 180 day flight, which would include a 7 to 14 day stay for proximity operations at the target NEO. More recently U.S. President Obama stated on April 15, 2010 that the next goal for human spaceflight will be to send human beings to a near-Earth asteroid by 2025. Given this direction from the White House, NASA has been involved in studying various strategies for NEO exploration in order to follow U.S. space exploration policy. Prior to sending a human mission, a series of robotic spacecraft would be launched to reduce the risk to crew, and enhance the planning for the proximity and surface operations at the NEO. The human mission would ideally follow five or more years later. This mission would be the first human expedition to an interplanetary body beyond the Earth-Moon system and would prove useful for testing technologies required for human missions to Mars and other solar system destinations. Piloted missions to NEOs would undoubtedly provide a great deal of technical and engineering data on spacecraft operations for future human space exploration while conducting in-depth scientific investigations of these primitive objects. The main scientific advantage of sending piloted missions to NEOs would be the flexibility of the crew to perform tasks and to adapt to situations in real time. A crewed vehicle would be able to test several different sample collection techniques and target specific areas of interest via extra-vehicular activities (EVAs) more efficiently than robotic spacecraft. Such capabilities greatly enhance the scientific return from these missions to NEOs, destinations vital to understanding the evolution and thermal histories of primitive bodies during the formation of the early solar system. Data collected from these missions would help constrain the suite of materials possibly delivered to the early Earth, and would identify potential source regions from which NEOs originate. In addition, the resulting scientific investigations would refine designs for future extraterrestrial resource extraction and utilization, and assist in the development of hazard mitigation techniques for planetary defense.

Abell, Paul A.↗

GPS/MEMS IMU/Microprocessor Board for Navigation

A miniaturized instrumentation package comprising a (1) Global Positioning System (GPS) receiver, (2) an inertial measurement unit (IMU) consisting largely of surface-micromachined sensors of the microelectromechanical systems (MEMS) type, and (3) a microprocessor, all residing on a single circuit board, is part of the navigation system of a compact robotic spacecraft intended to be released from a larger spacecraft [e.g., the International Space Station (ISS)] for exterior visual inspection of the larger spacecraft. Variants of the package may also be useful in terrestrial collision-detection and -avoidance applications. The navigation solution obtained by integrating the IMU outputs is fed back to a correlator in the GPS receiver to aid in tracking GPS signals. The raw GPS and IMU data are blended in a Kalman filter to obtain an optimal navigation solution, which can be supplemented by range and velocity data obtained by use of (l) a stereoscopic pair of electronic cameras aboard the robotic spacecraft and/or (2) a laser dynamic range imager aboard the ISS. The novelty of the package lies mostly in those aspects of the design of the MEMS IMU that pertain to controlling mechanical resonances and stabilizing scale factors and biases.

Gender, Thomas K.↗

Alignment Jig for the Precise Measurement of THz Radiation

A miniaturized instrumentation package comprising a (1) Global Positioning System (GPS) receiver, (2) an inertial measurement unit (IMU) consisting largely of surface-micromachined sensors of the microelectromechanical systems (MEMS) type, and (3) a microprocessor, all residing on a single circuit board, is part of the navigation system of a compact robotic spacecraft intended to be released from a larger spacecraft [e.g., the International Space Station (ISS)] for exterior visual inspection of the larger spacecraft. Variants of the package may also be useful in terrestrial collision-detection and -avoidance applications. The navigation solution obtained by integrating the IMU outputs is fed back to a correlator in the GPS receiver to aid in tracking GPS signals. The raw GPS and IMU data are blended in a Kalman filter to obtain an optimal navigation solution, which can be supplemented by range and velocity data obtained by use of (l) a stereoscopic pair of electronic cameras aboard the robotic spacecraft and/or (2) a laser dynamic range imager aboard the ISS. The novelty of the package lies mostly in those aspects of the design of the MEMS IMU that pertain to controlling mechanical resonances and stabilizing scale factors and biases.

Javadi, Hamid H.↗

Comparing Consider-Covariance Analysis with Sigma-Point Consider Filter and Linear-Theory Consider Filter Formulations

Recent literature in applied estimation theory reflects growing interest in the sigma-point (also called unscented ) formulation for optimal sequential state estimation, often describing performance comparisons with extended Kalman filters as applied to specific dynamical problems [c.f. 1, 2, 3]. Favorable attributes of sigma-point filters are described as including a lower expected error for nonlinear even non-differentiable dynamical systems, and a straightforward formulation not requiring derivation or implementation of any partial derivative Jacobian matrices. These attributes are particularly attractive, e.g. in terms of enabling simplified code architecture and streamlined testing, in the formulation of estimators for nonlinear spaceflight mechanics systems, such as filter software onboard deep-space robotic spacecraft. As presented in [4], the Sigma-Point Consider Filter (SPCF) algorithm extends the sigma-point filter algorithm to the problem of consider covariance analysis. Considering parameters in a dynamical system, while estimating its state, provides an upper bound on the estimated state covariance, which is viewed as a conservative approach to designing estimators for problems of general guidance, navigation and control. This is because, whether a parameter in the system model is observable or not, error in the knowledge of the value of a non-estimated parameter will increase the actual uncertainty of the estimated state of the system beyond the level formally indicated by the covariance of an estimator that neglects errors or uncertainty in that parameter. The equations for SPCF covariance evolution are obtained in a fashion similar to the derivation approach taken with standard (i.e. linearized or extended) consider parameterized Kalman filters (c.f. [5]). While in [4] the SPCF and linear-theory consider filter (LTCF) were applied to an illustrative linear dynamics/linear measurement problem, in the present work examines the SPCF as applied to nonlinear sequential consider covariance analysis, i.e. in the presence of nonlinear dynamics and nonlinear measurements. A simple SPCF for orbit determination, exemplifying an algorithm hosted in the guidance, navigation and control (GN&C) computer processor of a hypothetical robotic spacecraft, was implemented, and compared with an identically-parameterized (standard) extended, consider-parameterized Kalman filter. The onboard filtering scenario examined is a hypothetical spacecraft orbit about a small natural body with imperfectly-known mass. The formulations, relative complexities, and performances of the filters are compared and discussed.

Lisano, Michael E.↗

NASA’s Space Launch System: Enabling a New Generation of Lunar Exploration

Following two decades of operational experience in low-Earth orbit (LEO), NASA has turned its focus once again to deep space exploration. The Agency is building the Space Launch System (SLS) to take astronauts and cargo to the Moon and send robotic spacecraft deep into the solar system. Offering unmatched performance, departure energy and payload capacity, SLS is designed to evolve into progressively more powerful configurations, enabling a new generation of human exploration of the Moon in preparation for future missions to Mars. The first build of the Block 1 vehicle is nearly complete for Exploration Mission-1 (EM-1), the first integrated flight of SLS and the Orion crew vehicle. EM-1 will send an uncrewed Orion to a distant retrograde lunar orbit in order to test and verify new systems, and along the way will deploy 13 6U-class CubeSats in deep space along the upper stage disposal trajectory after separation from Orion. The Agency’s current plans call for the first three missions on the SLS manifest to utilize the Block 1 vehicle in crew and cargo configurations. A more powerful evolved vehicle, Block 1B, will provide additional mass and volume performance using a new Exploration Upper Stage (EUS). Block 1B will lift 34 to 40 metric tons (t) to trans-lunar injection (TLI), depending on crew or cargo configuration. The Block 1B crew configuration will offer as much payload volume as industry-standard 5 m-diameter fairings to co-manifested payloads in a Universal Stage Adapter (USA). The Block 1B cargo variant will accommodate 8.4 meter-diameter fairings in 62.7-foot (19.1 meter) or 90-foot (27.4 meter) lengths. Adding smallsat secondary payloads to ride along with primary and co-manifested payloads on future flights may be possible, depending on mass margins. Leveraging a flight-proven, well-understood propulsion system, SLS’s flexible architecture, unmatched performance and expansive payload accommodations will open exciting new mission possibilities in deep space. Launches of habitat modules for NASA’s new Gateway lunar outpost, the next generation of robotic spacecraft to the far reaches of the solar system, large-aperture deep space telescopes, probes to interstellar space and the return of astronauts to the Moon are all possible with SLS.

Creech, Stephen D.↗

Avionics for a Small Robotic Inspection Spacecraft

A report describes the tentative design of the avionics of the Mini-AERCam -- a proposed 7.5-in. (approximately 19-cm)-diameter spacecraft that would contain three digital video cameras to be used in visual inspection of the exterior of a larger spacecraft (a space shuttle or the International Space Station). The Mini-AERCam would maneuver by use of its own miniature thrusters under radio control by astronauts inside the larger spacecraft. The design of the Mini-AERCam avionics is subject to a number of constraints, most of which can be summarized as severely competing requirements to maximize radiation hardness and maneuvering, image-acquisition, and data-communication capabilities while minimizing cost, size, and power consumption. The report discusses the design constraints, the engineering approach to satisfying the constraints, and the resulting iterations of the design. The report places special emphasis on the design of a flight computer that would (1) acquire position and orientation data from a Global Positioning System receiver and a microelectromechanical gyroscope, respectively; (2) perform all flight-control (including thruster-control) computations in real time; and (3) control video, tracking, power, and illumination systems.

Abbott, Larry↗

Vibration damping of the Cassini spacecraft structure

Cassini is a large robotic spacecraft currently under development at the Jet Propulsion Laboratory (JPL) whose interplanetary scientific mission is to explore Saturn, its ring, and its moons. Cassini is scheduled to launch on a Titan IV rocket with a Centaur upper stage booster, and will be protected during ascent through the atmosphere by a lightweight aluminum payload fairing (PLF). As a result of the extreme noise levels generated by the powerful Titan IV at liftoff, and the acoustic transparency of the PLF, Cassini is predicted to experience sever acoustic levels. Furthermore, the high acoustic levels, coupled with the size and configuration of the spacecraft, will induce unacceptable random vibration levels on the structure and critical spacecraft components. Studies showed that the use of Tuned Vibration Absorbers (TVAs) would be effective in reducing vibration. A series of reverberant acoustic tests were performed on a partial development test model (DTM) of Cassini to evaluate the effectiveness of TVAs in reducing the structural vibration. The test results showed that significant vibration attenuation was achieved.

vibration damping↗

The Synergistic Engineering Environment

The Synergistic Engineering Environment (SEE) is a system of software dedicated to aiding the understanding of space mission operations. The SEE can integrate disparate sets of data with analytical capabilities, geometric models of spacecraft, and a visualization environment, all contributing to the creation of an interactive simulation of spacecraft. Initially designed to satisfy needs pertaining to the International Space Station, the SEE has been broadened in scope to include spacecraft ranging from those in low orbit around the Earth to those on deep-space missions. The SEE includes analytical capabilities in rigid-body dynamics, kinematics, orbital mechanics, and payload operations. These capabilities enable a user to perform real-time interactive engineering analyses focusing on diverse aspects of operations, including flight attitudes and maneuvers, docking of visiting spacecraft, robotic operations, impingement of spacecraft-engine exhaust plumes, obscuration of instrumentation fields of view, communications, and alternative assembly configurations. .

Cruz, Jonathan↗

Electronic Brain Design for Advanced Microspacecraft

A brief history of NASA robotic spacecraft computing architectures is given. Changing needs driving changes in features (10x reduction in cost, various increases in capability, 10x to 100x reduction in power, mass and volume) for spacecraft computing are discussed. A scaleable, parallel/neural computing architecture which addresses these changes is proposed. Evaluation of some of this architecture's components is detailed. Finally, future directions of exploration for this spacecraft computing architecture are considered.

robotic↗

Mathematical Model Development and Experimental Verification of Electromagnetic Force Actuators for use in Space Applications

This technical memorandum shows the development of the mathematics needed to model several types of electromagnetic force actuators that may be of interest for use in space applications. The actuators described are capable of providing attractive, repulsive, and longitudinal forces between the actuator and a variety of metal surfaces. Potential applications for these propellant free actuators include spacecraft docking, in-space fabrication, robotic spacecraft inspection and servicing, deflection of metallic debris, and interaction with iron core asteroids (e.g., landing, repelling, and relocating).

Robert C. Youngquist↗

Nonlinear Dynamic Behavior in the Cassini Spacecraft Modal Survey

In October 1997, the 6-ton robotic spacecraft, Cassini, will lift off from Cape Canaveral atop a Titan IV B rocket, beginning a 7-year journey to Saturn. Upon completion of that voyage, Cassini will send the Huygens probe into the atmosphere of Saturn's largest moon, Titan. Cassini will then spend years studying Saturn's vast realm of rings, icy moons, and magnetic fields. The size and complexity of this endeavor mandates the involvement of many organizations. The Jet Propulsion Laboratory (JPL) manages the project for NASA and is responsible for the spacecraft design, development, and assembly. The NASA Lewis Research Center is the launch system integrator. As is typical for such a spacecraft, a test-verified finite element model is required for loads analysis. JPL had responsibility for the Cassini modal survey and the development of the spacecraft test-verified finite element model. Test verification is a complex and sometimes subjective process. Because of this, NASA Lewis independently verified and validated the Cassini spacecraft modal survey.

Carney, Kelly S.↗

Catching a Rolling Stone: Dynamics and Control of a Spacecraft and an Asteroid

In a recent report, a robotic spacecraft mission is proposed for the purpose of collecting a small asteroid, or a small part of a large one, and transporting it to an orbit in the Earth-Moon system. Such an undertaking will require solutions to many of the engineering problems associated with deflection of an asteroid that poses a danger to Earth. In both cases, it may be necessary for a spacecraft to approach an asteroid from a nearby position, hover for some amount of time, move with the same angular velocity as the asteroid, descend, perhaps ascend, and finally arrest the angular velocity of the asteroid. Dynamics and control in each of these activities is analyzed in order to determine the velocity increments and control torque that must be provided by a reaction control system, and the mass of the propellant that will be consumed. Two attitude control algorithms are developed, one to deal with synchronizing the spacecraft s angular velocity with that of the asteroid, and the other to arrest the asteroid s angular velocity. A novel approach is proposed for saving fuel in the latter case.

Roithmayr, Carlos M.↗

Dshell++: A Component Based, Reusable Space System Simulation Framework

This paper describes the multi-mission Dshell++ simulation framework for high fidelity, physics-based simulation of spacecraft, robotic manipulation and mobility systems. Dshell++ is a C++/Python library which uses modern script driven object-oriented techniques to allow component reuse and a dynamic run-time interface for complex, high-fidelity simulation of spacecraft and robotic systems. The goal of the Dshell++ architecture is to manage the inherent complexity of physicsbased simulations while supporting component model reuse across missions. The framework provides several features that support a large degree of simulation configurability and usability.

Software↗

NASA Tech Briefs, February 2004

Topics include: Simulation Testing of Embedded Flight Software; Improved Indentation Test for Measuring Nonlinear Elasticity; Ultraviolet-Absorption Spectroscopic Biofilm Monitor; Electronic Tongue for Quantitation of Contaminants in Water; Radar for Measuring Soil Moisture Under Vegetation; Modular Wireless Data-Acquisition and Control System; Microwave System for Detecting Ice on Aircraft; Routing Algorithm Exploits Spatial Relations; Two-Finger EKG Method of Detecting Evasive Responses; Updated System-Availability and Resource-Allocation Program; Routines for Computing Pressure Drops in Venturis; Software for Fault-Tolerant Matrix Multiplication; Reproducible Growth of High-Quality Cubic-SiC Layers; Nonlinear Thermoelastic Model for SMAs and SMA Hybrid Composites; Liquid-Crystal Thermosets, a New Generation of High-Performance Liquid-Crystal Polymers; Formulations for Stronger Solid Oxide Fuel-Cell Electrolytes; Simulation of Hazards and Poses for a Rocker-Bogie Rover; Autonomous Formation Flight; Expandable Purge Chambers Would Protect Cryogenic Fittings; Wavy-Planform Helicopter Blades Make Less Noise; Miniature Robotic Spacecraft for Inspecting Other Spacecraft; Miniature Ring-Shaped Peristaltic Pump; Compact Plasma Accelerator; Improved Electrohydraulic Linear Actuators; A Software Architecture for Semiautonomous Robot Control; Fabrication of Channels for Nanobiotechnological Devices; Improved Thin, Flexible Heat Pipes; Miniature Radioisotope Thermoelectric Power Cubes; Permanent Sequestration of Emitted Gases in the Form of Clathrate Hydrates; Electrochemical, H2O2-Boosted Catalytic Oxidation System; Electrokinetic In Situ Treatment of Metal-Contaminated Soil; Pumping Liquid Oxygen by Use of Pulsed Magnetic Fields; Magnetocaloric Pumping of Liquid Oxygen; Tailoring Ion-Thruster Grid Apertures for Greater Efficiency; and Lidar for Guidance of a Spacecraft or Exploratory Robot.

Source record↗

Automation Rover for Extreme Environments

Almost 2,300 years ago the ancient Greeks built the Antikythera automaton. This purely mechanical computer accurately predicted past and future astronomical events long before electronics existed1. Automata have been credibly used for hundreds of years as computers, art pieces, and clocks. However, in the past several decades automata have become less popular as the capabilities of electronics increased, leaving them an unexplored solution for robotic spacecraft. The Automaton Rover for Extreme Environments (AREE) proposes an exciting paradigm shift from electronics to a fully mechanical system, enabling longitudinal exploration of the most extreme environments within the solar system.

automata↗

Current Design Criteria for MMOD Impact of Metallic Pressurized Tanks

Most spacecraft have at least one pressurized vessel on board. For robotic spacecraft, it is usually a liquid propellant tank or battery. For human spacecraft, there are also pressurized living quarters and life-support systems. One of the design considerations of such spacecraft is the possible damage that might occur in the event of an on-orbit impact by a micrometeoroid or orbital debris (MMOD) particle. While considerable energy and effort has been expended in the study of the response of nonpressurized spacecraft components to these kinds of impacts, relatively few studies have been conducted on the pressurized elements of such spacecraft. In addition, the design criteria currently used by the National Aeronautics and Space Administration (NASA) for pressurized tanks operating in the MMOD environment have not been tested or scrutinized since they were first proposed nearly 45 years ago. This paper reviews current NASA design criteria for pressurized vessels and offers suggestions for next steps in their further development.

orbital debris↗