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An inverse dynamic method yielding flexible manipulator state trajectories

An inverse dynamic equation for a flexible manipulator is derived in a state form. By dividing the inverse system into the causal part and the anticausal part, torque is calculated in the time domain for a certain end point trajectory, as well as trajectories of all state variables. The open loop control of the inverse dynamic method shows an excellent result in simulation. For practical applications, a control strategy adapting feedback tracking control to the inverse dynamic feedforward control is illustrated, and its good experimental result is presented.

Kwon, Dong-Soo

An inverse dynamic method yielding flexible manipulator state trajectories

An inverse dynamic equation for a flexible manipulator is derived in a state form. By dividing the inverse system into the causal part and the anticausal part, one can calculate torque in the time domain for a certain end-point trajectory, as well as trajectories of all state variables. The open-loop control of the inverse dynamic method shows an excellent result in simulation. For practical applications, a control strategy adapting feedback tracking control to the inverse dynamic feedforward control is illustrated, and experimental results are presented.

Kwon, Dong-Soo

The ASAC Flight Segment and Network Cost Models

To assist NASA in identifying research art, with the greatest potential for improving the air transportation system, two models were developed as part of its Aviation System Analysis Capability (ASAC). The ASAC Flight Segment Cost Model (FSCM) is used to predict aircraft trajectories, resource consumption, and variable operating costs for one or more flight segments. The Network Cost Model can either summarize the costs for a network of flight segments processed by the FSCM or can be used to independently estimate the variable operating costs of flying a fleet of equipment given the number of departures and average flight stage lengths.

Kaplan, Bruce J.

NASA Tech Briefs, November 2011

The topics include: 1) Flight Test Results from the Rake Airflow Gage Experiment on the F-15B; 2) Telemetry and Science Data Software System; 3) CropEx Web-Based Agricultural Monitoring and Decision Support; 4) High-Performance Data Analysis Tools for Sun-Earth Connection Missions; 5) Experiment in Onboard Synthetic Aperture Radar Data Processing; 6) Microfabrication of a High-Throughput Nanochannel Delivery/Filtration System; 7) Improved Design and Fabrication of Hydrated-Salt Pills; 8) Monolithic Flexure Pre-Stressed Ultrasonic Horns; 9) Cryogenic Quenching Process for Electronic Part Screening; 10) Broadband Via-Less Microwave Crossover Using Microstrip-CPW Transitions; 11) Wheel-Based Ice Sensors for Road Vehicles; 12) G-DYN Multibody Dynamics Engine; 13) Multibody Simulation Software Testbed for Small-Body Exploration and Sampling; 14) Propulsive Reaction Control System Model; 15) Licklider Transmission Protocol Implementation; 16) Core Recursive Hierarchical Image Segmentation; 17) Two-Stage Centrifugal Fan; 18) Combined Structural and Trajectory Control of Variable-Geometry Planetary Entry Systems; 19) Pressure Regulator With Internal Ejector Circulation Pump, Flow and Pressure Measurement Porting, and Fuel Cell System Integration Options; 20) Temperature-Sensitive Coating Sensor Based on Hematite; 21) Standardization of a Volumetric Displacement Measurement for Two-Body Abrasion Scratch Test Data Analysis; 22) Detection of Carbon Monoxide Using Polymer-Carbon Composite Films; 23) Substituted Quaternary Ammonium Salts Improve Low-Temperature Performance of Double-Layer Capacitors; 24) Sustainably Sourced, Thermally Resistant, Radiation Hard Biopolymer; 25) Integrated Lens Antennas for Multi-Pixel Receivers; 26) 180-GHz Interferometric Imager; 27) Maturation of Structural Health Management Systems for Solid Rocket Motors; 28) Validating Phasing and Geometry of Large Focal Plane Arrays; 29) Transverse Pupil Shifts for Adaptive Optics Non-Common Path Calibration; 30) Qualification of Fiber Optic Cables for Martian Extreme Temperature Environments; 31) Solid-State Spectral Light Source System; 32) Multiple-Event, Single-Photon Counting Imaging Sensor; 33) Surface Modeling to Support Small-Body Spacecraft Exploration and Proximity Operations; and 34) Achieving Exact and Constant Turnaround Ratio in a DDS-Based Coherent Transponder.

Source record

Seasonal Variations of the James Webb Space Telescope Orbital Dynamics

While spacecraft orbital variations due to the Earth's tilt and orbital eccentricity are well-known phenomena, the implications for the James Webb Space Telescope present unique features. We investigate the variability of the observatory trajectory characteristics, and present an explanation of some of these effects using invariant manifold theory and local approximation of the dynamics in terms of the restricted three-body problem.

launch windows

Robust Path-following Controller for Multirotor Vehicles in Uncertain Wind Conditions

This paper presents simulations of L1 adaptive controller on a multirotor vehicle for compensation of convective winds. There are increasing efforts to utilize unmanned vehicles for fighting wildfires, but such vehicles need to be able to compensate for convective updrafts and other uncertainties (e.g., wind shear and turbulence) caused by the wildfire. Other application domains, such as urban air mobility, also must account for convective or uncertain winds present in urban microclimates. Geometric controllers have great tracking performance properties in environments without uncertainties, but the tracking performance degrades when wind disturbances and external loads are present in the environment. Introducing L1 adaptive control into the controller architecture compensates for these wind disturbances and reduces the tracking error caused by such disturbances. The controller architecture is implemented on a small quadrotor. The simulations demonstrate the advantages of the L1 adaptive augmentation for a sample figure-eight trajectory while encountering unknown variable wind conditions with an external load.

John L Bullock

Robust Path-following Controller for Multirotor Vehicles in Uncertain Wind Conditions

This paper presents simulations of L1 adaptive controller on a multirotor vehicle for compensation of convective winds. There are increasing efforts to utilize unmanned vehicles for fighting wildfires, but such vehicles need to be able to compensate for convective updrafts and other uncertainties (e.g., wind shear and turbulence) caused by the wildfire. Other application domains, such as urban air mobility, also must account for convective or uncertain winds present in urban microclimates. Geometric controllers have great tracking performance properties in environments without uncertainties, but the tracking performance degrades when wind disturbances and external loads are present in the environment. Introducing L1 adaptive control into the controller architecture compensates for these wind disturbances and reduces the tracking error caused by such disturbances. The controller architecture is implemented on a small quadrotor. The simulations demonstrate the advantages of the L1 adaptive augmentation for a sample figure-eight trajectory while encountering unknown variable wind conditions with an external load.

John Bullock

Mars entry-to-landing trajectory optimization and closed loop guidance

The guidance strategy of the Mars Rover Sample Return mission is presented in detail. Aeromaneuver versus aerobrake trades are examined, and an aerobrake analysis is presented which takes into account targeting, guidance, flight control, trajectory profile, delivery accuracy. An aeromaneuver analysis is given which includes the entry corridor, maneuver footprint, guidance, preentry phase, constant drag phase, equilibrium guide phase, variable drag phase, influence of trajectory profile on the entry flight loads, parachute deployment conditions and strategies, and landing accuracy. The Mars terminal descent phase is analyzed.

Ilgen, Marc R.

Variable mixture ratio performance through nitrogen augmentation

High/variable mixture ratio O2/H2 candidate engine cycles are examined for earth-to-orbit vehicle application. Engine performance and power balance information are presented for the candidate cycles relative to chamber pressure, bulk density, and mixture ratio. Included in the cycle screening are concepts where a third fluid (liquid nitrogen) is used to achieve a variable mixture ratio over the trajectory from liftoff to earth orbit. The third fluid cycles offer a very low risk, fully reusable, low operation cost alternative to high/variable mixture ratio bipropellant cycles. Variable mixture ratio engines with extendible nozzle are slightly lower performing than a single mixture ratio engine (MR = 7:1) with extendible nozzle. Dual expander engines (MR = 7:1) have slightly better performance than the single mixture ratio engine. Dual fuel dual expander engines offer a 16 percent improvement over the single mixture ratio engine.

Beichel, R.

A Time-Regularized, Multiple Gravity-Assist Low-Thrust, Bounded-Impulse Model for Trajectory Optimization

The multiple gravity assist low-thrust (MGALT) trajectory model combines the medium-fidelity Sims-Flanagan bounded-impulse transcription with a patched-conics flyby model and is an important tool for preliminary trajectory design. While this model features fast state propagation via Keplers equation and provides a pleasingly accurate estimation of the total mass budget for the eventual flight suitable integrated trajectory it does suffer from one major drawback, namely its temporal spacing of the control nodes. We introduce a variant of the MGALT transcription that utilizes the generalized anomaly from the universal formulation of Keplers equation as a decision variable in addition to the trajectory phase propagation time. This results in two improvements over the traditional model. The first is that the maneuver locations are equally spaced in generalized anomaly about the orbit rather than time. The second is that the Kepler propagator now has the generalized anomaly as its independent variable instead of time and thus becomes an iteration-free propagation method. The new algorithm is outlined, including the impact that this has on the computation of Jacobian entries for numerical optimization, and a motivating application problem is presented that illustrates the improvements that this model has over the traditional MGALT transcription.

Optimization

A Time-Regularized Multiple Gravity-Assist Low-Thrust Bounded-Impulse Model for Trajectory Optimization

The multiple gravity assist low-thrust (MGALT) trajectory model combines the medium-fidelity Sims-Flanagan bounded-impulse transcription with a patched-conics flyby model and is an important tool for preliminary trajectory design. While this model features fast state propagation via Kepler's equation and provides a pleasingly accurate estimation of the total mass budget for the eventual flight-suitable integrated trajectory it does suffer from one major drawback, namely its temporal spacing of the control nodes. We introduce a variant of the MGALT transcription that utilizes the generalized anomaly from the universal formulation of Kepler's equation as a decision variable in addition to the trajectory phase propagation time. This results in two improvements over the traditional model. The first is that the maneuver locations are equally spaced in generalized anomaly about the orbit rather than time. The second is that the Kepler propagator now has the generalized anomaly as its independent variable instead of time and thus becomes an iteration-free propagation method. The new algorithm is outlined, including the impact that this has on the computation of Jacobian entries for numerical optimization, and a motivating application problem is presented that illustrates the improvements that this model has over the traditional MGALT transcription.

Optimization

Straight Ahead in Microgravity

This joint ESA-NASA study will address adaptive changes in spatial orientation related to the subjective straight ahead, and the use of a vibrotactile sensory aid to reduce perceptual errors. The study will be conducted before and after long-duration expeditions to the International Space Station (ISS) to examine how spatial processing of target location is altered following exposure to microgravity. This project specifically addresses the sensorimotor research gap "What are the changes in sensorimotor function over the course of a mission?" Six ISS crewmembers will be requested to participate in three preflight sessions (between 120 and 60 days prior to launch) and then three postflight sessions on R+0/1 day, R+4 +/-2 days, and R+8 +/-2 days. The three specific aims include: (a) fixation of actual and imagined target locations at different distances; (b) directed eye and arm movements along different spatial reference frames; and (c) the vestibulo-ocular reflex during translation motion with fixation targets at different distances. These measures will be compared between upright and tilted conditions. Measures will then be compared with and without a vibrotactile sensory aid that indicates how far one has tilted relative to the straight-ahead direction. The flight study was been approved by the medical review boards and will be implemented in the upcoming Informed Crew Briefings to solicit flight subject participation. Preliminary data has been recorded on 6 subjects during parabolic flight to examine the spatial coding of eye movements during roll tilt relative to perceived orientations while free-floating during the microgravity phase of parabolic flight or during head tilt in normal gravity. Binocular videographic recordings obtained in darkness allowed us to quantify the mean deviations in gaze trajectories along both horizontal and vertical coordinates relative to the aircraft and head orientations. During some parabolas, a vibrotactile sensory aid provided feedback of body orientation relative to the plane coordinates. RESULTS Both variability and curvature of gaze trajectories increased during roll tilt compared to the upright position. The saccades were less accurate during parabolic flight compared to measurements obtained in normal gravity. Although subjects were instructed to look off in the distance while performing the eye movements, fixation distance varied with vertical gaze direction independent of whether the saccades were made along perceived aircraft or head orientations. The increased errors in gaze trajectories along both perceived orientations during microgravity can be attributed to the otolith's role in spatial coding of eye movements. A change in an individual's egocentric reference might have negative consequences on evaluating the direction of an approaching object or on the accuracy of reaching movements or locomotion. Consequently, investigating how microgravity affects the target location will have theoretical, operational and even clinical implications for future space exploration missions. The use of vibrotactile feedback as a sensorimotor countermeasure is applicable to balance therapy applications for vestibular loss patients and the elderly to mitigate risks due to loss of orientation.

Wood, S. J.

Rapid Calculation of Spacecraft Trajectories Using Efficient Taylor Series Integration

A variable-order, variable-step Taylor series integration algorithm was implemented in NASA Glenn's SNAP (Spacecraft N-body Analysis Program) code. SNAP is a high-fidelity trajectory propagation program that can propagate the trajectory of a spacecraft about virtually any body in the solar system. The Taylor series algorithm's very high order accuracy and excellent stability properties lead to large reductions in computer time relative to the code's existing 8th order Runge-Kutta scheme. Head-to-head comparison on near-Earth, lunar, Mars, and Europa missions showed that Taylor series integration is 15.8 times faster than Runge- Kutta on average, and is more accurate. These speedups were obtained for calculations involving central body, other body, thrust, and drag forces. Similar speedups have been obtained for calculations that include J2 spherical harmonic for central body gravitation. The algorithm includes a step size selection method that directly calculates the step size and never requires a repeat step. High-order Taylor series integration algorithms have been shown to provide major reductions in computer time over conventional integration methods in numerous scientific applications. The objective here was to directly implement Taylor series integration in an existing trajectory analysis code and demonstrate that large reductions in computer time (order of magnitude) could be achieved while simultaneously maintaining high accuracy. This software greatly accelerates the calculation of spacecraft trajectories. At each time level, the spacecraft position, velocity, and mass are expanded in a high-order Taylor series whose coefficients are obtained through efficient differentiation arithmetic. This makes it possible to take very large time steps at minimal cost, resulting in large savings in computer time. The Taylor series algorithm is implemented primarily through three subroutines: (1) a driver routine that automatically introduces auxiliary variables and sets up initial conditions and integrates; (2) a routine that calculates system reduced derivatives using recurrence relations for quotients and products; and (3) a routine that determines the step size and sums the series. The order of accuracy used in a trajectory calculation is arbitrary and can be set by the user. The algorithm directly calculates the motion of other planetary bodies and does not require ephemeris files (except to start the calculation). The code also runs with Taylor series and Runge-Kutta used interchangeably for different phases of a mission.

Scott, James R.

Physical Invariants of Intelligence

A program of research is dedicated to development of a mathematical formalism that could provide, among other things, means by which living systems could be distinguished from non-living ones. A major issue that arises in this research is the following question: What invariants of mathematical models of the physics of systems are (1) characteristic of the behaviors of intelligent living systems and (2) do not depend on specific features of material compositions heretofore considered to be characteristic of life? This research at earlier stages has been reported, albeit from different perspectives, in numerous previous NASA Tech Briefs articles. To recapitulate: One of the main underlying ideas is to extend the application of physical first principles to the behaviors of living systems. Mathematical models of motor dynamics are used to simulate the observable physical behaviors of systems or objects of interest, and models of mental dynamics are used to represent the evolution of the corresponding knowledge bases. For a given system, the knowledge base is modeled in the form of probability distributions and the mental dynamics is represented by models of the evolution of the probability densities or, equivalently, models of flows of information. At the time of reporting the information for this article, the focus of this research was upon the following aspects of the formalism: Intelligence is considered to be a means by which a living system preserves itself and improves its ability to survive and is further considered to manifest itself in feedback from the mental dynamics to the motor dynamics. Because of the feedback from the mental dynamics, the motor dynamics attains quantum-like properties: The trajectory of the physical aspect of the system in the space of dynamical variables splits into a family of different trajectories, and each of those trajectories can be chosen with a probability prescribed by the mental dynamics. From a slightly different perspective, the mechanism of decision-making is feedback from the mental dynamics to the motor dynamics, and this mechanism provides a quantum-like collapse of a random motion into an appropriate deterministic state, such that entropy undergoes a pronounced decrease. The existence of this mechanism is considered to be an invariant of intelligent behavior of living systems, regardless of the origins and material compositions of the systems.

Zak, Michail

Interplanetary trajectory optimization

A procedure for minimizing total impulsive Delta-V for constrained multiple-flyby trajectories, which was originally developed for application to satellite tours, has been modified for application to interplanetary trajectories. The modification includes adding to the cost function the Delta-V required to escape from a parking orbit about the launch planet and the Delta-V required for insertion into orbit about the arrival planet. The hyperbolic excess velocity vector with respect to the launch planet and the launch date have been added to the set of independent variables for the optimization. Each trajectory originates at departure from the parking orbit rather than at a fixed position in space, as is the case for the satellite tour application. The multi-conic trajectory propagation techniques and the Newton optimization algorithm of the original method have been retained. Examples of the application of this new method are given for several types of Galileo interplanetary trajectory options, including Mars powered flyby, broken plane, VEGA, and Delta VEGA trajectories.

Damario, L. A.

Optimum Interplanetary Rendezvous Trajectories With Powerlimited Vehicles

The optimum-thrust equations for both variable and constant thrust are presented. These thrust programs are used to generate rendezvous trajectories from the Earth to Mars for various flight times and launch dates during the years 1968-71. The manner in which the propulsion requirements vary with flight time and launch date are considered, and a comparison of vehicle performance using the variable- and constant-thrust programs is presented. The optimization of the pro- pulsion system parameters is discussed, and the existence of optimum launch dates is interpreted in terms of certain transversality conditions derivable from the calculus of variations. A brief comparison of the advanced propulsion vehicle and the ballistic vehicle propulsion requirements is made for Earth-Mars rendezvous trajectories. An appendix considering the analytical basis for this work is included.

INTERPLANETARY TRAJECTORY

Study of Some Planetary Atmospheres Features by Probe Entry and Descent Simulations

Characterization of planetary atmospheres is analyzed by its effects in the entry and descent trajectories of probes. Emphasis is on the most important variables that characterize atmospheres e.g. density profile with altitude. Probe trajectories are numerically determined with ENTRAP, a developing multi-purpose computational tool for entry and descent trajectory simulations capable of taking into account many features and perturbations. Real data from Mars Pathfinder mission is used. The goal is to be able to determine more accurately the atmosphere structure by observing real trajectories and what changes are to expect in probe descent trajectories if atmospheres have different properties than the ones assumed initially.

Gil, P. J. S.

Autonomous manipulation on a robot: Summary of manipulator software functions

A six degree-of-freedom computer-controlled manipulator is examined, and the relationships between the arm's joint variables and 3-space are derived. Arm trajectories using sequences of third-degree polynomials to describe the time history of each joint variable are presented and two approaches to the avoidance of obstacles are given. The equations of motion for the arm are derived and then decomposed into time-dependent factors and time-independent coefficients. Several new and simplifying relationships among the coefficients are proven. Two sample trajectories are analyzed in detail for purposes of determining the most important contributions to total force in order that relatively simple approximations to the equations of motion can be used.

Lewis, R. A.