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NASA NTRS2016

Trajectory Design Employing Convex Optimization for Landing on Irregularly Shaped Asteroids

Mission proposals that land on asteroids are becoming popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site. The problem under investigation is how to design a fuel-optimal powered descent trajectory that can be quickly computed on- board the spacecraft, without interaction from ground control. An optimal trajectory designed immediately prior to the descent burn has many advantages. These advantages include the ability to use the actual vehicle starting state as the initial condition in the trajectory design and the ease of updating the landing target site if the original landing site is no longer viable. For long trajectories, the trajectory can be updated periodically by a redesign of the optimal trajectory based on current vehicle conditions to improve the guidance performance. One of the key drivers for being completely autonomous is the infrequent and delayed communication between ground control and the vehicle. Challenges that arise from designing an asteroid powered descent trajectory include complicated nonlinear gravity fields, small rotating bodies and low thrust vehicles. There are two previous studies that form the background to the current investigation. The first set looked in-depth at applying convex optimization to a powered descent trajectory on Mars with promising results.1, 2 This showed that the powered descent equations of motion can be relaxed and formed into a convex optimization problem and that the optimal solution of the relaxed problem is indeed a feasible solution to the original problem. This analysis used a constant gravity field. The second area applied a successive solution process to formulate a second order cone program that designs rendezvous and proximity operations trajectories.3, 4 These trajectories included a Newtonian gravity model. The equivalence of the solutions between the relaxed and the original problem is theoretically established. The proposed solution for designing the asteroid powered descent trajectory is to use convex optimization, a gravity model with higher fidelity than Newtonian, and an iterative solution process to design the fuel optimal trajectory. The solution to the convex optimization problem is the thrust profile, magnitude and direction, that will yield the minimum fuel trajectory for a soft landing at the target site, subject to various mission and operational constraints. The equations of motion are formulated in a rotating coordinate system and includes a high fidelity gravity model. The vehicle's thrust magnitude can vary between maximum and minimum bounds during the burn. Also, constraints are included to ensure that the vehicle does not run out of propellant, or go below the asteroid's surface, and any vehicle pointing requirements. The equations of motion are discretized and propagated with the trapezoidal rule in order to produce equality constraints for the optimization problem. These equality constraints allow the optimization algorithm to solve the entire problem, without including a propagator inside the optimization algorithm.

Pinson, Robin M.↗

NASA NTRS1978

Numerical spatial marching techniques for estimating duct attenuation and source pressure profiles

A numerical method was developed that could predict the pressure distribution of a ducted source from far field pressure inputs. Using an initial value formulation, the two-dimensional homogeneous Helmholtz wave equation (no steady flow) was solved using explicit marching techniques. The Von Neumann method was used to develop relationships which describe how sound frequency and grid spacing effect numerical stability. At the present time, stability considerations limit the approach to high frequency sound. Sample calculations for both hard and soft wall ducts compare favorably to known boundary value solutions. In addition, assuming that reflections in the duct are small, this initial value approach was successfully used to determine the attenuation of a straight soft wall duct. Compared to conventional finite difference or finite element boundary value approaches, the numerical marching technique is orders of magnitude shorter in computation time and required computer storage and can be easily employed in problems involving high frequency sound.

Baumeister, K. J.↗

NASA NTRS1978

Numerical spatial marching techniques for estimating duct attenuation and source pressure profiles

A numerical method is developed that could predict the pressure distribution of a ducted source from far-field pressure inputs. Using an initial value formulation, the two-dimensional homogeneous Helmholtz wave equation (no steady flow) is solved using explicit marching techniques. The Von Neumann method is used to develop relationships which describe how sound frequency and grid spacing effect numerical stability. At the present time, stability considerations limit the approach to high frequency sound. Sample calculations for both hard and soft wall ducts compare favorably to known boundary value solutions. In addition, assuming that reflections in the duct are small, this initial value approach is successfully used to determine the attenuation of a straight soft wall duct. Compared to conventional finite difference or finite element boundary value approaches, the numerical marching technique is orders of magnitude shorter in computation time and required computer storage and can be easily employed in problems involving high frequency sound.

Baumeister, K. J.↗

NASA NTRS2011

The Fast Scattering Code (FSC): Validation Studies and Program Guidelines

The Fast Scattering Code (FSC) is a frequency domain noise prediction program developed at the NASA Langley Research Center (LaRC) to simulate the acoustic field produced by the interaction of known, time harmonic incident sound with bodies of arbitrary shape and surface impedance immersed in a potential flow. The code uses the equivalent source method (ESM) to solve an exterior 3-D Helmholtz boundary value problem (BVP) by expanding the scattered acoustic pressure field into a series of point sources distributed on a fictitious surface placed inside the actual scatterer. This work provides additional code validation studies and illustrates the range of code parameters that produce accurate results with minimal computational costs. Systematic noise prediction studies are presented in which monopole generated incident sound is scattered by simple geometric shapes - spheres (acoustically hard and soft surfaces), oblate spheroids, flat disk, and flat plates with various edge topologies. Comparisons between FSC simulations and analytical results and experimental data are presented.

Tinetti, Ana F.↗

NASA NTRS2024

Modeling Soft X‐Ray Emissions at the Dayside Magnetopause

In this study, we simulate the Solar Wind Charge Exchange (SWCX) soft X-ray emissions at dayside magnetosheath and cusps by using magnetohydrodynamic (MHD) and LAtmos TEst Particle (LaTeP) models. MHD models are unable to resolve the particle kinetic effects, such as the different behaviors of ions with different q/m, or distinguish the magnetospheric plasma from the solar wind plasma. We investigate these effects with the LaTeP model. As the LaTeP model does not self-compute magnetic and electric field, the magnetic and electric field data obtained from Open Geospace General Circulation Model (OpenGGCM) and Lagrangian version of the piecewise parabolic method (PPMLR) MHD model are used as the input to LaTeP model. The soft X-ray emissivity maps simulated from pure OpenGGCM and PPMLR MHD approaches and from LaTeP-OpenGGCM and LaTeP-PPMLR approaches are presented and compared. The results indicate that the LaTeP model can well resolve the kinetic effects and can be used to investigate the individual spectral characteristics. Therefore, the LaTeP model is a complementary approach for simulating the X-ray emissions near the dayside magnetopause. We also calculate the ratio of integrated OVII/OVIII line intensities, produced by charge exchange of O7+ ions and O8+ ions, respectively. We find a relatively higher ratio at the bow shock compared to the surrounding areas, suggesting that this ratio can be an effective parameter to identify the bow shock location.

Qiuyu Xu↗

NASA NTRS2003

Simulation System for Training in Laparoscopic Surgery

A computer-based simulation system creates a visual and haptic virtual environment for training a medical practitioner in laparoscopic surgery. Heretofore, it has been common practice to perform training in partial laparoscopic surgical procedures by use of a laparoscopic training box that encloses a pair of laparoscopic tools, objects to be manipulated by the tools, and an endoscopic video camera. However, the surgical procedures simulated by use of a training box are usually poor imitations of the actual ones. The present computer-based system improves training by presenting a more realistic simulated environment to the trainee. The system includes a computer monitor that displays a real-time image of the affected interior region of the patient, showing laparoscopic instruments interacting with organs and tissues, as would be viewed by use of an endoscopic video camera and displayed to a surgeon during a laparoscopic operation. The system also includes laparoscopic tools that the trainee manipulates while observing the image on the computer monitor (see figure). The instrumentation on the tools consists of (1) position and orientation sensors that provide input data for the simulation and (2) actuators that provide force feedback to simulate the contact forces between the tools and tissues. The simulation software includes components that model the geometries of surgical tools, components that model the geometries and physical behaviors of soft tissues, and components that detect collisions between them. Using the measured positions and orientations of the tools, the software detects whether they are in contact with tissues. In the event of contact, the deformations of the tissues and contact forces are computed by use of the geometric and physical models. The image on the computer screen shows tissues deformed accordingly, while the actuators apply the corresponding forces to the distal ends of the tools. For the purpose of demonstration, the system has been set up to simulate the insertion of a flexible catheter in a bile duct. [As thus configured, the system can also be used to simulate other endoscopic procedures (e.g., bronchoscopy and colonoscopy) that include the insertion of flexible tubes into flexible ducts.] A hybrid approach has been followed in developing the software for real-time simulation of the visual and haptic interactions (1) between forceps and the catheter, (2) between the forceps and the duct, and (3) between the catheter and the duct. The deformations of the duct are simulated by finite-element and modalanalysis procedures, using only the most significant vibration modes of the duct for computing deformations and interaction forces. The catheter is modeled as a set of virtual particles uniformly distributed along the center line of the catheter and connected to each other via linear and torsional springs and damping elements. The interactions between the forceps and the duct as well as the catheter are simulated by use of a ray-based haptic-interaction- simulating technique in which the forceps are modeled as connected line segments.

Basdogan, Cagatay↗

NASA NTRS1991

Multi-stage decoding for multi-level block modulation codes

In this paper, we investigate various types of multi-stage decoding for multi-level block modulation codes, in which the decoding of a component code at each stage can be either soft-decision or hard-decision, maximum likelihood or bounded-distance. Error performance of codes is analyzed for a memoryless additive channel based on various types of multi-stage decoding, and upper bounds on the probability of an incorrect decoding are derived. Based on our study and computation results, we find that, if component codes of a multi-level modulation code and types of decoding at various stages are chosen properly, high spectral efficiency and large coding gain can be achieved with reduced decoding complexity. In particular, we find that the difference in performance between the suboptimum multi-stage soft-decision maximum likelihood decoding of a modulation code and the single-stage optimum decoding of the overall code is very small: only a fraction of dB loss in SNR at the probability of an incorrect decoding for a block of 10(exp -6). Multi-stage decoding of multi-level modulation codes really offers a way to achieve the best of three worlds, bandwidth efficiency, coding gain, and decoding complexity.

Lin, Shu↗

NASA NTRS2005

Parachute Testing for the NASA X-38 Crew Return Vehicle

NASA's X-38 program was an in-house technology demonstration program to develop a Crew Return Vehicle (CRV) for the International Space Station capable of returning seven crewmembers to Earth when the Space Shuttle was not present at the station. The program, managed out of NASA's Johnson Space Center, was started in 1995 and was cancelled in 2003. Eight flights with a prototype atmospheric vehicle were successfully flown at Edwards Air Force Base, demonstrating the feasibility of a parachute landing system for spacecraft. The intensive testing conducted by the program included testing of large ram-air parafoils. The flight test techniques, instrumentation, and simulation models developed during the parachute test program culminated in the successful demonstration of a guided parafoil system to land a 25,000 Ib spacecraft. The test program utilized parafoils of sizes ranging from 750 to 7500 p. The guidance, navigation, and control system (GN&C) consisted of winches, laser or radar altimeter, global positioning system (GPS), magnetic compass, barometric altimeter, flight computer, and modems for uplink commands and downlink data. The winches were used to steer the parafoil and to perform the dynamic flare maneuver for a soft landing. The laser or radar altimeter was used to initiate the flare. In the event of a GPS failure, the software navigated by dead reckoning using the compass and barometric altimeter data. The GN&C test beds included platforms dropped from cargo aircraft, atmospheric vehicles released from a 8-52, and a Buckeye powered parachute. This paper will describe the test program and significant results.

Stein, Jenny M.↗

NASA NTRS2015

Rapid Generation of Optimal Asteroid Powered Descent Trajectories Via Convex Optimization

Pinson, Robin↗

NASA NTRSDate not supplied

Explaining Soft-Goal Conflicts through Constraint Relaxations

Recent work suggests to explain trade-offs between soft goals in terms of their conflicts, i. e., minimal unsolvable soft-goal subsets. But this does not explain the conflicts themselves: Why can a given set of soft-goals not be jointly achieved? Here we approach that question in terms of the underlying constraints on plans in the task at hand, namely resource availability and time windows. In this context, a natural form of explanation for a soft-goal conflict is a minimal constraint relaxation under which the conflict disappears (“if the deadline was 1 hour later, it would work”). We explore algorithms for computing such explanations. A baseline is to simply loop over all relaxed tasks and compute the conflicts for each separately. We improve over this by two algorithms that leverage information – conflicts, reachable states – across relaxed tasks. We show that these algorithms can exponentially outperform the baseline in theory, and we run experiments confirming that advantage in practice.

Planning↗

NASA NTRS1992

Imaging of the hip joint. Computed tomography versus magnetic resonance imaging

The authors reviewed the applications and limitations of computed tomography (CT) and magnetic resonance (MR) imaging in the assessment of the most common hip disorders. Magnetic resonance imaging is the most sensitive technique in detecting osteonecrosis of the femoral head. Magnetic resonance reflects the histologic changes associated with osteonecrosis very well, which may ultimately help to improve staging. Computed tomography can more accurately identify subchondral fractures than MR imaging and thus remains important for staging. In congenital dysplasia of the hip, the position of the nonossified femoral head in children less than six months of age can only be inferred by indirect signs on CT. Magnetic resonance imaging demonstrates the cartilaginous femoral head directly without ionizing radiation. Computed tomography remains the imaging modality of choice for evaluating fractures of the hip joint. In some patients, MR imaging demonstrates the fracture even when it is not apparent on radiography. In neoplasm, CT provides better assessment of calcification, ossification, and periosteal reaction than MR imaging. Magnetic resonance imaging, however, represents the most accurate imaging modality for evaluating intramedullary and soft-tissue extent of the tumor and identifying involvement of neurovascular bundles. Magnetic resonance imaging can also be used to monitor response to chemotherapy. In osteoarthrosis and rheumatoid arthritis of the hip, both CT and MR provide more detailed assessment of the severity of disease than conventional radiography because of their tomographic nature. Magnetic resonance imaging is unique in evaluating cartilage degeneration and loss, and in demonstrating soft-tissue alterations such as inflammatory synovial proliferation.

Review↗

NASA NTRS1986

Laser docking system flight experiment

Experiments necessary in the development of the Laser Docking System (LDS) are described. The LDS would be mounted in the Orbiter payload bay, along with a grid connected by fiber optic link to a computer in the cabin. The tests would be performed to aid in the design of an operational sensor which could track a passive target accurately enough to permit soft docking. Additional data would be gained regarding the LDS performance in space, the effects of Orbiter RCS plume impingement on the target, and refinements needed for the flight hardware. A working model which includes an IR laser steered by galvanometer-driven motors for bouncing beams off retroreflectors mounted on targets is described, together with a 300 ft long indoor test facility. Tests on Orbiter flights would first be in a wholly automatic mode and then in a man-in-the-loop mode.

Erwin, Harry O.↗

NASA NTRS2016

Trajectory Design Employing Convex Optimization for Landing on Irregularly Shaped Asteroids

Mission proposals that land spacecraft on asteroids are becoming increasingly popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site with pinpoint precision. The problem under investigation is how to design a propellant optimal powered descent trajectory that can be quickly computed onboard the spacecraft, without interaction from the ground control. The propellant optimal control problem in this work is to determine the optimal finite thrust vector to land the spacecraft at a specified location, in the presence of a highly nonlinear gravity field, subject to various mission and operational constraints. The proposed solution uses convex optimization, a gravity model with higher fidelity than Newtonian, and an iterative solution process for a fixed final time problem. In addition, a second optimization method is wrapped around the convex optimization problem to determine the optimal flight time that yields the lowest propellant usage over all flight times. Gravity models designed for irregularly shaped asteroids are investigated. Success of the algorithm is demonstrated by designing powered descent trajectories for the elongated binary asteroid Castalia.

Pinson, Robin M.↗

NASA NTRS1986

Finite element modelling of non-linear magnetic circuits using Cosmic NASTRAN

The general purpose Finite Element Program COSMIC NASTRAN currently has the ability to model magnetic circuits with constant permeablilities. An approach was developed which, through small modifications to the program, allows modelling of non-linear magnetic devices including soft magnetic materials, permanent magnets and coils. Use of the NASTRAN code resulted in output which can be used for subsequent mechanical analysis using a variation of the same computer model. Test problems were found to produce theoretically verifiable results.

Sheerer, T. J.↗

NASA NTRS1990

ISIS and META projects

ISIS and META are two distributed systems projects at Cornell University. The ISIS project, has developed a new methodology, virtual synchrony, for writing robust distributed software. This approach is directly supported by the ISIS Toolkit, a programming system that is distributed to over 300 academic and industrial sites. Several interesting applications that exploit the strengths of ISIS, including an NFS-compatible replicated file system, are being developed. The META project, is about distributed control in a soft real time environment incorporating feedback. This domain encompasses examples as diverse as monitoring inventory and consumption on a factory floor and performing load-balancing on a distributed computing system. One of the first uses of META is for distributed application management: the tasks of configuring a distributed program, dynamically adapting to failures, and monitoring its performance. Recent progress and current plans are presented. This approach to distributed computing, a philosophy that is believed to significantly distinguish the work from that of others in the field, is explained.

Birman, Kenneth↗

NASA NTRS2014

Noise Scaling and Community Noise Metrics for the Hybrid Wing Body Aircraft

An aircraft system noise assessment was performed for the hybrid wing body aircraft concept, known as the N2A-EXTE. This assessment is a result of an effort by NASA to explore a realistic HWB design that has the potential to substantially reduce noise and fuel burn. Under contract to NASA, Boeing designed the aircraft using practical aircraft design princip0les with incorporation of noise technologies projected to be available in the 2020 timeframe. NASA tested 5.8% scale-mode of the design in the NASA Langley 14- by 22-Foot Subsonic Tunnel to provide source noise directivity and installation effects for aircraft engine and airframe configurations. Analysis permitted direct scaling of the model-scale jet, airframe, and engine shielding effect measurements to full-scale. Use of these in combination with ANOPP predictions enabled computations of the cumulative (CUM) noise margins relative to FAA Stage 4 limits. The CUM margins were computed for a baseline N2A-EXTE configuration and for configurations with added noise reduction strategies. The strategies include reduced approach speed, over-the-rotor line and soft-vane fan technologies, vertical tail placement and orientation, and modified landing gear designs with fairings. Combining the inherent HWB engine shielding by the airframe with added noise technologies, the cumulative noise was assessed at 38.7 dB below FAA Stage 4 certification level, just 3.3 dB short of the NASA N+2 goal of 42 dB. This new result shows that the NASA N+2 goal is approachable and that significant reduction in overall aircraft noise is possible through configurations with noise reduction technologies and operational changes.

Burley, Casey L.↗

NASA NTRS1976

The interaction between a solid body and viscous fluid by marker-and-cell method

A computational method for solving nonlinear problems relating to impact and penetration of a rigid body into a fluid type medium is presented. The numerical techniques, based on the Marker-and-Cell method, gives the pressure and velocity of the flow field. An important feature in this method is that the force and displacement of the rigid body interacting with the fluid during the impact and sinking phases are evaluated from the boundary stresses imposed by the fluid on the rigid body. A sample problem of low velocity penetration of a rigid block into still water is solved by this method. The computed time histories of the acceleration, pressure, and displacement of the block show food agreement with experimental measurements. A sample problem of high velocity impact of a rigid block into soft clay is also presented.

Cheng, R. Y. K.↗

NASA NTRS1990

ISIS and META projects

The ISIS project has developed a new methodology, virtual synchony, for writing robust distributed software. High performance multicast, large scale applications, and wide area networks are the focus of interest. Several interesting applications that exploit the strengths of ISIS, including an NFS-compatible replicated file system, are being developed. The META project is distributed control in a soft real-time environment incorporating feedback. This domain encompasses examples as diverse as monitoring inventory and consumption on a factory floor, and performing load-balancing on a distributed computing system. One of the first uses of META is for distributed application management: the tasks of configuring a distributed program, dynamically adapting to failures, and monitoring its performance. Recent progress and current plans are reported.

Birman, Kenneth↗