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Real-time trajectory optimization on parallel processors

A parallel algorithm has been developed for rapidly solving trajectory optimization problems. The goal of the work has been to develop an algorithm that is suitable to do real-time, on-line optimal guidance through repeated solution of a trajectory optimization problem. The algorithm has been developed on an INTEL iPSC/860 message passing parallel processor. It uses a zero-order-hold discretization of a continuous-time problem and solves the resulting nonlinear programming problem using a custom-designed augmented Lagrangian nonlinear programming algorithm. The algorithm achieves parallelism of function, derivative, and search direction calculations through the principle of domain decomposition applied along the time axis. It has been encoded and tested on 3 example problems, the Goddard problem, the acceleration-limited, planar minimum-time to the origin problem, and a National Aerospace Plane minimum-fuel ascent guidance problem. Execution times as fast as 118 sec of wall clock time have been achieved for a 128-stage Goddard problem solved on 32 processors. A 32-stage minimum-time problem has been solved in 151 sec on 32 processors. A 32-stage National Aerospace Plane problem required 2 hours when solved on 32 processors. A speed-up factor of 7.2 has been achieved by using 32-nodes instead of 1-node to solve a 64-stage Goddard problem.

Psiaki, Mark L.

Massively Parallel and Scalable Implicit Time Integration Algorithms for Structural Dynamics

Explicit codes are often used to simulate the nonlinear dynamics of large-scale structural systems, even for low frequency response, because the storage and CPU requirements entailed by the repeated factorizations traditionally found in implicit codes rapidly overwhelm the available computing resources. With the advent of parallel processing, this trend is accelerating because of the following additional facts: (a) explicit schemes are easier to parallelize than implicit ones, and (b) explicit schemes induce short range interprocessor communications that are relatively inexpensive, while the factorization methods used in most implicit schemes induce long range interprocessor communications that often ruin the sought-after speed-up. However, the time step restriction imposed by the Courant stability condition on all explicit schemes cannot yet be offset by the speed of the currently available parallel hardware. Therefore, it is essential to develop efficient alternatives to direct methods that are also amenable to massively parallel processing because implicit codes using unconditionally stable time-integration algorithms are computationally more efficient when simulating the low-frequency dynamics of aerospace structures.

Farhat, Charbel

Cross-Cutting Flight Infrastructure Improvements on M2020

Mars2020 (M2020) was formulated as a mission that leveraged as much Mars Science Laboratory (MSL) heritage as possible, while focusing major new development efforts on the original and unique elements needed to accomplish the different mission objectives. Well publicized examples of high profile new developments include precision landing, the sampling and caching system, the specific instrument suite, improved mobility via Autonomous Navigation, and later the addition of the Ingenuity helicopter. Less well known are the refinements to the core flight infrastructure, primarily in the cross-cutting functions of Telecom, Avionics, Data Management, Communications Behaviors, and Parameter Management. These enhancements are introduced predominately via flight software, and represent increases in capability that justified their inclusion in an otherwise heritage-focused project environment.Perseverance’s cross-cutting flight infrastructure improvements fall into and across the following five categories. First is a trimming of the software footprint of infrastructure modules, in order to make room for memory demands elsewhere in the system. Second is the minimization of data volume to be downlinked, through various methods such as the incorporation of new compression options. Third is the maximization of the available downlink bandwidth for data, by curtailing content-less data (fill) and introducing an improved UHF proximity link protocol. Fourth is a reduction in vulnerabilities, through increased file system redundancy, robustness, and software process monitoring. Fifth is an increase in operations efficiency by lowering file system mount times, improving parallelism between simultaneous events, minimizing the time to recover from file system errors, streamlining the purging of obsolete data, and reducing the number of commands to service parameters by a factor of 100.Individually, none of the cross-cutting infrastructure improvements are likely to garner headlines, but collectively they appreciably improve the safety and operability of Perseverance over its predecessor. This paper will describe the improvements, their promise, and where applicable, their actual impact in operations.

Bohannon, Emily

A parallel algorithm for switch-level timing simulation on a hypercube multiprocessor

The parallel approach to speeding up simulation is studied, specifically the simulation of digital LSI MOS circuitry on the Intel iPSC/2 hypercube. The simulation algorithm is based on RSIM, an event driven switch-level simulator that incorporates a linear transistor model for simulating digital MOS circuits. Parallel processing techniques based on the concepts of Virtual Time and rollback are utilized so that portions of the circuit may be simulated on separate processors, in parallel for as large an increase in speed as possible. A partitioning algorithm is also developed in order to subdivide the circuit for parallel processing.

Rao, Hariprasad Nannapaneni

Massively Parallel Algorithms for Real-Time Wavefront Control of a Dense Adaptive Optics System

In this paper massively parallel algorithms and architectures for real-time wavefront control of a dense adaptive optic system (SELENE) are presented. We have already shown that the computation of a near optimal control algorithm for SELENE can be reduced to the solution of a discrete Poisson equation on a regular domain. Although this represents an optimal computation, due the large size of the system and the high sampling rate requirement, the implementation of this control algorithm poses a computationally challenging problem since it demands a sustained computational throughput of the order of 10 GFlops. We develop a novel algorithm, designated as Fast Invariant Imbedding algorithm, which offers a massive degree of parallelism with simple communication and synchronization requirements. Due to these features, our algorithm is significantly more efficient than other Fast Poisson Solvers for implementation on massively parallel architectures.

massively

Trajectory optimization for real-time guidance. I - Time-varying LQR on a parallel processor

A key algorithmic element of a real-time trajectory optimization hardware/software implementation, the quadratic program (QP) solver element, is presented. The purpose of the effort is to make nonlinear trajectory optimization fast enough to provide real-time commands during guidance of a vehicle such as an aeromaneuvering orbiter. Many methods of nonlinear programming require the solution of a QP at each iteration. In the trajectory optimization case the QP has a special dynamic programming structure, a LQR-like structure. QP algorithm speed is increased by taking advantage of this special structure and by parallel implementation.

Psiaki, Mark L.

Overview and extensions of a system for routing directed graphs on SIMD architectures

Many problems can be described in terms of directed graphs that contain a large number of vertices where simple computations occur using data from adjacent vertices. A method is given for parallelizing such problems on an SIMD machine model that uses only nearest neighbor connections for communication, and has no facility for local indirect addressing. Each vertex of the graph will be assigned to a processor in the machine. Rules for a labeling are introduced that support the use of a simple algorithm for movement of data along the edges of the graph. Additional algorithms are defined for addition and deletion of edges. Modifying or adding a new edge takes the same time as parallel traversal. This combination of architecture and algorithms defines a system that is relatively simple to build and can do fast graph processing. All edges can be traversed in parallel in time O(T), where T is empirically proportional to the average path length in the embedding times the average degree of the graph. Additionally, researchers present an extension to the above method which allows for enhanced performance by allowing some broadcasting capabilities.

Tomboulian, Sherryl

Parallel algorithms for simulating continuous time Markov chains

We have previously shown that the mathematical technique of uniformization can serve as the basis of synchronization for the parallel simulation of continuous-time Markov chains. This paper reviews the basic method and compares five different methods based on uniformization, evaluating their strengths and weaknesses as a function of problem characteristics. The methods vary in their use of optimism, logical aggregation, communication management, and adaptivity. Performance evaluation is conducted on the Intel Touchstone Delta multiprocessor, using up to 256 processors.

Nicol, David M.

A Parallel Pipelined Renderer for the Time-Varying Volume Data

This paper presents a strategy for efficiently rendering time-varying volume data sets on a distributed-memory parallel computer. Time-varying volume data take large storage space and visualizing them requires reading large files continuously or periodically throughout the course of the visualization process. Instead of using all the processors to collectively render one volume at a time, a pipelined rendering process is formed by partitioning processors into groups to render multiple volumes concurrently. In this way, the overall rendering time may be greatly reduced because the pipelined rendering tasks are overlapped with the I/O required to load each volume into a group of processors; moreover, parallelization overhead may be reduced as a result of partitioning the processors. We modify an existing parallel volume renderer to exploit various levels of rendering parallelism and to study how the partitioning of processors may lead to optimal rendering performance. Two factors which are important to the overall execution time are re-source utilization efficiency and pipeline startup latency. The optimal partitioning configuration is the one that balances these two factors. Tests on Intel Paragon computers show that in general optimal partitionings do exist for a given rendering task and result in 40-50% saving in overall rendering time.

Chiueh, Tzi-Cker

High Performance Programming Using Explicit Shared Memory Model on Cray T3D1

The Cray T3D system is the first-phase system in Cray Research, Inc.'s (CRI) three-phase massively parallel processing (MPP) program. This system features a heterogeneous architecture that closely couples DEC's Alpha microprocessors and CRI's parallel-vector technology, i.e., the Cray Y-MP and Cray C90. An overview of the Cray T3D hardware and available programming models is presented. Under Cray Research adaptive Fortran (CRAFT) model four programming methods (data parallel, work sharing, message-passing using PVM, and explicit shared memory model) are available to the users. However, at this time data parallel and work sharing programming models are not available to the user community. The differences between standard PVM and CRI's PVM are highlighted with performance measurements such as latencies and communication bandwidths. We have found that the performance of neither standard PVM nor CRI s PVM exploits the hardware capabilities of the T3D. The reasons for the bad performance of PVM as a native message-passing library are presented. This is illustrated by the performance of NAS Parallel Benchmarks (NPB) programmed in explicit shared memory model on Cray T3D. In general, the performance of standard PVM is about 4 to 5 times less than obtained by using explicit shared memory model. This degradation in performance is also seen on CM-5 where the performance of applications using native message-passing library CMMD on CM-5 is also about 4 to 5 times less than using data parallel methods. The issues involved (such as barriers, synchronization, invalidating data cache, aligning data cache etc.) while programming in explicit shared memory model are discussed. Comparative performance of NPB using explicit shared memory programming model on the Cray T3D and other highly parallel systems such as the TMC CM-5, Intel Paragon, Cray C90, IBM-SP1, etc. is presented.

Simon, Horst D.

Parallel processing architecture for computing inverse differential kinematic equations of the PUMA arm

In advanced robot control problems, on-line computation of inverse Jacobian solution is frequently required. Parallel processing architecture is an effective way to reduce computation time. A parallel processing architecture is developed for the inverse Jacobian (inverse differential kinematic equation) of the PUMA arm. The proposed pipeline/parallel algorithm can be inplemented on an IC chip using systolic linear arrays. This implementation requires 27 processing cells and 25 time units. Computation time is thus significantly reduced.

Hsia, T. C.

Six Years of Parallel Computing at NAS (1987 - 1993): What Have we Learned?

In the fall of 1987 the age of parallelism at NAS began with the installation of a 32K processor CM-2 from Thinking Machines. In 1987 this was described as an "experiment" in parallel processing. In the six years since, NAS acquired a series of parallel machines, and conducted an active research and development effort focused on the use of highly parallel machines for applications in the computational aerosciences. In this time period parallel processing for scientific applications evolved from a fringe research topic into the one of main activities at NAS. In this presentation I will review the history of parallel computing at NAS in the context of the major progress, which has been made in the field in general. I will attempt to summarize the lessons we have learned so far, and the contributions NAS has made to the state of the art. Based on these insights I will comment on the current state of parallel computing (including the HPCC effort) and try to predict some trends for the next six years.

Simon, Horst D.

Correlation between calmodulin activity and gravitropic sensitivity in primary roots of maize

Recent evidence indicates a role for calcium and calmodulin in the gravitropic response of primary roots of maize (Zea mays, L.). We examined this possibility by testing the relationship between calmodulin activity and gravitropic sensitivity in roots of the maize cultivars Merit and B73 x Missouri 17. Roots of the Merit cultivar require light to the gravitropically competent. The gravitropic response of the Missouri cultivar is independent of light. The occurrence of calmodulin in primary roots of these maize cultivars was tested by affinity gel chromatography followed by sodium dodecyl sulfate-polyacrylamide gel electrophoresis with bovine brain calmodulin as standard. The distribution of calmodulin activity was measured using both the phosphodiesterase and NAD kinase assays for calmodulin. These assays were performed on whole tissue segments, crude extracts, and purified extracts. In light-grown seedlings of the Merit cultivar or in either dark- or light-grown seedlings of the Missouri cultivar, calmodulin activity per millimeter of root tissue was about 4-fold higher in the apical millimeter than in the subtending 3 millimeters. Calmodulin activity was very low in the apical millimeter of roots of dark-grown (gravitropically nonresponsive) seedlings of the Merit cultivar. Upon illumination, the calmodulin activity in the apical millimeter increased to a level comparable to that of light-grown seedlings and the roots became gravitropically competent. The time course of the development of gravitropic sensitivity following illumination paralleled the time course of the increase in calmodulin activity in the apical millimeter of the root. The results are consistent with the suggestion that calmodulin plays an important role in the gravitropic response of roots.

NASA Program Space Biology

Visual reaction times during prolonged angular acceleration parallel the subjective perception of rotation

The effect of prolonged angular acceleration on choice reaction time to an accelerating visual stimulus was investigated, with 10 commercial airline pilots serving as subjects. The pattern of reaction times during and following acceleration was compared with the pattern of velocity estimates reported during identical trials. Both reaction times and velocity estimates increased at the onset of acceleration, declined prior to the termination of acceleration, and showed an aftereffect. These results are inconsistent with the torsion-pendulum theory of semicircular canal function and suggest that the vestibular adaptation is of central origin.

Mattson, D. L.

Time-partitioning simulation models for calculation on parallel computers

A technique allowing time-staggered solution of partial differential equations is presented in this report. Using this technique, called time-partitioning, simulation execution speedup is proportional to the number of processors used because all processors operate simultaneously, with each updating of the solution grid at a different time point. The technique is limited by neither the number of processors available nor by the dimension of the solution grid. Time-partitioning was used to obtain the flow pattern through a cascade of airfoils, modeled by the Euler partial differential equations. An execution speedup factor of 1.77 was achieved using a two processor Cray X-MP/24 computer.

Milner, Edward J.

Time-partitioning simulation models for calculation of parallel computers

A technique allowing time-staggered solution of partial differential equations is presented in this report. Using this technique, called time-partitioning, simulation execution speedup is proportional to the number of processors used because all processors operate simultaneously, with each updating of the solution grid at a different time point. The technique is limited by neither the number of processors available nor by the dimension of the solution grid. Time-partitioning was used to obtain the flow pattern through a cascade of airfoils, modeled by the Euler partial differential equations. An execution speedup factor of 1.77 was achieved using a two processor Cray X-MP/24 computer.

Milner, Edward J.

The Role of Magnetic Shear in Reconnection-driven Flare Energy Release

Using observations from the Solar Dynamics Observatory's Atmosphere Imaging Assembly and the Ramaty High Energy Solar Spectroscopic Imager, we present novel measurements of the shear of post-reconnection flare loops (PRFLs) in SOL20141218T21:40 and study its evolution with respect to magnetic reconnection and flare emission. Two quasi-parallel ribbons form adjacent to the magnetic polarity inversion line (PIL), spreading in time first parallel to the PIL and then mostly in a perpendicular direction. We measure the magnetic reconnection rate from the ribbon evolution, and also the shear angle of a large number of PRFLs observed in extreme ultraviolet passbands (≲1 MK). For the first time, the shear angle measurements are conducted using several complementary techniques allowing for cross validation of the results. In this flare, the total reconnection rate is much enhanced before a sharp increase in the hard X-ray emission, and the median shear decreases from 60°–70° to 20°, on a timescale of 10 minutes. We find a correlation between the shear-modulated total reconnection rate and the nonthermal electron flux. These results confirm the strong-to-weak shear evolution suggested in previous observational studies and reproduced in numerical models, and also confirm that, in this flare, reconnection is not an efficient producer of energetic nonthermal electrons during the first 10 minutes when the strongly sheared PRFLs are formed. We conclude that an intermediate shear angle, ≤40°, is needed for efficient particle acceleration via reconnection, and we propose a theoretical interpretation.

Solar magnetic reconnection