Engineering topics
Publications and source records attributed to Jain, A..
two new methods developed for molecular dynamics simulations of very large proteins are applied to a series of proteins ranging up to the protein capsid of tomato bushy stunt virus.
The present recursive algorithm for solving molecular systems' dynamical equations of motion employs internal variable models that reduce such simulations' computation time by an order of magnitude, relative to Cartesian models. Extensive use is made of spatial operator methods recently developed for analysis and simulation of the dynamics of multibody systems. A factor-of-450 speedup over the conventional O(N-cubed) algorithm is demonstrated for the case of a polypeptide molecule with 400 residues.
This paper presents an approach to modeling the dynamics of flexible multibody systems such as flexible spacecraft and limber space robotic systems. A large number of degrees of freedom and complex dynamic interactions are typical in these systems. This paper uses spatial operators to develop efficient recursive algorithms for the dynamics of these systems. This approach very efficiently manages complexity by means of a hierarchy of mathematical operations.
This paper describes the Dynamics Algorithms for Real-Time Simulation (DARTS) real-time hardware-in-the-loop dynamics simulator for the National Aeronautics and Space Administration's Cassini spacecraft. The spacecraft model consists of a central flexible body with a number of articulated rigid-body appendages. The demanding performance requirements from the spacecraft control system require the use of a high fidelity simulator for control system design and testing. The DARTS algorithm provides a new algorithmic and hardware approach to the solution of this hardware-in-the-loop simulation problem. It is based upon the efficient spatial algebra dynamics for flexible multibody systems. A parallel and vectorized version of this algorithm is implemented on a low-cost, multiprocessor computer to meet the simulation timing requirements.
Part 1 of this paper presented the requirements for the real-time simulation of Cassini spacecraft along with some discussion of the DARTS algorithm. Here, in Part 2 we discuss the development and implementation of parallel/vectorized DARTS algorithm and architecture for real-time simulation. Development of the fast algorithms and architecture for real-time hardware-in-the-loop simulation of spacecraft dynamics is motivated by the fact that it represents a hard real-time problem, in the sense that the correctness of the simulation depends on both the numerical accuracy and the exact timing of the computation. For a given model fidelity, the computation should be computed within a predefined time period. Further reduction in computation time allows increasing the fidelity of the model (i.e., inclusion of more flexible modes) and the integration routine.
Linearized dynamics models for manipulators are useful in robot analysis, motion planning, and control applications. Techniques from the spatial operator algebra are used to obtain closed form operator expressions for two types of linearized dynamics models, the linearized inverse and forward dynamics models. Spatially recursive algorithms of O(n) and O(n-squared) complexity for the computation of the perturbation vector and coefficient matrices for the linearized inverse dynamics model are developed first. Subsequently, operator factorization and inversion identities are used to develop corresponding closed-form expressions for the linearized forward dynamics model (LFDM). Once again, these are used to develop algorithms of O(n) and O(n-squared) complexity for the computation of the perturbation vector and the coefficient matrices. The algorithms for the LFDM do not require the explicit computation of the mass matrix nor its numerical inversion and are also of lower complexity than the conventional O(n-cubed) algorithms.
This paper uses spatial operators to develop new spatially recursive dynamics algorithms for flexible multibody systems. The operator description of the dynamics is identical to that for rigid multibody systems. Assumed-mode models are used for the deformation of each individual body. The algorithms are based on two spatial operator factorizations of the system mass matrix. The first (Newton-Euler) factorization of the mass matrix leads to recursive algorithms for the inverse dynamics, mass matrix evaluation, and composite-body forward dynamics for the systems. The second (innovations) factorization of the mass matrix, leads to an operator expression for the mass matrix inverse and to a recursive articulated-body forward dynamics algorithm. The primary focus is on serial chains, but extensions to general topologies are also described. A comparison of computational costs shows that the articulated-body, forward dynamics algorithm is much more efficient than the composite-body algorithm for most flexible multibody systems.
Deep BV RI CCD photometry was performed on a 1 sq deg region of M 31. A catalog of photometry and astrometry of a total of 361,281 stars is presented, with typical completion limits of BV RI = (22.3, 22.2, 22.2, 20.9). Photometric accuracy is about 2 percent at V = 19. This catalog allows detailed studies of stellar populations and reddening. The data are currently being used to assist in finding the optical counterparts of Einstein and ROSAT X-ray sources.
A recently developed spatial operator algebra approach to modeling and analysis of multibody robotic systems is used to develop O(n) recursive algorithms that compute the operational space mass matrix and the operational space coriolis/centrifugal and gravity terms of an n-link serial manipulator. These algorithms enable an O(n) recursive implementation of operational space control.
The Spatial Operator Algebra framework for the dynamics of general multibody systems is described. The use of a spatial operator-based methodology permits the formulation of the dynamical equations of motion of multibody systems in a concise and systematic way. The dynamical equations of progressively more complex grid multibody systems are developed in an evolutionary manner beginning with a serial chain system, followed by a tree topology system and finally, systems with arbitrary closed loops. Operator factorizations and identities are used to develop novel recursive algorithms for the forward dynamics of systems with closed loops. Extensions required to deal with flexible elements are also discussed.
A recently developed spatial operator algebra for manipulator modeling, control, and trajectory design is discussed. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of a manipulator. Inversion of operators can be efficiently obtained via techniques of recursive filtering and smoothing. The operator algebra provides a high-level framework for describing the dynamic and kinematic behavior of a manipulator and for control and trajectory design algorithms. The interpretation of expressions within the algebraic framework leads to enhanced conceptual and physical understanding of manipulator dynamics and kinematics.
A study is made of the kinematics and dynamics of under-actuated manipulators. The presence of passive hinges causes the kinematics and dynamics of these manipulators to be considerably more complex when compared with fully actuated manipulators. Techniques from the spatial operator algebra are used to develop expressions for the generalized Jacobian, the mass matrix, and an efficient inverse dynamics computational algorithm.
Due to their structural flexibility, spacecraft and space manipulators are multibody systems with complex dynamics and possess a large number of degrees of freedom. Here the spatial operator algebra methodology is used to develop a new dynamics formulation and spatially recursive algorithms for such flexible multibody systems. A key feature of the formulation is that the operator description of the flexible system dynamics is identical in form to the corresponding operator description of the dynamics of rigid multibody systems. A significant advantage of this unifying approach is that it allows ideas and techniques for rigid multibody systems to be easily applied to flexible multibody systems. The algorithms use standard finite-element and assumed modes models for the individual body deformation. A Newton-Euler Operator Factorization of the mass matrix of the multibody system is first developed. It forms the basis for recursive algorithms such as for the inverse dynamics, the computation of the mass matrix, and the composite body forward dynamics for the system. Subsequently, an alternative Innovations Operator Factorization of the mass matrix, each of whose factors is invertible, is developed. It leads to an operator expression for the inverse of the mass matrix, and forms the basis for the recursive articulated body forward dynamics algorithm for the flexible multibody system. For simplicity, most of the development here focuses on serial chain multibody systems. However, extensions of the algorithms to general topology flexible multibody systems are described. While the computational cost of the algorithms depends on factors such as the topology and the amount of flexibility in the multibody system, in general, it appears that in contrast to the rigid multibody case, the articulated body forward dynamics algorithm is the more efficient algorithm for flexible multibody systems containing even a small number of flexible bodies. The variety of algorithms described here permits a user to choose the algorithm which is optimal for the multibody system at hand. The availability of a number of algorithms is even more important for real-time applications, where implementation on parallel processors or custom computing hardware is often necessary to maximize speed.
The authors consider the dynamical modeling of robot manipulators whose joint actuators consist of motors driving the joints through gears. The dynamical models for such manipulators are significantly more complex than those for direct drive manipulators. The authors develop recursive O(n) inverse and forward dynamics algorithms as well as recursive O(n2) algorithms for the computation of the mass matrix for geared manipulators. It is shown that, despite the added complexity of the dynamical models for geared manipulators, the algorithms closely resemble the corresponding algorithms for direct drive manipulators, and that the additional algorithmic or computational complexity is relatively insignificant. As a consequence, with little additional cost, existing direct drive algorithms can be easily extended to handle the effects of gearing at the joints.
A spatial operator algebra for modeling the control and trajectory design of manipulation is discussed, with emphasis on its analytical formulation and implementation in the Ada programming language. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of the manipulator. Inversion is obtained using techniques of recursive filtering and smoothing. The operator alegbra provides a high-level framework for describing the dynamic and kinematic behavior of a manipulator and control and trajectory design algorithms. Implementable recursive algorithms can be immediately derived from the abstract operator expressions by inspection, thus greatly simplifying the transition from an abstract problem formulation and solution to the detailed mechanization of a specific algorithm.
Assembly robots combine the benefits of speed and accuracy with the capability of adaptation to changes in the work environment. However, an impediment to the use of robots is the complexity of the man-machine interface. This interface can be improved by providing a means of using a priori-knowledge and reasoning capabilities for controlling and monitoring the tasks performed by robots. Robots ought to be able to perform complex assembly tasks with the help of only supervisory guidance from human operators. For such supervisory quidance, it is important to express the commands in terms of the effects desired, rather than in terms of the motion the robot must undertake in order to achieve these effects. A suitable knowledge representation can facilitate the conversion of task level descriptions into explicit instructions to the robot. Such a system would use symbolic relationships describing the a priori information about the robot, its environment, and the tasks specified by the operator to generate the commands for the robot.
A synthetic aperture radar (SAR) employed for delta k measurement of ocean current from a spacecraft without the need for a narrow beam and long observation times. The SAR signal is compressed to provide image data for different sections of the chirp band width, equivalent to frequencies and a common area for the separate image fields is selected. The image for the selected area at each frequency is deconvolved to obtain the image signals for the different frequencies and the same area. A product of pairs of signals is formed, Fourier transformed and squared. The spectrum thus obtained from different areas for the same pair of frequencies are added to provide an improved signal to noise ratio. The shift of the peak from the center of the spectrum is measured and compared to the expected shift due to the phase velocity of the Bragg scattering wave. Any difference is a measure of current velocity v sub o (delta k).
Good resolution and high signal/noise ratio anticipated. Report describes orbiting sidelooking radar that measures ocean currents in direction toward or away from it. Radar relies on relationship between Doppler shifts and lengths and frequencies of ocean waves.