Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

INTRODUCTION: Brief History. Multifingered Hands and Dextrous Manipulation. Outline of the Book. Bibliography. RIGID BODY MOTION: Rigid Body Transformations. Rotational Motion in R3. Rigid Motion in R3. Velocity of a Rigid Body. Wrenches and Reciprocal Screws. MANIPULATOR KINEMATICS: Introduction. Forward Kinematics. Inverse Kinematics. The Manipulator Jacobian. Redundant and Parallel Manipulators. ROBOT DYNAMICS AND CONTROL: Introduction. Lagrange's Equations. Dynamics of Open-Chain Manipulators. Lyapunov Stability Theory. Position Control and Trajectory Tracking. Control of Constrained Manipulators. MULTIFINGERED HAND KINEMATICS: Introduction to Grasping. Grasp Statics. Force-Closure. Grasp Planning. Grasp Constraints. Rolling Contact Kinematics. HAND DYNAMICS AND CONTROL: Lagrange's Equations with Constraints. Robot Hand Dynamics. Redundant and Nonmanipulable Robot Systems. Kinematics and Statics of Tendon Actuation. Control of Robot Hands. NONHOLONOMIC BEHAVIOR IN ROBOTIC SYSTEMS: Introduction. Controllability and Frobenius' Theorem. Examples of Nonholonomic Systems. Structure of Nonholonomic Systems. NONHOLONOMIC MOTION PLANNING: Introduction. Steering Model Control Systems Using Sinusoids. General Methods for Steering. Dynamic Finger Repositioning. FUTURE PROSPECTS: Robots in Hazardous Environments. Medical Applications for Multifingered Hands. Robots on a Small Scale: Microrobotics. APPENDICES: Lie Groups and Robot Kinematics. A Mathematica Package for Screw Calculus. Bibliography. Index Each chapter also includes a Summary, Bibliography, and Exercises

http://www.cds.caltech.edu/%7Emurray/books/MLS/pdf/mls94-complete.pdf

A Mathematical Introduction to Robotic Manipulation

https://www.cs.duke.edu/brd/Teaching/Bio/asmb/Papers/NMR/NOE-auto-assignments/Dyana01.pdf

Torsion angle dynamics for nmr structure calculation with the new program dyana

We describe a learning-based approach to hand-eye coordination for robotic grasping from monocular images. To learn hand-eye coordination for grasping, we trained a large convolutional neural netwo...

https://journals.sagepub.com/doi/pdf/10.1177/0278364917710318

Learning Hand-Eye Coordination for Robotic Grasping with Deep Learning and Large-Scale Data Collection

This chapter gives an introduction to automated nuclear magnetic resonance (NMR) structure calculation with the program CYANA. Given a sufficiently complete list of assigned chemical shifts and one or several lists of cross-peak positions and columns from two-, three-, or four-dimensional nuclear Overhauser effect spectroscopy (NOESY) spectra, the assignment of the NOESY cross-peaks and the three-dimensional structure of the protein in solution can be calculated automatically with CYANA.

Automated NMR structure calculation with CYANA.

A recently developed spatial operator algebra for manipu lator modeling, control, and trajectory design is dis cussed. 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 concep tual and physical understanding of manipulator dynamics and kinematics. Furthermore, implementable recursive algorithms can be immediately derived from the abstract operator expressions by inspection. Thus the transition from an abstract problem formulation and solution to the detailed mechanizat...

/pdf/a-spatial-operator-algebra-for-manipulator-modeling-and-4lwmw0x48q.pdf

A spatial operator algebra for manipulator modeling and control

There has been a growing interest in the development of new and efficient algorithms for multibody dynamics in recent years. Serial rigid multibody systems form the basic subcomponents of general multibody systems, and a variety of algorithms to solve the serial chain forward dynamics problem have been proposed. In this paper, the economy of representation and analysis tools provided by the spatial operator algebra are used to clarify the inherent structure of these algorithms, to identify those that are similar, and to study the relationships among the ones that are distinct. For the purposes of this study, the algorithms are categorized into three classes: algorithms that require the explicit computation of the mass matrix, algorithms that are completely recursive in nature, and algorithms of intermediate complexity. In addition, alternative factorizations for the mass matrix and closed form expressions for its inverse are derived. These results provide a unifying perspective, within which these diverse dynamics algorithms arise naturally as a consequence of a progressive exploitation of the structure of the mass matrix.

Unified formulation of dynamics for serial rigid multibody systems

A fast recursive algorithm for molecular dynamics simulation

A diagonal equation for robot dynamics is developed by combining mass matrix factorization results with classical Lagrangian mechanics. Diagonalization implies that at each fixed time instant the equation at each joint is decoupled from all of the other joint equations. The equation involves two important variables: a vector of total joint rotational rates and a corresponding vector of working joint moments. The nonlinear Coriolis term depends on the joint angles and the rates. The total joint rates are related to the relative joint-angle rates by a linear spatial operator. The total rate at a given joint k reflects the total rotational velocity about the joint, and includes the combined effects from all the links between joint k and the base. Similarly, the working moments are related to the applied moments by the spatial operator . The working moment at a given joint is that part of the applied moment which does actual mechanical work. The diagonal equations are obtained by using the mass matrix factorization in the system Lagrangian. >

Diagonalized Lagrangian robot dynamics

The dynamics and kinematics of manipulators that have fewer actuators than degrees of freedom are studied. These underactuated manipulators arise in a number of important applications such as free-flying space robots, hyperredundant manipulators, manipulators with structural flexibility, etc. In the analysis such underactuated manipulators are decomposed into component active and passive arms. This decomposition allows techniques previously developed for regular (fully actuated) manipulators to be applied to underactuated systems. Spatial operator identities are used to develop closed-form expressions for the generalized accelerations for the system. These expressions form the basis for a recursive O(N) dynamics algorithm. The structure of this algorithm is a hybrid of known forward and inverse dynamics algorithms for regular manipulators. Expressions and computational algorithms are also developed for the generalized and disturbance Jacobians for underactuated manipulators. The application of the results in the paper to space manipulators is also described. >

Abhinandan Jain

Papers

A spatial operator algebra for manipulator modeling and control

Unified formulation of dynamics for serial rigid multibody systems

A fast recursive algorithm for molecular dynamics simulation

Diagonalized Lagrangian robot dynamics

An analysis of the kinematics and dynamics of underactuated manipulators