On the equivalence of three trajectory optimization schemes

Equivalence of perturbation method, Newtons method, and adjoint-perturbation method for solving boundary value problems from variational calculus treatment of optimal control problem

An indirect optimization method with improved convergence characteristics

A method is presented for obtaining numerical solutions to a certain class of two-point boundary value problems which arise in optimal control theory. The problems are characterized by systems of nonlinear ordinary differential equations with nonlinear boundary conditions

Trajectory computational techniques emphasizing existence, uniqueness, and construction of solutions to boundary problems for ordinary differential equations Final report

Trajectory computational techniques emphasizing existence, uniqueness, and construction of solutions to boundary problems for ordinary differential equation

Quasi-linearization approach for the under-actuated robots

A novel technique to reduce energy consumption for industrial robots by using redundancy and under-actuated configurations is introduced in this paper. The study concentrates on kinematics including a passive axis which causes a highly nonlinear coupling of the Coriolis and centrifugal forces and high inertia coupling. The challenge of meeting the requirements of position accuracy, precision, and repeatability combined with the requirements for the speed, acceleration, and torque is coped with by solving a sequence of linear two point boundary value problems for controlling the movement of the end effector between two points. The advantages of this method are the ability of reducing the computation time dramatically, computer storage, and linearizing the nonlinear model. Furthermore the optimal trajectories are identified with minimizing energy consumption and enabling high speed capability. Numerical simulations are conducted to validate the theoretical analysis

Non-oscillatory Spatial Solutions Criterion for Convection-Diffusion Problem

The fact that the convection-diffusion problems are essential in nature is supported by the presence of such problems in vast number of applications in both science as well as engineering. Some of these applications involve the computational domain’s grid structure issues in the numerical experiment of fluid dynamics. The paper highlights the important role of convection-diffusion flow parameters in the construction of the grid structure. We propose the a priori criterion formulation to avoid non-oscillatory solutions which is based on both Peclet and grid  numbers, and serves as a systematic approach in setting grid related parameters of interest. Aiming at a more efficient process in choosing grid structure for computational domain, the criterion functions as a standard which also eliminates heuristic process in the scalar concentration prediction. The test cases’ calculated results verify the consistency of the criterion

A shooting algorithm for problems with singular arcs

In this article we propose a shooting algorithm for a class of optimal control problems for which all control variables appear linearly. The shooting system has, in the general case, more equations than unknowns and the Gauss-Newton method is used to compute a zero of the shooting function. This shooting algorithm is locally quadratically convergent if the derivative of the shooting function is one-to-one at the solution. The main result of this paper is to show that the latter holds whenever a sufficient condition for weak optimality is satisfied. We note that this condition is very close to a second order necessary condition. For the case when the shooting system can be reduced to one having the same number of unknowns and equations (square system) we prove that the mentioned sufficient condition guarantees the stability of the optimal solution under small perturbations and the invertibility of the Jacobian matrix of the shooting function associated to the perturbed problem. We present numerical tests that validate our method.Comment: No. RR-7763 (2011); Journal of Optimization, Theory and Applications, published as 'Online first', January 201

FY 1991 scientific and technical reports, articles, papers, and presentations

Formal NASA technical reports, papers published in technical journals, and presentations by MSFC personnel in FY 1991 are presented. Papers of MSFC contractors are also included. The information in this report may be of value to the scientific and engineering community in determining what information has been published and what is available

Liquid rocket engine axial-flow turbopumps

The axial pump is considered in terms of the total turbopump assembly. Stage hydrodynamic design, pump rotor assembly, pump materials for liquid hydrogen applications, and safety factors as utilized in state of the art pumps are among the topics discussed. Axial pump applications are included

Failure Analysis of the Method of Adjoint Systems to Determine Optimal Trajectories

Failure analysis of adjoint systems method for determining optimal trajectorie

A Quantitative Methodology for Vetting Dark Network Intelligence Sources for Social Network Analysis

Social network analysis (SNA) is used by the DoD to describe and analyze social networks, leading to recommendations for operational decisions. However, social network models are constructed from various information sources of indeterminate reliability. Inclusion of unreliable information can lead to incorrect models resulting in flawed analysis and decisions. This research develops a methodology to assist the analyst by quantitatively identifying and categorizing information sources so that determinations on including or excluding provided data can be made. This research pursued three main thrusts. It consolidated binary similarity measures to determine social network information sources\u27 concordance and developed a methodology to select suitable measures dependent upon application considerations. A methodology was developed to assess the validity of individual sources of social network data. This methodology utilized source pairwise comparisons to measure information sources\u27 concordance and a weighting schema to account for sources\u27 unique perspectives of the underlying social network. Finally, the developed methodology was tested over a variety of generated networks with varying parameters in a design of experiments paradigm (DOE). Various factors relevant to conditions faced by SNA analysts potentially employing this methodology were examined. The DOE was comprised of a 24 full factorial design augmented with a nearly orthogonal Latin hypercube. A linear model was constructed using quantile regression to mitigate the non-normality of the error terms