Engineering Commons^™

Trajectory Planning For Coordinated Rendezvous Of Unmanned Air Vehicles, Timothy W. Mclain, Randal W. Beard

Faculty Publications

A trajectory generation strategy that facilitates the coordination of multiple unmanned air vehicles is developed. Of particular interest is the planning of threat-avoiding trajectories that result in the simultaneous arrival of multiple UAVs at their targets. In this approach, paths to the target are modeled using the physical analogy of a chain. A unique strength of the planning approach is the ability to specify or alter the path length by adding or subtracting links from the chain. Desirable paths to the target are obtained by simulating the dynamics of the chain where threats apply repulsive forces to the chain and …

Fuel Saving Strategies For Separated Spacecraft Interferometry, Timothy Mclain, Randal W. Beard, Christopher A. Bailey

Faculty Publications

Separated spacecraft interferometry missions will require spacecraft to move in a coordinated fashion to ensure minimal and balanced consumption of fuel. This paper develops strategies for determining interferometry mission plans that result in significant fuel savings over standard approaches. Simulation results demonstrate that valuable reductions in fuel consumption can be realized by combining the retargeting and imaging maneuvers required to image multiple stellar sources. Fuel-optimal imaging strategies have been developed for two-spacecraft interferometry missions similar to the proposed Space Technology 3 mission using chained local optimization methods. Based on these strategies, sampling pattern guidelines for space-borne interferometry missions have been …

Statistical Continuum Theory For Large Plastic Deformation Of Polycrystalline Materials, Brent L. Adams, S. Ahzi, H. Garmestani, S. Lin

Faculty Publications

This paper focuses on the application of statistical continuum mechanics to the prediction of mechanical response of polycrystalline materials and microstructure evolution under large plastic deformations. A statistical continuum mechanics formulation is developed by applying a Green's function solution to the equations of stress equilibrium in an infinite domain. The distribution and morphology of grains (crystals) in polycrystalline materials is represented by a set of correlation functions that are described by the corresponding probability functions. The elastic deformation is neglected and a viscoplastic power law is employed for crystallographic slip in single crystals. In this formulation, two- and three-point probability …

Fuel Optimization For Constrained Rotation Of Satellite Formations, Timothy Mclain, Randal W. Beard, Fred Y. Hadaegh

Faculty Publications

This paper considers the problem of reorienting a constellation of spacecraft such that the fuel distributed across the constellation is both conserved and expended uniformly. Results are derived for constellations with an arbitrary number of spacecraft, assuming that the constellation is in free space, that the spacecraft mass is time invariant, and that the thrusters can produce thrust in any direction. An open-loop control algorithm is derived by minimizing a cost function that trades off total fuel minimization and fuel equalization. The associated optimization problem is shown to be amenable to standard algorithms. Simulation results using a four-spacecraft constellation are …

Nonlinear Robust Missile Autopilot Design Using Successive Galerkin Approximation, Timothy Mclain, Randal W. Beard

Faculty Publications

The application of a new nonlinear robust control strategy to the design of missile autopilots is presented. The control approach described and demonstrated here is based upon the numerical solution of the Hamilton-Jacobi-Isaacs equation by Successive Galerkin Approximation. Using this approach, feedback controllers are computed by an iterative application of a numerical Galerkin-type PDE solver. Application of this approach to the design of a pitch-axis autopilot for a missile having uncertain pitch moment and lift force is described.

Successive Galerkin Approximation Of The Isaacs Equation, Timothy Mclain, Randal W. Beard, John T. Wen

Faculty Publications

The successive Galerkin approximation (SGA) algorithm has recently been developed for approximating solutions to the Hamilton-Jacobi-Isaacs equation. The algorithm produces feedback control laws that are stabilizing on a well-defined region of state space. The objective of this paper is to demonstrate the application of the SGA algorithm to two simple examples. The examples serve several purposes: first they illustrate how the algorithm is applied in a setting that is simple enough to write out in detail, second they demonstrate the convergence of the algorithm in a setting where the actual solution can be derived analytically.

Successive Galerkin Approximation Of A Nonlinear Optimal Attitude Control, Timothy Mclain, Randal W. Beard, Johnathan Lawton

Faculty Publications

This paper presents the application of the successive Galerkin approximation (SGA) to the Hamilton-Jacobi-Bellman equation to obtain solutions of the optimal attitude control problem. Galerkin's method approximates the value function by a truncated Galerkin series expansion. To do so, a truncated Galerkin basis set is formed. A sufficient number of functions must be included in this Galerkin basis set in order to guarantee that the solution will be a stabilizing control. By increasing the size of the Galerkin basis the quality of the approximation is improved at the cost of rapid growth in the computation load of the SGA. A …

Synthesis And Experimental Testing Of A Nonlinear Optimal Tracking Controller, Timothy Mclain, Randal W. Beard, Christopher A. Bailey

Faculty Publications

This paper presents a novel approach for developing tracking controllers for nonlinear systems. The approach involves the numerical solution, by Galerkin approximation, of the time-varying Hamilton-Jacobi-Bellman (HJB) equation and results in a nonlinear controller approximating the optimal tracking control law for a specified desired trajectory and cost function. Experimental results are presented for a nonlinear pendulum system.

Observations Of Lattice Curvature Near The Interface Of A Deformed Aluminium Bicrystal, Brent L. Adams, W. E. King, S. Sun

Faculty Publications

This work was partially supported by MRSEC Program of the National Science Foundation (DMR-9632556), and under the auspices of the US Department of Energy and Lawrence Livermore National Laboratory under contract W-7405- Eng-48. S. Sun gratefully acknowledges the comments of Professor E. T. Onat, Professor B. T. Chu and Professor W. Tong of the Mechanical Engineering Department at Yale University, and their valuable guidance in the process of completing this project as a doctoral dissertation. The assistance of B. El-Dasher of Carnegie-Mellon University is also gratefully acknowledged. Reported here is a study of the pattern of lattice curvature near the …

Spin-Up In A Tank Induced By A Rotating Bluff Body, R. Daniel Maynes, J. Klewicki, P. Mcmurty

Faculty Publications

Spin-up of a turbulent flow in a cylindrical tank caused by a rotating bluff body has been investigated using flow visualization, fluid velocity measurements, and hydrodynamic torque measurements. During the spin-up process three distinct temporal regimes exist. These regimes are: (i) a build-up regime where the torque and the tangential velocity fluctuations in the close proximity of the body remain constant; (ii) a decay regime where these quantities decay with power-law relations; and (iii) a mean flow steady state where these values remain relatively constant. Experiments were conducted in two tanks differing in volume by a factor of 80 and …

The Evolution Of Probability Functions In An Inelasticly Deforming Two-Phase Medium, Brent L. Adams, H. Garmestani, S. Lin

Faculty Publications

A formulation is introduced here for the evolution of correlation functions in an inelastically deforming two phase medium. Probability functions play a major role in describing the statistical distribution of different phases in a heterogeneous medium in the development of statistical continuum theory. Proper formulation of statistical continuum model for inelastic deformation requires better understanding of the evolution of the corresponding probability functions. A two point probability function representation is used to approximate the statistical correlation functions. The evolution of these functions requires the information from higher order probability functions, in this case, a three point probability function. A decomposition …

Successive Galerkin Approximation Algorithms For Nonlinear Optimal And Robust Control, Timothy Mclain, Randal W. Beard

Faculty Publications

Nonlinear optimal control and nonlinear H infinity control are two of the most significant paradigms in nonlinear systems theory. Unfortunately, these problems require the solution of Hamilton-Jacobi equations, which are extremely difficult to solve in practice. To make matters worse, approximation techniques for these equations are inherently prone to the so-called 'curse of dimensionality'. While there have been many attempts to approximate these equations, solutions resulting in closed-loop control with well-defined stability and robustness have remained elusive. This paper describes a recent breakthrough in approximating the Hamilton-Jacobi-Bellman and Hamilton-Jacobi-Isaacs equations. Successive approximation and Galerkin approximation methods are combined to derive …

Nonlinear Optimal Control Design Of A Missile Autopilot, Tim Mclain, Randal W. Beard

Faculty Publications

The application of a new nonlinear optimal control strategy to the design of missile autopilots is presented. The control approach described and demonstrated here is based upon the numerical solution of the Hamilton-Jacobi-Bellman equation by Successive Galerkin Approximation. Using this approach, feedback controllers are computed by an iterative application of a numerical Galerkin-type PDE solver. Simulation results demonstrating the application of this approach to the design of a missile autopilot are presented.

Development And Experimental Validation Of An Underwater Manipulator Hydrodynamic Model, Timothy W. Mclain, Stephen M. Rock

Faculty Publications

Hydrodynamic forces can be large and hence have a significant effect on the dynamic performance of underwater manipulation systems. this paper investigates these forces for a cylindrical single-link arm undergoing motions that are characteristics of a robotic manipulator. Based on flow visualization, theoretical analysis, and experimental measurements, a new model is developed that describes these forces. This model differs from previous models in that the drag and added-mass coefficients are state-dependent functions that depend on the distance traveled by the arm. A factor of four improvement in accuracy is demonstrated over standard constant-coefficient models.

Successive Galerkin Approximations To The Nonlinear Optimal Control Of An Underwater Robotic Vehicle, Timothy Mclain, Randal W. Beard

Faculty Publications

The application of a new nonlinear optimal control strategy to the station-keeping control of an underwater robotic vehicle is considered. The control approach described and demonstrated here is based upon the numerical approximation of solutions to the Hamilton-Jacobi-Bellman equation. These solutions are computed by an iterative application of Galerkin's method. Preliminary simulation results demonstrating the application of this approach to the control of an underwater vehicle in the horizontal plane are presented.

Fuel Equalized Retargeting For Separated Spacecraft Interferometry, Timothy Mclain, Randal W. Beard, Fred Y. Hadaegh

Faculty Publications

Motivated by NASA's proposed Deep Space 3 interferometer mission, the paper considers the problem of reorienting a constellation of spacecraft such that the total fuel distributed across the constellation is both conserved and expended uniformly. The spacecraft constellation is controlled to reorient as if it were a rigid body. Two approaches to fuel equalization are investigated. The first approach picks a point of rotation a priori that optimizes an objective function that trades off minimum-fuel maneuvers and maneuvers that equalize the fuel. Since the point of rotation is selected a priori and is fixed during the rotation, this approach is …

A Practical Algorithm For Designing H∞ Control Laws, Timothy Mclain, Randal W. Beard

Faculty Publications

We describe an approximation method for the Hamilton-Jacobi-Isaacs (HJI) equation that results in feedback control. The approximation is accomplished via a two-step successive Galerkin approximation scheme. An application of the technique to the control of the forward motion of an underwater vehicle is described.

Determination Of The Asymmetry Parameter And Scattering Coefficient Of Turbid Media From Spatially Resolved Reflectance Measurments, Matthew R. Jones, Yukio Yamada

Faculty Publications

We present a technique for determining the asymmetry parameter and scattering coefficient of turbid media from spatially resolved reflectance measurements. This technique will contribute to the development of medical applications in which it is necessary to predict the distribution and propagation of light in tissue. Based on Monte Carlo simulations, we derived correlations which relate the reduced scattering coefficient and the asymmetry parameter to the relative reflectance curve. Initial estimates of the optical properties are obtained from these correlations. Final values are obtained by adjusting the optical parameters and repeating the Monte Carlo simulations until the simulated reflectance pattern matches …

Statistical Continuum Theory For Inelastic Behavior Of A Two-Phase Medium, Brent L. Adams, H. Garmestani, S. Lin

Faculty Publications

This work was supported in part (B.L. Adams) by the MRSEC Program of the National Science Foundation under Award no. DMR-9632556. Further support was provided by the Center for Materials Research and Technology (MARTECH at FSU) and Center for Nonlinear and Nonequilibrium Sciences (CENNAS at FAMU). A statistical contiuum mechanics formulation is presented to predict the inelastic behavior of a medium consisting of two isotropic phases. The phase distribution and morphology are represented by a two-point probability function. The isotropic behavior of the single phase medium is represented by a power law relationship between the strain rate and the resolved …

Extracting The Relative Grain Boundary Free Energy And Mobility Functions From The Geometry Of Microstructures, Brent L. Adams, D. Kinderlehrer, W. W. Mullins, Anthony D. Rollett, Shlomo Ta'asan

Faculty Publications

This work was supported primarily by the MRSEC Program of the National Science Foundation under Award Number DMR-9632556. This paper describes a method for extracting, from measurements of a polycrystal, the relative excess free energy and the relative mobility of the grain boundaries as functions of the crystallographic type (five degrees of freedom) and relevant thermodynamic variables. The method requires the simultaneous measurement of both the geometry and the crystallography of a large number of grain boundary intersections; the crystallographic information may be obtained from orientation imaging microscopy (OIM). For simplicity, the intersections will be assumed to be triple junctions …

Robotic Tcf And Rigid-Body Calibration Methods, Edward Red, Xuguang Wang

Faculty Publications

For off-line programming to work, systematic methods must be developed to account for non-ideal performance of the parts and devices in the manufacturing cell. Although much of the literature focuses on robot inaccuracy, this paper considers practical methods for the tool control frame (TCF) calibration and rigid-body compensation required to close the inverse kinematics loop for target driven tasks.

Nonlinear Optimal Control Of A Hydraulically Actuated Positioning System, Timothy Mclain, Randal W. Beard

Faculty Publications

In this paper, the nonlinear optimal control problem is formulated for the position control of an electrohydraulic servo system. The optimal control is given by the solution to the Hamilton-Jacobi-Bellman equation, which in this case cannot be solved explicitly. An alternative method, based upon successive Galerkin approximation, is used to obtain an approximate optimal solution. Preliminary simulation results, demonstrating the application of this approach to the position control of a hydraulically actuated device, are presented.

On-Line Cartesian Trajectory Control Of Mechanisms Along Complex Curves, Edward Red, Zhaoxue Yang

Faculty Publications

New methods have been developed to control a mechanism's realtime Cartesian motion along spatially complex curves such as Non-Uniform Rational B-splines (NURBS). The methods dynamically map the critical trajectory parameters between parameter space, Cartesian space, and joint space. Trajectory models that relate Cartesian tool speeds and accelerations to joint speeds and accelerations have been generalized so that they can be applied to most classes of robots and CNC mechanisms.

Extracting The Grain Boundary Character/Free Energy Relationship From The Microstructure: Pure <100> And <111> Tilt Boundaries, Brent L. Adams, S. Costiner, D. Kinderlehrer, W. W. Mullins, Shlomo Ta'asan

Faculty Publications

This work was supported primarily by the MRSEC Program of the National Science Foundation under Award Number DMR-9632556. Analysis is described to extract the excess free energy of grain boundaries from the mesotexture of well-equilibrated polycrystalline samples. The approach is based upon the force and torque balances at triple junctions described in the classical work of Herring. The main advantage of the approach is that the free energy function is obtained over the full fundamental zone of grain boundary types. For the purposes of exposition, the method is described for specified two-parameter hypersurfaces in the fundamental zone for cubic polycrystals …

Bounding Elastic Constants Of An Orthotropic Polycrystal Using Measurements Of The Microstructure, Brent L. Adams, M. J. Beran, T. A. Mason, Ted Olsen

Faculty Publications

We show how information about the elastic stiffness and compliance of an orthotropic polycrystal may be obtained from measurements of the statistical properties of the microstructure. We begin by discussing the statistical properties of the governing equations and the hierarchy that results when the equations are averaged. Perturbation solutions are obtained in terms of low-order statistical information. Using methods previously developed, we derive bounds for the elastic stiffnesses and compliances. A heirarchy of bounds is derived using the statistical information obtained from measurements of the microstructure. We discuss the methods used to obtain the correlation functions of the microstructure and …

Grain-Boundary Structure Effects On Intergranular Stress Corrosion Cracking Of Alloy X-750, Brent L. Adams, Ted Olsen, N. Panayotou, Y. Pan

Faculty Publications

This work was supported by the Department of Energy under Grant No. DE-FG02-88ER 45355. TO was supported by the National Science Foundation during her 1993-94 stay at the Institute for Advanced Studies (Princeton) under grant DMS-9304580. The authors wish to acknowledge helpful discussion with Carol Nichols, John Hack, Gino Palumbo, Karl Aust, and Gary Was. It is well known that the properties and behavior of grain boundaries are strongly affected by local chemistry and atomic structure. This paper focuses on the mesoscale description of grain boundary structure (i.e. the five crystallographic degrees of freedom) and correlations with intergranular stress corrosion …

Experiments In The Coordinated Control Of An Underwater Arm/Vehicle System, Timothy W. Mclain, Stephen M. Rock, Michael J. Lee

Faculty Publications

The addition of manipulators to small autonomous underwater vehicles (AUVs) can pose significant control challenges due to hydrodynamic interactions between the arm and the vehicle. Experiments conducted at the monterey Bay Aquarium Research Institute (MBARI) using the OTTER vehicle have shown that dynamical interactions between an arm and a vehicle can be very significant. For the experiments reported in this paper, a single-link "arm" was mounted on OTTER. Tests showed that for 90-degree, two-second repetitive slews of the arm, the vehicle would move as much as 18 degrees in roll and 14 degrees in yaw when no vehicle control was …

Otter: A Testbed Submersible For Robotics Research, Tim Mclain, H H. Wang, R L. Marks, S D. Fleischer, D W. Miles, G A. Sapilewski, S M. Rock, M J. Lee, R C. Burton

Faculty Publications

Untethered, unmanned submersibles (UUSs) have the potential of becoming useful tools in nuclear reactor inspection and repair and waste-site cleanup and survey, in addition to subsea exploration. Classical "hand-in-glove" control methods used currently by tethered, remotely-operated vehicles (ROVs) are unsuitable for UUS systems which have, at best, limited communications. The Stanford Aerospace Robotics Laboratory (ARL) has joined with the Monterey Bay Aquarium Research Institute (MBARI) in a program to develop new methods of controlling UUS systems.

As a part of this effort, a submersible testbed has been built to test and develop new technologies that will make UUSs useful tools …

Characterization Of The Near-Interface Region Of Chemical Vapor Deposited Diamond Films On Silicon By Backscatter Kikuchi Diffraction, Brent L. Adams, K. Kunze, S. Geier, R. Hessmer, M. Schreck, B. Rauschembach, B. Stritzker

Faculty Publications

The lattice orientations near the interface of chemical vapor deposited diamond films on Si(001) have been studied by orientation imaging microscopy. This technique is based on the automated analysis of electron backscatter Kikuchi diffraction patterns. The electron beam has been scanned in discrete steps over the reverse side of the diamond film after having removed the substrate. The obtained data have allowed us to determine the texture and to visualize quantitatively the orientational arrangement of and among individual diamond crystallites in the near-interface region. A comparison with the orientation of the substrate has proved the existence of epitaxially nucleated grains. …

Characterization Of The Near-Interface Region Of Chemical Vapor Deposited Diamond Films On Silicon By Backscatter Kikuchi Diffraction, Brent L. Adams, K. Kunze, S. Geier, R. Hessmer, B. Rauschembach, M. Schreck, B. Stritzker

Faculty Publications

B.L.A. and K.K. gratefully acknowledge support under a Materials Research Group Award by the National Science Foundation No. DMR-9001278. Also the software support by Th. Bollmeier is greatly appreciated. The lattice orientations near the interface of chemical vapor deposited diamond films on Si(001) have been studied by orientation imaging microscopy. This technique is based on the automated analysis of electron backscatter Kikuchi diffraction patterns. The electron beamhas been scanned in discrete steps over the reverse side of the diamond film after having removed the substrate. The obtained data have allowed us to determine the texture and to visualize quantitatively the …