A modal approach to hyper-redundant manipulator kinematics

This paper presents novel and efficient kinematic modeling techniques for “hyper-redundant” robots. This approach is based on a “backbone curve” that captures the robot's macroscopic geometric features. The inverse kinematic, or “hyper-redundancy resolution,” problem reduces to determining the time varying backbone curve behavior. To efficiently solve the inverse kinematics problem, the authors introduce a “modal” approach, in which a set of intrinsic backbone curve shape functions are restricted to a modal form. The singularities of the modal approach, modal non-degeneracy conditions, and modal switching are considered. For discretely segmented morphologies, the authors introduce “fitting” algorithms that determine the actuator displacements that cause the discrete manipulator to adhere to the backbone curve. These techniques are demonstrated with planar and spatial mechanism examples. They have also been implemented on a 30 degree-of-freedom robot prototype

Caution or activism? Monetary policy strategies in an open economy

We examine optimal policy in an open-economy model with uncertainty and learning, where monetary policy actions affect the economy through the real exchange rate channel. Our results show that the degree of caution or activism in optimal policy depends on whether central banks are in coordinated or uncoordinated equilibrium. If central banks coordinate their policy actions then activism is optimal. In contrast, if there is no coordination, caution prevails. In the latter case caution is optimal because it helps central banks to avoid exposing themselves to manipulative actions by other central banks

Control of large flexible spacecraft by the independent modal-space control method

The problem of control of a large-order flexible structure in the form of a plate-like lattice by the Independent Modal-Space Control (IMSC) method is presented. The equations of motion are first transformed to the modal space, thus obtaining internal (plant) decoupling of the system. Then, the control laws are designed in the modal space for each mode separately, so that the modal equations of motion are rendered externally (controller) decoupled. This complete decoupling applies both to rigid-body modes and elastic modes. The application of linear optimal control, in conjunction with a quadratic performance index, is first reviewed. A solution for high-order systems is proposed here by the IMSC method, whereby the problem is reduced to a number of modal minimum-fuel problems for the controlled modes

Robust H-infinity sliding mode control for nonlinear stochastic systems with multiple data packet losses

This is the post-print version of this Article. The official published version can be accessed from the link below - Copyright @ 2012 John Wiley & SonsIn this paper, an ∞ sliding mode control (SMC) problem is studied for a class of discrete-time nonlinear stochastic systems with multiple data packet losses. The phenomenon of data packet losses, which is assumed to occur in a random way, is taken into consideration in the process of data transmission through both the state-feedback loop and the measurement output. The probability for the data packet loss for each individual state variable is governed by a corresponding individual random variable satisfying a certain probabilistic distribution over the interval [0 1]. The discrete-time system considered is also subject to norm-bounded parameter uncertainties and external nonlinear disturbances, which enter the system state equation in both matched and unmatched ways. A novel stochastic discrete-time switching function is proposed to facilitate the sliding mode controller design. Sufficient conditions are derived by means of the linear matrix inequality (LMI) approach. It is shown that the system dynamics in the specified sliding surface is exponentially stable in the mean square with a prescribed ∞ noise attenuation level if an LMI with an equality constraint is feasible. A discrete-time SMC controller is designed capable of guaranteeing the discrete-time sliding mode reaching condition of the specified sliding surface with probability 1. Finally, a simulation example is given to show the effectiveness of the proposed method.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., the National Natural Science Foundation of China under Grant 61028008 and the Alexander von Humboldt Foundation of German

Synthesis of Linear Reversible Circuits and EXOR-AND-based Circuits for Incompletely Specified Multi-Output Functions

At this time the synthesis of reversible circuits for quantum computing is an active area of research. In the most restrictive quantum computing models there are no ancilla lines and the quantum cost, or latency, of performing a reversible form of the AND gate, or Toffoli gate, increases exponentially with the number of input variables. In contrast, the quantum cost of performing any combination of reversible EXOR gates, or CNOT gates, on n input variables requires at most O(n2/log2n) gates. It was under these conditions that EXOR-AND-EXOR, or EPOE, synthesis was developed. In this work, the GF(2) logic theory used in EPOE is expanded and the concept of an EXOR-AND product transform is introduced. Because of the generality of this logic theory, it is adapted to EXOR-AND-OR, or SPOE, synthesis. Three heuristic spectral logic synthesis algorithms are introduced, implemented in a program called XAX, and compared with previous work in classical logic circuits of up to 26 inputs. Three linear reversible circuit methods are also introduced and compared with previous work in linear reversible logic circuits of up to 100 inputs

Maximally-localized Wannier functions for entangled energy bands

We present a method for obtaining well-localized Wannier-like functions (WFs) for energy bands that are attached to or mixed with other bands. The present scheme removes the limitation of the usual maximally-localized WFs method (N. Marzari and D. Vanderbilt, Phys. Rev. B 56, 12847 (1997)) that the bands of interest should form an isolated group, separated by gaps from higher and lower bands everywhere in the Brillouin zone. An energy window encompassing N bands of interest is specified by the user, and the algorithm then proceeds to disentangle these from the remaining bands inside the window by filtering out an optimally connected N-dimensional subspace. This is achieved by minimizing a functional that measures the subspace dispersion across the Brillouin zone. The maximally-localized WFs for the optimal subspace are then obtained via the algorithm of Marzari and Vanderbilt. The method, which functions as a postprocessing step using the output of conventional electronic-structure codes, is applied to the s and d bands of copper, and to the valence and low-lying conduction bands of silicon. For the low-lying nearly-free-electron bands of copper we find WFs which are centered at the tetrahedral interstitial sites, suggesting an alternative tight-binding parametrization.Comment: 13 pages, with 9 postscript figures embedded. Uses REVTEX and epsf macro

Optimal Control for Open Quantum Systems: Qubits and Quantum Gates

This article provides a review of recent developments in the formulation and execution of optimal control strategies for the dynamics of quantum systems. A brief introduction to the concept of optimal control, the dynamics of of open quantum systems, and quantum information processing is followed by a presentation of recent developments regarding the two main tasks in this context: state-specific and state-independent optimal control. For the former, we present an extension of conventional theory (Pontryagin's principle) to quantum systems which undergo a non-Markovian time-evolution. Owing to its importance for the realization of quantum information processing, the main body of the review, however, is devoted to state-independent optimal control. Here, we address three different approaches: an approach which treats dissipative effects from the environment in lowest-order perturbation theory, a general method based on the time--evolution superoperator concept, as well as one based on the Kraus representation of the time-evolution superoperator. Applications which illustrate these new methods focus on single and double qubits (quantum gates) whereby the environment is modeled either within the Lindblad equation or a bath of bosons (spin-boson model). While these approaches are widely applicable, we shall focus our attention to solid-state based physical realizations, such as semiconductor- and superconductor-based systems. While an attempt is made to reference relevant and representative work throughout the community, the exposition will focus mainly on work which has emerged from our own group.Comment: 27 pages, 18 figure

Design optimization of transonic airfoils

Numerical optimization procedures were considered for the design of airfoils in transonic flow based on the transonic small disturbance (TSD) and Euler equations. A sequential approximation optimization technique was implemented with an accurate approximation of the wave drag based on the Nixon's coordinate straining approach. A modification of the Euler surface boundary conditions was implemented in order to efficiently compute design sensitivities without remeshing the grid. Two effective design procedures producing converged designs in approximately 10 global iterations were developed: interchanging the role of the objective function and constraint and the direct lift maximization with move limits which were fixed absolute values of the design variables

Guidance, flight mechanics and trajectory optimization. Volume 10 - Dynamic programming

Dynamic programming and multistage decision processes in guidance, flight mechanics, and trajectory optimizatio