(SoE) School of Engineering

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Shiv Nadar University

Design procedures based on exact eigenstructure assignment are not suitable because of very high computational requirements. A computation-effective control design procedure for eigenstructure assignment using aggregation is presented. Dominant eigenvalues are placed at specified locations in the complex plane and the non-dominant eigenvalues are placed in a specified disk. The proposed design procedure is applied to the trajectory tracking problem of a robot manipulator. An error-pattern based payload estimation and compensation scheme is also proposed to improve performance robustness. © 1993 Taylor & Francis Group, LLC.

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Electrical Engineering

International Journal of Systems Science

Eigenstructure assignment in robot tracking applications

A new nondestructive technique for the determination of the depth of the proton exchanged (PE) layer in LiNbO3 is reported. The techniques relies on the difference in phase of measured pyroelectric voltages, induced by a modulated laser beam incident on the exchanged and unexchanged regions. Measurements of PE layer thickness in a Z-cut LiNbO3 sample have been corroborated by prevalent, more elaborate, optical characterisation techniques. © 1993, The Institution of Electrical Engineers. All rights reserved.

Electronics Letters

Etermination of depth of proton exchanged layer in LiNbO3, from laser induced pyroelectric signals

We report a new nondestructive technique for the determination of depth of proton exchanged (PE) layers in LiNbO3. Relying on the difference in the magnitudes of measured pyroelectric voltages, induced by an intensity modulated laser beam, on the exchanged and unexchanged regions, the depth of the PE layer has been measured and corroborated by a conventional optical characterization method.

Fulltext

Applied Physics Letters

Proton exchanged depth determination in LiNbO3 from laser induced pyroelectric voltage measurements

To make an appropriate choice of linear model for the development of real‐time control of robot manipulators, four direct linearization schemes have been studied here on the basis of computation and accuracy. Accuracy is assured in the state linearization method, whereas the rate linearization method leads to a satisfactory trade‐off between computational effort and accuracy. In the case of high‐velocity motions, a combination of state and rate linearization is proposed. Copyright © 1992 Wiley Periodicals, Inc., A Wiley Company

Journal of Robotic Systems

Linearized dynamic models for trajectory control of robot manipulators

We present an optimal algorithm for sorting n integers in the range [1, nc] (for any constant c) for the EREW PRAM model where the word length is nε, for any ε&gt;0. Using this algorithm, the best known upper bound for integer sorting on the (O(log n) word length) EREW PRAM model is improved. In addition, a novel parallel range reduction algorithm which results in a near optimal randomized integer sorting algorthm is presented. For the case when the keys are uniformly distributed integers in an arbitrary range, we give an algorithm whose expected running time is optimal. © 1992 Springer-Verlag.

Acta Informatica

On parallel integer sorting

We present parallel algorithms for some fundamental problems in computational geometry which have a running time of O(log n) using n processors, with very high probability (approaching 1 as n → ∞). These include planar-point location, triangulation, and trapezoidal decomposition. We also present optimal algorithms for three-dimensional maxima and two-set dominance counting by an application of integer sorting. Most of these algorithms run on a CREW PRAM model and have optimal processor-time product which improve on the previously best-known algorithms of Atallah and Goodrich [5] for these problems. The crux of these algorithms is a useful data structure which emulates the plane-sweeping paradigm used for sequential algorithms. We extend some of the techniques used by Reischuk [26] and Reif and Valiant [25] for flashsort algorithm to perform divide and conquer in a plane very efficiently leading to the improved performance by our approach. © 1992 Springer-Verlag New York Inc.

Algorithmica

Optimal randomized parallel algorithms for computational geometry

We present algorithms for maintaining data structures supporting fast (polylogarithmic) point-location and ray-shooting queries in arrangements of hyperplanes. This data structure allows for deletion and insertion of hyperplanes. Our algorithms use random bits in the construction of the data structure but do not make any assumptions about the update sequence or the hyperplanes in the input. The query bound for our data structure is Õ(polylog(n)), where n is the number of hyperplanes at any given time, and the Õ notation indicates that the bound holds with high probability, where the probability is solely with respect to randomization in the data structure. By high probability we mean that the probability of error is inversely proportional to a large degree polynomial in n. The space requirement is Õ(nd). The cost of update is Õ(nd-1 log n. The expected cost of update is O(nd-1); the expectation is again solely with respect to randomization in the data structure. Our algorithm is extremely simple. We also give a related algorithm with optimal Õ(log n) query time, expected O(nd) space requirement, and amortized O(nd-1) expected cost of update. Moreover, our approach has a versatile quality which is likely to have further applications to other dynamic algorithms. For d=2, 3 we also show how to obtain polylogarithmic update time in the CRCW PRAM model so that the processor-time product matches (within a polylogarithmic factor) the sequential update time. © 1992 Springer-Verlag New York Inc.

Discrete & Computational Geometry

Dynamic point location in arrangements of hyperplanes

We give an alternate implementation of the fractional cascading data-structure of Chazelle and Guibas to do iterativesearch for a key in multiple ordered lists. The construction of our data-structure uses randomization and simplifies the algorithm of Chazelle and Guibas vastly making it practical to implement. Although our bounds are asymptotically similar to the earlier ones, there are improvements in the constant factors. Our analysis is novel and captures some of the inherent difficulties associated with the fractional casading data structure. In particular, we use tools from branching process theory and derive some useful asymptotic bounds. The probability of deviation from the expected performance bounds decreases rapidly with number of keys. © Springer-Verlag Berlin Heidelberg 1992.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Fractional cascading simplified

The tracking problem for a robotic manipulator with uncertain dynamics is considered. The proposed control scheme utilizes manipulator ‚inverse’ as an adaptive feedforward controller, the controller gains are updated to cow with variations in the manipulator inverse due to changes the operating point A feedback conlroller that provides arbitrary assignment of all eigenvalues and certain parts o f 3 closed-loop eigenvector structure: Is also used. Eigenstructure assignment is used to enhance closed-loop stability and to achieve robust tracking. Simulation results are presented in support of the proposed control scheme. The results demonstrate satisfactory performance of the controller despite variations in payload. © 1991 Taylor & Francis Group, LLC.

Robust trajectory control of a robot manipulator

The Skip-list data-structure was proposed by Pugh as an alternate to balanced binary search trees. This remarkably simple data-structure uses randomization and Pugh proved that the expected performance is comparable to the balanced trees. In this note we prove that the performance can be further guaranteed in the following sense: the probability of the search time or space complexity exceeding their expected values, approaches 0 rapidly as the number of keys increases. © 1991.