The Experts below are selected from a list of 24183 Experts worldwide ranked by ideXlab platform
Debasish Roy - One of the best experts on this subject based on the ideXlab platform.
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An accurate numerical integration scheme for finite Rotations using Rotation Vector parametrization
Journal of the Franklin Institute, 2010Co-Authors: Susanta Ghosh, Debasish RoyAbstract:A numerical integration procedure for Rotational motion using a Rotation Vector parametrization is explored from an engineering perspective by using rudimentary Vector analysis. The incremental Rotation Vector, angular velocity and acceleration correspond to different tangent spaces of the Rotation manifold at different times and have a non-Vectorial character. We rewrite the equation of motion in terms of Vectors lying in the same tangent space, facilitating Vector space operations consistent with the underlying geometric structure. While any integration algorithm (that works within a Vector space setting) may be used, we presently employ a family of explicit Runge-Kutta algorithms to solve this equation. While this work is primarily motivated out of a need for highly accurate numerical solutions of dissipative Rotational systems of engineering interest, we also compare the numerical performance of the present scheme with some of the invariant preserving schemes, namely ALGO-C1, STW, LIEMIDEA] and SUBCYC-M. Numerical results show better local accuracy via the present approach vis-a-vis the preserving algorithms. It is also noted that the preserving algorithms do not simultaneously preserve all constants of motion. We incorporate adaptive time-stepping within the present scheme and this in turn enables still higher accuracy and a `near preservation' of constants of motion over significantly longer intervals. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
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A frame-invariant scheme for the geometrically exact beam using Rotation Vector parametrization
Computational Mechanics, 2009Co-Authors: Susanta Ghosh, Debasish RoyAbstract:While frame-invariant solutions for arbitrarily large Rotational deformations have been reported through the orthogonal matrix parametrization, derivation of such solutions purely through a Rotation Vector parametrization, which uses only three parameters and provides a parsimonious storage of Rotations, is novel and constitutes the subject of this paper. In particular, we employ interpolations of relative Rotations and a new Rotation Vector update for a strain-objective finite element formulation in the material framework. We show that the update provides either the desired Rotation Vector or its complement. This rules out an additive interpolation of total Rotation Vectors at the nodes. Hence, interpolations of relative Rotation Vectors are used. Through numerical examples, we show that combining the proposed update with interpolations of relative Rotations yields frame-invariant and path-independent numerical solutions. Advantages of the present approach vis-a-vis the updated Lagrangian formulation are also analyzed.
Susanta Ghosh - One of the best experts on this subject based on the ideXlab platform.
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An accurate numerical integration scheme for finite Rotations using Rotation Vector parametrization
Journal of the Franklin Institute, 2010Co-Authors: Susanta Ghosh, Debasish RoyAbstract:A numerical integration procedure for Rotational motion using a Rotation Vector parametrization is explored from an engineering perspective by using rudimentary Vector analysis. The incremental Rotation Vector, angular velocity and acceleration correspond to different tangent spaces of the Rotation manifold at different times and have a non-Vectorial character. We rewrite the equation of motion in terms of Vectors lying in the same tangent space, facilitating Vector space operations consistent with the underlying geometric structure. While any integration algorithm (that works within a Vector space setting) may be used, we presently employ a family of explicit Runge-Kutta algorithms to solve this equation. While this work is primarily motivated out of a need for highly accurate numerical solutions of dissipative Rotational systems of engineering interest, we also compare the numerical performance of the present scheme with some of the invariant preserving schemes, namely ALGO-C1, STW, LIEMIDEA] and SUBCYC-M. Numerical results show better local accuracy via the present approach vis-a-vis the preserving algorithms. It is also noted that the preserving algorithms do not simultaneously preserve all constants of motion. We incorporate adaptive time-stepping within the present scheme and this in turn enables still higher accuracy and a `near preservation' of constants of motion over significantly longer intervals. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
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A frame-invariant scheme for the geometrically exact beam using Rotation Vector parametrization
Computational Mechanics, 2009Co-Authors: Susanta Ghosh, Debasish RoyAbstract:While frame-invariant solutions for arbitrarily large Rotational deformations have been reported through the orthogonal matrix parametrization, derivation of such solutions purely through a Rotation Vector parametrization, which uses only three parameters and provides a parsimonious storage of Rotations, is novel and constitutes the subject of this paper. In particular, we employ interpolations of relative Rotations and a new Rotation Vector update for a strain-objective finite element formulation in the material framework. We show that the update provides either the desired Rotation Vector or its complement. This rules out an additive interpolation of total Rotation Vectors at the nodes. Hence, interpolations of relative Rotation Vectors are used. Through numerical examples, we show that combining the proposed update with interpolations of relative Rotations yields frame-invariant and path-independent numerical solutions. Advantages of the present approach vis-a-vis the updated Lagrangian formulation are also analyzed.
Lu Zhi-dong - One of the best experts on this subject based on the ideXlab platform.
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Application and Optimization of Rotation Vector Algorithm under Dynamic Motion
Computer Simulation, 2008Co-Authors: Lu Zhi-dongAbstract:A new optimization algorithm for SDINS (Strapdown Inertial Navigation System) based on mlti-samples Rotation Vector under high dynamic coning motion is presented in this paper. For attitude-update-matrix of SDINS, the coning motion is the worst working condition, and results in the math platform seriously drift, even SINS invalidation. On the other hand, the algorithm drift is reached to least under other conditions so long as it is least under coning motion. The result shows that the drift of optimization algorithm is lower than that before, and with more samples and higher attitude-update-matrix accuracy. Also, the drift of algorithm is obviously reduced comparing with simple-sample and double-sample.
Zhao Zhong - One of the best experts on this subject based on the ideXlab platform.
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Simulation of Improved Rotation Vector Algorithm in Coning Motion
Computer Simulation, 2010Co-Authors: Zhao ZhongAbstract:The attitude algorithm plays an important role in strap-down navigation system algorithms.The main method of improving precision of attitude algorithms based on Rotation Vector is to add the output hits of gyro in one update cycle of the Rotation Vector.However,the method by increasing hits will totally cause data acquisition and data transmission computing of navigation computer increasing greatly.This paper deals with some research on improving algorithms precision without adding the output hits of gyro in one Rotation Vector update cycle.Also higher order items are added in Rotation Vector expression,and a new style of algorithm is designed in this paper.Finally,the simulation of oringinal and improved methods is gived and the comparison is made.
Liang Jin Wan - One of the best experts on this subject based on the ideXlab platform.
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Application of Rotation Vector in SINS Algorithms
Applied Mechanics and Materials, 2014Co-Authors: Liang Jin Wan, Chun DongAbstract:Updating attitude precisely in time is the primary task of strapdown inertial navigation system(SINS) algorithms. This paper mainly studied the application of Rotation Vector in three different methods of data fusion respectively named linear interpolation, gradient descent and complementary filter for attitude-updating, using low-cost MEMS inertial sensors in SINS. Meanwhile, an idea that the quaternion attitude could be updated by constructing micro-Rotation quaternion from Rotation Vector in the sampling interval is proposed. The idea is based on geometric interpretation of space Rotation transformation, while the general method is the differential equations of quaternion about Rotation Vector. Therefore the new method is an approximation method within enough short update interval, but its best superiority is the higher speed of attitude-updating than general method with little loss of accuracy because of no necessary to solve differential equations. The experimental results also show the effectiveness and accuracy of three improved algorithms with the new idea.
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Application of Rotation Vector algorithm for SINS attitude updating
2014 12th International Conference on Signal Processing (ICSP), 2014Co-Authors: Zhiqun Wang, Xunhe Yin, Liang Jin WanAbstract:The primary task of strap down inertial navigation system (SINS) algorithms is updating attitude timely and precisely. This paper presents an ARM based quad copter, using low-cost MEMS inertial sensors. In this paper we propose to use three methods, namely linear interpolation, gradient descent and complementary filter for attitude-updating. Meanwhile, an idea that the quaternion attitude could be updated by constructing micro-Rotation quaternion from Rotation Vector in the sampling interval is proposed. The idea is based on geometric interpretation of space Rotation transformation, while the general method is the differential equations of quaternion about Rotation Vector. Therefore the new method is an approximation method within enough short update intervals. Experiments on different methods show the effectiveness and accuracy of three improved algorithms with the Rotation Vector algorithm.
