subject:(Quaternion)

1. Huang, Liji. Quaternion equations and quaternion polynomial matrices.

Degree: Mathematics, 2013, University of Manitoba

URL: http://hdl.handle.net/1993/14907

We mainly consider finding formula solutions to quaternion equations and calculating the generalized inverses of quaternion polynomial matrices. Advisors/Committee Members: Zhang, Yang (Mathematics) (supervisor), Williams, Joe (Mathematics).

Subjects/Keywords: Quaternion

…quaternion equation" (Tait, 1890). However, Tait’s lifetime friend, William Thomson… …illustration on the matter "...I compare a quaternion formula to a pocketmap, a capital thing to… …mathematician Alexander McAulay, a quaternion advocate, stated that "...not much advance in… …quaternion orientation representations in today’s computer graphics and modeling community 3 1.1… …of the 3232 publications containing the word “quaternion” or “quaternionic” in the title…

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APA (6^th Edition):

Huang, L. (2013). Quaternion equations and quaternion polynomial matrices. (Masters Thesis). University of Manitoba. Retrieved from http://hdl.handle.net/1993/14907

Chicago Manual of Style (16^th Edition):

Huang, Liji. “Quaternion equations and quaternion polynomial matrices.” 2013. Masters Thesis, University of Manitoba. Accessed January 22, 2021. http://hdl.handle.net/1993/14907.

MLA Handbook (7^th Edition):

Huang, Liji. “Quaternion equations and quaternion polynomial matrices.” 2013. Web. 22 Jan 2021.

Vancouver:

Huang L. Quaternion equations and quaternion polynomial matrices. [Internet] [Masters thesis]. University of Manitoba; 2013. [cited 2021 Jan 22]. Available from: http://hdl.handle.net/1993/14907.

Council of Science Editors:

Huang L. Quaternion equations and quaternion polynomial matrices. [Masters Thesis]. University of Manitoba; 2013. Available from: http://hdl.handle.net/1993/14907

University of Texas – Austin

2. Mendes De Almeida Neto, Marcelino. Quaternion regression and finite-time controllers for attitude dynamics.

Degree: PhD, Aerospace Engineering, 2020, University of Texas – Austin

URL: http://dx.doi.org/10.26153/tsw/7431

► This dissertation presents two major research contributions to the field of attitude dynamics and control. The first topic comprises of estimating the angular velocity of… (more)

Subjects/Keywords: Quaternion; Attitude control; Attitude estimation; Slam; Quaternion regression; Finite time control

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APA (6^th Edition):

Mendes De Almeida Neto, M. (2020). Quaternion regression and finite-time controllers for attitude dynamics. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://dx.doi.org/10.26153/tsw/7431

Chicago Manual of Style (16^th Edition):

Mendes De Almeida Neto, Marcelino. “Quaternion regression and finite-time controllers for attitude dynamics.” 2020. Doctoral Dissertation, University of Texas – Austin. Accessed January 22, 2021. http://dx.doi.org/10.26153/tsw/7431.

MLA Handbook (7^th Edition):

Mendes De Almeida Neto, Marcelino. “Quaternion regression and finite-time controllers for attitude dynamics.” 2020. Web. 22 Jan 2021.

Vancouver:

Mendes De Almeida Neto M. Quaternion regression and finite-time controllers for attitude dynamics. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2020. [cited 2021 Jan 22]. Available from: http://dx.doi.org/10.26153/tsw/7431.

Council of Science Editors:

Mendes De Almeida Neto M. Quaternion regression and finite-time controllers for attitude dynamics. [Doctoral Dissertation]. University of Texas – Austin; 2020. Available from: http://dx.doi.org/10.26153/tsw/7431

University of Oklahoma

3. Wiebe, Jordan. Arithmetic in Quaternion Algebras and Quaternionic Modular Forms.

Degree: PhD, 2019, University of Oklahoma

URL: http://hdl.handle.net/11244/319651

► This dissertation has two parts. In the first part, we revisit the correspondence between spaces of modular forms and orders in quaternion algebras addressed first… (more)

Subjects/Keywords: Number theory; Quaternion algebras; Orders in quaternion algebras; Modular forms

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APA (6^th Edition):

Wiebe, J. (2019). Arithmetic in Quaternion Algebras and Quaternionic Modular Forms. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/319651

Chicago Manual of Style (16^th Edition):

Wiebe, Jordan. “Arithmetic in Quaternion Algebras and Quaternionic Modular Forms.” 2019. Doctoral Dissertation, University of Oklahoma. Accessed January 22, 2021. http://hdl.handle.net/11244/319651.

MLA Handbook (7^th Edition):

Wiebe, Jordan. “Arithmetic in Quaternion Algebras and Quaternionic Modular Forms.” 2019. Web. 22 Jan 2021.

Vancouver:

Wiebe J. Arithmetic in Quaternion Algebras and Quaternionic Modular Forms. [Internet] [Doctoral dissertation]. University of Oklahoma; 2019. [cited 2021 Jan 22]. Available from: http://hdl.handle.net/11244/319651.

Council of Science Editors:

Wiebe J. Arithmetic in Quaternion Algebras and Quaternionic Modular Forms. [Doctoral Dissertation]. University of Oklahoma; 2019. Available from: http://hdl.handle.net/11244/319651

Ruhr Universität Bochum

4. Niestroj, Fabian Oliver. 3D-Inertial-Messsysteme für Karosserie-Bewegungsanalysen in Kraftfahrzeug-Crashtests.

Degree: 2012, Ruhr Universität Bochum

URL: http://nbn-resolving.de/urn/resolver.pl?urn=urn:nbn:de:hbz:294-40960

► Im Rahmen der Dissertation ist ein 3D-Inertial-Messsystem für Karosserie-Bewegungsanalysen in Kraftfahrzeug-Crashtests entwickelt worden. Das Messsystem umfasst Sensorsysteme mit Inertialsensoren für Beschleunigungen und Drehraten, einen Datenrekorder… (more)

Subjects/Keywords: Inertialvermessung; Bewegungsanalyse; Crash-Test; Quaternion; Fahrzeugverhalten

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APA (6^th Edition):

Niestroj, F. O. (2012). 3D-Inertial-Messsysteme für Karosserie-Bewegungsanalysen in Kraftfahrzeug-Crashtests. (Thesis). Ruhr Universität Bochum. Retrieved from http://nbn-resolving.de/urn/resolver.pl?urn=urn:nbn:de:hbz:294-40960

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Niestroj, Fabian Oliver. “3D-Inertial-Messsysteme für Karosserie-Bewegungsanalysen in Kraftfahrzeug-Crashtests.” 2012. Thesis, Ruhr Universität Bochum. Accessed January 22, 2021. http://nbn-resolving.de/urn/resolver.pl?urn=urn:nbn:de:hbz:294-40960.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Niestroj, Fabian Oliver. “3D-Inertial-Messsysteme für Karosserie-Bewegungsanalysen in Kraftfahrzeug-Crashtests.” 2012. Web. 22 Jan 2021.

Vancouver:

Niestroj FO. 3D-Inertial-Messsysteme für Karosserie-Bewegungsanalysen in Kraftfahrzeug-Crashtests. [Internet] [Thesis]. Ruhr Universität Bochum; 2012. [cited 2021 Jan 22]. Available from: http://nbn-resolving.de/urn/resolver.pl?urn=urn:nbn:de:hbz:294-40960.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Niestroj FO. 3D-Inertial-Messsysteme für Karosserie-Bewegungsanalysen in Kraftfahrzeug-Crashtests. [Thesis]. Ruhr Universität Bochum; 2012. Available from: http://nbn-resolving.de/urn/resolver.pl?urn=urn:nbn:de:hbz:294-40960

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Anna University

5. Sujaritha M. Quaternion representation of color and texture integration based image segmentation approaches.

Degree: 2013, Anna University

URL: http://shodhganga.inflibnet.ac.in/handle/10603/13804

► Image segmentation is one of the most investigated subjects in the field of computer vision since it plays a crucial role in the development of… (more)

Subjects/Keywords: Quaternion; texture integration; image segmentation approaches

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APA (6^th Edition):

M, S. (2013). Quaternion representation of color and texture integration based image segmentation approaches. (Thesis). Anna University. Retrieved from http://shodhganga.inflibnet.ac.in/handle/10603/13804

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

M, Sujaritha. “Quaternion representation of color and texture integration based image segmentation approaches.” 2013. Thesis, Anna University. Accessed January 22, 2021. http://shodhganga.inflibnet.ac.in/handle/10603/13804.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

M, Sujaritha. “Quaternion representation of color and texture integration based image segmentation approaches.” 2013. Web. 22 Jan 2021.

Vancouver:

M S. Quaternion representation of color and texture integration based image segmentation approaches. [Internet] [Thesis]. Anna University; 2013. [cited 2021 Jan 22]. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/13804.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

M S. Quaternion representation of color and texture integration based image segmentation approaches. [Thesis]. Anna University; 2013. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/13804

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Houston

6. Phadnis, Mandar 1988-. Feedback Control of CubeSat for Attitude and Trajectory Corrections.

Degree: MSin Electrical Engineering, Electrical Engineering, 2013, University of Houston

URL: http://hdl.handle.net/10657/1553

► In order to analyze the performance of Cube Satellites with regards to orbit maintenance and attitude maneuvers, a three unit (3U) CubeSat with a mass… (more)

Subjects/Keywords: CubeSat; Small Satellites; Quaternion; Nonlinear; Spherical harmonics

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APA (6^th Edition):

Phadnis, M. 1. (2013). Feedback Control of CubeSat for Attitude and Trajectory Corrections. (Masters Thesis). University of Houston. Retrieved from http://hdl.handle.net/10657/1553

Chicago Manual of Style (16^th Edition):

Phadnis, Mandar 1988-. “Feedback Control of CubeSat for Attitude and Trajectory Corrections.” 2013. Masters Thesis, University of Houston. Accessed January 22, 2021. http://hdl.handle.net/10657/1553.

MLA Handbook (7^th Edition):

Phadnis, Mandar 1988-. “Feedback Control of CubeSat for Attitude and Trajectory Corrections.” 2013. Web. 22 Jan 2021.

Vancouver:

Phadnis M1. Feedback Control of CubeSat for Attitude and Trajectory Corrections. [Internet] [Masters thesis]. University of Houston; 2013. [cited 2021 Jan 22]. Available from: http://hdl.handle.net/10657/1553.

Council of Science Editors:

Phadnis M1. Feedback Control of CubeSat for Attitude and Trajectory Corrections. [Masters Thesis]. University of Houston; 2013. Available from: http://hdl.handle.net/10657/1553

University of Manchester

7. Hopkinson, Jeremy Franklin Lawrence. Quoric manifolds.

Degree: PhD, 2012, University of Manchester

URL: https://www.research.manchester.ac.uk/portal/en/theses/quoric-manifolds(e2ba0b95-ea55-4cb7-a98e-4f7426ce52cd).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.553503

► Davis and Januszkiewicz introduced in 1981 a family of compact real manifolds, the Quasi-Toric Manifolds, with a group action by a torus, a direct product… (more)

▼ Davis and Januszkiewicz introduced in 1981 a family of compact real manifolds, the Quasi-Toric Manifolds, with a group action by a torus, a direct product of circle (T) groups. Their manifolds have an orbit space which is a simple polytope with a distinct isotropy subgroup associated to each face of the polytope, subject to some consistency conditions. They defined a characteristic function which captured the properties of the isotropy subgroups, and showed that their manifolds can be classified by the polytope and characteristic function. They further showed that the cohomology ring of the manifold can be written down directly from properties derived from the polytope and the characteristic function. This work considers the question of how far the circle group T can be replaced by the group of unit quaternions Q in the construction and description of quasi-toric manifolds. Unlike T, the group Q is not commutative, so the actions of Q n on the product H n of the set of quaternions using quaternionic multiplication are studied in detail. Then, in direct analogy to the quasi-toric manifolds, a family of compact real manifolds, the Quoric Manifolds, is introduced which have an action by Q n, and whose orbit space is a polytope. A characteristic functor is defined on the faces of the polytope which captures the properties of the isotropy classes of the orbits of the action. It is shown that quoric manifolds can be classified in a manner similar to the quasi-toric manifolds, by the polytope and characteristic functor. A restricted family, the global quoric manifolds, which satisfy an additional condition are defined. It is shown that an infinite number of polytopes exist in any dimension over which a global quoric manifold can be defined. It is shown that any global quoric manifold can be described as a quotient space of a moment angle complex over the polytope, and that its integral cohomology ring can be calculated, taking a form analagous to that in the quasi-toric case.

Subjects/Keywords: 516.07; Manifold; quaternion; group action; classification; cohomology

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APA (6^th Edition):

Hopkinson, J. F. L. (2012). Quoric manifolds. (Doctoral Dissertation). University of Manchester. Retrieved from https://www.research.manchester.ac.uk/portal/en/theses/quoric-manifolds(e2ba0b95-ea55-4cb7-a98e-4f7426ce52cd).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.553503

Chicago Manual of Style (16^th Edition):

Hopkinson, Jeremy Franklin Lawrence. “Quoric manifolds.” 2012. Doctoral Dissertation, University of Manchester. Accessed January 22, 2021. https://www.research.manchester.ac.uk/portal/en/theses/quoric-manifolds(e2ba0b95-ea55-4cb7-a98e-4f7426ce52cd).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.553503.

MLA Handbook (7^th Edition):

Hopkinson, Jeremy Franklin Lawrence. “Quoric manifolds.” 2012. Web. 22 Jan 2021.

Vancouver:

Hopkinson JFL. Quoric manifolds. [Internet] [Doctoral dissertation]. University of Manchester; 2012. [cited 2021 Jan 22]. Available from: https://www.research.manchester.ac.uk/portal/en/theses/quoric-manifolds(e2ba0b95-ea55-4cb7-a98e-4f7426ce52cd).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.553503.

Council of Science Editors:

Hopkinson JFL. Quoric manifolds. [Doctoral Dissertation]. University of Manchester; 2012. Available from: https://www.research.manchester.ac.uk/portal/en/theses/quoric-manifolds(e2ba0b95-ea55-4cb7-a98e-4f7426ce52cd).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.553503

Delft University of Technology

8. van Steijn, Z.A. (author). Quaternion PCA and sparse PCA for shape variability.

Degree: 2020, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:a47738b0-f72b-4052-a7d3-8cf2f3997100

►

Principal component analysis (PCA) is commonly used in the fields of computer graphics and geometry processing for constructing subspaces that represent the variability present in… (more)

▼

Principal component analysis (PCA) is commonly used in the fields of computer graphics and geometry processing for constructing subspaces that represent the variability present in a dataset. Examples of such datasets are configurations of a non-rigid object, poses of a deformable character or snapshots from a simulation. By applying PCA to the dataset, one can generate a lower-dimensional space in which the data samples can be approximated well. Similar to PCA, one can also apply a sparse PCA technique to the geometric data. These methods aim to find components that do not only describe the deformations present in the data well, but are also sparse and localized. One of the problems related to PCA and sparse PCA is that they do not take the correlation between the x, y and z coordinates of each vertex into account when constructing the subspace. Furthermore, the methods are not invariant to rigid motion (rotations and translations) of the data samples, which means that rigid registration has to often be applied to the samples as a preprocessing step. Ideally, we would like to construct a subspace that is invariant to these rigid motions. This project investigates whether quaternions can be used to solve these problems. By describing each vertex as a pure quaternion, we show how quaternion PCA can be applied to geometric data and introduce a quaternion method of snapshots for improved computational efficiency. Additionally, we derive multiple quaternion sparse PCA techniques, which are inspired by the Sparse Localized Deformation Components (SPLOCS) method. Experimental results show that the quaternion PCA and sparse PCA methods are able to describe a richer space of deformations using fewer components. Furthermore, we show that quaternion PCA leads to improved rigid motion invariance.

Computer Science

Advisors/Committee Members: Hildebrandt, K.A. (mentor), Eisemann, E. (graduation committee), Liem, C.C.S. (graduation committee), Delft University of Technology (degree granting institution).

Subjects/Keywords: Principal Component Analysis; Dimensionality reduction; Quaternions; Quaternion PCA; Sparse PCA; Quaternion sparse PCA; Geometry processing

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APA (6^th Edition):

van Steijn, Z. A. (. (2020). Quaternion PCA and sparse PCA for shape variability. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:a47738b0-f72b-4052-a7d3-8cf2f3997100

Chicago Manual of Style (16^th Edition):

van Steijn, Z A (author). “Quaternion PCA and sparse PCA for shape variability.” 2020. Masters Thesis, Delft University of Technology. Accessed January 22, 2021. http://resolver.tudelft.nl/uuid:a47738b0-f72b-4052-a7d3-8cf2f3997100.

MLA Handbook (7^th Edition):

van Steijn, Z A (author). “Quaternion PCA and sparse PCA for shape variability.” 2020. Web. 22 Jan 2021.

Vancouver:

van Steijn ZA(. Quaternion PCA and sparse PCA for shape variability. [Internet] [Masters thesis]. Delft University of Technology; 2020. [cited 2021 Jan 22]. Available from: http://resolver.tudelft.nl/uuid:a47738b0-f72b-4052-a7d3-8cf2f3997100.

Council of Science Editors:

van Steijn ZA(. Quaternion PCA and sparse PCA for shape variability. [Masters Thesis]. Delft University of Technology; 2020. Available from: http://resolver.tudelft.nl/uuid:a47738b0-f72b-4052-a7d3-8cf2f3997100

University of Dayton

9. Long, Cameron E. Quaternion Temporal Convolutional Neural Networks.

Degree: MSin Computer Engineering, Electrical and Computer Engineering, 2019, University of Dayton

URL: http://rave.ohiolink.edu/etdc/view?acc_num=dayton1565303216180597

► Sequence Processing and Modeling are a domain of problems recently receiving significant attention for significant advancements in research and technology. While traditionally sequence processing using… (more)

Subjects/Keywords: Computer Science; Engineering; Quaternion Temporal Convolutional Network; QTCN; Quaternion Neural Network; Sequence Processing; Machine Learning

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APA (6^th Edition):

Long, C. E. (2019). Quaternion Temporal Convolutional Neural Networks. (Masters Thesis). University of Dayton. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=dayton1565303216180597

Chicago Manual of Style (16^th Edition):

Long, Cameron E. “Quaternion Temporal Convolutional Neural Networks.” 2019. Masters Thesis, University of Dayton. Accessed January 22, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=dayton1565303216180597.

MLA Handbook (7^th Edition):

Long, Cameron E. “Quaternion Temporal Convolutional Neural Networks.” 2019. Web. 22 Jan 2021.

Vancouver:

Long CE. Quaternion Temporal Convolutional Neural Networks. [Internet] [Masters thesis]. University of Dayton; 2019. [cited 2021 Jan 22]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=dayton1565303216180597.

Council of Science Editors:

Long CE. Quaternion Temporal Convolutional Neural Networks. [Masters Thesis]. University of Dayton; 2019. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=dayton1565303216180597

University of Pretoria

10. [No author]. The development of the quaternion normal distribution .

Degree: 2011, University of Pretoria

URL: http://upetd.up.ac.za/thesis/available/etd-06272011-164137/

► In this dissertation an overview on the real representation of quaternions in distribution theory is given. The density functions of the p-variate and matrix-variate quaternion… (more)

Subjects/Keywords: Wilks's statistic; Quaternion wishart distribution; Real representation; Characteristic function; Quaternion matrix-variate beta type i distribution; Meijer's g-function; Quaternion normal distribution; UCTD

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APA (6^th Edition):

author], [. (2011). The development of the quaternion normal distribution . (Masters Thesis). University of Pretoria. Retrieved from http://upetd.up.ac.za/thesis/available/etd-06272011-164137/

Chicago Manual of Style (16^th Edition):

author], [No. “The development of the quaternion normal distribution .” 2011. Masters Thesis, University of Pretoria. Accessed January 22, 2021. http://upetd.up.ac.za/thesis/available/etd-06272011-164137/.

MLA Handbook (7^th Edition):

author], [No. “The development of the quaternion normal distribution .” 2011. Web. 22 Jan 2021.

Vancouver:

author] [. The development of the quaternion normal distribution . [Internet] [Masters thesis]. University of Pretoria; 2011. [cited 2021 Jan 22]. Available from: http://upetd.up.ac.za/thesis/available/etd-06272011-164137/.

Council of Science Editors:

author] [. The development of the quaternion normal distribution . [Masters Thesis]. University of Pretoria; 2011. Available from: http://upetd.up.ac.za/thesis/available/etd-06272011-164137/

University of Pretoria

11. Loots, Mattheus Theodor. The development of the quaternion normal distribution.

Degree: Statistics, 2011, University of Pretoria

URL: http://hdl.handle.net/2263/25903

► In this dissertation an overview on the real representation of quaternions in distribution theory is given. The density functions of the p-variate and matrix-variate quaternion… (more)

Subjects/Keywords: Wilks's statistic; Quaternion wishart distribution; Real representation; Characteristic function; Quaternion matrix-variate beta type i distribution; Meijer's g-function; Quaternion normal distribution; UCTD

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APA (6^th Edition):

Loots, M. T. (2011). The development of the quaternion normal distribution. (Masters Thesis). University of Pretoria. Retrieved from http://hdl.handle.net/2263/25903

Chicago Manual of Style (16^th Edition):

Loots, Mattheus Theodor. “The development of the quaternion normal distribution.” 2011. Masters Thesis, University of Pretoria. Accessed January 22, 2021. http://hdl.handle.net/2263/25903.

MLA Handbook (7^th Edition):

Loots, Mattheus Theodor. “The development of the quaternion normal distribution.” 2011. Web. 22 Jan 2021.

Vancouver:

Loots MT. The development of the quaternion normal distribution. [Internet] [Masters thesis]. University of Pretoria; 2011. [cited 2021 Jan 22]. Available from: http://hdl.handle.net/2263/25903.

Council of Science Editors:

Loots MT. The development of the quaternion normal distribution. [Masters Thesis]. University of Pretoria; 2011. Available from: http://hdl.handle.net/2263/25903

University of Washington

12. Lee, Unsik. State-Constrained Rotational and Translational Motion Control with Applications to Monolithic and Distributed Spacecraft.

Degree: PhD, 2014, University of Washington

URL: http://hdl.handle.net/1773/25416

► The main research in this dissertation deals with translationally and rotationally constrained motion planning within aerospace literature. The topology of such a configuration manifold for… (more)

▼ The main research in this dissertation deals with translationally and rotationally constrained motion planning within aerospace literature. The topology of such a configuration manifold for a rigid body system is fundamentally challenging from a control perspective. This is because a rotational configuration space is a boundless but compact manifold that has no globally continuous feedback control law. This becomes more troublesome when planning a re-orientation in the presence of rotationally constrained zones. This is of paramount importance as these constraints frequently arise in many space science missions such as space telescope or interferometers; it also poses a challenging computational task for the spacecraft's guidance, navigation, and control subsystem. The complexity of such problems is elevated due to the fact that removing the constrained zones from the boundless compact manifold results in a non-convex region. In the first part of this dissertation, a novel guidance algorithm is proposed to handle multiple types of attitude constrained zones. Two types of attitude constrained zones are as developed and we show that such attitude constrained zones can be represented as convex regions. The advantage of the proposed approach hinges upon the development of the novel strictly convex logarithmic barrier potential functional that is subsequently used for constructing two types of control laws. The second part handles the problem of achieving identical orientation for a group of spacecraft in the presence of rotationally constrained zones. A distributed algorithm for consensus of multiple agents is developed where the shared state is assumed to be constrained in a distinct compact convex set and then augment to fit in the constrained reorientation framework presented earlier. This consensus algorithm is applicable when each spacecraft is required to satisfy its own constraints while also synchronizing with other spacecraft. Two sets of simulations of synchronizing space interferometers with identical and independent rotationally constrained zones are presented. In the final part, as an extension to the first part of the dissertation, a general framework for the analysis of rotationally and translationally constrained spacecraft control problems is presented. The general dynamics of the rigid body is addressed in terms of unit dual quaternions parameterizing position- and attitude-dependent variables, and an almost globally stable control law is developed for unconstrained rigid-body dynamics via a convex energy like Lyapunov function. The novelty of a unit dual quaternion based approach hinges on the fact that translationally and rotationally constrained zones can be formulated as convex representable subsets. Moreover, a convex programming approach is proposed to control synthesis of a planet lander that has the aforementioned constrained zones as its mission requirements. The numerical simulations validates that the proposed approach successfully find feasible trajectories satisfying all constraints. Advisors/Committee Members: Mesbahi, Mehran (advisor).

Subjects/Keywords: astrodynamics; attitude control; constrained motion control; distributed control; dual quaternion; quaternion; Aerospace engineering; aeronautics and astronautics

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APA (6^th Edition):

Lee, U. (2014). State-Constrained Rotational and Translational Motion Control with Applications to Monolithic and Distributed Spacecraft. (Doctoral Dissertation). University of Washington. Retrieved from http://hdl.handle.net/1773/25416

Chicago Manual of Style (16^th Edition):

Lee, Unsik. “State-Constrained Rotational and Translational Motion Control with Applications to Monolithic and Distributed Spacecraft.” 2014. Doctoral Dissertation, University of Washington. Accessed January 22, 2021. http://hdl.handle.net/1773/25416.

MLA Handbook (7^th Edition):

Lee, Unsik. “State-Constrained Rotational and Translational Motion Control with Applications to Monolithic and Distributed Spacecraft.” 2014. Web. 22 Jan 2021.

Vancouver:

Lee U. State-Constrained Rotational and Translational Motion Control with Applications to Monolithic and Distributed Spacecraft. [Internet] [Doctoral dissertation]. University of Washington; 2014. [cited 2021 Jan 22]. Available from: http://hdl.handle.net/1773/25416.

Council of Science Editors:

Lee U. State-Constrained Rotational and Translational Motion Control with Applications to Monolithic and Distributed Spacecraft. [Doctoral Dissertation]. University of Washington; 2014. Available from: http://hdl.handle.net/1773/25416

13. Zenteno Torres, Jazmin. Sliding mode control with fault tolerance capacities : application to a rendezvous mission in a circular orbit : Commande et commande tolérante aux fautes par modes glissants : application à une mission de rendez-vous en orbite circulaire.

Degree: Docteur es, Automatique, Productique, Signal et Image, Ingénierie cognitique, 2020, Bordeaux

URL: http://www.theses.fr/2020BORD0063

►

De nombreux travaux de recherche ont ´et´e conduits dans le domaine de synthèse de lois de commande par modes glissants. Différentes approches de commande été… (more)

▼

De nombreux travaux de recherche ont ´et´e conduits dans le domaine de synthèse de lois de commande par modes glissants. Différentes approches de commande été proposées dans la litérature, telles que l’algorithme Super-Twisting (STA) et sa version récente, l’algorithme généralisé Super-Twisting (GSTA). Les travaux de recherche présentés dans ce mémoire de thèse s’inscriventdans ces méthodes pour résoudre le problème de commande et de commande tolérante aux fautes, pour une mission spatiale. La mission considère une cible passive et un chasseur. L’objectif visé est de synthétiser les lois de contrôle d’attitude et de mouvement relatif, tolérantes aux pannes. Les approches proposées abordent la problématique des modes flexibles des panneaux solaires etdes phénomènes de ballottement du carburant dans les réservoirs.Dans un premier travail, une loi de commande de type STA est proposée dans une configuration dite de backstepping. Dans un second travail, une loi de commande tolérante aux fautes basée sur les modes glissants du second ordre, est proposée. La solution est basée sur l’algorithme GSTA ,placé en boucle externe de compensation de défauts utilisant un estimateur de défauts non linéaire. Le problème de saturation des actionneurs est également abordé et une solution basée sur la géométrie polytopique, est proposée. Les éléments clés de l’approche tolérante aux pannes sont, i) d’une part la solution ne nécessite pas de diagnostiquer les fautes et donc n’utilise pas d’algorithme de détection et de localisation de défauts, et ii), d’autre part, l’approche est basée sur le formalisme duquaternion dual qui permet de tenir compte des effets de couplage attitude/mouvement relatif. Des critères orientés mission, illustrent les résultats obtenus au travers d’une campagne de simulation réaliste.

Increasing attention has grown with regards to Sliding Mode Controllers (SMC). In order to reduce the so-called chattering effect, the Super-Twisting Algorithm (STA) has been proposed, recently. In this work, a controller based on the STA in a backstepping setup, is proposed for spacecraft rendezvous in a circular orbit. A key feature is that the chaser is not treated as a point mass, given that the effects of the flexible modes and propellant sloshing phenomena are considered. The results obtained are taken further, given that the guarantee of robustness against perturbations is not enough when it comes to critical systems, through the second ordersliding mode controllers technique. It is shown that the technique enables to solve to problem of fault tolerant control. The solution is based on the Generalized Super-Twisting Algorithm (GSTA) with an anti-windup strategy and a nonlinear observer and the dual quaternion formalism. The main reason of employing a GSTA is because it offers more robustness against state dependentperturbations (sloshing phenomena and flexible modes) than the STA. In addition, with the help of the anti-windup strategy, the control law does not saturate the thrusters, avoiding instablity when faults occur.…

Advisors/Committee Members: Henry, David (thesis director).

Subjects/Keywords: Modes glissants; Commandes tolérantes aux fautes; Quaternion dual; Mission spatiale; Sliding modes; Fault tolerant control; Dual quaternion; Aerospace application

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Zenteno Torres, J. (2020). Sliding mode control with fault tolerance capacities : application to a rendezvous mission in a circular orbit : Commande et commande tolérante aux fautes par modes glissants : application à une mission de rendez-vous en orbite circulaire. (Doctoral Dissertation). Bordeaux. Retrieved from http://www.theses.fr/2020BORD0063

Chicago Manual of Style (16^th Edition):

Zenteno Torres, Jazmin. “Sliding mode control with fault tolerance capacities : application to a rendezvous mission in a circular orbit : Commande et commande tolérante aux fautes par modes glissants : application à une mission de rendez-vous en orbite circulaire.” 2020. Doctoral Dissertation, Bordeaux. Accessed January 22, 2021. http://www.theses.fr/2020BORD0063.

MLA Handbook (7^th Edition):

Zenteno Torres, Jazmin. “Sliding mode control with fault tolerance capacities : application to a rendezvous mission in a circular orbit : Commande et commande tolérante aux fautes par modes glissants : application à une mission de rendez-vous en orbite circulaire.” 2020. Web. 22 Jan 2021.

Vancouver:

Zenteno Torres J. Sliding mode control with fault tolerance capacities : application to a rendezvous mission in a circular orbit : Commande et commande tolérante aux fautes par modes glissants : application à une mission de rendez-vous en orbite circulaire. [Internet] [Doctoral dissertation]. Bordeaux; 2020. [cited 2021 Jan 22]. Available from: http://www.theses.fr/2020BORD0063.

Council of Science Editors:

Zenteno Torres J. Sliding mode control with fault tolerance capacities : application to a rendezvous mission in a circular orbit : Commande et commande tolérante aux fautes par modes glissants : application à une mission de rendez-vous en orbite circulaire. [Doctoral Dissertation]. Bordeaux; 2020. Available from: http://www.theses.fr/2020BORD0063

The Ohio State University

14. Werner, Nicholas J. Integer-Valued Polynomials over Quaternion Rings.

Degree: PhD, Mathematics, 2010, The Ohio State University

URL: http://rave.ohiolink.edu/etdc/view?acc_num=osu1274923342

► When D is an integral domain with field of fractions K, the ring Int(D) of integer-valued polynomials over D is defined to be the set… (more)

Subjects/Keywords: Mathematics; integer-valued polynomial; quaternion; Hurwitz quaternion; Hurwitz integer

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APA (6^th Edition):

Werner, N. J. (2010). Integer-Valued Polynomials over Quaternion Rings. (Doctoral Dissertation). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1274923342

Chicago Manual of Style (16^th Edition):

Werner, Nicholas J. “Integer-Valued Polynomials over Quaternion Rings.” 2010. Doctoral Dissertation, The Ohio State University. Accessed January 22, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu1274923342.

MLA Handbook (7^th Edition):

Werner, Nicholas J. “Integer-Valued Polynomials over Quaternion Rings.” 2010. Web. 22 Jan 2021.

Vancouver:

Werner NJ. Integer-Valued Polynomials over Quaternion Rings. [Internet] [Doctoral dissertation]. The Ohio State University; 2010. [cited 2021 Jan 22]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1274923342.

Council of Science Editors:

Werner NJ. Integer-Valued Polynomials over Quaternion Rings. [Doctoral Dissertation]. The Ohio State University; 2010. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1274923342

Université du Québec à Montréal

15. Poitras, Luc. Origines algébrique et géométrique des nombres complexes et leur extension aux quaternions : fondements de la géométrie.

Degree: 2007, Université du Québec à Montréal

URL: http://www.archipel.uqam.ca/4762/1/M10011.pdf

► La première partie de ce mémoire relève les principaux problèmes de nature algébrique et géométrique qu'ont dû résoudre les mathématiciens avant d'accepter l'existence des nombres… (more)

Subjects/Keywords: Nombre complexe; Histoire; Géométrie; Quaternion

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Poitras, L. (2007). Origines algébrique et géométrique des nombres complexes et leur extension aux quaternions : fondements de la géométrie. (Thesis). Université du Québec à Montréal. Retrieved from http://www.archipel.uqam.ca/4762/1/M10011.pdf

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Poitras, Luc. “Origines algébrique et géométrique des nombres complexes et leur extension aux quaternions : fondements de la géométrie.” 2007. Thesis, Université du Québec à Montréal. Accessed January 22, 2021. http://www.archipel.uqam.ca/4762/1/M10011.pdf.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Poitras, Luc. “Origines algébrique et géométrique des nombres complexes et leur extension aux quaternions : fondements de la géométrie.” 2007. Web. 22 Jan 2021.

Vancouver:

Poitras L. Origines algébrique et géométrique des nombres complexes et leur extension aux quaternions : fondements de la géométrie. [Internet] [Thesis]. Université du Québec à Montréal; 2007. [cited 2021 Jan 22]. Available from: http://www.archipel.uqam.ca/4762/1/M10011.pdf.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Poitras L. Origines algébrique et géométrique des nombres complexes et leur extension aux quaternions : fondements de la géométrie. [Thesis]. Université du Québec à Montréal; 2007. Available from: http://www.archipel.uqam.ca/4762/1/M10011.pdf

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Université du Québec à Montréal

16. Poitras, Luc. Origines algébrique et géométrique des nombres complexes et leur extension aux quaternions : fondements de la géométrie.

Degree: 2007, Université du Québec à Montréal

URL: http://archipel.uqam.ca/4762/1/M10011.pdf

► La première partie de ce mémoire relève les principaux problèmes de nature algébrique et géométrique qu'ont dû résoudre les mathématiciens avant d'accepter l'existence des nombres… (more)

Subjects/Keywords: Nombre complexe; Histoire; Géométrie; Quaternion

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Poitras, L. (2007). Origines algébrique et géométrique des nombres complexes et leur extension aux quaternions : fondements de la géométrie. (Thesis). Université du Québec à Montréal. Retrieved from http://archipel.uqam.ca/4762/1/M10011.pdf

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Poitras, Luc. “Origines algébrique et géométrique des nombres complexes et leur extension aux quaternions : fondements de la géométrie.” 2007. Thesis, Université du Québec à Montréal. Accessed January 22, 2021. http://archipel.uqam.ca/4762/1/M10011.pdf.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Poitras, Luc. “Origines algébrique et géométrique des nombres complexes et leur extension aux quaternions : fondements de la géométrie.” 2007. Web. 22 Jan 2021.

Vancouver:

Poitras L. Origines algébrique et géométrique des nombres complexes et leur extension aux quaternions : fondements de la géométrie. [Internet] [Thesis]. Université du Québec à Montréal; 2007. [cited 2021 Jan 22]. Available from: http://archipel.uqam.ca/4762/1/M10011.pdf.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Poitras L. Origines algébrique et géométrique des nombres complexes et leur extension aux quaternions : fondements de la géométrie. [Thesis]. Université du Québec à Montréal; 2007. Available from: http://archipel.uqam.ca/4762/1/M10011.pdf

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Vienna

17. Döller, Victoria. Über maximale Ordnungen in Normrestalgebren.

Degree: 2013, University of Vienna

URL: http://othes.univie.ac.at/27681/

►

Diese Arbeit beschäftigt sich mit maximalen Ordnungen in Normrestalgebren über algebraischen Zahlkörpern. Diese Algebren können als Verallgemeinerung der Quaternionenalgebren aufgefasst werden. Im ersten Teil der… (more)

Subjects/Keywords: 31.14 Zahlentheorie; Ordnung / Quaternionenalgebra / Zyklische Algebra; order / quaternion algebra / cyclic algebra

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APA (6^th Edition):

Döller, V. (2013). Über maximale Ordnungen in Normrestalgebren. (Thesis). University of Vienna. Retrieved from http://othes.univie.ac.at/27681/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Döller, Victoria. “Über maximale Ordnungen in Normrestalgebren.” 2013. Thesis, University of Vienna. Accessed January 22, 2021. http://othes.univie.ac.at/27681/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Döller, Victoria. “Über maximale Ordnungen in Normrestalgebren.” 2013. Web. 22 Jan 2021.

Vancouver:

Döller V. Über maximale Ordnungen in Normrestalgebren. [Internet] [Thesis]. University of Vienna; 2013. [cited 2021 Jan 22]. Available from: http://othes.univie.ac.at/27681/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Döller V. Über maximale Ordnungen in Normrestalgebren. [Thesis]. University of Vienna; 2013. Available from: http://othes.univie.ac.at/27681/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Luleå University of Technology

18. Fresk, Emil. Modeling, Control and Experimentation of a Variable Pitch Quadrotor.

Degree: 2013, Luleå University of Technology

URL: http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-47963

►

The aim of this thesis is to present a novel quaternion based control scheme for the attitude control problem of a quadrotor equipped with… (more)

Subjects/Keywords: Technology; Teknik; control; quadrotor; variable pitch propeller; quaternion; attitude problem

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APA (6^th Edition):

Fresk, E. (2013). Modeling, Control and Experimentation of a Variable Pitch Quadrotor. (Thesis). Luleå University of Technology. Retrieved from http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-47963

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Fresk, Emil. “Modeling, Control and Experimentation of a Variable Pitch Quadrotor.” 2013. Thesis, Luleå University of Technology. Accessed January 22, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-47963.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Fresk, Emil. “Modeling, Control and Experimentation of a Variable Pitch Quadrotor.” 2013. Web. 22 Jan 2021.

Vancouver:

Fresk E. Modeling, Control and Experimentation of a Variable Pitch Quadrotor. [Internet] [Thesis]. Luleå University of Technology; 2013. [cited 2021 Jan 22]. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-47963.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Fresk E. Modeling, Control and Experimentation of a Variable Pitch Quadrotor. [Thesis]. Luleå University of Technology; 2013. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-47963

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Delft University of Technology

19. Hazra, Shriya (author). Autonomous Guidance for Asteroid Descent using Successive Convex Optimisation: Dual Quaternion Approach.

Degree: 2019, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:98cd2661-7e9c-46b5-a651-adcc467d30c4

► With the onset of the age of space travel, asteroid missions have been steadily gaining interest. The pristine nature of asteroids due to their preserved… (more)

▼ With the onset of the age of space travel, asteroid missions have been steadily gaining interest. The pristine nature of asteroids due to their preserved state since the formation of the Solar System is an opportunity to unravel many mysteries about the Solar System. Also with the ever-growing need for resources, asteroids prove to be a plentiful source. With the discovery of asteroids in the close vicinity of our planet and a probable threat to the preservation of life, a need for defence missions has also arisen. The ever-growing need for better computational speed and accuracy has led to the development of new representations for attitude and position of the spacecraft in the past. The usual methods of representations of position and attitude (pose) are the Cartesian coordinates and quaternions. A recent development is the simultaneous representation of the pose of the spacecraft using dual quaternions which are eight-dimensional vectors. In this thesis, an attempt to incorporate these state-of-the-art guidance technologies to asteroid missions has been made. The novelty in this thesis is, using dual quaternions for SC pose and attitude representation to autonomously guide the spacecraft for mapping an asteroid and perform a touch and go descent using sampling-based motion predictive optimisation and successive convexification respectively. After the development and verification of these algorithms, different scenarios have been designed to find out the robustness of the dynamic successive convexification method. The scenarios have been run by both the Cartesian quaternion and dual quaternion based algorithms. They are found to behave similarly in their results, besides the latter being computationally more expensive as proved by different theses so far. The algorithm performs better than the one developed by Szmuk et al. (2017), but faces difficulties with badly scaled problems as is the nature of missions to asteroids. The software used for the thesis is ECOS, which faces numerical problems in these mission scenarios even when the problem is feasible and has an optimal result. The availability of a solution to the optimal control problem depends on the scaling of the penalty weights used in the cost function to penalise virtual controls and trust region, which are used to prevent infeasibility and bound the problem, respectively. It also depends on finding an appropriate final time for the descent along with the number of nodes for discretisation. This research proves, that successive convexification indeed provides a speedy solution for an autonomous precision descent but needs further work to make it robust and stable. The outcome of this thesis is to carry out further research to understand the complex relations, between the scale of the problem, simulation parameters for the optimal control problem and final time to make the algorithm robust and safe for an autonomous mission. Another important future research prospect is to incorporate the sampling based model predictive optimisation, for the SC to… Advisors/Committee Members: Sagliano, Marco (mentor), Mooij, Erwin (graduation committee), Delft University of Technology (degree granting institution).

Subjects/Keywords: successive convexification; convex optimisation; dual quaternion; motion planning; asteroids

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Hazra, S. (. (2019). Autonomous Guidance for Asteroid Descent using Successive Convex Optimisation: Dual Quaternion Approach. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:98cd2661-7e9c-46b5-a651-adcc467d30c4

Chicago Manual of Style (16^th Edition):

Hazra, Shriya (author). “Autonomous Guidance for Asteroid Descent using Successive Convex Optimisation: Dual Quaternion Approach.” 2019. Masters Thesis, Delft University of Technology. Accessed January 22, 2021. http://resolver.tudelft.nl/uuid:98cd2661-7e9c-46b5-a651-adcc467d30c4.

MLA Handbook (7^th Edition):

Hazra, Shriya (author). “Autonomous Guidance for Asteroid Descent using Successive Convex Optimisation: Dual Quaternion Approach.” 2019. Web. 22 Jan 2021.

Vancouver:

Hazra S(. Autonomous Guidance for Asteroid Descent using Successive Convex Optimisation: Dual Quaternion Approach. [Internet] [Masters thesis]. Delft University of Technology; 2019. [cited 2021 Jan 22]. Available from: http://resolver.tudelft.nl/uuid:98cd2661-7e9c-46b5-a651-adcc467d30c4.

Council of Science Editors:

Hazra S(. Autonomous Guidance for Asteroid Descent using Successive Convex Optimisation: Dual Quaternion Approach. [Masters Thesis]. Delft University of Technology; 2019. Available from: http://resolver.tudelft.nl/uuid:98cd2661-7e9c-46b5-a651-adcc467d30c4

University of South Florida

20. Martori, Amanda Lynn. A Wearable Motion Analysis System to Evaluate Gait Deviations.

Degree: 2013, University of South Florida

URL: https://scholarcommons.usf.edu/etd/4724

► A Wearable Motion Analysis System (WMAS) was developed to evaluate gait, particularly parameters that are indicative of mild traumatic brain injury. The WMAS consisted on… (more)

Subjects/Keywords: APDM; IMU; knee angle; quaternion; sensors; Mechanical Engineering

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Martori, A. L. (2013). A Wearable Motion Analysis System to Evaluate Gait Deviations. (Thesis). University of South Florida. Retrieved from https://scholarcommons.usf.edu/etd/4724

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Martori, Amanda Lynn. “A Wearable Motion Analysis System to Evaluate Gait Deviations.” 2013. Thesis, University of South Florida. Accessed January 22, 2021. https://scholarcommons.usf.edu/etd/4724.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Martori, Amanda Lynn. “A Wearable Motion Analysis System to Evaluate Gait Deviations.” 2013. Web. 22 Jan 2021.

Vancouver:

Martori AL. A Wearable Motion Analysis System to Evaluate Gait Deviations. [Internet] [Thesis]. University of South Florida; 2013. [cited 2021 Jan 22]. Available from: https://scholarcommons.usf.edu/etd/4724.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Martori AL. A Wearable Motion Analysis System to Evaluate Gait Deviations. [Thesis]. University of South Florida; 2013. Available from: https://scholarcommons.usf.edu/etd/4724

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Waterloo

21. Zi Yang, Sham. Quaternion Algebras and Quadratic Forms.

Degree: 2008, University of Waterloo

URL: http://hdl.handle.net/10012/3656

► The main goal of this Masters' thesis is to explore isomorphism types of quaternion algebras using the theory of quadratic forms, number theory and algebra.… (more)

Subjects/Keywords: quadratic forms; quaternion algebras

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APA (6^th Edition):

Zi Yang, S. (2008). Quaternion Algebras and Quadratic Forms. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/3656

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Zi Yang, Sham. “Quaternion Algebras and Quadratic Forms.” 2008. Thesis, University of Waterloo. Accessed January 22, 2021. http://hdl.handle.net/10012/3656.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Zi Yang, Sham. “Quaternion Algebras and Quadratic Forms.” 2008. Web. 22 Jan 2021.

Vancouver:

Zi Yang S. Quaternion Algebras and Quadratic Forms. [Internet] [Thesis]. University of Waterloo; 2008. [cited 2021 Jan 22]. Available from: http://hdl.handle.net/10012/3656.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Zi Yang S. Quaternion Algebras and Quadratic Forms. [Thesis]. University of Waterloo; 2008. Available from: http://hdl.handle.net/10012/3656

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Georgia

22. Thompson, Katherine Elizabeth. Explicit representation results for quadratic forms over qq and qq(sqrt{5}) by analytic methods.

Degree: 2014, University of Georgia

URL: http://hdl.handle.net/10724/30677

► In this thesis, we examine representation of positive integers by certain definite quaternary quadratic forms Q over ZZ and ZZ [(1+ sqrt{5})/2] by studying the… (more)

Subjects/Keywords: Number theory; Quadratic forms; Modular forms; Quaternion algebras

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APA (6^th Edition):

Thompson, K. E. (2014). Explicit representation results for quadratic forms over qq and qq(sqrt{5}) by analytic methods. (Thesis). University of Georgia. Retrieved from http://hdl.handle.net/10724/30677

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Thompson, Katherine Elizabeth. “Explicit representation results for quadratic forms over qq and qq(sqrt{5}) by analytic methods.” 2014. Thesis, University of Georgia. Accessed January 22, 2021. http://hdl.handle.net/10724/30677.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Thompson, Katherine Elizabeth. “Explicit representation results for quadratic forms over qq and qq(sqrt{5}) by analytic methods.” 2014. Web. 22 Jan 2021.

Vancouver:

Thompson KE. Explicit representation results for quadratic forms over qq and qq(sqrt{5}) by analytic methods. [Internet] [Thesis]. University of Georgia; 2014. [cited 2021 Jan 22]. Available from: http://hdl.handle.net/10724/30677.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Thompson KE. Explicit representation results for quadratic forms over qq and qq(sqrt{5}) by analytic methods. [Thesis]. University of Georgia; 2014. Available from: http://hdl.handle.net/10724/30677

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Georgia Tech

23. Issac, Yanal. A quaternion approach to the modal analysis and reduced-order modeling of three-dimensional fluid systems.

Degree: PhD, Aerospace Engineering, 2020, Georgia Tech

URL: http://hdl.handle.net/1853/63702

► In 1967, Lumley derived the proper orthogonal decomposition (POD) in an attempt to provide a mathematical description of patterns that emerge in turbulent flow, which… (more)

▼ In 1967, Lumley derived the proper orthogonal decomposition (POD) in an attempt to provide a mathematical description of patterns that emerge in turbulent flow, which he called coherent structures. The POD method derived by Lumley has deep mathematical roots, is statistically based, and has analytical foundations that provide a rigorous mathematical framework for the extraction and description of coherent structures. However, it was not until 1987, when Sirovich provided a numerically tractable implementation of the POD method capable of tackling large data sets such as the ones encountered in modern day engineering problems, did the POD gain much attention. In recent years, the wide spread success of the POD method has greatly elevated the status of the POD method. Today, the POD method is considered as benchmark procedure, and is at the bedrock of modal analysis and reduced-order modeling of fluid systems. Since its inception, numerous applications, adaptions and variations of the POD have been devised. However, little attention has been paid to addressing the three-dimensional nature of fluid systems. In fact, George states that the POD is agnostic to the nature of the data, as it does not matter whether the data is velocity, pressure or temperature. The aim of this thesis was to explore a fundamentally different approach to the POD that is better suited for three-dimensional fluid systems; an approach that does not compromise the mathematical rigor associated with the concept of coherent structures defined by Lumley. The approach investigated in this thesis replaces the traditional field of real numbers \R, with a four-dimensional non-commutative division algebra ℍ, known as the quaternion division algebra. To the knowledge of the author, this thesis is the first to incorporate quaternions into Lumley's mathematical framework. The introduction of quaternions into Lumley's mathematical framework, generalizes the proper orthogonal decomposition to the quaternion proper orthogonal decomposition (QPOD) while preserving its favorable features and extending the POD to higher dimensional spaces. In the work of this thesis it was shown that a quaternion approach abstracts Lumley's mathematical representation of coherent structures at a fundamental level. These abstracted representations, defined for the first time in the work of this thesis are termed quaternion coherent structures, exhibit interesting properties and result in a fascinating phenomena termed the kaleidoscope effect which is not present in the traditional definition of coherent structures. Furthermore, it was numerically and mathematical shown that the QPOD method can better distill the essential dynamics present in a data set and can create more accurate rank-m approximations as compared the POD method. The results presented in this thesis provide compelling evidence advocating for the use of quaternions in the context of modal analysis and reduced-order modeling of three-dimensional fluid systems. In addition a… Advisors/Committee Members: Mavris, Dimitri (advisor), Silva, Walter (committee member), Eppink, Jenna (committee member), Sankar, Lakshmi (committee member), Pinon-Fischer, Olivia (committee member).

Subjects/Keywords: Reduced-order modeling; Model-order reduction; Quaternion; Proper orthogonal decomposition

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APA (6^th Edition):

Issac, Y. (2020). A quaternion approach to the modal analysis and reduced-order modeling of three-dimensional fluid systems. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/63702

Chicago Manual of Style (16^th Edition):

Issac, Yanal. “A quaternion approach to the modal analysis and reduced-order modeling of three-dimensional fluid systems.” 2020. Doctoral Dissertation, Georgia Tech. Accessed January 22, 2021. http://hdl.handle.net/1853/63702.

MLA Handbook (7^th Edition):

Issac, Yanal. “A quaternion approach to the modal analysis and reduced-order modeling of three-dimensional fluid systems.” 2020. Web. 22 Jan 2021.

Vancouver:

Issac Y. A quaternion approach to the modal analysis and reduced-order modeling of three-dimensional fluid systems. [Internet] [Doctoral dissertation]. Georgia Tech; 2020. [cited 2021 Jan 22]. Available from: http://hdl.handle.net/1853/63702.

Council of Science Editors:

Issac Y. A quaternion approach to the modal analysis and reduced-order modeling of three-dimensional fluid systems. [Doctoral Dissertation]. Georgia Tech; 2020. Available from: http://hdl.handle.net/1853/63702

24. Yang, Sungpil. Robustness properties of quaternion-based attitude control systems.

Degree: PhD, Aerospace Engineering, 2016, University of Texas – Austin

URL: http://hdl.handle.net/2152/38095

► Both stabilizing and tracking solutions of the rigid-body attitude control problem, using various attitude representations, are now well understood. Based on the sensor availability, numerous… (more)

▼ Both stabilizing and tracking solutions of the rigid-body attitude control problem, using various attitude representations, are now well understood. Based on the sensor availability, numerous full-state feedback or gyro-free output feedback controllers have been proposed and studied. In the dissertation, we revisit classical proportional-derivative (PD) type attitude controllers when the system is subject to uncertainties like time-delay in the feedback loop, measurement errors, external disturbance torques and modeling uncertainties. We not only analyze existing PD-type controllers while considering various types of uncertainties, but also design tracking controllers robust to the system parameter uncertainties. We adopt the quaternion representation for the attitude kinematics so that we can avoid the geometric singularities coming with minimal 3-dimensional parameter representations. For stability and robustness analysis of the PD-type controllers, we do not rely on the linear system framework in which the original dynamics are considered as the sum of the nominal linear part and the nonlinear perturbation part. Instead, another approach is suggested as suitable for the quaternion kinematic representation so that results are not restricted to a neighborhood of the origin. We first deal with one of the common Lyapunov functions used for quaternion-based attitude control problem. Then, through the strictification process, a new Lyapunov function is constructed which can be analyzed based on the standard Lyapunov stability analysis method. As a result, we establish sufficient conditions for locally stability or boundedness of the system subject to aforementioned uncertainties for both PD full-state feedback and PD-like gyro-free output feedback controllers. When our scope is narrowed to the system parameter uncertainties, we propose adaptive controllers that track predefined reference trajectories and estimate the unknown inertial parameters. Specifically, we apply a dynamic scaling-based Immersion and Invariance method for the first time to the attitude tracking problem. We also provide a way to control and estimate the upper bound of a dynamic scaling factor which has not yet been seen in the literature. Advisors/Committee Members: Akella, Maruthi Ram, 1972- (advisor), Bakolas, Efstathios (committee member), Arapostathis, Aristotle (committee member), Acikmese, Behcet (committee member), Mazenc, Frederic (committee member).

Subjects/Keywords: Attitude control; Quaternion kinematics; Robustness; Adaptive control; Uncertainties; Delay; Disturbances

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APA (6^th Edition):

Yang, S. (2016). Robustness properties of quaternion-based attitude control systems. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/38095

Chicago Manual of Style (16^th Edition):

Yang, Sungpil. “Robustness properties of quaternion-based attitude control systems.” 2016. Doctoral Dissertation, University of Texas – Austin. Accessed January 22, 2021. http://hdl.handle.net/2152/38095.

MLA Handbook (7^th Edition):

Yang, Sungpil. “Robustness properties of quaternion-based attitude control systems.” 2016. Web. 22 Jan 2021.

Vancouver:

Yang S. Robustness properties of quaternion-based attitude control systems. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2016. [cited 2021 Jan 22]. Available from: http://hdl.handle.net/2152/38095.

Council of Science Editors:

Yang S. Robustness properties of quaternion-based attitude control systems. [Doctoral Dissertation]. University of Texas – Austin; 2016. Available from: http://hdl.handle.net/2152/38095

Kent State University

25. Almutairi, Najat Bandar. ON MULTILINEAR POLYNOMIALS EVALUATED ON QUATERNION ALGEBRA.

Degree: MS, College of Arts and Sciences / Department of Mathematical Science, 2016, Kent State University

URL: http://rave.ohiolink.edu/etdc/view?acc_num=kent1454279474

The purpose of this thesis is to describe the image of quaternion algebra under multilinearpolynomials. In it, we provide a proof that the image of multilinear non-centralpolynomials contains ai + bj + ck for all real numbers a, b and c. Advisors/Committee Members: Chebotar, Mikhail (Advisor).

Subjects/Keywords: Mathematics; quaternion algebra; multilinear polynomials; image of multilinear polynomials; central polynomial

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APA (6^th Edition):

Almutairi, N. B. (2016). ON MULTILINEAR POLYNOMIALS EVALUATED ON QUATERNION ALGEBRA. (Masters Thesis). Kent State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=kent1454279474

Chicago Manual of Style (16^th Edition):

Almutairi, Najat Bandar. “ON MULTILINEAR POLYNOMIALS EVALUATED ON QUATERNION ALGEBRA.” 2016. Masters Thesis, Kent State University. Accessed January 22, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=kent1454279474.

MLA Handbook (7^th Edition):

Almutairi, Najat Bandar. “ON MULTILINEAR POLYNOMIALS EVALUATED ON QUATERNION ALGEBRA.” 2016. Web. 22 Jan 2021.

Vancouver:

Almutairi NB. ON MULTILINEAR POLYNOMIALS EVALUATED ON QUATERNION ALGEBRA. [Internet] [Masters thesis]. Kent State University; 2016. [cited 2021 Jan 22]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=kent1454279474.

Council of Science Editors:

Almutairi NB. ON MULTILINEAR POLYNOMIALS EVALUATED ON QUATERNION ALGEBRA. [Masters Thesis]. Kent State University; 2016. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=kent1454279474

26. Morchid, Mohamed. Représentations robustes de documents bruités dans des espaces homogènes : Robust representation of noisy documents in homogeneous spaces.

Degree: Docteur es, Sciences et agrosciences, 2014, Avignon

URL: http://www.theses.fr/2014AVIG0202

► En recherche d’information, les documents sont le plus souvent considérés comme des "sacs-de-mots". Ce modèle ne tient pas compte de la structure temporelle du document… (more)

▼ En recherche d’information, les documents sont le plus souvent considérés comme des "sacs-de-mots". Ce modèle ne tient pas compte de la structure temporelle du document et est sensible aux bruits qui peuvent altérer la forme lexicale. Ces bruits peuvent être produits par différentes sources : forme peu contrôlée des messages des sites de micro-blogging, messages vocaux dont la transcription automatique contient des erreurs, variabilités lexicales et grammaticales dans les forums du Web. . . Le travail présenté dans cette thèse s’intéresse au problème de la représentation de documents issus de sources bruitées.La thèse comporte trois parties dans lesquelles différentes représentations des contenus sont proposées. La première partie compare une représentation classique utilisant la fréquence des mots à une représentation de haut-niveau s’appuyant sur un espace de thèmes. Cette abstraction du contenu permet de limiter l’altération de la forme de surface du document bruité en le représentant par un ensemble de caractéristiques de haut-niveau. Nos expériences confirment que cette projection dans un espace de thèmes permet d’améliorer les résultats obtenus sur diverses tâches de recherche d’information en comparaison d’une représentation plus classique utilisant la fréquence des mots.Le problème majeur d’une telle représentation est qu’elle est fondée sur un espace de thèmes dont les paramètres sont choisis empiriquement.La deuxième partie décrit une nouvelle représentation s’appuyant sur des espaces multiples et permettant de résoudre trois problèmes majeurs : la proximité des sujets traités dans le document, le choix difficile des paramètres du modèle de thèmes ainsi que la robustesse de la représentation. Partant de l’idée qu’une seule représentation des contenus ne peut pas capturer l’ensemble des informations utiles, nous proposons d’augmenter le nombre de vues sur un même document. Cette multiplication des vues permet de générer des observations "artificielles" qui contiennent des fragments de l’information utile. Une première expérience a validé cette approche multi-vues de la représentation de textes bruités. Elle a cependant l’inconvénient d’être très volumineuse,redondante, et de contenir une variabilité additionnelle liée à la diversité des vues. Dans un deuxième temps, nous proposons une méthode s’appuyant sur l’analyse factorielle pour fusionner les vues multiples et obtenir une nouvelle représentation robuste,de dimension réduite, ne contenant que la partie "utile" du document tout en réduisant les variabilités "parasites". Lors d’une tâche de catégorisation de conversations,ce processus de compression a confirmé qu’il permettait d’augmenter la robustesse de la représentation du document bruité.Cependant, lors de l’élaboration des espaces de thèmes, le document reste considéré comme un "sac-de-mots" alors que plusieurs études montrent que la position d’un terme au sein du document est importante. Une représentation tenant compte de cette structure temporelle du document est proposée dans la troisième partie.… Advisors/Committee Members: Linarès, Georges (thesis director), Dufour, Richard (thesis director).

Subjects/Keywords: Représentation robuste; Document bruité; Analyse latente de Dirichlet; Allocation latente de Dirichlet; Multivues; Analyse factorielle; Quaternion; Robust representation; Noisy document; Latent Dirichlet allocation; Multi-views; Factor analysis; Quaternion; 06.454

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Morchid, M. (2014). Représentations robustes de documents bruités dans des espaces homogènes : Robust representation of noisy documents in homogeneous spaces. (Doctoral Dissertation). Avignon. Retrieved from http://www.theses.fr/2014AVIG0202

Chicago Manual of Style (16^th Edition):

Morchid, Mohamed. “Représentations robustes de documents bruités dans des espaces homogènes : Robust representation of noisy documents in homogeneous spaces.” 2014. Doctoral Dissertation, Avignon. Accessed January 22, 2021. http://www.theses.fr/2014AVIG0202.

MLA Handbook (7^th Edition):

Morchid, Mohamed. “Représentations robustes de documents bruités dans des espaces homogènes : Robust representation of noisy documents in homogeneous spaces.” 2014. Web. 22 Jan 2021.

Vancouver:

Morchid M. Représentations robustes de documents bruités dans des espaces homogènes : Robust representation of noisy documents in homogeneous spaces. [Internet] [Doctoral dissertation]. Avignon; 2014. [cited 2021 Jan 22]. Available from: http://www.theses.fr/2014AVIG0202.

Council of Science Editors:

Morchid M. Représentations robustes de documents bruités dans des espaces homogènes : Robust representation of noisy documents in homogeneous spaces. [Doctoral Dissertation]. Avignon; 2014. Available from: http://www.theses.fr/2014AVIG0202

27. Henriksson, Manne. Estimation of heading using magnetometer and GPS.

Degree: Signals and Systems Group, 2013, Uppsala University

URL: http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-207585

►

One important part of inertial navigation is the estimation of the direction relative to the Earth’s geographic North Pole, the so called heading. In… (more)

▼

One important part of inertial navigation is the estimation of the direction relative to the Earth’s geographic North Pole, the so called heading. In this project, a gyroscope and an accelerometer were used together in an Extended Kalman Filter with a quaternion as the state space variable, representing the attitude. Given the attitude of the system, measurements from a magnetometer were rotated to a horizontal coordinate frame in order to calculate the direction toward Earth’s magnetic North Pole. Comparing this direction with the angle toward the Geographic North Pole given by a GPS, the local magnetic declination was estimated with the purpose of correcting the heading in the future. Different methods for detecting disturbances on the magnetometer in order to automatically decide when it is to be trusted was discussed and evaluated. Routines for easily performing sensor calibration was created. The outcome of the project was a well working attitude estimation, simply performed calibration routines and a set of methods working together to detect magnetometer disturbances.

En viktig del av ett tröghetsnavigeringssystem är skattningen av riktningen relativt jordens geografiska nordpol, den så kallade bäringen. I detta projekt användes ett gyroskop och en accelerometer tillsammans i ett Extended Kalman filter med en quaternion som tillståndsvariabel för att representera attityden. Givet systemets attityd roterades mätningar från en magnetometer till ett horisontellt koordinatsystem för att beräkna riktningen mot magnetiska nordpolen. Genom att jämföra denna riktning med vinkeln mot geografiska nordpolen kunde den lokala magnetiska deklinationen skattas för att sedan användas i framtiden för att korrigera bäringen. Olika metoder för att detektera störningar på magnetometern för att automatiskt bestämma när den är störd diskuteras och utvärderas. Rutiner för att enkelt kalibrera sensorerna skapades. Projektets resultat var en väl fungerande attitydestimering, enkla kalibreringsmetoder samt ett par metoder för att detektera störningar på magnetometern.

Subjects/Keywords: Inertial navigation; magnetometer; heading; quaternion; bäring; magnetometer; tröghetsnavigering; quaternion

…rotation is introduced since it will be used for rotating the measurement data. A quaternion will… …some quaternion theory follows next. Finally, theory necessary for describing the calibration… …presented in the next section. 13 2.7 Quaternions The quaternion will be used for describing… …presented. 2.7.1 History and definition The quaternion was discovered by the Irish… …number can be said to have rank 2, a pure real part and a pure imaginary part. A quaternion is…

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APA (6^th Edition):

Henriksson, M. (2013). Estimation of heading using magnetometer and GPS. (Thesis). Uppsala University. Retrieved from http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-207585

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Henriksson, Manne. “Estimation of heading using magnetometer and GPS.” 2013. Thesis, Uppsala University. Accessed January 22, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-207585.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Henriksson, Manne. “Estimation of heading using magnetometer and GPS.” 2013. Web. 22 Jan 2021.

Vancouver:

Henriksson M. Estimation of heading using magnetometer and GPS. [Internet] [Thesis]. Uppsala University; 2013. [cited 2021 Jan 22]. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-207585.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Henriksson M. Estimation of heading using magnetometer and GPS. [Thesis]. Uppsala University; 2013. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-207585

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

28. Chandra, Rohit. Application of Dual Quaternion for Bimanual Robotic Tasks : Application des quaternions duaux aux tâches robotiques bi-bras.

Degree: Docteur es, Robotique, 2019, Clermont Auvergne

URL: http://www.theses.fr/2019CLFAC042

► L'approche classique pour le contrôle coopératif dans l’espace de travail d’un manipulateur bi-bras a été revisitée. En particulier, une nouvelle approche pour la formulation symétrique… (more)

▼ L'approche classique pour le contrôle coopératif dans l’espace de travail d’un manipulateur bi-bras a été revisitée. En particulier, une nouvelle approche pour la formulation symétrique de la coordination bi-bras à l'aide du concept "virtual sticks" a été proposée à l'aide d'un torseur cinématique en utilisant des quaternions duaux. Le contrôle couplé dans l'espace de travail coopératif qui est proposé, i.e. le contrôle simultané, en position et en orientation, des points de consigne de l'espace de travail relatif et absolu a été comparé à un contrôleur proportionnel découplé traitant séparément les erreurs de position et d'orientation. Le contrôleur couplé a démontré un meilleur suivi de la pose et de l'orientation en termes de précision et de stabilité comparé au contrôleur découplé pour les tâches exigeant un fonctionnement plus rapide dans l'espace de travail relatif des manipulateurs bi-bras.L'approche de modélisation et de contrôle de l'espace de travail d’une tâche coopérative, en exploitant les torseurs cinématiques et des quaternions duaux, a été étendue à la modélisation de la coopération des doigts d'une main robotique anthropomorphique. De plus, le couplage des articulations des doigts sous-actionnés de la main robotique a été représenté à l’aide de la "jacobienne couplée" du doigt. La "jacobienne couplée" du doigt robotique a été utilisée pour le contrôle cinématique inverse, tout en lui permettant une intégration facile avec un bras robotique.L'idée d'un traitement couplé des variables en position et en orientation a été capitalisée en utilisant la conception d'une trajectoire de second ordre utilisant des quaternions duaux. Le contrôleur de trajectoire ainsi conçu est capable de suivre les points de consigne en pose en vitesse et en accélération, de l'effecteur en utilisant le modèle dynamique inverse du robot. Le contrôleur couplé en taux d’accélération résolue ("resolved rate acceleration") s'est avéré capable d'un contrôle de trajectoire plus précis, particulièrement en termes d'erreurs liées à l'orientation, que le contrôleur découplé classique qui traitait séparément les points de consigne en position et en orientation et ignorait l'effet de la rotation sur le mouvement de translation. De plus, cela a également permis de réduire les oscillations de la commande du couple des articulations lorsque le contrôleur a été implémenté pour le contrôle de l'un des bras du robot bi-bras Baxter.Enfin, un cadre complet pour la coordination des systèmes robotiques bi-bras a été proposé avec l'ajout d'un planificateur de tâches coopératives. La simplicité du torseur cinématique a également été exploitée pour la génération de trajectoires généralisées du second ordre pour des tâches nécessitant un mouvement simplifié, comme la translation, la rotation et la torsion autour d'un axe hélicoïdale arbitraire donné dans un repère connu. La méthode de génération de trajectoires a été étendue pour représenter les contraintes liées aux tâches impliquant un contact entre les objets en utilisant le concept de mécanisme… Advisors/Committee Members: Mezouar, Youcef (thesis director).

Subjects/Keywords: Quaternions; Manipulation; Dual-arm Manipulation; Collaborative robot; Kinematics; Screw-theory; Dual-quaternion; Quaternion; Anthropomorphic robotic hand; Dynamics; Computed torque control; Spatial Dynamics; Trajectory tracking; Deformable objects

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APA (6^th Edition):

Chandra, R. (2019). Application of Dual Quaternion for Bimanual Robotic Tasks : Application des quaternions duaux aux tâches robotiques bi-bras. (Doctoral Dissertation). Clermont Auvergne. Retrieved from http://www.theses.fr/2019CLFAC042

Chicago Manual of Style (16^th Edition):

Chandra, Rohit. “Application of Dual Quaternion for Bimanual Robotic Tasks : Application des quaternions duaux aux tâches robotiques bi-bras.” 2019. Doctoral Dissertation, Clermont Auvergne. Accessed January 22, 2021. http://www.theses.fr/2019CLFAC042.

MLA Handbook (7^th Edition):

Chandra, Rohit. “Application of Dual Quaternion for Bimanual Robotic Tasks : Application des quaternions duaux aux tâches robotiques bi-bras.” 2019. Web. 22 Jan 2021.

Vancouver:

Chandra R. Application of Dual Quaternion for Bimanual Robotic Tasks : Application des quaternions duaux aux tâches robotiques bi-bras. [Internet] [Doctoral dissertation]. Clermont Auvergne; 2019. [cited 2021 Jan 22]. Available from: http://www.theses.fr/2019CLFAC042.

Council of Science Editors:

Chandra R. Application of Dual Quaternion for Bimanual Robotic Tasks : Application des quaternions duaux aux tâches robotiques bi-bras. [Doctoral Dissertation]. Clermont Auvergne; 2019. Available from: http://www.theses.fr/2019CLFAC042

Brno University of Technology

29. Bečka, Pavel. Kvaternionové algebry: Quaternion algebras.

Degree: 2019, Brno University of Technology

URL: http://hdl.handle.net/11012/66050

► This thesis deals with quaternion algebras. A quaternion algebra is a four dimensional vector space with basis 1, i, j, k and multiplication defined as… (more)

Subjects/Keywords: kvaternionová algebra; řád; maximální řád; SAGE; diskriminant kvaternionové algebry; Hilbertv symbol; quaternion algebra; order; maximal order; SAGE; discriminant of quaternion algebra; Hilbert symbol

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Bečka, P. (2019). Kvaternionové algebry: Quaternion algebras. (Thesis). Brno University of Technology. Retrieved from http://hdl.handle.net/11012/66050

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Bečka, Pavel. “Kvaternionové algebry: Quaternion algebras.” 2019. Thesis, Brno University of Technology. Accessed January 22, 2021. http://hdl.handle.net/11012/66050.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Bečka, Pavel. “Kvaternionové algebry: Quaternion algebras.” 2019. Web. 22 Jan 2021.

Vancouver:

Bečka P. Kvaternionové algebry: Quaternion algebras. [Internet] [Thesis]. Brno University of Technology; 2019. [cited 2021 Jan 22]. Available from: http://hdl.handle.net/11012/66050.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Bečka P. Kvaternionové algebry: Quaternion algebras. [Thesis]. Brno University of Technology; 2019. Available from: http://hdl.handle.net/11012/66050

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Southern California

30. Choi, Homin. Dynamic modeling and simulations of rigid-flexible coupled systems using quaternion dynamics.

Degree: PhD, Aerospace and Mechanical Engineering (Dynamics and Control), 2014, University of Southern California

URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/421237/rec/2126

► In this study, a three‐dimensional dynamic modeling and simulation of a satellite that consists of coupled rigid‐flexible bodies is presented. In the modeling of this… (more)

▼ In this study, a three‐dimensional dynamic modeling and simulation of a satellite that consists of coupled rigid‐flexible bodies is presented. In the modeling of this coupled system, the satellite is assumed to be a rigid body; and solar arrays, antennas or booms are assumed to be flexible bodies. Coupling the equations of motions of the rigid body and the flexible bodies is accomplished by using the finite element method (FEM). Since the satellite rotates in space, the conventional FEM has a singularity problem caused by rotational sequences of Euler angles. To solve this problem, quaternion‐based FEM is used in this study. Quaternion is well known as its singularity‐free representation of bodies in three‐dimensional motions. The governing equations of motions are derived from Lagrange equation, and derivatives in the equations are explicitly solved for accurate results. ❧ Although quaternions are singularity‐free in modeling and analysis of rigid bodies in three‐dimensional motion, description of torques may lead to an unbounded response of a quaternion‐based model. In this study, theorems on the conditions of torque‐induced singularity in four coordinate systems—inertial frame, body frame, Euler basis, and dual Euler basis—are derived. According to the theorems, torques applied in an inertial frame or a body frame or an Euler basis will never cause unbounded motion. Torques applied in a dual Euler basis, however, may lead to unbounded motion. ❧ Numerical simulations of free and forced vibrations are conducted for the quaternion‐based dynamic models of one rigid body and rigid‐flexible coupled bodies. For the dynamic model of one rigid body, the simulation results show that there is no singularity in free vibrations, but when external torque is applied in dual Euler bases, singularity occurs. However, when the torque is applied in the other coordinate systems, there is no singularity. For the dynamic model of rigid‐flexible coupled bodies, torque is applied only in the body frame in this simulation, so both free and forced vibrations have no singularity. Advisors/Committee Members: Yang, Bingen (Ben) (Committee Chair), Flashner, Henryk (Committee Member), Wang, Chunming (Committee Member).

Subjects/Keywords: multi-body dynamics; rigid body dynamics; quaternions; quaternion singularity; Euler angles; Euler angle singularity; torque induced singularity; rigid-flexible coupled systems; quaternion-based FEM; satellite orientation

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APA (6^th Edition):

Choi, H. (2014). Dynamic modeling and simulations of rigid-flexible coupled systems using quaternion dynamics. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/421237/rec/2126

Chicago Manual of Style (16^th Edition):

Choi, Homin. “Dynamic modeling and simulations of rigid-flexible coupled systems using quaternion dynamics.” 2014. Doctoral Dissertation, University of Southern California. Accessed January 22, 2021. http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/421237/rec/2126.

MLA Handbook (7^th Edition):

Choi, Homin. “Dynamic modeling and simulations of rigid-flexible coupled systems using quaternion dynamics.” 2014. Web. 22 Jan 2021.

Vancouver:

Choi H. Dynamic modeling and simulations of rigid-flexible coupled systems using quaternion dynamics. [Internet] [Doctoral dissertation]. University of Southern California; 2014. [cited 2021 Jan 22]. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/421237/rec/2126.

Council of Science Editors:

Choi H. Dynamic modeling and simulations of rigid-flexible coupled systems using quaternion dynamics. [Doctoral Dissertation]. University of Southern California; 2014. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/421237/rec/2126

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