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Dynamics of Human Head and Eye Rotations Under Donders' Constraint
The rotation of human head and the eye are modeled as a perfect sphere with the rotation actuated by external torques. For the head movement, the axis of rotation is constrained by a law proposed in the 19th century by Donders. For the saccadic eye movement, Donders' Law is restricted to a law...
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Published in: | IEEE transactions on automatic control 2012-10, Vol.57 (10), p.2478-2489 |
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description | The rotation of human head and the eye are modeled as a perfect sphere with the rotation actuated by external torques. For the head movement, the axis of rotation is constrained by a law proposed in the 19th century by Donders. For the saccadic eye movement, Donders' Law is restricted to a law that goes by the name of Listing's Law. In this paper, head movement and saccadic eye movement are modeled using principles from classical mechanics and the associated Euler Lagrange's equations (EL) are analyzed. Geodesic curves are obtained in the space of allowed orientations for the head and the eye and projections of these curves on the space S 2 of pointing directions of the eye/head are shown. A potential function and a damping term has been added to the geodesic dynamics from EL and the resulting head and eye trajectories settle down smoothly towards the unique point of minimum potential. The minimum point can be altered to regulate the end point of the trajectories (potential control). Throughout the paper, the restricted dynamics of the eye and the head movement have been compared with the unrestricted rotational dynamics on SO(3) and the corresponding EL equations have been analyzed. A version of the Donders' Theorem, on the possible head orientations for a specific head direction, has been stated and proved in Appendix I. In the case of eye movement, Donders' Theorem restricts to the well known Listing's Theorem. In Appendix II, a constraint on the angular velocity and the angular acceleration vectors is derived for the head movement satisfying Donders' constraint. A statement of this constraint that goes by the name "half angle rule," has been derived. |
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K. ; Wijayasinghe, I. B.</creator><creatorcontrib>Ghosh, B. K. ; Wijayasinghe, I. B.</creatorcontrib><description>The rotation of human head and the eye are modeled as a perfect sphere with the rotation actuated by external torques. For the head movement, the axis of rotation is constrained by a law proposed in the 19th century by Donders. For the saccadic eye movement, Donders' Law is restricted to a law that goes by the name of Listing's Law. In this paper, head movement and saccadic eye movement are modeled using principles from classical mechanics and the associated Euler Lagrange's equations (EL) are analyzed. Geodesic curves are obtained in the space of allowed orientations for the head and the eye and projections of these curves on the space S 2 of pointing directions of the eye/head are shown. A potential function and a damping term has been added to the geodesic dynamics from EL and the resulting head and eye trajectories settle down smoothly towards the unique point of minimum potential. The minimum point can be altered to regulate the end point of the trajectories (potential control). Throughout the paper, the restricted dynamics of the eye and the head movement have been compared with the unrestricted rotational dynamics on SO(3) and the corresponding EL equations have been analyzed. A version of the Donders' Theorem, on the possible head orientations for a specific head direction, has been stated and proved in Appendix I. In the case of eye movement, Donders' Theorem restricts to the well known Listing's Theorem. In Appendix II, a constraint on the angular velocity and the angular acceleration vectors is derived for the head movement satisfying Donders' constraint. A statement of this constraint that goes by the name "half angle rule," has been derived.</description><identifier>ISSN: 0018-9286</identifier><identifier>EISSN: 1558-2523</identifier><identifier>DOI: 10.1109/TAC.2012.2186183</identifier><identifier>CODEN: IETAA9</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Applied sciences ; Artificial intelligence ; Biological and medical sciences ; Biomechanics. Biorheology ; Computer science; control theory; systems ; Differential geometry ; Donders' law ; Dynamic tests ; Dynamics ; Equations ; Euler Lagrange equation ; Exact sciences and technology ; Eye and associated structures. Visual pathways and centers. Vision ; Eye movements ; eye/head movement ; Eyes & eyesight ; Fundamental and applied biological sciences. Psychology ; geodesics ; Geometry ; half angle rule ; Head ; Head movement ; Law ; Listing's Law ; Mathematical analysis ; Mathematical model ; Mathematical models ; Mathematics ; Measurement ; Muscles ; Pattern recognition. Digital image processing. Computational geometry ; potential control ; Quaternions ; Riemannian Metric ; Sciences and techniques of general use ; Theorems ; Tissues, organs and organisms biophysics ; Trajectories ; Vectors ; Vertebrates: nervous system and sense organs</subject><ispartof>IEEE transactions on automatic control, 2012-10, Vol.57 (10), p.2478-2489</ispartof><rights>2015 INIST-CNRS</rights><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Oct 2012</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c354t-2ffe56693aa45625b1fa43429a9d15d3314c814a47368d1eb5c5a949048064053</citedby><cites>FETCH-LOGICAL-c354t-2ffe56693aa45625b1fa43429a9d15d3314c814a47368d1eb5c5a949048064053</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/6144709$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,54774</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=26443231$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Ghosh, B. K.</creatorcontrib><creatorcontrib>Wijayasinghe, I. B.</creatorcontrib><title>Dynamics of Human Head and Eye Rotations Under Donders' Constraint</title><title>IEEE transactions on automatic control</title><addtitle>TAC</addtitle><description>The rotation of human head and the eye are modeled as a perfect sphere with the rotation actuated by external torques. For the head movement, the axis of rotation is constrained by a law proposed in the 19th century by Donders. For the saccadic eye movement, Donders' Law is restricted to a law that goes by the name of Listing's Law. In this paper, head movement and saccadic eye movement are modeled using principles from classical mechanics and the associated Euler Lagrange's equations (EL) are analyzed. Geodesic curves are obtained in the space of allowed orientations for the head and the eye and projections of these curves on the space S 2 of pointing directions of the eye/head are shown. A potential function and a damping term has been added to the geodesic dynamics from EL and the resulting head and eye trajectories settle down smoothly towards the unique point of minimum potential. The minimum point can be altered to regulate the end point of the trajectories (potential control). Throughout the paper, the restricted dynamics of the eye and the head movement have been compared with the unrestricted rotational dynamics on SO(3) and the corresponding EL equations have been analyzed. A version of the Donders' Theorem, on the possible head orientations for a specific head direction, has been stated and proved in Appendix I. In the case of eye movement, Donders' Theorem restricts to the well known Listing's Theorem. In Appendix II, a constraint on the angular velocity and the angular acceleration vectors is derived for the head movement satisfying Donders' constraint. A statement of this constraint that goes by the name "half angle rule," has been derived.</description><subject>Applied sciences</subject><subject>Artificial intelligence</subject><subject>Biological and medical sciences</subject><subject>Biomechanics. Biorheology</subject><subject>Computer science; control theory; systems</subject><subject>Differential geometry</subject><subject>Donders' law</subject><subject>Dynamic tests</subject><subject>Dynamics</subject><subject>Equations</subject><subject>Euler Lagrange equation</subject><subject>Exact sciences and technology</subject><subject>Eye and associated structures. Visual pathways and centers. Vision</subject><subject>Eye movements</subject><subject>eye/head movement</subject><subject>Eyes & eyesight</subject><subject>Fundamental and applied biological sciences. Psychology</subject><subject>geodesics</subject><subject>Geometry</subject><subject>half angle rule</subject><subject>Head</subject><subject>Head movement</subject><subject>Law</subject><subject>Listing's Law</subject><subject>Mathematical analysis</subject><subject>Mathematical model</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Measurement</subject><subject>Muscles</subject><subject>Pattern recognition. Digital image processing. Computational geometry</subject><subject>potential control</subject><subject>Quaternions</subject><subject>Riemannian Metric</subject><subject>Sciences and techniques of general use</subject><subject>Theorems</subject><subject>Tissues, organs and organisms biophysics</subject><subject>Trajectories</subject><subject>Vectors</subject><subject>Vertebrates: nervous system and sense organs</subject><issn>0018-9286</issn><issn>1558-2523</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><recordid>eNpdkE1Lw0AQhhdRsFbvgpcFEb2k7uxXNseaVisUBGnPYZpsICXZ1N3k0H9vQosHT8PMPPMyPITcA5sBsOR1M09nnAGfcTAajLggE1DKRFxxcUkmjIGJEm70NbkJYT-0WkqYkLfF0WFT5YG2JV31DTq6slhQdAVdHi39bjvsqtYFunWF9XTRjiU803SYdR4r192SqxLrYO_OdUq278tNuorWXx-f6Xwd5ULJLuJlaZXWiUCUSnO1gxKlkDzBpABVCAEyNyBRxkKbAuxO5QoTmTBpmJZMiSl5OeUefPvT29BlTRVyW9fobNuHDIRWIAXwEX38h-7b3rvhuwyYYXEsQMFAsROV-zYEb8vs4KsG_XGAslFqNkjNRqnZWepw8nQOxpBjXXp0eRX-7vggVXAxRj-cuMpa-7fWIGXMEvELYdt7wQ</recordid><startdate>20121001</startdate><enddate>20121001</enddate><creator>Ghosh, B. K.</creator><creator>Wijayasinghe, I. B.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>F28</scope></search><sort><creationdate>20121001</creationdate><title>Dynamics of Human Head and Eye Rotations Under Donders' Constraint</title><author>Ghosh, B. K. ; Wijayasinghe, I. B.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c354t-2ffe56693aa45625b1fa43429a9d15d3314c814a47368d1eb5c5a949048064053</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Applied sciences</topic><topic>Artificial intelligence</topic><topic>Biological and medical sciences</topic><topic>Biomechanics. Biorheology</topic><topic>Computer science; control theory; systems</topic><topic>Differential geometry</topic><topic>Donders' law</topic><topic>Dynamic tests</topic><topic>Dynamics</topic><topic>Equations</topic><topic>Euler Lagrange equation</topic><topic>Exact sciences and technology</topic><topic>Eye and associated structures. Visual pathways and centers. Vision</topic><topic>Eye movements</topic><topic>eye/head movement</topic><topic>Eyes & eyesight</topic><topic>Fundamental and applied biological sciences. Psychology</topic><topic>geodesics</topic><topic>Geometry</topic><topic>half angle rule</topic><topic>Head</topic><topic>Head movement</topic><topic>Law</topic><topic>Listing's Law</topic><topic>Mathematical analysis</topic><topic>Mathematical model</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Measurement</topic><topic>Muscles</topic><topic>Pattern recognition. Digital image processing. Computational geometry</topic><topic>potential control</topic><topic>Quaternions</topic><topic>Riemannian Metric</topic><topic>Sciences and techniques of general use</topic><topic>Theorems</topic><topic>Tissues, organs and organisms biophysics</topic><topic>Trajectories</topic><topic>Vectors</topic><topic>Vertebrates: nervous system and sense organs</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ghosh, B. K.</creatorcontrib><creatorcontrib>Wijayasinghe, I. B.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Xplore</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts – Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><jtitle>IEEE transactions on automatic control</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ghosh, B. K.</au><au>Wijayasinghe, I. B.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Dynamics of Human Head and Eye Rotations Under Donders' Constraint</atitle><jtitle>IEEE transactions on automatic control</jtitle><stitle>TAC</stitle><date>2012-10-01</date><risdate>2012</risdate><volume>57</volume><issue>10</issue><spage>2478</spage><epage>2489</epage><pages>2478-2489</pages><issn>0018-9286</issn><eissn>1558-2523</eissn><coden>IETAA9</coden><abstract>The rotation of human head and the eye are modeled as a perfect sphere with the rotation actuated by external torques. For the head movement, the axis of rotation is constrained by a law proposed in the 19th century by Donders. For the saccadic eye movement, Donders' Law is restricted to a law that goes by the name of Listing's Law. In this paper, head movement and saccadic eye movement are modeled using principles from classical mechanics and the associated Euler Lagrange's equations (EL) are analyzed. Geodesic curves are obtained in the space of allowed orientations for the head and the eye and projections of these curves on the space S 2 of pointing directions of the eye/head are shown. A potential function and a damping term has been added to the geodesic dynamics from EL and the resulting head and eye trajectories settle down smoothly towards the unique point of minimum potential. The minimum point can be altered to regulate the end point of the trajectories (potential control). Throughout the paper, the restricted dynamics of the eye and the head movement have been compared with the unrestricted rotational dynamics on SO(3) and the corresponding EL equations have been analyzed. A version of the Donders' Theorem, on the possible head orientations for a specific head direction, has been stated and proved in Appendix I. In the case of eye movement, Donders' Theorem restricts to the well known Listing's Theorem. In Appendix II, a constraint on the angular velocity and the angular acceleration vectors is derived for the head movement satisfying Donders' constraint. A statement of this constraint that goes by the name "half angle rule," has been derived.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TAC.2012.2186183</doi><tpages>12</tpages></addata></record> |
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subjects | Applied sciences Artificial intelligence Biological and medical sciences Biomechanics. Biorheology Computer science control theory systems Differential geometry Donders' law Dynamic tests Dynamics Equations Euler Lagrange equation Exact sciences and technology Eye and associated structures. Visual pathways and centers. Vision Eye movements eye/head movement Eyes & eyesight Fundamental and applied biological sciences. Psychology geodesics Geometry half angle rule Head Head movement Law Listing's Law Mathematical analysis Mathematical model Mathematical models Mathematics Measurement Muscles Pattern recognition. Digital image processing. Computational geometry potential control Quaternions Riemannian Metric Sciences and techniques of general use Theorems Tissues, organs and organisms biophysics Trajectories Vectors Vertebrates: nervous system and sense organs |
title | Dynamics of Human Head and Eye Rotations Under Donders' Constraint |
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