{"id":79,"date":"2024-04-04T08:01:28","date_gmt":"2024-04-04T05:01:28","guid":{"rendered":"https:\/\/sisu.ut.ee\/rosak\/asend-ja-kinemaatika\/"},"modified":"2024-04-04T08:03:55","modified_gmt":"2024-04-04T05:03:55","slug":"asend-ja-kinemaatika","status":"publish","type":"page","link":"https:\/\/sisu.ut.ee\/rosak\/asend-ja-kinemaatika\/","title":{"rendered":"2. Asend ja kinemaatika"},"content":{"rendered":"<blockquote>\n<p>\n\t\t<span id=\"docs-internal-guid-6d52aada-7fff-3d37-ff37-2980d317fef2\">Kinemaatika on <strong>teadus liikumisest<\/strong>. Robootikas t\u00e4hendab see positsiooni ja orientatsiooni, kiirust, kiirendust ja k\u00f5iki mehhanismi k\u00f5rgemaid tuletisi. J\u00e4rgnevalt uurime erinevaid viise roboti positsiooni ja orientatsiooni kirjeldamiseks.<\/span>\n\t<\/p>\n<p>\n\t\t<em>\u00d5ppematerjali vaatamiseks klikka vahepealkirjadele.<\/em>\n\t<\/p>\n<\/blockquote>\n<p>\n\t<\/p><div class=\"accordion mb-3\">\n        <div class=\"accordion-item accordion-item--white\">\n        <h2 class=\"accordion-header\" id=\"accordion-69d4a4d8ce12b-heading\">\n            <button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#accordion-69d4a4d8ce12b-collapse\" aria-expanded=\"true\" aria-controls=\"accordion-69d4a4d8ce12b-collapse\"><strong>1. Mis on asend?<\/strong><\/button>\n        <\/h2>\n        <div id=\"accordion-69d4a4d8ce12b-collapse\" class=\"accordion-collapse collapse\" aria-labelledby=\"accordion-69d4a4d8ce12b-heading\">\n            <div class=\"accordion-body\"><span id=\"docs-internal-guid-7387a1bc-7fff-bfe0-6232-50498ff62139\">Liigendid v\u00f5imaldavad roboti l\u00fclidel olla erinevates positsioonides ja orientatsioonides. L\u00fcli positsioon on selle asukoht ruumis; orientatsioon on l\u00fcli p\u00f6\u00f6ratuse suund ja kaugus. Koos moodustavad need l\u00fcli<\/span> <strong>asendi<\/strong> (ingl k. <em>pose<\/em>).\n\n<blockquote>\n<p>\n\t\t<strong><span id=\"docs-internal-guid-c9240e7e-7fff-0c2d-a9ac-a198e72f5b0d\">Positsioon + orientatsioon = asend<\/span><\/strong>\n\t<\/p>\n<\/blockquote>\n<p>\n\t<\/p><\/div>\n        <\/div>\n        <\/div>\n    <\/div>\n\n<p>\n\t<\/p><div class=\"accordion mb-3\">\n        <div class=\"accordion-item accordion-item--white\">\n        <h2 class=\"accordion-header\" id=\"accordion-69d4a4d8ce131-heading\">\n            <button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#accordion-69d4a4d8ce131-collapse\" aria-expanded=\"true\" aria-controls=\"accordion-69d4a4d8ce131-collapse\"><strong>2. Ruumikoordinaadid robootikas<\/strong><\/button>\n        <\/h2>\n        <div id=\"accordion-69d4a4d8ce131-collapse\" class=\"accordion-collapse collapse\" aria-labelledby=\"accordion-69d4a4d8ce131-heading\">\n            <div class=\"accordion-body\">T\u00fc\u00fcpiline jadamanipulaatori kasutamise \u00fclesanne on selle m\u00f5juri \u00f5igesse asukohta viimine. Seda asukohta saab kirjeldada erinevates koordinaats\u00fcsteemides. Enimtuntud koordinaats\u00fcsteem on <strong>ruumikoordinaadid<\/strong> (ingl k. <em>Cartesian space<\/em>), milles asukohta kirjeldatakse x-, y- ja z-teljes.\n\n<p>\n\tSelles kolme ristuva teljega kolmem\u00f5\u00f5tmelises ruumis on lihtne kirjeldada suvalise punkti asukohta. Samuti on selles koordinaats\u00fcsteemis lihtne m\u00e4\u00e4rata manipulaatori m\u00f5juri asukohta.\n<\/p>\n<p>\n\t<img loading=\"lazy\" decoding=\"async\" width=\"2147\" height=\"1995\" class=\"alignnone wp-image-169\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinematics_cartesian_axes_513aad6ee4b81a99dc8722581216523f.png\" title=\"kinematics_cartesian_axes_513aad6ee4b81a99dc8722581216523f.png\" alt=\".\" srcset=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinematics_cartesian_axes_513aad6ee4b81a99dc8722581216523f.png 2147w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinematics_cartesian_axes_513aad6ee4b81a99dc8722581216523f-300x279.png 300w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinematics_cartesian_axes_513aad6ee4b81a99dc8722581216523f-1024x952.png 1024w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinematics_cartesian_axes_513aad6ee4b81a99dc8722581216523f-768x714.png 768w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinematics_cartesian_axes_513aad6ee4b81a99dc8722581216523f-1536x1427.png 1536w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinematics_cartesian_axes_513aad6ee4b81a99dc8722581216523f-2048x1903.png 2048w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinematics_cartesian_axes_513aad6ee4b81a99dc8722581216523f-1920x1784.png 1920w\" sizes=\"auto, (max-width: 2147px) 100vw, 2147px\">\n<\/p>\n<p>\n\t<\/p><\/div>\n        <\/div>\n        <\/div>\n    <\/div>\n\n<p>\n\t<\/p><div class=\"accordion mb-3\">\n        <div class=\"accordion-item accordion-item--white\">\n        <h2 class=\"accordion-header\" id=\"accordion-69d4a4d8ce135-heading\">\n            <button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#accordion-69d4a4d8ce135-collapse\" aria-expanded=\"true\" aria-controls=\"accordion-69d4a4d8ce135-collapse\"><strong>3. Liigendiolek ja liigendiruum<\/strong><\/button>\n        <\/h2>\n        <div id=\"accordion-69d4a4d8ce135-collapse\" class=\"accordion-collapse collapse\" aria-labelledby=\"accordion-69d4a4d8ce135-heading\">\n            <div class=\"accordion-body\">Kui valime manipulaatori m\u00f5juri asukoha ruumikoordinaatides, siis m\u00e4\u00e4rame me ainult roboti \u00fche osa kohta positsiooni, aga mitte kogu roboti asendi. Kui soovime kirjeldada roboti k\u00f5igi l\u00fclide asendit, peame m\u00e4\u00e4ratlema rohkem punkte. Piisab, kui kirjeldame iga liigendi asendi, selle asemel, et m\u00e4\u00e4rata k\u00f5igi l\u00fclide asukohta.\n\n<p>\n\tKui teame jadamanipulaatori iga p\u00f6\u00f6rdliigendi nurka, saame \u00fcheselt kirjeldada roboti iga osa asendit. Seda liigendite nurkade kogumit nimetatakse <strong>liigendi olekuks<\/strong> (ingl k. <em>joint state<\/em>). Liigendi olekut teades on v\u00f5imalik taasluua kogu roboti asend.\n<\/p>\n<p>\n\t<span id=\"docs-internal-guid-fe5e8bed-7fff-7baa-e047-e791670402a9\">K\u00f5igi v\u00f5imalike liigendiolekute kogumit nimetatakse <\/span><span><strong>liigendiruumiks<\/strong> (ingl k. <\/span><em><span>joint space<\/span><\/em><span>).<\/span>\n<\/p>\n<p>\n\t<img loading=\"lazy\" decoding=\"async\" width=\"4607\" height=\"3725\" class=\"alignnone wp-image-170\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinetics_joint_state_illustration_994e8b3cf643102b187fc9f07aa07c84.png\" title=\"kinetics_joint_state_illustration_994e8b3cf643102b187fc9f07aa07c84.png\" alt=\".\" srcset=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinetics_joint_state_illustration_994e8b3cf643102b187fc9f07aa07c84.png 4607w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinetics_joint_state_illustration_994e8b3cf643102b187fc9f07aa07c84-300x243.png 300w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinetics_joint_state_illustration_994e8b3cf643102b187fc9f07aa07c84-1024x828.png 1024w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinetics_joint_state_illustration_994e8b3cf643102b187fc9f07aa07c84-768x621.png 768w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinetics_joint_state_illustration_994e8b3cf643102b187fc9f07aa07c84-1536x1242.png 1536w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinetics_joint_state_illustration_994e8b3cf643102b187fc9f07aa07c84-2048x1656.png 2048w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinetics_joint_state_illustration_994e8b3cf643102b187fc9f07aa07c84-1920x1552.png 1920w\" sizes=\"auto, (max-width: 4607px) 100vw, 4607px\">\n<\/p>\n<p>\n\t<\/p><\/div>\n        <\/div>\n        <\/div>\n    <\/div>\n\n<p>\n\t<\/p><div class=\"accordion mb-3\">\n        <div class=\"accordion-item accordion-item--white\">\n        <h2 class=\"accordion-header\" id=\"accordion-69d4a4d8ce139-heading\">\n            <button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#accordion-69d4a4d8ce139-collapse\" aria-expanded=\"true\" aria-controls=\"accordion-69d4a4d8ce139-collapse\"><strong>4. P\u00e4rikinemaatika<\/strong><\/button>\n        <\/h2>\n        <div id=\"accordion-69d4a4d8ce139-collapse\" class=\"accordion-collapse collapse\" aria-labelledby=\"accordion-69d4a4d8ce139-heading\">\n            <div class=\"accordion-body\">Liigendiruumis on meil info iga liigendi nurga kohta. Kui teame, millised l\u00fclid iga liigendi k\u00fclge \u00fchenduvad, saame teada, milline on iga l\u00fcli suhteline asend sellega \u00fchendatud l\u00fclide suhtes. Teoorias saame selle j\u00e4rgi leida manipulaatori m\u00f5juri asendi, aga kuidas?\n\n<p>\n\tSelle jaoks on <strong>p\u00e4rikinemaatika<\/strong> (ingl k. <em>forward kinematics<\/em>). P\u00e4rikinemaatikat ja roboti kirjeldust kasutades saame viia info liigendiruumist koordinaatruumi. N\u00e4iteks teades liigendiolekut saame arvutada manipulaatori m\u00f5juri asendi koordinaatruumis. P\u00e4rikinemaatika on \u00fcsna lihtne ja kasutab tavalist trigonomeetriat. Tavaliselt tehakse neid arvutusi maatriksite korrutamise abil.\n<\/p>\n<p>\n\t<img loading=\"lazy\" decoding=\"async\" width=\"6040\" height=\"8216\" class=\"alignnone wp-image-171\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinetics_forwardkin_illustration_98b40736164a5a15871ba79fe6579ec7.png\" title=\"kinetics_forwardkin_illustration_98b40736164a5a15871ba79fe6579ec7.png\" alt=\".\" srcset=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinetics_forwardkin_illustration_98b40736164a5a15871ba79fe6579ec7.png 6040w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinetics_forwardkin_illustration_98b40736164a5a15871ba79fe6579ec7-221x300.png 221w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinetics_forwardkin_illustration_98b40736164a5a15871ba79fe6579ec7-753x1024.png 753w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinetics_forwardkin_illustration_98b40736164a5a15871ba79fe6579ec7-768x1045.png 768w\" sizes=\"auto, (max-width: 6040px) 100vw, 6040px\">\n<\/p>\n<p>\n\t<\/p><\/div>\n        <\/div>\n        <\/div>\n    <\/div>\n\n<p>\n\t<\/p><div class=\"accordion mb-3\">\n        <div class=\"accordion-item accordion-item--white\">\n        <h2 class=\"accordion-header\" id=\"accordion-69d4a4d8ce13c-heading\">\n            <button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#accordion-69d4a4d8ce13c-collapse\" aria-expanded=\"true\" aria-controls=\"accordion-69d4a4d8ce13c-collapse\"><strong>5. <span id=\"docs-internal-guid-5b65fb1d-7fff-66cd-b893-cee1187b94ea\">P\u00f6\u00f6rdkinemaatika<\/span><\/strong><\/button>\n        <\/h2>\n        <div id=\"accordion-69d4a4d8ce13c-collapse\" class=\"accordion-collapse collapse\" aria-labelledby=\"accordion-69d4a4d8ce13c-heading\">\n            <div class=\"accordion-body\">Tihti on robootikutel vaja lahendada p\u00e4rikinemaatikale vastupidine \u00fclesanne. N\u00e4iteks v\u00f5ib meil olla vaja viia roboti haarats j\u00e4rgmise eseme haaramiseks sobivasse asukohta. Eseme asukoht on kirjeldatud koordinaatruumis ja meil on vaja seada roboti liigendid \u00f5igete nurkade alla.\n\n<p>\n\tOletame, et me teame, kuhu meil on vaja viia roboti m\u00f5jur. Meil on vaja seada k\u00f5ik roboti liigendid ja l\u00fclid selliselt, et m\u00f5jur j\u00f5uaks vajalikku punkti. See t\u00e4hendab, et meil on vaja leida liigendiruumist selline liigendiolek, kus roboti m\u00f5jur on soovitud koordinaatruumi punktis. Info viimine koordinaatruumist liigendiruumi ongi <strong>p\u00f6\u00f6rdkinemaatika<\/strong> (ingl k. <em>inverse kinematics<\/em>).\n<\/p>\n<p>\n\t<img loading=\"lazy\" decoding=\"async\" width=\"6040\" height=\"8216\" class=\"alignnone wp-image-172\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinetics_inversekin_illustration_791de3992df17bc4f329e8493abe4e1b.png\" title=\"kinetics_inversekin_illustration_791de3992df17bc4f329e8493abe4e1b.png\" alt=\".\" srcset=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinetics_inversekin_illustration_791de3992df17bc4f329e8493abe4e1b.png 6040w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinetics_inversekin_illustration_791de3992df17bc4f329e8493abe4e1b-221x300.png 221w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinetics_inversekin_illustration_791de3992df17bc4f329e8493abe4e1b-753x1024.png 753w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinetics_inversekin_illustration_791de3992df17bc4f329e8493abe4e1b-768x1045.png 768w\" sizes=\"auto, (max-width: 6040px) 100vw, 6040px\">\n<\/p>\n<p>\n\t<\/p><\/div>\n        <\/div>\n        <\/div>\n    <\/div>\n\n<p>\n\t<\/p><div class=\"accordion mb-3\">\n        <div class=\"accordion-item accordion-item--white\">\n        <h2 class=\"accordion-header\" id=\"accordion-69d4a4d8ce140-heading\">\n            <button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#accordion-69d4a4d8ce140-collapse\" aria-expanded=\"true\" aria-controls=\"accordion-69d4a4d8ce140-collapse\"><strong>6. <span id=\"docs-internal-guid-a456230b-7fff-4e64-1a93-efc91a473c83\">P\u00f6\u00f6rdkinemaatika probleemid<\/span><\/strong><\/button>\n        <\/h2>\n        <div id=\"accordion-69d4a4d8ce140-collapse\" class=\"accordion-collapse collapse\" aria-labelledby=\"accordion-69d4a4d8ce140-heading\">\n            <div class=\"accordion-body\"><span id=\"docs-internal-guid-fd80e6f2-7fff-85de-792c-f6eed5adb6fd\">P\u00f6\u00f6rdkinemaatika rakendamisel tekivad m\u00f5ned probleemid. Soovitud asukohta j\u00f5udmiseks v\u00f5ib robotil olla vaja keerata ennast veidratel viisidel, mida ei ole lihtne arvutada. Me ei saa isegi olla kindlad, kas roboti m\u00f5juril on f\u00fc\u00fcsiliselt v\u00f5imalik soovitud koordinaatidele j\u00f5uda. Ja mis juhtub, kui liigendiruumis on soovitud punkti j\u00f5udmiseks mitu erinevat liigendiolekut? Erinevalt p\u00e4rikinemaatikast on p\u00f6\u00f6rdkinemaatika arvutuslikult keeruline \u00fclesanne.<\/span>\n\n<p>\n\t<span id=\"docs-internal-guid-f6b8a673-7fff-b93b-bfe8-0fc5478f0e70\">\u00d5nneks on p\u00f6\u00f6rdkinemaatika rakendamiseks olemas mitmeid tarkvaralisi lahendusi.<\/span>\n<\/p>\n<p>\n\t<img loading=\"lazy\" decoding=\"async\" width=\"3648\" height=\"3018\" class=\"alignnone wp-image-173\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinetics_inversekin_problems_833f3d4e2227d38bbdfd2e797d8497fc.png\" title=\"kinetics_inversekin_problems_833f3d4e2227d38bbdfd2e797d8497fc.png\" alt=\".\" srcset=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinetics_inversekin_problems_833f3d4e2227d38bbdfd2e797d8497fc.png 3648w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinetics_inversekin_problems_833f3d4e2227d38bbdfd2e797d8497fc-300x248.png 300w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinetics_inversekin_problems_833f3d4e2227d38bbdfd2e797d8497fc-1024x847.png 1024w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinetics_inversekin_problems_833f3d4e2227d38bbdfd2e797d8497fc-768x635.png 768w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinetics_inversekin_problems_833f3d4e2227d38bbdfd2e797d8497fc-1536x1271.png 1536w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinetics_inversekin_problems_833f3d4e2227d38bbdfd2e797d8497fc-2048x1694.png 2048w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/560\/kinetics_inversekin_problems_833f3d4e2227d38bbdfd2e797d8497fc-1920x1588.png 1920w\" sizes=\"auto, (max-width: 3648px) 100vw, 3648px\">\n<\/p>\n<p>\n\t<\/p><\/div>\n        <\/div>\n        <\/div>\n    <\/div>\n","protected":false},"excerpt":{"rendered":"<p>Kinemaatika on teadus liikumisest. Robootikas t\u00e4hendab see positsiooni ja orientatsiooni, kiirust, kiirendust ja k\u00f5iki mehhanismi k\u00f5rgemaid tuletisi. J\u00e4rgnevalt uurime erinevaid viise roboti positsiooni ja orientatsiooni kirjeldamiseks. \u00d5ppematerjali vaatamiseks klikka vahepealkirjadele. 1. Mis on asend? Liigendid v\u00f5imaldavad roboti l\u00fclidel olla erinevates &#8230;<\/p>\n","protected":false},"author":98,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"class_list":["post-79","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/sisu.ut.ee\/rosak\/wp-json\/wp\/v2\/pages\/79","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sisu.ut.ee\/rosak\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sisu.ut.ee\/rosak\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sisu.ut.ee\/rosak\/wp-json\/wp\/v2\/users\/98"}],"replies":[{"embeddable":true,"href":"https:\/\/sisu.ut.ee\/rosak\/wp-json\/wp\/v2\/comments?post=79"}],"version-history":[{"count":1,"href":"https:\/\/sisu.ut.ee\/rosak\/wp-json\/wp\/v2\/pages\/79\/revisions"}],"predecessor-version":[{"id":322,"href":"https:\/\/sisu.ut.ee\/rosak\/wp-json\/wp\/v2\/pages\/79\/revisions\/322"}],"wp:attachment":[{"href":"https:\/\/sisu.ut.ee\/rosak\/wp-json\/wp\/v2\/media?parent=79"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}