{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T04:10:49Z","timestamp":1777435849380,"version":"3.51.4"},"reference-count":23,"publisher":"SAGE Publications","issue":"12","license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Advanced Robotic Systems"],"published-print":{"date-parts":[[2015,12]]},"abstract":"<jats:p>Humanoid soccer robots must be able to carry out their tasks in a highly dynamic environment which requires responsive omnidirectional walking. This paper explains a new omnidirectional walking engine for a humanoid soccer robot that mainly consists of a foot planner, a zero moment point (ZMP) trajectory generator, a centre of mass (CoM) calculator and an active balance feedback loop. An analytical approach is presented for generating the CoM trajectory, in which the cart-table motion of the equations is solved using the Fourier approximation of the ZMP. With this approach, we propose using a new time segmentation approach in order to parametrize the double-support phase. An active balance method is also proposed which keeps the robot's trunk upright when faced with environmental disturbances.<\/jats:p>\n                  <jats:p>The walking engine is tested on both simulated and real NAO robots. Our results are encouraging given the fact that the robot performs favourably, walking quickly and in a stable manner in any direction in comparison with the best RoboCup 3D soccer simulation teams for which the same simulator is used. In addition, the proposed analytical Fourier-based approach is compared with the well-established numerical ZMP dynamics control method. Our results show that the presented analytical approach involves less time and complexity and better accuracy compared with the ZMP preview control method.<\/jats:p>","DOI":"10.5772\/61314","type":"journal-article","created":{"date-parts":[[2016,1,7]],"date-time":"2016-01-07T06:54:56Z","timestamp":1452149696000},"update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":6,"title":["Development of an Omnidirectional Walk Engine for Soccer Humanoid Robots"],"prefix":"10.1177","volume":"12","author":[{"given":"Nima","family":"Snafii","sequence":"first","affiliation":[{"name":"IEETA - Instituto de Engenharia Eletr\u00f3nica e Telem\u00e1tica de Aveiro, Universidade de Aveiro, Portugal"},{"name":"LIACC - Laborat\u00f3rio de Intelig\u00eancia Artificial e Ci\u00eancia de Computadores, Universidade do Porto, Portugal"},{"name":"DEI\/FEUP - Departamento de Engenharia Inform\u00e1tica, Faculdade de Engenharia, Universidade do Porto, Portugal"}]},{"given":"Abbas","family":"Abdolmaleki","sequence":"additional","affiliation":[{"name":"IEETA - Instituto de Engenharia Eletr\u00f3nica e Telem\u00e1tica de Aveiro, Universidade de Aveiro, Portugal"},{"name":"LIACC - Laborat\u00f3rio de Intelig\u00eancia Artificial e Ci\u00eancia de Computadores, Universidade do Porto, Portugal"},{"name":"DETI\/UA - Departamento de Eletr\u00f3nica, Telecomunica\u00e7\u00f5es e Inform\u00e1tica, Universidade de Aveiro, Portugal"}]},{"given":"Nuno","family":"Lau","sequence":"additional","affiliation":[{"name":"IEETA - Instituto de Engenharia Eletr\u00f3nica e Telem\u00e1tica de Aveiro, Universidade de Aveiro, Portugal"},{"name":"DETI\/UA - Departamento de Eletr\u00f3nica, Telecomunica\u00e7\u00f5es e Inform\u00e1tica, Universidade de Aveiro, Portugal"}]},{"given":"Luis Paulo","family":"Reis","sequence":"additional","affiliation":[{"name":"LIACC - Laborat\u00f3rio de Intelig\u00eancia Artificial e Ci\u00eancia de Computadores, Universidade do Porto, Portugal"},{"name":"DSI\/EEUM - Departamento de Sistemas de Informa\u00e7\u00e3o, Escola de Engenharia da Universidade do Minho, Portugal"}]}],"member":"179","published-online":{"date-parts":[[2015,1]]},"reference":[{"key":"e_1_3_3_2_2","volume-title":"Biped locomotion: dynamics, stability, control and application","author":"Vukobratovic Miomir","year":"2012","unstructured":"Vukobratovic Miomir, Borovac Branislav, Surla Dusan, Stokic Dragan. 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