{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T09:55:07Z","timestamp":1777715707049,"version":"3.51.4"},"reference-count":44,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2007,4,1]],"date-time":"2007-04-01T00:00:00Z","timestamp":1175385600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[2007,4]]},"abstract":"<jats:p>Efficient algorithms for collision-free energy sub-optimal path planning for formations of spacecraft flying in deep space are presented. The idea is to introduce a set of way-points through which the spacecraft are required to pass, combined with parameterizations of the trajectories which are energy-optimal for each spacecraft. The resulting constrained optimization problem is formulated as a quasi-quadratic parameter optimization problem in terms of the way-points parameters. The mathematical structure of the problem is further exploited to develop gradient-based algorithms in which the gradients are computed analytically. The collision avoidance constraints are approximated such that closed form solutions are generated. This combination results in fast and robust numerical algorithms which work very well for scenarios involving a large number of spacecraft (e.g. 20).<\/jats:p>","DOI":"10.1177\/0278364907076709","type":"journal-article","created":{"date-parts":[[2007,4,10]],"date-time":"2007-04-10T11:20:12Z","timestamp":1176204012000},"page":"405-430","source":"Crossref","is-referenced-by-count":25,"title":["Deep Space Formation Flying Spacecraft Path Planning"],"prefix":"10.1177","volume":"26","author":[{"given":"Cornel","family":"Sultan","sequence":"first","affiliation":[{"name":"United Technologies Research Center, East Hartford, CT, 06108, USA"}]},{"given":"Sanjeev","family":"Seereram","sequence":"additional","affiliation":[{"name":"Scientific Systems Company Inc., Woburn, MA, 01801, USA and"}]},{"given":"Raman K.","family":"Mehra","sequence":"additional","affiliation":[{"name":"Scientific Systems Company Inc., Woburn, MA, 01801, USA and"}]}],"member":"179","published-online":{"date-parts":[[2007,4,1]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1177\/027836499701600604"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.2514\/2.4528"},{"key":"atypb3","volume-title":"Proceedings of Astronomical Interferometry Meeting, Kona, HI","author":"Beichman, C.A."},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.2514\/6.2000-5194"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.2514\/1.4306"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.2514\/2.4950"},{"key":"atypb7","volume-title":"Proceedings of the 12th AIAA\/USU Annual Conference on Small Satellites","author":"Das, A."},{"key":"atypb8","volume-title":"Proceedings of the Conference on Decision and Control","author":"Dunbar, W."},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.2514\/2.4732"},{"key":"atypb10","volume-title":"Proceedings of the Flight Mechanics Symposium","author":"Folta, D."},{"key":"atypb11","volume-title":"Proceedings IEEE\/RSJ International Conf erence on Intelligent Robots and Systems","author":"Foskey, M."},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.2514\/2.4678"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.2514\/2.4856"},{"key":"atypb14","first-page":"20","volume":"103","author":"Fridlund, C.V.M.","year":"2000","journal-title":"ESA Bulletin"},{"key":"atypb15","volume-title":"Proceedings of 5th International Workshop on Algorithmic Foundations of Robotics (WAFR)","author":"Garber, M."},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1142\/S0218195999000285"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1177\/027836402320556421"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.2514\/2.4982"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.2514\/2.4874"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1109\/70.508439"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1109\/70.660866"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.2514\/2.5059"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.aa.16.090178.000453"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.2514\/6.2004-4785"},{"key":"atypb25","volume-title":"AIAA Guidance, Navigation, and Control Conference and Exhibition"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1109\/9.664155"},{"key":"atypb27","volume-title":"Linear and Nonlinear Programming","author":"Luenberger, D.G.","year":"1984"},{"key":"atypb28","volume-title":"Intercorrelated Satellite Observations Related to Solar Events","author":"Manno, V.","year":"1969"},{"key":"atypb29","volume-title":"Proceedings of the International Symposium Formation Flying","author":"McQuade, F."},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.2514\/2.4721"},{"key":"atypb31","volume-title":"Proceedings of AIAA Guidance, Navigation, and Control Conference","author":"Phillips, J.M."},{"key":"atypb32","volume-title":"Proceedings of the American Control Conference","author":"Prasanth, R."},{"key":"atypb33","volume-title":"Proceedings of the Inernational. 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