{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,6,19]],"date-time":"2023-06-19T22:15:41Z","timestamp":1687212941670},"reference-count":14,"publisher":"Walter de Gruyter GmbH","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,1,28]]},"abstract":"<jats:title>Zusammenfassung<\/jats:title>\n               <jats:p>Der Beitrag stellt einen Algorithmus zur Generierung von mehrfach stetig differenzierbaren Trajektorien auf Basis von B-Splines vor, deren Funktionswerte und Ableitungen innerhalb von konstanten Grenzen liegen. Die Trajektorien k\u00f6nnen f\u00fcr Systeme genutzt werden, bei denen Grenzen in den Ableitungen des Systemeingangs vorliegen. Dies trifft beispielsweise auf Modelle zu, bei denen ein Antrieb mit Begrenzungen in der Position, Geschwindigkeit und Beschleunigung als Systemeingang genutzt wird.<\/jats:p>\n               <jats:p>Zur Generierung werden Parameter, Startwerte der Trajektorie sowie die konstanten Grenzen ben\u00f6tigt. Eine quadratische Optimierung liefert die St\u00fctzpunkte der B-Spline-Kurve, die dadurch definiert ist. Die implizit begrenzten B-Splines k\u00f6nnen ideal in Optimalsteuerungsproblemen und modellpr\u00e4diktiven Regelungen als Steuertrajektorie eingesetzt werden. Durch die implizite Ber\u00fccksichtigung von Nebenbedingungen k\u00f6nnen ebensolche aus dem eigentlichen Optimierungsproblem entfallen. Daraus resultiert eine Verringerung der Komplexit\u00e4t des Optimalsteuerungsproblems bzw. der modellpr\u00e4diktiven Regelung was wiederum zu einer schnelleren Berechnungszeit f\u00fchrt.<\/jats:p>\n               <jats:p>Die implizit begrenzten B-Splines werden im Beitrag vorgestellt und exemplarisch in einer modellpr\u00e4diktiven Regelung mit einem robotischen System angewandt. Sie f\u00fchren zu einer deutlich schnelleren Berechnungszeit im Vergleich zur Nutzung von B-Splines mit expliziten Nebenbedingungen im Optimierungsproblem.<\/jats:p>","DOI":"10.1515\/auto-2019-0067","type":"journal-article","created":{"date-parts":[[2019,12,21]],"date-time":"2019-12-21T09:04:45Z","timestamp":1576919085000},"page":"72-85","source":"Crossref","is-referenced-by-count":1,"title":["Trajektoriengenerator zur Erzeugung beschr\u00e4nkter B-Splines"],"prefix":"10.1515","volume":"68","author":[{"given":"Andreas","family":"Seefried","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Systemdynamik und Regelungstechnik , DLR Oberpfaffenhofen , Wessling , Deutschland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andreas","family":"Pfeiffer","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Systemdynamik und Regelungstechnik , DLR Oberpfaffenhofen , Wessling , Deutschland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2019,12,21]]},"reference":[{"key":"2021062112572147906_j_auto-2019-0067_ref_001_w2aab3b7b1b1b6b1ab2b1b1Aa","doi-asserted-by":"crossref","unstructured":"A. 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