On the Generation of Smooth Three-Dimensional Rigid Body Motions

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dc.contributor.authorKumar, Vijay
dc.contributor.authorŽefran, Miloš
dc.contributor.authorCroke, Christopher
dc.date2023-05-17T05:22:23.000
dc.date.accessioned2023-05-22T23:47:29Z
dc.date.available2023-05-22T23:47:29Z
dc.date.issued1998-08-01
dc.date.submitted2010-09-13T07:38:48-07:00
dc.description.abstractThis paper addresses the problem of generating smooth trajectories between an initial and final position and orientation in space. The main idea is to define a functional depending on velocity or its derivatives that measures the smoothness of a trajectory and find trajectories that minimize this functional. In order to ensure that the computed trajectories are independent of the parameterization of positions and orientations, we use the notions of Riemannian metric and covariant derivatives from differential geometry and formulate the problem as a variational problem on the Lie group of spatial rigid body displacements, SE (3). We show that by choosing an appropriate measure of smoothness, the trajectories can be made to satisfy boundary conditions on the velocities or higher order derivatives. Dynamically smooth trajectories can be obtained by incorporating the inertia of the system into the definition of the Riemannian metric. We state the necessary conditions for the shortest distance, minimum acceleration and minimum jerk trajectories. Analytical expressions for the smooth trajectories are derived for some special cases. We also provide several examples of the general case where the trajectories are computed numerically.
dc.description.commentsSuggested Citation: Zefran, M., V. Kumar and C. Croke. "On the generation of smooth three-dimensional rigid body motions." IEEE Transactions on Robotics and Automation, Vol. 14(4). p. 576-589. © 1998 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
dc.identifier.urihttps://repository.upenn.edu/handle/20.500.14332/39961
dc.legacy.articleid1254
dc.legacy.fieldstrue
dc.legacy.fulltexturlhttps://repository.upenn.edu/cgi/viewcontent.cgi?article=1254&context=meam_papers&unstamped=1
dc.source.issue244
dc.source.journalDepartmental Papers (MEAM)
dc.source.peerreviewedtrue
dc.source.statuspublished
dc.subject.otherGRASP
dc.subject.otherEngineering
dc.subject.otherMechanical Engineering
dc.titleOn the Generation of Smooth Three-Dimensional Rigid Body Motions
dc.typeArticle
digcom.contributor.authorŽefran, Miloš
digcom.contributor.authorisAuthorOfPublication|email:kumar@grasp.upenn.edu|institution:University of Pennsylvania|Kumar, Vijay
digcom.contributor.authorisAuthorOfPublication|email:CCROKE@MATH.UPENN.EDU|institution:University of Pennsylvania|Croke, Christopher
digcom.identifiermeam_papers/244
digcom.identifier.contextkey1554214
digcom.identifier.submissionpathmeam_papers/244
digcom.typearticle
dspace.entity.typePublication
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relation.isAuthorOfPublication3baa51e5-8e46-41ad-8508-56c025d0f9f1
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relation.isAuthorOfPublication.latestForDiscovery3baa51e5-8e46-41ad-8508-56c025d0f9f1
upenn.schoolDepartmentCenterDepartmental Papers (MEAM)
upenn.schoolDepartmentCenterGeneral Robotics, Automation, Sensing and Perception Laboratory
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