The construction of analytic diffeomorphisms for exact robot navigation on star worlds

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Departmental Papers (ESE)
General Robotics, Automation, Sensing and Perception Laboratory
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The authors consider the construction of navigation functions on configuration spaces whose geometric expressiveness is rich enough for navigation amidst real-world obstacles. They describe a general methodology which extends the construction of navigation functions on sphere worlds to any smoothly deformable space. According to this methodology, the problem of constructing a navigation function is reduced to the construction of a transformation mapping a given space into its model sphere world. The transformation must satisfy certain regularity conditions guaranteeing invariance of the navigation function properties. The authors demonstrate this idea by constructing navigation functions on star worlds: n-dimensional star shaped subsets of En punctured by any finite number of smaller disjoint n-dimensional stars. This construction yields automatically a bounded torque feedback control law which is guaranteed to guide the robot to destination point from almost every initial position without hitting any obstacle.

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1989-05-14
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2023-05-17T02:17:26.000
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Copyright 1989 IEEE. Reprinted from Proceedings of the IEEE International Conference on Robotics and Automation, Volume 1, 1989, pages 21-26. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or 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 must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it. NOTE: At the time of publication, author Daniel Koditschek was affiliated with Yale University. Currently, he is a faculty member in the Department of Electrical and Systems Engineering at the University of Pennsylvania.
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