Departmental Papers (ESE)


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


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.

Document Type

Conference Paper

Subject Area

GRASP, Kodlab

Date of this Version

May 1989


Copyright 1989 IEEE. Reprinted from Proceedings of the IEEE International Conference on Robotics and Automation, Volume 1, 1989, pages 21-26.

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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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Date Posted: 06 June 2008

This document has been peer reviewed.