Exact robot navigation using cost functions: the case of distinct spherical boundaries in En

The utility of artificial potential functions is explored as a means of translating automatically a robot task description into a feedback control law to drive the robot actuators. A class of functions is sought which will guide a point robot amid any finite number of spherically bounded obstacles in Euclidean n-space toward an arbitrary destination point. By introducing a set of additional constraints, the subclass of navigation functions is defined. This class is dynamically sound in the sense that the actual mechanical system will inherit the essential aspects of the qualitative behavior of the gradient lines of the cost function. An existence proof is given by constructing a one parameter family of such functions; the parameter is used to guarantee the absence of local minima. Comments Copyright 1988 IEEE. Reprinted from Proceedings of the IEEE International Conference on Robotics and Automation, Volume 3, 1988, pages 1791-1796. 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 [email protected]. 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. This conference paper is available at ScholarlyCommons: http://repository.upenn.edu/ese_papers/391 Exact Robot Navigation using Cost Functions: The Case of Distinct Spherical Boundaries in E” Elon R imon and Dimiel E. Koditschek Center for Sys tems Science Yale University, Depa r tmen t of Electrical Engineering Abstrarct The utility of artificial potential functions is explored, as a mean of translating automatically a robot task description into a feedback control law to drive the robot actuators. We seek a class of cost functions which will guide a point robot amidst any finite number of spherically bounded obstacles in Euclidean n-space toward an arbitrary destination point. By introducing a set of additional constraints, the subclass of navigation functions is defined. This class is “dynamically sound” in the sense tha t the actual mechanical system will inherit the essential asHogan [ll] in the context of force control. The methodology was developed independently by Arimoto in Japan [13], and by Soviet investigators as well [14]. This paper introduces the notion of a navigation function (to be defined precisely in Section 2.1), which encompasses the more stringent requirements described above. A lengthier dist.iission of the motivation for this investigation is provided i n the earlier paper [3], which explores the possibility of k priori topological obstructions to the project. Here, we present a construction and proof tha t it correctly solves the problem stated above. pects of the qualitative behavior of the gradient lines of the cost function. An existence proof is given, by the construction used t o guarantee the absence of local minima. Of course, the much more general problem of constructwith arbitrary polynomial boundary (given perfect information) has already been completely solved 171. Moreover, a near of a oneparameter family of such functions; the parameter is ing a path between two points in a ’pace obstructed by sets