Shortest paths for a robot with nonholonomic and field-of-view constraints

Authors:
Paolo Salaris;Daniele Fontanelli;Lucia Pallottino;Antonio Bicchi
Affiliations:
Interdepartmental Research Center "Enrico Piaggio," University of Pisa, Pisa, Italy;Department of Engineering and Information Science, University of Trento, Trento, Italy;Interdepartmental Research Center "Enrico Piaggio," University of Pisa, Pisa, Italy;Interdepartmental Research Center "Enrico Piaggio," University of Pisa, Pisa, Italy
Venue:
IEEE Transactions on Robotics
Year:
2010

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Abstract

This paper presents a complete characterization of shortest paths to a goal position for a robot with unicycle kinematics and an on-board camera with limited field-of-view (FOV), which must keep a given feature in sight. Previous work on this subject has shown that the search for a shortest path can be limited to simple families of trajectories. In this paper, we provide a complete optimal synthesis for the problem, i.e., a language of optimal control words, and a global partition of the motion plane induced by shortest paths, such that aword in the optimal language is univocally associated with a region and completely describes the shortest path from any starting point in that region to the goal point. An efficient algorithm to determine the region in which the robot is at any time is also provided.