Abstract
This paper considers the problem of finding the shortest tour to cover a given set of inverted cone views with apex angle alpha and height H when their apex points lie on a planar surface. This is a novel variant of the 3D Traveling Salesman Problem with intersecting Neighborhoods (TSPN) called Cone-Tspn. When the cones are allowed to tilt by an angle epsilon we have the tilted Cone-Tspn problem, to which we present an algorithm that returns a solution with an approximation ratio of Oleft(frac 1+tanalpha 1-tanepsilontanalpha left(1+logfrac max(H) min(H) right)right). We demonstrate through simulations that our algorithm can be implemented in a practical way and by exploiting the structure of the cones we can achieve shorter tours. Finally, we present results from covering a reflective surface (lake area) that shows the importance of selecting different view angles under strong sunlight specularities.
| Original language | English (US) |
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| Title of host publication | 2018 IEEE International Conference on Robotics and Automation, ICRA 2018 |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 3910-3915 |
| Number of pages | 6 |
| ISBN (Electronic) | 9781538630815 |
| DOIs | |
| State | Published - Sep 10 2018 |
| Event | 2018 IEEE International Conference on Robotics and Automation, ICRA 2018 - Brisbane, Australia Duration: May 21 2018 → May 25 2018 |
Publication series
| Name | Proceedings - IEEE International Conference on Robotics and Automation |
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| ISSN (Print) | 1050-4729 |
Conference
| Conference | 2018 IEEE International Conference on Robotics and Automation, ICRA 2018 |
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| Country/Territory | Australia |
| City | Brisbane |
| Period | 5/21/18 → 5/25/18 |
Bibliographical note
Funding Information:This work is supported in part by NSF Award #1525045 and a grant from Minnesota State LCCMR Program.
Publisher Copyright:
© 2018 IEEE.