TY - GEN

T1 - Navigation among visually connected sets of partially distinguishable landmarks

AU - Erickson, Lawrence H.

AU - Lavalle, Steven M

PY - 2012/1/1

Y1 - 2012/1/1

N2 - A robot navigates in a polygonal region populated by a set of partially distinguishable landmarks. The robot's motion primitives consist of actions of the form "drive toward a landmark of class x". To effectively navigate, the robot must always be able to see a landmark. Also, if the robot sees two landmarks of the same class, its motion primitives become ambiguous. Finally, if the robot wishes to navigate from landmark s0 to landmark sgoal with a simple graph search algorithm, then there must be a sequence of landmarks [s0, s1, s2,..., s k = sgoal], in which landmark si is visible from si-1. Given these three conditions, how many landmark classes are required for navigation in a given polygon P? We call this minimum number of landmark classes the connected landmark class number, denoted χCL(P). We study this problem for the monotone polygons, an important family of polygons that are frequently generated as intermediate steps in other decomposition algorithms. We demonstrate that for all odd k, there exists a monotone polygon Mk with 3/4 (k2 + 2k + 1) vertices such that χCL(P) ≥ k. We also demonstrate that for any n-vertex monotone polygon P, χCL(P) ≤ n/3 + 12.

AB - A robot navigates in a polygonal region populated by a set of partially distinguishable landmarks. The robot's motion primitives consist of actions of the form "drive toward a landmark of class x". To effectively navigate, the robot must always be able to see a landmark. Also, if the robot sees two landmarks of the same class, its motion primitives become ambiguous. Finally, if the robot wishes to navigate from landmark s0 to landmark sgoal with a simple graph search algorithm, then there must be a sequence of landmarks [s0, s1, s2,..., s k = sgoal], in which landmark si is visible from si-1. Given these three conditions, how many landmark classes are required for navigation in a given polygon P? We call this minimum number of landmark classes the connected landmark class number, denoted χCL(P). We study this problem for the monotone polygons, an important family of polygons that are frequently generated as intermediate steps in other decomposition algorithms. We demonstrate that for all odd k, there exists a monotone polygon Mk with 3/4 (k2 + 2k + 1) vertices such that χCL(P) ≥ k. We also demonstrate that for any n-vertex monotone polygon P, χCL(P) ≤ n/3 + 12.

UR - http://www.scopus.com/inward/record.url?scp=84864459222&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84864459222&partnerID=8YFLogxK

U2 - 10.1109/ICRA.2012.6224694

DO - 10.1109/ICRA.2012.6224694

M3 - Conference contribution

AN - SCOPUS:84864459222

SN - 9781467314039

T3 - Proceedings - IEEE International Conference on Robotics and Automation

SP - 4829

EP - 4835

BT - 2012 IEEE International Conference on Robotics and Automation, ICRA 2012

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2012 IEEE International Conference on Robotics and Automation, ICRA 2012

Y2 - 14 May 2012 through 18 May 2012

ER -