TY - JOUR
T1 - Reaching a goal with directional uncertainty
AU - de Berg, Mark
AU - Guibas, Leonidas
AU - Halperin, Dan
AU - Overmars, Mark
AU - Schwarzkopf, Otfried
AU - Sharir, Micha
AU - Teillaud, Monique
N1 - Funding Information:
*This research was supported by the Netherlands’ Organization for Scientific Research (NWO) and partially by ESPRIT Basic Research Actions No. 6546 (project PROMotion) and No. 7141 (project ALCOM II: Aigorithms and Complexity). Part of the research was done during the Second Utrecht Workshop on Computational Geometry and its Application, supported by NWO. L.G. acknowledges support by NSF grant CCR-9215219,b y a grant from the Stanford SIMA Consortium, and by grants from the Digitial Equipment, Mitsubishi, and Toshiba Corporations. D.H. was supported by a Rothschild Postdoctoral Fellowship, by a grant from the Stanford Integrated Manufacturing Association (SIMA), and by NSF/ARPA Research Grant IRI-9306544. Work on this paper by M.S. has been supported by National Science Foundation Grant CCR-91-22103, and by grants from the U.S.-Israeli Binational Science Foundation, the Fund for Basic Research administered by the Israeli Academy of Sciences, and the G.I.F., the German-Israeli Foundation for Scientific Research and Development. l Corresponding author. Email: [email protected].
PY - 1995/4/3
Y1 - 1995/4/3
N2 - We study two problems related to planar motion planning for robots with imperfect control, where, if the robot starts a linear movement in a certain commanded direction, we only know that its actual movement will be confined in a cone of angle α centered around the specified direction. First, we consider a single goal region, namely the "region at infinity", and a set of polygonal obstacles, modeled as a set S of n line segments. We are interested in the region Rα(S) from where we can reach infinity with a directional uncertainty of α. We prove that the maximum complexity of Rα(S) is O( n α5). Second, we consider a collection of k polygonal goal regions of total complexity m, but without any obstacles. Here we prove an O(k3m) bound on the complexity of the region from where we can reach a goal region with a directional uncertainty of α. For both situations we also prove lower bounds on the maximum complexity, and we give efficient algorithms for computing the regions.
AB - We study two problems related to planar motion planning for robots with imperfect control, where, if the robot starts a linear movement in a certain commanded direction, we only know that its actual movement will be confined in a cone of angle α centered around the specified direction. First, we consider a single goal region, namely the "region at infinity", and a set of polygonal obstacles, modeled as a set S of n line segments. We are interested in the region Rα(S) from where we can reach infinity with a directional uncertainty of α. We prove that the maximum complexity of Rα(S) is O( n α5). Second, we consider a collection of k polygonal goal regions of total complexity m, but without any obstacles. Here we prove an O(k3m) bound on the complexity of the region from where we can reach a goal region with a directional uncertainty of α. For both situations we also prove lower bounds on the maximum complexity, and we give efficient algorithms for computing the regions.
UR - http://www.scopus.com/inward/record.url?scp=0029634168&partnerID=8YFLogxK
U2 - 10.1016/0304-3975(94)00237-D
DO - 10.1016/0304-3975(94)00237-D
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AN - SCOPUS:0029634168
SN - 0304-3975
VL - 140
SP - 301
EP - 317
JO - Theoretical Computer Science
JF - Theoretical Computer Science
IS - 2
ER -