A variational approach to path planning in three dimensions using level set methods

被引:10
作者
Cecil, T
Marthaler, DE
机构
[1] Univ Texas, ICES, Austin, TX 78712 USA
[2] Northrop Grumman Corp, ACS, UMS, Rancho Bernardo, CA USA
关键词
D O I
10.1016/j.jcp.2005.05.015
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
In this paper we extend the two-dimensional methods set forth in [T. Cecil, D. Marthaler, A variational approach to search and path planning using level set methods, UCLA CAM Report, 04-61, 2004], proposing a variational approach to a path planning problem in three dimensions using a level set framework. After defining an energy integral over the path, we use gradient flow on the defined energy and evolve the entire path until a locally optimal steady state is reached. We follow the framework for motion of curves in three dimensions set forth in [P. Burchard, L.-T. Cheng, B. Merriman, S. Osher, Motion of curves in three spatial dimensions using a level set approach, J. Comput. Phys. 170(2) (2001) 720-741], modified appropriately to take into account that we allow for paths with positive, varying widths. Applications of this method extend to robotic motion and visibility problems, for example. Numerical methods and algorithms are given, and examples are presented. (c) 2005 Elsevier Inc. All rights reserved.
引用
收藏
页码:179 / 197
页数:19
相关论文
共 37 条
[1]  
ALTSCHULER SJ, 1991, J DIFFER GEOM, V34, P491
[2]  
[Anonymous], IEEE T IMAGE PROCESS
[3]   Motion of curves in three spatial dimensions using a level set approach [J].
Burchard, P ;
Cheng, LT ;
Merriman, B ;
Osher, S .
JOURNAL OF COMPUTATIONAL PHYSICS, 2001, 170 (02) :720-741
[4]  
Canny J.F., 1988, Complexity of Robot Motion Planning
[5]  
CECIL T, 2004, 0461 UCLA CAM
[6]   Motion of curves constrained on surfaces using a level-set approach [J].
Cheng, LT ;
Burchard, P ;
Merriman, B ;
Osher, S .
JOURNAL OF COMPUTATIONAL PHYSICS, 2002, 175 (02) :604-644
[7]  
CHENG LT, 2004, 0403 UCLA CAM
[8]  
CRANDALL MG, 1984, MATH COMPUT, V43, P1, DOI 10.1090/S0025-5718-1984-0744921-8
[9]   VISCOSITY SOLUTIONS OF HAMILTON-JACOBI EQUATIONS [J].
CRANDALL, MG ;
LIONS, PL .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 277 (01) :1-42
[10]  
EARL MG, 2002, P 41 IEEE C DEC CONT