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

Authors:
Thomas Cecil;Daniel E. Marthaler
Affiliations:
ICES, University of Texas - Austin, University Station, C0200, Austin, TX 78712, United States;ACS-UMS, Northrop Grumman Corp, Rancho Bernardo, CA, United States
Venue:
Journal of Computational Physics
Year:
2006

Citing 12
Cited 9

Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations

Journal of Computational Physics
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations

SIAM Journal on Numerical Analysis
A viscosity solutions approach to shape-from-shading

SIAM Journal on Numerical Analysis
A level set approach for computing solutions to incompressible two-phase flow

Journal of Computational Physics
A PDE-based fast local level set method

Journal of Computational Physics
Implicit and nonparametric shape reconstruction from unorganized data using a variational level set method

Computer Vision and Image Understanding
Motion of curves in three spatial dimensions using a level set approach

Journal of Computational Physics
Optimal Algorithm for Shape from Shading and Path Planning

Journal of Mathematical Imaging and Vision
Motion of curves constrained on surfaces using a level-set approach

Journal of Computational Physics
Geometric optics in a phase-space-based level set and Eulerian framework

Journal of Computational Physics
Discretization of Dirac delta functions in level set methods

Journal of Computational Physics
Active contours without edges

IEEE Transactions on Image Processing

Simplex free adaptive tree fast sweeping and evolution methods for solving level set equations in arbitrary dimension

Journal of Computational Physics
Node fault robustness for heterogeneous dynamic sensor networks

IMACS'08 Proceedings of the 7th WSEAS International Conference on Instrumentation, Measurement, Circuits and Systems
A unified approach for heterogeneity and node fault robustness in dynamic sensor networks

WSEAS TRANSACTIONS on COMMUNICATIONS
Mobile sensors networks under communication constraints

WSEAS TRANSACTIONS on SYSTEMS
Redundant coverage for noise reduction in dynamic sensor networks

WSEAS TRANSACTIONS on SYSTEMS
Measurement noise reduction in dynamic sensor networks

ICS'08 Proceedings of the 12th WSEAS international conference on Systems
A decentralized protocol for wireless communication in mobile sensor networks

ICCOM Proceedings of the 13th WSEAS international conference on Communications
A local information based protocol for networks data exchange with application to mobile sensor networks

WSEAS TRANSACTIONS on COMMUNICATIONS
A direct variational method for planning monotonically optimal paths for redundant manipulators in constrained workspaces

Robotics and Autonomous Systems

Quantified Score

Hi-index	31.45

Visualization

Abstract

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.