A Variational Approach to Path Planning in Three Dimensions Using Level Set Methods

Abstract

In this paper we extend the two dimensional methods set forth in 4, 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 2, 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.

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Document Details

Document Type
Technical Report
Publication Date
Dec 08, 2004
Accession Number
ADA438263

Entities

People

  • Daniel E. Marthaler
  • T. Cecil

Organizations

  • University of Texas at Austin

Tags

Communities of Interest

  • Air Platforms
  • Autonomy
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Aircrafts
  • Algorithms
  • Artificial Intelligence
  • Boundaries
  • Collision Avoidance
  • Computer Programming
  • Coordinate Systems
  • Curvature
  • Grids
  • Heuristic Methods
  • Image Processing
  • Motion Planning
  • Optimization
  • Robotics
  • Steady State
  • Three Dimensional
  • Topology

Readers

  • Fluid Dynamics.
  • Robotics and Automation.
  • Systems Analysis and Design

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms
  • Autonomy