3D Motion Planning (Motion Planning Problems)
Revision as of 10:29, 15 February 2023 by Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:3D Motion Planning (Motion Planning Problems)}} == Description == Given a set of horizontal (that is, parallel to the xy-plane) non-intersecting, non-touching triangle obstacles in 3-space, and a vertical line segment as a robot, determine whether the robot can be moved, using translations only, from a source to a goal position without colliding with the obstacles. == Related Problems == Related: Planar Motion Planning == Parameters == <pre>n:...")
Description
Given a set of horizontal (that is, parallel to the xy-plane) non-intersecting, non-touching triangle obstacles in 3-space, and a vertical line segment as a robot, determine whether the robot can be moved, using translations only, from a source to a goal position without colliding with the obstacles.
Related Problems
Related: Planar Motion Planning
Parameters
n: number of triangle obstacles
Table of Algorithms
Currently no algorithms in our database for the given problem.
Reductions FROM Problem
| Problem | Implication | Year | Citation | Reduction |
|---|---|---|---|---|
| Triangles Cover Triangle | if: to-time $N^{2-\epsilon}$ for some $\epsilon > {0}$ then: from-time: $N^{2-\epsilon'}$ for some $\epsilon' > {0}$ |
1995 | https://doi-org.ezproxy.canberra.edu.au/10.1016/0925-7721(95)00022-2 | link |