Motion Planning i n Virtual Environments. Dan Halperin Yesha Sivan TA: Alon Shalita. Spring 2007. Basics of Motion Planning (D.H.). Motion planning: the basic problem.
Dan HalperinYesha Sivan
TA: Alon Shalita
Basics of Motion Planning (D.H.)
Let B be a system (the robot) with k degrees of freedom moving in a known environment cluttered with obstacles. Given free start and goal placements for B decide whether there is a collision free motion for B from start to goal and if so plan such a motion.
roadmap [Canny 87]:
a singly exponential solution,
nk(log n)dO(k^2) expected time
translational motion planning for a polygon
among polygos using exact Minkowski sums
We are given two polygons P and Q with mandn vertices respectively. If both polygons are convex, the complexity of their sum is m + n, and we can compute it in (m + n) time using a very simple procedure.
If only one of the polygons is convex, the complexity of their sum is (mn).
If both polygons are non-convex, the complexity of their sum is (m2n2).
The maze solver that we saw last week uses CGAL’s Minkowski sum package
prevalent methods: sampling-based planners
We start with the archetype: probabilistic roadmap (PRM)