3.2 Rigid-Body Transformations

Any of the techniques from Section 3.1 can be used to define both the obstacle region and the robot. Let $ {\cal O}$ refer to the obstacle region, which is a subset of $ {\cal W}$. Let $ {\cal A}$ refer to the robot, which is a subset of $ {\mathbb{R}}^2$ or $ {\mathbb{R}}^3$, matching the dimension of $ {\cal W}$. Although $ {\cal O}$ remains fixed in the world, $ {\cal W}$, motion planning problems will require ``moving'' the robot, $ {\cal A}$.


Steven M LaValle 2012-04-20