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, ${\cal A}$.