7.2 Multiple Robots

Suppose that multiple robots share the same world, ${\cal W}$. A path must be computed for each robot that avoids collisions with obstacles and with other robots. In Chapter 4, each robot could be a rigid body, ${\cal A}$, or it could be made of $k$ attached bodies, ${\cal A}_1$, $\ldots$, ${\cal A}_k$. To avoid confusion, superscripts will be used in this section to denote different robots. The $i$th robot will be denoted by ${\cal A}^i$. Suppose there are $m$ robots, ${\cal A}^1$, ${\cal A}^2$, $\ldots$, ${\cal A}^m$. Each robot, ${\cal A}^i$, has its associated C-space, ${\cal C}^i$, and its initial and goal configurations, $q^i_{init}$ and $q^i_{goal}$, respectively.