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.