Suppose that multiple robots share the same world, . 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, , or it could be made of attached bodies, , , . To avoid confusion, superscripts will be used in this section to denote different robots. The th robot will be denoted by . Suppose there are robots, , , , . Each robot, , has its associated C-space, , and its initial and goal configurations, and , respectively.