 
Summary: Coverage of a Planar Point Set with Multiple Constrained Robots
Nilanjan Chakraborty Srinivas Akella John Wen
Abstract An important problem that arises in many appli
cations is: Given k robots with known processing footprint to
process a set of N points in the plane, find trajectories for
each robot satisfying the geometric, kinematic, and dynamic
constraints such that the time required to cover the points
(processing time plus travel time) is minimized. This problem
is a hybrid discretecontinuous optimization problem and is
hard to solve optimally even for k = 1. One approach is
to treat this as a two stage problem where the first stage
is to find the best possible path satisfying the geometric
constraints and then convert it into a trajectory satisfying
the differential constraints. In this paper, we consider an
industrial microelectronics manufacturing system of k(= 2)
robots, with square footprints, that are constrained to translate
along a line while satisfying proximity constraints. The points
lie on a planar base plate that can translate along the plane
normal to the direction of motion of the robots. We solve the
geometric problem of path generation for the robots using a two
