Collision avoidance of mobile robots by using initial time delays

This paper addresses a collision avoidance problem in a multi-robot system. Each robot has a set of possible trajectories, each trajectory fulfilling its individual task. The trajectories consist of sequences of regions to be followed, and the time for moving inside each region is known. The problem is to avoid inter-robot collisions by imposing initial time delays for each trajectory. Two solutions are developed, depending on the possibility of imposing a certain trajectory from the available set of paths for each robot. The solutions have the form of mixed integer linear programming optimizations that return the initial time delays and, when necessary, the chosen trajectory for each robot. Finally, we perform a statistical study on the proposed solutions and we conclude that one formulation is preferable to the others.