Reciprocal root locus approach to path planning for multiple mobile robots

Given the available mobile robots and the tasks to be executed, at the highest planning level, the first problem is the assignment of tasks to the robots or AGVs, and the second one is path planning. If the robots are equipped with sensors and with some computing capability then each robot can manage local planning and partially obstacle avoidance. Hence at the highest level only the planner is needed for specifying missions. In this case a quick planning is desirable for computing feasible paths in a given work-space without congestion. The proposed solution is based on the theory of conformal transformations that can be employed in order to map the given work-space in a more appealing geometric setting. Assuming the work-space is a semicircle, the path planning is solved by using the reciprocal root locus technique used in the theory of optimal control of linear time-invariant discrete systems. Some examples are given to illustrate the proposed technique and its efficiency