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We consider a problem called task ordering with path uncertainty (TOP-U)where multiple robots are provided with a set of task locations to visit in abounded environment, but the length of the path between a pair of tasklocations is initially known only coarsely by the robots. The objective of therobots is to find the order of tasks that reduces the path length (or, energyexpended) to visit the task locations in such a scenario. To solve thisproblem, we propose an abstraction called a task reachability graph (TRG) thatintegrates the task ordering with the path planning by the robots. The TRG isupdated dynamically based on inter-task path costs calculated using asampling-based motion planner, and, a Hidden Markov Model (HMM)-based techniquethat calculates the belief in the current path costs based on the environmentperceived by the robot's sensors and task completion information received fromother robots. We then describe a Markov Decision Process (MDP)-based algorithmthat can select the paths that reduce the overall path length to visit the tasklocations and a coordination algorithm that resolves path conflicts betweenrobots. We have shown analytically that our task selection algorithm finds thelowest cost path returned by the motion planner, and, that our proposedcoordination algorithm is deadlock free. We have also evaluated our algorithmon simulated Corobot robots within different environments while varying thenumber of task locations, obstacle geometries and number of robots, as well ason physical Corobot robots. Our results show that the TRG-based approach canperform considerably better in planning and locomotion times, and number ofre-plans, while traveling almost-similar distances as compared to a closestfirst, no uncertainty (CFNU) task selection algorithm.

Integrated Task and Motion Planning for Multiple Robots under Path and Communication Uncertainties