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

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 a bounded environment, but the length of the path between a pair of task locations is initially known only coarsely by the robots. The objective of the robots is to find the order of tasks that reduces the path length (or, energy expended) to visit the task locations in such a scenario. To solve this problem, we propose an abstraction called a task reachability graph (TRG) that integrates the task ordering with the path planning by the robots. The TRG is updated dynamically based on inter-task path costs calculated using a sampling-based motion planner, and, a Hidden Markov Model (HMM)-based technique that calculates the belief in the current path costs based on the environment perceived by the robot's sensors and task completion information received from other robots. We then describe a Markov Decision Process (MDP)-based algorithm that can select the paths that reduce the overall path length to visit the task locations and a coordination algorithm that resolves path conflicts between robots. We have shown analytically that our task selection algorithm finds the lowest cost path returned by the motion planner, and, that our proposed coordination algorithm is deadlock free. We have also evaluated our algorithm on simulated Corobot robots within different environments while varying the number of task locations, obstacle geometries and number of robots, as well as on physical Corobot robots. Our results show that the TRG-based approach can perform considerably better in planning and locomotion times, and number of re-plans, while traveling almost-similar distances as compared to a closest first, no uncertainty (CFNU) task selection algorithm.