Efficient Robot Planning for Achieving Multiple Independent Partially Observable Tasks That Evolve over Time

We focus on domains where a robot is required to accomplish a set of tasks that are partially observable and evolve independently of each other according to their dynamics. An example domain is a restaurant setting where a robot waiter should take care of an ongoing stream of tasks, namely serving a number of tables, including delivering food to the tables and checking on customers. An action that the robot should take next at any point of time typically depends on the duration of possible actions, the state of each table, and how these tables evolve over time, e.g., the food becomes cold after a few time steps. As most of these domains are dynamic and tasks are frequently being added and removed, the robot typically needs to plan for a short h-step horizon to quickly decide on the next action and replans at each time step. A conventional approach to deal with this problem is to combine all the tasks' states and robot actions into one large model and to compute an h-step optimal policy for this combined model. For the problems that we are interested in, the number of tasks, e.g., the number of tables in the restaurant domain, can be large making this planning approach computationally impractical. The observation that we make however is that in many domains the number of tasks that the robot can accomplish within h-steps is very limited. We present an algorithm that exploits this observation and decomposes the problem into a series of much smaller planning problems, the solution to which gives us an optimal solution. We demonstrate the efficiency of our algorithm on the restaurant domain.