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This paper addresses the problem of dynamic allocation of robot resources to tasks with hierarchical representations and multiple types of execution constraints, with the goal of enabling single-robot multitasking capabilities. Although the vast majority of robot platforms are equipped with more than one sensor (cameras, lasers, sonars) and several actuators (wheels/legs, two arms), which would in principle allow the robot to concurrently work on multiple tasks, existing methods are limited to allocating robots in their entirety to only one task at a time. This approach employs only a subset of a robot's sensors and actuators, leaving other robot resources unused. Our aim is to enable a robot to make full use of its capabilities by having an individual robot multitask, distributing its sensors and actuators to multiple concurrent activities. We propose a new architectural framework based on Hierarchical Task Trees that supports multitasking through a new representation of robot behaviors that explicitly encodes the robot resources (sensors and actuators) and the environmental conditions needed for execution. This architecture was validated on a two-arm, mobile, PR2 humanoid robot, performing tasks with multiple types of execution constraints. 

Partially observable Markov decision processes (POMDPs) provide a flexible representation for real-world decision and control problems. However, POMDPs are notoriously difficult to solve, especially when the state and observation spaces are continuous or hybrid, which is often the case for physical systems. While recent online sampling-based POMDP algorithms that plan with observation likelihood weighting have shown practical effectiveness, a general theory characterizing the approximation error of the particle filtering techniques that these algorithms use has not previously been proposed. Our main contribution is bounding the error between any POMDP and its corresponding finite sample particle belief MDP (PB-MDP) approximation. This fundamental bridge between PB-MDPs and POMDPs allows us to adapt any sampling-based MDP algorithm to a POMDP by solving the corresponding particle belief MDP, thereby extending the convergence guarantees of the MDP algorithm to the POMDP. Practically, this is implemented by using the particle filter belief transition model as the generative model for the MDP solver. While this requires access to the observation density model from the POMDP, it only increases the transition sampling complexity of the MDP solver by a factor of O(C), where C is the number of particles. Thus, when combined with sparse sampling MDP algorithms, this approach can yield algorithms for POMDPs that have no direct theoretical dependence on the size of the state and observation spaces. In addition to our theoretical contribution, we perform five numerical experiments on benchmark POMDPs to demonstrate that a simple MDP algorithm adapted using PB-MDP approximation, Sparse-PFT, achieves performance competitive with other leading continuous observation POMDP solvers.