The field of Human-Robot Collaboration (HRC) has seen a considerable amount of progress in the recent years. Although genuinely collaborative platforms are far from being deployed in real-world scenarios, advances in control and perception algorithms have progressively popularized robots in manufacturing settings, where they work side by side with human peers to achieve shared tasks. Unfortunately, little progress has been made toward the development of systems that are proactive in their collaboration, and autonomously take care of some of the chores that compose most of the collaboration tasks. In this work, we present a collaborative system capable of assisting the human partner with a variety of supportive behaviors in spite of its limited perceptual and manipulation capabilities and incomplete model of the task. Our framework leverages information from a high-level, hierarchical model of the task. The model, that is shared between the human and robot, enables transparent synchronization between the peers and understanding of each other's plan. More precisely, we derive a partially observable Markov model from the high-level task representation. We then use an online solver to compute a robot policy, that is robust to unexpected observations such as inaccuracies of perception, failures in object manipulations, as well as discovers hidden user preferences. We demonstrate that the system is capable of robustly providing support to the human in a furniture construction task.
 In this paper, we bring techniques from operations research to bear on the problem of choosing optimal actions in partially observable stochastic domains. We begin by introducing the theory of Markov decision processes (mdps) and partially observable MDPs (pomdps). We then outline a novel algorithm for solving pomdps off line and show how, in some cases, a finite-memory controller can be extracted from the solution to a POMDP. We conclude with a discussion of how our approach relates to previous work, the complexity of finding exact solutions to pomdps, and of some possibilities for finding approximate solutions. We consider the problem of using real-time feedback from contact sensors to create closed-loop pushing actions. To do so, we formulate the problem as a partially observable Markov decision process POMDP with a transition model based on a physics simulator and a reward function that drives the robot towards a successful grasp. We demonstrate that it is intractable to solve the full POMDP with traditional techniques and introduce a novel decomposition of the policy into pre- and post-contact stages to reduce the computational complexity. Our method uses an offline point-based solver on a variable-resolution discretization of the state space to solve for a post-contact policy as a pre-computation step. Then, at runtime, we use an A* search to compute a pre-contact trajectory. We prove that the value of the resulting policy is within a bound of the value of the optimal policy and give intuition about when it performs well. Additionally, we show the policy produced by our algorithm achieves a successful grasp more quickly and with higher probability than a baseline QMDP policy on two different objects in simulation. Finally, we validate our simulation results on a real robot using commercially available tactile sensors.