Many robotic systems deal with uncertainty by performing a sequence of information gathering actions. In this work, we focus on the problem of efficiently constructing such a sequence by drawing an explicit connection to submodularity. Ideally, we would like a method that finds the optimal sequence, taking the minimum amount of time while providing sufficient information. Finding this sequence, however, is generally intractable. As a result, many well-established methods select actions greedily. Surprisingly, this often performs well. Our work first explains this high performance -- we note a commonly used metric, reduction of Shannon entropy, is submodular under certain assumptions, rendering the greedy solution comparable to the optimal plan in the offline setting. However, reacting online to observations can increase performance. Recently developed notions of adaptive submodularity provide guarantees for a greedy algorithm in this online setting. In this work, we develop new methods based on adaptive submodularity for selecting a sequence of information gathering actions online. In addition to providing guarantees, we can capitalize on submodularity to attain additional computational speedups. We demonstrate the effectiveness of these methods in simulation and on a robot.
@cite_28 @cite_3 select a sequence of uncertainty reducing tactile actions through forward search in a POMDP. Possible actions consist of pre-specified world-relative trajectories @cite_28 , motions based on the current highest probability state. Actions are selected using either information gain or probability of success as a metric @cite_29 , with a forward search depth of up to three actions. Aggressive pruning and clustering of observations makes online selection tractable. While Hsiao considers a small, focused set of actions (typically ) at a greater depth, we consider a broad set of actions (typically ) at a search depth of one action.
@cite_28 @cite_29 @cite_3
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In this paper, we present an approach for robustly grasping objects under positional uncertainty. We maintain a belief state (a probability distribution over world states), model the problem as a partially observable Markov decision process (POMDP), and select actions with a receding horizon using forward search through the belief space. Our actions are world-relative trajectories, or fixed trajectories expressed relative to the most-likely state of the world. We localize the object, ensure its reachability, and robustly grasp it at a goal position by using information-gathering, reorientation, and goal actions. We choose among candidate actions in a tractable way online by computing and storing the observation models needed for belief update offline. This framework is used to successfully grasp objects (including a powerdrill and a Brita pitcher) despite significant uncertainty, both in simulation and with an actual robot arm. 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. We propose a new approach to the problem of searching a space of policies for a Markov decision process (MDP) or a partially observable Markov decision process (POMDP), given a model. Our approach is based on the following observation: Any (PO)MDP can be transformed into an "equivalent" POMDP in which all state transitions (given the current state and action) are deterministic. This reduces the general problem of policy search to one in which we need only consider POMDPs with deterministic transitions. We give a natural way of estimating the value of all policies in these transformed POMDPs. Policy search is then simply performed by searching for a policy with high estimated value. We also establish conditions under which our value estimates will be good, recovering theoretical results similar to those of Kearns, Mansour and Ng (1999), but with "sample complexity" bounds that have only a polynomial rather than exponential dependence on the horizon time. Our method applies to arbitrary POMDPs, including ones with infinite state and action spaces. We also present empirical results for our approach on a small discrete problem, and on a complex continuous state continuous action problem involving learning to ride a bicycle. We present a novel POMDP planning algorithm called heuristic search value iteration (HSVI). HSVI is an anytime algorithm that returns a policy and a provable bound on its regret with respect to the optimal policy. HSVI gets its power by combining two well-known techniques: attention-focusing search heuristics and piecewise linear convex representations of the value function. HSVI's soundness and convergence have been proven. On some bench-mark problems from the literature, HSVI displays speedups of greater than 100 with respect to other state-of-the-art POMDP value iteration algorithms. We also apply HSVI to a new rover exploration problem 10 times larger than most POMDP problems in the literature.