Planning robust executions under uncertainty is a fundamental challenge for building autonomous robots. Partially Observable Markov Decision Processes (POMDPs) provide a standard framework for modeling uncertainty in many robot applications. A key algorithmic problem for POMDPs is policy synthesis. While this problem has traditionally been posed w.r.t. optimality objectives, many robot applications are better modeled by POMDPs where the objective is a boolean requirement. In this paper, we study the latter problem in a setting where the requirement is a safe-reachability property, which states that with a probability above a certain threshold, it is possible to eventually reach a goal state while satisfying a safety requirement. The central challenge in our problem is that it requires reasoning over a vast space of probability distributions. What's more, it has been shown that policy synthesis of POMDPs with reachability objectives is undecidable in general. To address these challenges, we introduce the notion of a goal-constrained belief space, which only contains beliefs (probability distributions over states) reachable from the initial belief under desired executions. This constrained space is generally much smaller than the original belief space. Our approach compactly represents this space over a bounded horizon using symbolic constraints, and employs an incremental Satisfiability Modulo Theories (SMT) solver to efficiently search for a valid policy over it. We evaluate our method using a case study involving a partially observable robotics domain with uncertain obstacles. Our results suggest that it is possible to synthesize policies over large belief spaces with a small number of SMT solver calls by focusing on goal-constrained belief space, and our method o ers a stronger guarantee of both safety and reachability than alternative unconstrained constrained POMDP formulations.
POMDPs @cite_29 provide a principled mathematical framework for modeling a variety of robotics problems in the face of uncertainty. Many POMDP algorithms @cite_5 @cite_27 @cite_9 @cite_36 @cite_34 @cite_4 for robot applications focus on discounted reward objectives. Recent work @cite_38 @cite_24 @cite_22 has investigated of POMDPs with temporal logic specifications, where the goal is to check whether a temporal logic objective can be ensured with probability 1. Our approach can be seen as synthesizing policies for large POMDP problems with basic temporal logic objectives (safe-reachability), but not limited to almost-sure satisfaction analysis. Though we may formulate a safe-reachability objective as an optimization problem by assigning negative rewards for unsafe states and positive rewards for goal states, this formulation does not always yield good policies @cite_0 .
@cite_38 @cite_4 @cite_22 @cite_36 @cite_29 @cite_9 @cite_24 @cite_0 @cite_27 @cite_5 @cite_34
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We consider partially observable Markov decision processes (POMDPs), that are a standard framework for robotics applications to model uncertainties present in the real world, with temporal logic specifications. All temporal logic specifications in linear-time temporal logic (LTL) can be expressed as parity objectives. We study the qualitative analysis problem for POMDPs with parity objectives that asks whether there is a controller (policy) to ensure that the objective holds with probability 1 (almost-surely). While the qualitative analysis of POMDPs with parity objectives is undecidable, recent results show that when restricted to finite-memory policies the problem is EXPTIME-complete. While the problem is intractable in theory, we present a practical approach to solve the qualitative analysis problem. We designed several heuristics to deal with the exponential complexity, and have used our implementation on a number of well-known POMDP examples for robotics applications. Our results provide the first practical approach to solve the qualitative analysis of robot motion planning with LTL properties in the presence of uncertainty. Partially observable Markov decision processes (POMDPs) are used in many robotic task classes from soccer to household chores. Determining an approximately optimal action policy for POMDPs is PSPACE-complete, and the exponential growth of computation time prohibits solving large tasks. This paper describes two techniques to extend the range of robotic tasks that can be solved using a POMDP. Our first technique reduces the motion constraints of a robot and, then, uses state-of-the-art robotic motion planning techniques to respect the true motion constraints at runtime. We then propose a novel task decomposition that can be applied to some indoor robotic tasks. This decomposition transforms a long time horizon task into a set of shorter tasks. We empirically demonstrate the performance gain provided by these two techniques through simulated execution in a variety of environments. Comparing a direct formulation of a POMDP to solving our proposed reductions, we conclude that the techniques proposed in this paper can provide significant enhancement to current POMDP solution techniques, extending the POMDP instances that can be solved to include large continuous-state robotic tasks. Partially observable Markov decision processes (POMDPs) provide a principled, general framework for robot motion planning in uncertain and dynamic environments. They have been applied to various robotic tasks. However, solving POMDPs exactly is computationally intractable. A major challenge is to scale up POMDP algorithms for complex robotic tasks. Robotic systems often have mixed observability : even when a robotâs state is not fully observable, some components of the state may still be so. We use a factored model to represent separately the fully and partially observable components of a robotâs state and derive a compact lower-dimensional representation of its belief space. This factored representation can be combined with any point-based algorithm to compute approximate POMDP solutions. Experimental results show that on standard test problems, our approach improves the performance of a leading point-based POMDP algorithm by many times. In order to be fully robust and responsive to a dynamically changing real-world environment, intelligent robots will need to engage in a variety of simultaneous reasoning modalities. In particular, in this paper we consider their needs to i) reason with commonsense knowledge, ii) model their nondeter-ministic action outcomes and partial observability, and iii) plan toward maximizing long-term rewards. On one hand, Answer Set Programming (ASP) is good at representing and reasoning with commonsense and default knowledge, but is ill-equipped to plan under probabilistic uncertainty. On the other hand, Partially Observable Markov Decision Processes (POMDPs) are strong at planning under uncertainty toward maximizing long-term rewards, but are not designed to incorporate commonsense knowledge and inference. This paper introduces the CORPP algorithm which combines P-log, a probabilistic extension of ASP, with POMDPs to integrate commonsense reasoning with planning under uncertainty. Our approach is fully implemented and tested on a shopping request identification problem both in simulation and on a real robot. Compared with existing approaches using P-log or POMDPs individually, we observe significant improvements in both efficiency and accuracy.