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.
 We present an approximate POMDP solution method for robot planning in partially observable environments. Our algorithm belongs to the family of point-based value iteration solution techniques for POMDP, in which planning is performed only on a sampled set of reachable belief points. We describe a simple, randomized procedure that performs value update steps that strictly improve the value of all belief points in each step. We demonstrate our algorithm on a robotic delivery task in an office environment and on several benchmark problems, for which we compute solutions that are very competitive to those of state-of-the-art methods in terms of speed and solution quality. POMDPs are standard models for probabilistic planning problems, where an agent interacts with an uncertain environment. We study the problem of almost-sure reachability, where given a set of target states, the question is to decide whether there is a policy to ensure that the target set is reached with probability 1 (almost-surely). While in general the problem is EXPTIME-complete, in many practical cases policies with a small amount of memory suffice. Moreover, the existing solution to the problem is explicit, which first requires to construct explicitly an exponential reduction to a belief-support MDP. In this work, we first study the existence of observation-stationary strategies, which is NP-complete, and then small-memory strategies. We present a symbolic algorithm by an efficient encoding to SAT and using a SAT solver for the problem. We report experimental results demonstrating the scalability of our symbolic (SAT-based) approach. POMDPs provide a principled framework for planning under uncertainty, but are computationally intractable, due to the "curse of dimensionality" and the "curse of history". This paper presents an online POMDP algorithm that alleviates these difficulties by focusing the search on a set of randomly sampled scenarios. A Determinized Sparse Partially Observable Tree (DESPOT) compactly captures the execution of all policies on these scenarios. Our Regularized DESPOT (R-DESPOT) algorithm searches the DESPOT for a policy, while optimally balancing the size of the policy and its estimated value obtained under the sampled scenarios. We give an output-sensitive performance bound for all policies derived from a DESPOT, and show that R-DESPOT works well if a small optimal policy exists. We also give an anytime algorithm that approximates R-DESPOT. Experiments show strong results, compared with two of the fastest online POMDP algorithms. Source code along with experimental settings are available at http: bigbird.comp.nus.edu.sg pmwiki farm appl .  Partially observable Markov decision processes (POMDPs) have been successfully applied to various robot motion planning tasks under uncertainty. However, most existing POMDP algorithms assume a discrete state space, while the natural state space of a robot is often continuous. This paper presents Monte Carlo Value Iteration (MCVI) for continuous-state POMDPs. MCVI samples both a robot’s state space and the corresponding belief space, and avoids inefficient a priori discretization of the state space as a grid. Both theoretical results and preliminary experimental results indicate that MCVI is a promising new approach for robot motion planning under uncertainty. 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. This work seeks to address the problem of planning in the presence of uncertainty and constraints. Such problems arise in many situations, including the basis of this work, which involves planning for a team of first responders (both humans and robots) operating in an urban environment. The problem is framed as a Partially-Observable Markov Decision Process (POMDP) with constraints, and it is shown that even in a relatively simple planning problem, modeling constraints as large penalties does not lead to good solutions. The main contribution of the work is a new online algorithm that explicitly ensures constraint feasibility while remaining computationally tractable. Its performance is demonstrated on an example problem and it is demonstrated that our online algorithm generates policies comparable to an offline constrained POMDP algorithm. IN Proc. Robotics: Science & Systems, 2008 Abstract—Motion planning in uncertain and dynamic environ- ments is an essential capability for autonomous robots. Partially observable Markov decision processes (POMDPs) provide a principled mathematical framework for solving such problems, but they are often avoided in robotics due to high computational complexity. Our goal is to create practical POMDP algorithms and software for common robotic tasks. To this end, we have developed a new point-based POMDP algorithm that exploits the notion of optimally reachable belief spaces to improve com- putational efficiency. In simulation, we successfully applied the algorithm to a set of common robotic tasks, including instances of coastal navigation, grasping, mobile robot exploration, and target tracking, all modeled as POMDPs with a large number of states. In most of the instances studied, our algorithm substantially outperformed one of the fastest existing point-based algorithms. A software package implementing our algorithm will soon be released at http: motion.comp.nus.edu.sg projects pomdp pomdp.html. The partially observable Markov decision process (POMDP) provides a principled general framework for robot planning under uncertainty. Leveraging the idea of Monte Carlo sampling, recent POMDP planning algorithms have scaled up to various challenging robotic tasks, including, real-time online planning for autonomous vehicles. To further improve online planning performance, this paper presents IS-DESPOT, which introduces importance sampling to DESPOT, a state-of-the-art sampling-based POMDP algorithm for planning under uncertainty. Importance sampling improves DESPOT’s performance when there are critical, but rare events, which are difficult to sample. We prove that IS-DESPOT retains the theoretical guarantee of DESPOT. We demonstrate empirically that importance sampling significantly improves the performance of online POMDP planning for suitable tasks. We also present a general method for learning the importance sampling distribution. 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.