Tag Archives: Pomdps

Building POMDPs under logical constraints

Bo Wu, Xiaobin Zhang, Hai Lin, Supervisor synthesis of POMDP via automata learning, . Automatica, Volume 129, 2021 DOI: 10.1016/j.automatica.2021.109654.

Partially observable Markov decision process (POMDP) is a comprehensive modeling framework that captures uncertainties from sensing noises, actuation errors, and environments. Traditional POMDP planning finds an optimal policy for reward maximization. However, for safety-critical applications, it is often necessary to guarantee system performance described by high-level temporal logic specifications. Hence, we are motivated to develop a supervisor synthesis framework for POMDP with respect to given formal specifications. We propose an iterative learning-based algorithm, which can learn a permissive policy in the form of a deterministic finite automaton. A human–robot collaboration case study validates the proposed algorithm.

POMDPs to combine human semantic sensing with robot sensing

Luke Burks, Nisar Ahmed, Ian Loefgren, Luke Barbier, Jeremy Muesing, Jamison McGinley, Sousheel Vunnam, Collaborative human-autonomy semantic sensing through structured POMDP planning, . Robotics and Autonomous Systems, Volume 140, 2021 DOI: 10.1016/j.robot.2021.103753.

Autonomous unmanned systems and robots must be able to actively leverage all available information sources — including imprecise but readily available semantic observations provided by human collaborators. This work develops and validates a novel active collaborative human–machine sensing solution for robotic information gathering and optimal decision making problems, with an example implementation of a dynamic target search scenario. Our approach uses continuous partially observable Markov decision process (CPOMDP) planning to generate vehicle trajectories that optimally exploit imperfect detection data from onboard sensors, as well as semantic natural language observations that can be specifically requested from human sensors. The key innovations are a method for the inclusion of a human querying/sensing model in a CPOMDP based autonomous decision making process, as well as a scalable hierarchical Gaussian mixture model formulation for efficiently solving CPOMDPs with semantic observations in continuous dynamic state spaces. Unlike previous state-of-the-art approaches this allows planning in large, complex, highly segmented environments. Our solution is demonstrated and validated with a real human–robot team engaged in dynamic indoor target search and capture scenarios on a custom testbed..

Improving POMDP solving efficiency by eliminating variables in the state structure

Eric A. Hansen, An integrated approach to solving influence diagrams and finite-horizon partially observable decision processes, . Artificial Intelligence, Volume 294, 2021 DOI: 10.1016/j.artint.2020.103431.

We show how to integrate a variable elimination approach to solving influence diagrams with a value iteration approach to solving finite-horizon partially observable Markov decision processes (POMDPs). The integration of these approaches creates a variable elimination algorithm for influence diagrams that has much more relaxed constraints on elimination order, which allows improved scalability in many cases. The new algorithm can also be viewed as a generalization of the value iteration algorithm for POMDPs that solves non-Markovian as well as Markovian problems, in addition to leveraging a factored representation for improved efficiency. The development of a single algorithm that integrates and generalizes both of these classic algorithms, one for influence diagrams and the other for POMDPs, unifies these two approaches to solving Bayesian decision problems in a way that combines their complementary advantages.

A hierarchical POMDP system for robot manipulation

Wenrui Zhao, Weidong Chen, Hierarchical POMDP planning for object manipulation in clutter, . Robotics and Autonomous Systems, Volume 139, 2021 DOI: 10.1016/j.robot.2021.103736.

Object manipulation planning in clutter suffers from perception uncertainties due to occlusion, as well as action constraints required by collision avoidance. Partially observable Markov decision process (POMDP) provides a general model for planning under uncertainties. But a manipulation task usually have a large action space, which not only makes task planning intractable but also brings significant motion planning effort to check action feasibility. In this work, a new kind of hierarchical POMDP is presented for object manipulation tasks, in which a brief abstract POMDP is extracted and utilized together with the original POMDP. And a hierarchical belief tree search algorithm is proposed for efficient online planning, which constructs fewer belief nodes by building part of the tree with the abstract POMDP and invokes motion planning fewer times by determining action feasibility with observation function of the abstract POMDP. A learning mechanism is also designed in case there are unknown probabilities in transition and observation functions. This planning framework is demonstrated with an object fetching task and the performance is empirically validated by simulations and experiments.

Classification with decision trees based on POMDPs

Shlomi Maliah, Guy Shani, Using POMDPs for learning cost sensitive decision trees, . Artificial Intelligence, Volume 292, 2021 DOI: 10.1016/j.artint.2020.103400.

In classification, an algorithm learns to classify a given instance based on a set of observed attribute values. In many real world cases testing the value of an attribute incurs a cost. Furthermore, there can also be a cost associated with the misclassification of an instance. Cost sensitive classification attempts to minimize the expected cost of classification, by deciding after each observed attribute value, which attribute to measure next. In this paper we suggest Partially Observable Markov Decision Processes (POMDPs) as a modeling tool for cost sensitive classification. POMDPs are typically solved through a policy over belief states. We show how a relatively small set of potentially important belief states can be identified, and define an MDP over these belief states. To identify these potentially important belief states, we construct standard decision trees over all attribute subsets, and the leaves of these trees become the state space of our tree-based MDP. At each phase we decide on the next attribute to measure, balancing the cost of the measurement and the classification accuracy. We compare our approach to a set of previous approaches, showing our approach to work better for a range of misclassification costs.

Expressing POMDPs policies through Knowledge-Based programs

Bruno Zanuttini, Jérôme Lang, Abdallah Saffidine, François Schwarzentruber Knowledge-based programs as succinct policies for partially observable domains. Artificial Intelligence, Volume 288, 2020 DOI: 10.1016/j.artint.2020.103365.

We suggest to express policies for contingent planning by knowledge-based programs (KBPs). KBPs, introduced by Fagin et al. (1995) [32], are high-level protocols describing the actions that the agent should perform as a function of their current knowledge: branching conditions are epistemic formulas that are interpretable by the agent. The main aim of our paper is to show that KBPs can be seen as a succinct language for expressing policies in single-agent contingent planning. KBP are conceptually very close to languages used for expressing policies in the partially observable planning literature: like them, they have conditional and looping structures, with actions as atomic programs and Boolean formulas on beliefs for choosing the execution path. Now, the specificity of KBPs is that branching conditions refer to the belief state and not to the observations. Because of their structural proximity, KBPs and standard languages for representing policies have the same power of expressivity: every standard policy can be expressed as a KBP, and every KBP can be “unfolded” into a standard policy. However, KBPs are more succinct, more readable, and more explainable than standard policies. On the other hand, they require more online computation time, but we show that this is an unavoidable tradeoff. We study knowledge-based programs along four criteria: expressivity, succinctness, complexity of online execution, and complexity of verification.

Including the models into the state of a POMDP for learning them (using POMCPs in a robotic application)

Akinobu Hayashi, Dirk Ruiken, Tadaaki Hasegawa, Christian Goerick, Reasoning about uncertain parameters and agent behaviors through encoded experiences and belief planning, Artificial Intelligence, Volume 280, 2020 DOI: 10.1016/j.artint.2019.103228.

Robots are expected to handle increasingly complex tasks. Such tasks often include interaction with objects or collaboration with other agents. One of the key challenges for reasoning in such situations is the lack of accurate models that hinders the effectiveness of planners. We present a system for online model adaptation that continuously validates and improves models while solving tasks with a belief space planner. We employ the well known online belief planner POMCP. Particles are used to represent hypotheses about the current state and about models of the world. They are sufficient to configure a simulator to provide transition and observation models. We propose an enhanced particle reinvigoration process that leverages prior experiences encoded in a recurrent neural network (RNN). The network is trained through interaction with a large variety of object and agent parametrizations. The RNN is combined with a mixture density network (MDN) to process the current history of observations in order to propose suitable particles and models parametrizations. The proposed method also ensures that newly generated particles are consistent with the current history. These enhancements to the particle reinvigoration process help alleviate problems arising from poor sampling quality in large state spaces and enable handling of dynamics with discontinuities. The proposed approach can be applied to a variety of domains depending on what uncertainty the decision maker needs to reason about. We evaluate the approach with experiments in several domains and compare against other state-of-the-art methods. Experiments are done in a collaborative multi-agent and a single agent object manipulation domain. The experiments are performed both in simulation and on a real robot. The framework handles reasoning with uncertain agent behaviors and with unknown object and environment parametrizations well. The results show good performance and indicate that the proposed approach can improve existing state-of-the-art methods.

Quantizing a continuous POMDP into a finite MDP to preserve optimality

Naci Saldi; Serdar Yüksel; Tamás Linder, Asymptotic Optimality of Finite Model Approximations for Partially Observed Markov Decision Processes With Discounted Cost, IEEE Transactions on Automatic Control ( Volume: 65, Issue: 1, Jan. 2020), DOI: 10.1109/TAC.2019.2907172.

We consider finite model approximations of discrete-time partially observed Markov decision processes (POMDPs) under the discounted cost criterion. After converting the original partially observed stochastic control problem to a fully observed one on the belief space, the finite models are obtained through the uniform quantization of the state and action spaces of the belief space Markov decision process (MDP). Under mild assumptions on the components of the original model, it is established that the policies obtained from these finite models are nearly optimal for the belief space MDP, and so, for the original partially observed problem. The assumptions essentially require that the belief space MDP satisfies a mild weak continuity condition. We provide an example and introduce explicit approximation procedures for the quantization of the set of probability measures on the state space of POMDP (i.e., belief space).

Improving on-line Monte Carlo POMDP (DESTOP in particular) in discrete spaces through the use of importance sampling, and a nice summary of the problem and of current on-line POMDP approaches

Luo, Y., Bai, H., Hsu, D., & Lee, W. S., Importance sampling for online planning under uncertainty, The International Journal of Robotics Research, 38(2–3), 162–181, 2019 DOI: 10.1177/0278364918780322.

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.

On the need to replanning in POMDPs when applied to real systems, due to imperfect sensing and computational cost of online planning

Ali-akbar Agha-mohammadi et al., SLAP: Simultaneous Localization and Planning Under Uncertainty via Dynamic Replanning in Belief Space, IEEE Transactions on Robotics, vol. 34, no. 5, DOI: 10.1109/TRO.2018.2838556.

Simultaneous localization and planning (SLAP) is a crucial ability for an autonomous robot operating under uncertainty. In its most general form, SLAP induces a continuous partially observable Markov decision process (POMDP), which needs to be repeatedly solved online. This paper addresses this problem and proposes a dynamic replanning scheme in belief space. The underlying POMDP, which is continuous in state, action, and observation space, is approximated offline via sampling-based methods, but operates in a replanning loop online to admit local improvements to the coarse offline policy. This construct enables the proposed method to combat changing environments and large localization errors, even when the change alters the homotopy class of the optimal trajectory. It further outperforms the state-of-the-art Feedback-based Information RoadMap (FIRM) method by eliminating unnecessary stabilization steps. Applying belief space planning to physical systems brings with it a plethora of challenges. A key focus of this paper is to implement the proposed planner on a physical robot and show the SLAP solution performance under uncertainty, in changing environments and in the presence of large disturbances, such as a kidnapped robot situation.