Performance guaranteed human-robot collaboration through correct-by-design

Performance guaranteed human-robot collaboration with POMDP supervisory control

Partially Observable Markov Decision Process (POMDP) has been widely used in the robotics to model uncertainties from sensors, actuators and the environment. However, such comprehensiveness makes the planning in POMDP generally very difficult. Existing work often searches for an optimal control policy with respect to predefined reward functions, which may require a large memory and is computationally expensive. We propose to use formal methods and learn a Deterministic Finite Automaton (DFA) as a supervisor to regulate the behavior of a Partially Observable Markov Decision Process (POMDP), such that it satisfies the given specification in Probabilistic Computation Tree Logic (PCTL). For such a purpose, we modify the L* learning algorithm and define oracles for membership queries and conjectures. We further show that the termination and correctness of the design algorithm are guaranteed. A simple example is used for illustration.

The ability to reason about and respond to their own emotional states can enhance the believability of Non-Player Characters (NPCs). In this paper, we use a Partially Observable Markov Decision Process (POMDP)-based framework to model emotion over time. A two-level appraisal model, involving quick and reactive vs. slow and deliberate appraisals, is proposed for the creation of affective autonomous characters based on POMDPs, wherein the probability of goal satisfaction is used in an appraisal and reappraisal process for emotion generation. We not only extend Probabilistic Computation Tree Logic (PCTL) for reasoning about the properties of emotional states based on POMDPs but also illustrate how four reactive (primary) emotions and nine deliberate (secondary) emotions can be derived by combining PCTL with the belief-desire theory of emotion. The results of an empirical study suggest that the proposed model can be used to create characters that appear to be more believable and more intelligent.

During the last decades, collaborative robots capable of operating out of their cages are widely used in industry to assist humans in mundane and harsh manufacturing tasks. Although such robots are inherently safe by design, they are commonly accompanied by external sensors and other cyber-physical systems, to facilitate close cooperation with humans, which frequently render the collaborative ecosystem unsafe and prone to hazards. We introduce a method that capitalizes on partially observable Markov decision processes (POMDP) to amalgamate nominal actions of the system along with unsafe control actions posed by the System Theoretic Process Analysis (STPA). A decision-making mechanism that constantly prompts the system into a safer state is realized by providing situation awareness about the safety levels of the collaborative ecosystem by associating the system safety awareness with specific groups of selected actions. POMDP compensates the partial observability and uncertainty of the current state of the collaborative environment and creates safety screening policies that tend to make decisions that balance the system from unsafe to safe states in real time during the operational phase. The theoretical framework is assessed on a simulated human–robot collaborative scenario and proved capable of identifying loss and success scenarios.

Resolving structural uncertainty in natural resources management using POMDP approaches

This thesis presents a recent research on the problem of environmental modeling for both localization and map building for wheel-based, differential driven, fully autonomous and self-contained mobile robots. The robots behave in an indoor office environment. They have a multi-sensor setup where the encoders are used for odometry and two exteroperceptive sensors, a 360° laser scanner and a monocular vision system, are employed to perceive the surrounding. The whole approach is feature based meaning that instead of directly using the raw data from the sensor features are firstly extracted. This allows the filtering of noise from the sensors and permits taking account of the dynamics in the environment. Furthermore, a properly chosen feature extraction has the characteristic of better isolating informative patterns. When describing these features care has to be taken that the uncertainty from the measurements is taken into account. The representation of the environment is crucial for mobile robot navigation. The model defines which perception capabilities are required and also which navigation technique is allowed to be used. The presented environmental model is both metric and topological. By coherently combining the two paradigms the advantages of both methods are added in order to face the drawbacks of a single approach. The capabilities of the hybrid approach are exploited to model an indoor office environment where metric information is used locally in structures (rooms, offices), which are naturally defined by the environment itself while the topology of the whole environment is resumed separately thus avoiding the need of global metric consistency. The hybrid model permits the use of two different and complementary approaches for localization, map building and planning. This combination permits the grouping of all the characteristics which enables the following goals to be met: Precision, robustness and practicability. Metric approaches are, per definition, precise. The use of an Extended Kalman Filter (EKF) permits to have a precision which is just bounded by the quality of the sensor data. Topological approaches can easily handle large environments because they do not heavily rely on dead reckoning. Global consistency can, therefore, be maintained for large environments. Consistent mapping, which handle large environments, is achieved by choosing a topological localization approach, based on a Partially Observable Markov Decision Process (POMDP), which is extended to simultaneous localization and map building. The theory can be mathematically proven by making some assumptions. However, as stated during the whole work, at the end the robot itself has to show how good the theory is when used in the real world. For this extensive experimentation for a total of more than 9 km is performed with fully autonomous self-contained robots. These experiments are then carefully analyzed. With the metric approach precision with error bounds of about 1 cm and less than 1 degree is further confirmed by ground truth measurements with a mean error of less than 1 cm. The topological approach is successfully tested by simultaneous localization and map building where the automatically created maps turned out to work better than the a priori maps. Relocation and closing the loop are also successfully tested.

Ambiguous partially observable Markov decision processes: Structural results and applications

Aiming to reduce energy consumption, minimize transmission latency, and optimize the long-term performance of Wireless Sensor Networks (WSN), this paper proposes an improved routing model of Directed Diffusion. We formulated the routing issue as a partially observable Markov decision process (POMDP), such that the optimal nodes selection policy yielded by maximizing the expected reward. Since the solution of POMDP is ready-made, the attention is concentrated only on the formulation of the routing issue into a POMDP model, more specifically, the definition of the tuple which contains states, actions, observations, transition probabilities, observation probabilities, and reward function. Our experimental study shows that the POMDP-based Directed Diffusion routing outperforms other routing techniques in terms of three widely used metrics including average dissipated energy, average delay, and average lifetime.

In this article, we study the problem of controlling a partially observed Markov decision process (POMDP) to either aid or hinder the estimation of its state trajectory. We encode the estimation objectives via the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">smoother entropy</i> , which is the conditional entropy of the state trajectory given measurements and controls. Consideration of the smoother entropy contrasts with previous approaches that instead resort to marginal (or instantaneous) state entropies due to tractability concerns. By establishing novel expressions for the smoother entropy in terms of the POMDP belief state, we show that both the problems of minimizing and maximizing the smoother entropy in POMDPs can surprisingly be reformulated as belief-state Markov decision processes with concave cost and value functions. The significance of these reformulations is that they render the smoother entropy a tractable optimization objective, with structural properties amenable to the use of standard POMDP solution techniques for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">both</i> active estimation and obfuscation. Simulations illustrate that optimization of the smoother entropy leads to superior trajectory estimation and obfuscation compared to alternative approaches.

The framework of partially observable Markov decision processes (POMDPs) offers a standard approach to model uncertainty in many robot tasks. Traditionally, POMDPs are formulated with optimality objectives. In this article, we study a different formulation of POMDPs with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Boolean objectives</i> . For robotic domains that require a correctness guarantee of accomplishing tasks, Boolean objectives are natural formulations. We investigate the problem of POMDPs with a common Boolean objective: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">safe reachability</i> , requiring that the robot eventually reaches a goal state with a probability above a threshold while keeping the probability of visiting unsafe states below a different threshold. Our approach builds upon the previous work that represents POMDPs with Boolean objectives using symbolic constraints. We employ a satisfiability modulo theories (SMTs) solver to efficiently search for solutions, i.e., policies or conditional plans that specify the action to take contingent on every possible event. A full policy or conditional plan is generally expensive to compute. To improve computational efficiency, we introduce the notion of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">partial conditional plans</i> that cover sampled events to approximate a full conditional plan. Our approach constructs a partial conditional plan parameterized by a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">replanning probability</i> . We prove that the failure rate of the constructed partial conditional plan is bounded by the replanning probability. Our approach allows users to specify an appropriate bound on the replanning probability to balance efficiency and correctness. Moreover, we update this bound properly to quickly detect whether the current partial conditional plan meets the bound and avoid unnecessary computation. In addition, to further improve the efficiency, we cache partial conditional plans for sampled belief states and reuse these cached plans if possible. We validate our approach in several robotic domains. The results show that our approach outperforms a previous policy synthesis approach for POMDPs with safe-reachability objectives in these domains. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article was motivated by two observations. On the one hand, in robotics applications where uncertainty in sensing and actions is present, the solution to the classical partially observable Markov decision process (POMDP) formulation is expensive to compute in general. On the other hand, in certain practical scenarios, formulations other than the classical POMDP make a lot of sense and can provide flexibility in balancing efficiency and correctness. This article considers a modified POMDP formulation that includes a Boolean objective, namely safe reachability. This article uses the notion of a partial conditional plan. Rather than explicitly enumerating all possible observations to construct a full conditional plan, this work samples a subset of all observations to ensure bounded replanning probability. Our theoretical and empirical results show that the failure rate of the constructed partial conditional plan is bounded by the replanning probability. Moreover, these partial conditional plans can be cached to further improve the performance. Our results suggest that for domains where replanning is easy, increasing the replanning probability bound usually leads to better scalability, and for domains where replanning is difficult or impossible in some states, we can decrease the bound and allocate more computation time to achieve a higher success rate. Hence, in certain cases, the practitioner can take advantage of their knowledge of the problem domain to scale to larger problems. Preliminary physical experiments suggest that this approach is applicable to real-world robotic domains, but it requires a discrete representation of the workspace. How to deal with continuous workspace directly is an interesting future direction.

Partially observable Markov decision processes (POMDPs) have recently become popular among many AI researchers because they serve as a natural model for planning under uncertainty. Value iteration ...

&lt;p&gt;Partially Observable Markov Decision Processes (POMDPs) is a modeling framework that allow decision makers to make decisions in uncertain environments. This framework is particularly suited for sequential decision making problems for which the uncertainties are revealed in stages. Constrained POMDPs (CPOMDPs) extend this framework by also accounting for various restrictions in the environment. This PhD thesis focuses on POMDPs, CPOMDPs and its extensions, proposes novel solution methods and studies applications of POMDPs in disease screening. First, we focus on developing efficient versions of the well-known algorithms for POMDPs. POMDPs are notoriously difficult to solve optimally, and exact solution algorithms typically fail to solve the instances with more than a few core states. In this regard, we consider scalable algorithms solve the POMDP problems. Specifically, we propose distributed and parallel versions of the exact solution methods such as Monahan's algorithm and the incremental pruning algorithm as well as the heuristics such as Lovejoy's upper bound and lower bound methods. Next, we study the CPOMDPs and propose linear programming-based solution methods as a flexible approach for those. We perform a detailed numerical study with five different problem instances to showcase the viability of the proposed solution approach for CPOMDPs. Lastly, we propose multi-objective CPOMDP models for the breast cancer screening problem. These CPOMDP models extend the previously proposed POMDP models for breast cancer screening by considering different screening modalities and simultaneously optimizing for expected total quality-adjusted life years maximization and life-time risk minimization objectives.&lt;/p&gt;

Iteratively solving a set of linear programs (LPs) is a common strategy for solving various decision-making problems in Artificial Intelligence, such as planning in multi-objective or partially observable Markov Decision Processes (MDPs). A prevalent feature is that the solutions to these LPs become increasingly similar as the solving algorithm converges, because the solution computed by the algorithm approaches the fixed point of a Bellman backup operator. In this paper, we propose to speed up the solving process of these LPs by bootstrapping based on similar LPs solved previously. We use these LPs to initialize a subset of relevant LP constraints, before iteratively generating the remaining constraints. The resulting algorithm is the first to consider such information sharing across iterations. We evaluate our approach on planning in Multi-Objective MDPs (MOMDPs) and Partially Observable MDPs (POMDPs), showing that it solves fewer LPs than the state of the art, which leads to a significant speed-up. Moreover, for MOMDPs we show that our method scales better in both the number of states and the number of objectives, which is vital for multi-objective planning.

In recent years, Markov decision processes (MDPs) and partially observable Markov decision processes (POMDPs) have found important applications to medical decision making in the context of prevention, screening, and treatment of diseases. In this chapter, we provide a review of state-of-the-art models and methods that have been applied to chronic diseases. We provide a tutorial about how to formulate and solve these important problems emphasizing some of the challenges specific to chronic diseases such as diabetes, heart disease, and cancer. Then, we illustrate important considerations for model formulation and solution methods through two examples. The first example is an MDP model for optimal control of drug treatment decisions for managing the risk of heart disease and stroke in patients with type 2 diabetes. The second example is a POMDP model for optimal design of biomarker-based screening policies in the context of prostate cancer. We end the chapter with a discussion of the challenges of using MDPs and POMDPs for medical contexts and describe some important future directions for research.

Dealing with aleatoric uncertainty is key in many domains involving sequential decision making, e.g., planning in AI, network protocols, and symbolic program synthesis. This paper presents a general-purpose model-based framework to obtain policies operating in uncertain environments in a fully automated manner. The new concept of coloured Markov Decision Processes (MDPs) enables a succinct representation of a wide range of synthesis problems. A coloured MDP describes a collection of possible policy configurations with their structural dependencies. The framework covers the synthesis of (a) programmatic policies from probabilistic program sketches and (b) finite-state controllers representing policies for partially observable MDPs (POMDPs), including decentralised POMDPs as well as constrained POMDPs. We show that all these synthesis problems can be cast as exploring memoryless policies in the corresponding coloured MDP. This exploration uses a symbiosis of two orthogonal techniques: abstraction refinement—using a novel refinement method—and counter-example generalisation. Our approach outperforms dedicated synthesis techniques on some problems and significantly improves an earlier version of this framework.