We introduce a parallel offline algorithm for computing hybrid conditional plans, called HCP-ASP, oriented towards robotics applications. HCP-ASP relies on modeling actuation actions and sensing actions in an expressive nonmonotonic language of answer set programming (ASP), and computation of the branches of a conditional plan in parallel using an ASP solver. In particular, thanks to external atoms, continuous feasibility checks (like collision checks) are embedded into formal representations of actuation actions and sensing actions in ASP; and thus each branch of a hybrid conditional plan describes a feasible execution of actions to reach their goals. Utilizing nonmonotonic constructs and nondeterministic choices, partial knowledge about states and nondeterministic effects of sensing actions can be explicitly formalized in ASP; and thus each branch of a conditional plan can be computed by an ASP solver without necessitating a conformant planner and an ordering of sensing actions in advance. We apply our method in a service robotics domain and report experimental evaluations. Furthermore, we present performance comparisons with other compilation based conditional planners on standardized benchmark domains. This paper is under consideration for acceptance in TPLP.
@cite_13: This paper introduces a highly competitive contingent planner, that uses the novel idea of encoding belief states as disjunctive normal form formulae ( 2009), for the search for solutions in the belief state space. In ( 2009), a complete transition function for computing successor belief states in the presence of incomplete information has been defined. This work extends the function to handle non-deterministic and sensing actions in the AND OR forward search paradigm for contingent planning solutions. The function allows one, under reasonable assumptions, to compute successor belief states efficiently, i.e., in polynomial time. The paper also presents a novel variant of an AND OR search algorithm, called PrAO (Pruning AND OR search), which allows the planner to significantly prune the search space; furthermore, by the time a solution is found, the remaining search graph is also the solution tree for the contingent planing problem. The strength of these techniques is confirmed by the empirical results obtained from a large set of benchmarks available in the literature.
@cite_18: In this paper we present a new approach to the problem of planning with incomplete information and sensing. Our approach is based on a higher level, "knowledge-based", representation of the planner's knowledge and of the domain actions. In particular, in our approach we use a set of formulas from a first-order modal logic of knowledge to represent the planner's incomplete knowledge state. Actions are then represented as updates to this collection of formulas. Hence, actions are being modelled in terms of how they modify the knowledge state of the planner rather than in terms of how they modify the physical world. We have constructed a planner to utilize this representation and we use it to show that on many common problems this more abstract representation is perfectly adequate for solving the planning problem, and that in fact it scales better and supports features that make it applicable to much richer domains and problems.
@cite_14: 
@cite_33: In contingent planning problems, agents have partial information about their state and use sensing actions to learn the value of some variables. When sensing and actuation are separated, plans for such problems can often be viewed as a tree of sensing actions, separated by conformant plans consisting of non-sensing actions that enable the execution of the next sensing action. This leads us to propose a heuristic, online method for contingent planning which focuses on identifying the next useful sensing action. The key part of our planner is a novel landmarks-based heuristic for selecting the next sensing action, together with a projection method that uses classical planning to solve the intermediate conformant planning problems. This allows our planner to operate without an explicit model of belief space or the use of existing translation techniques, both of which can require exponential space. The resulting Heuristic Contingent Planner (HCP) solves many more problems than state-of-the-art, translation-based online contingent planners, and in most cases much faster.
@cite_8: Planning with partial observability can be formulated as a non-deterministic search problem in belief space. The problem is harder than classical planning as keeping track of beliefs is harder than keeping track of states, and searching for action policies is harder than searching for action sequences. In this work, we develop a framework for partial observability that avoids these limitations and leads to a planner that scales up to larger problems. For this, the class of problems is restricted to those in which 1) the non-unary clauses representing the uncertainty about the initial situation are invariant, and 2) variables that are hidden in the initial situation do not appear in the body of conditional effects, which are all assumed to be deterministic. We show that such problems can be translated in linear time into equivalent fully observable non-deterministic planning problems, and that an slight extension of this translation renders the problem solvable by means of classical planners. The whole approach is sound and complete provided that in addition, the state-space is connected. Experiments are also reported.
@cite_32: In contingent planning under partial observability with sensing actions, agents actively use sensing to discover meaningful facts about the world. For this class of problems the solution can be represented as a plan tree, branching on various possible observations. Recent successful approaches translate the partially observable contingent problem into a non-deterministic fully observable problem, and then use a planner for non-deterministic planning. While this approach has been successful in many domains, the translation may become very large, encumbering the task of the non-deterministic planner. In this paper we suggest a different approach — using an online contingent solver repeatedly to construct a plan tree. We execute the plan returned by the online solver until the next observation action, and then branch on the possible observed values, and replan for every branch independently. In many cases a plan tree can be exponential in the number of state variables, but still, the tree has a structure that allows us to compactly represent it using a directed graph. We suggest a mechanism for tailoring such a graph that reduces both the computational effort and the storage space. Furthermore, unlike recent state of the art offline planners, our approach is not bounded to a specific class of contingent problems, such as limited problem width, or simple contingent problems. We present a set of experiments, showing our approach to scale better than state of the art offline planners.
@cite_23: Replanning via determinization is a recent, popular approach for online planning in MDPs. In this paper we adapt this idea to classical, non-stochastic domains with partial information and sensing actions, presenting a new planner: SDR (Sample, Determinize, Replan). At each step we generate a solution plan to a classical planning problem induced by the original problem. We execute this plan as long as it is safe to do so. When this is no longer the case, we replan. The classical planning problem we generate is based on the translation-based approach for conformant planning introduced by Palacios and Geffner. The state of the classical planning problem generated in this approach captures the belief state of the agent in the original problem. Unfortunately, when this method is applied to planning problems with sensing, it yields a non-deterministic planning problem that is typically very large. Our main contribution is the introduction of state sampling techniques for overcoming these two problems. In addition, we introduce a novel, lazy, regressionbased method for querying the agent's belief state during run-time. We provide a comprehensive experimental evaluation of the planner, showing that it scales better than the state-of-the-art CLG planner on existing benchmark problems, but also highlighting its weaknesses with new domains. We also discuss its theoretical guarantees.
@cite_5: The problem of planning in the presence of sensing has been addressed in recent years as a nondeterministic search problem in belief space. In this work, we use ideas advanced recently for compiling conformant problems into classical ones for introducing a different approach where contingent problems P are mapped into non-deterministic problems X(P) in state space. We also identify a contingent width parameter, and show that for problems P with bounded contingent width, the translation is sound, polynomial, and complete. We then solve X(P) by using a relaxation X+(P) that is a classical planning problem. The formulation is tested experimentally over contingent benchmarks where it is shown to yield a planner that scales up better than existing contingent planners.
@cite_16: Conditional planning enables planning for the sensing actions and their possible outcomes in addition to actuation actions, and allows for addressing uncertainties due to partial observability at the time of offline planning. Therefore, the plans (called conditional plans) computed by conditional planners can be viewed as trees of (deterministic) actuation actions and (nondeterministic) sensing actions. Hybrid conditional planning extends conditional planning further by integrating low-level feasibility checks into executability conditions of actuation actions in conditional plans. We introduce a novel hybrid conditional planning method, which extends hybrid sequential planning with nondeterministic sensing actions and utilizes this extension to compute branches of a conditional plan in parallel. We evaluate this method in a service robotics domain, by means of a set of experiments over dynamic simulations, from the perspectives of computational efficiency and plan quality.
@cite_10: Some recent works in conditional planning have proposed reachability heuristics to improve planner scalability, but many lack a formal description of the properties of their distance estimates. To place previous work in context and extend work on heuristics for conditional planning, we provide a formal basis for distance estimates between belief states. We give a definition for the distance between belief states that relies on aggregating underlying state distance measures. We give several techniques to aggregate state distances and their associated properties. Many existing heuristics exhibit a subset of the properties, but in order to provide a standardized comparison we present several generalizations of planning graph heuristics that are used in a single planner. We compliment our belief state distance estimate framework by also investigating efficient planning graph data structures that incorporate BDDs to compute the most effective heuristics. We developed two planners to serve as test-beds for our investigation. The first, CAltAlt, is a conformant regression planner that uses A* search. The second, POND, is a conditional progression planner that uses AO* search. We show the relative effectiveness of our heuristic techniques within these planners. We also compare the performance of these planners with several state of the art approaches in conditional planning.
@cite_25: Planning with sensing actions under partial observability is a computationally challenging problem that is fundamental to the realization of AI tasks in areas as diverse as robotics, game playing, and diagnostic problem solving. Recent work on generating plans for partially observable domains has advocated for online planning, claiming that offline plans are often too large to generate. Here we push the envelope on this challenging problem, proposing a technique for generating conditional (aka contingent) plans offline. The key to our planner's success is the reliance on state-of-the-art techniques for fully observable non-deterministic (FOND) planning. In particular, we use an existing compilation for converting a planning problem under partial observability and sensing to a FOND planning problem. With a modified FOND planner in hand, we are able to scale beyond previous techniques for generating conditional plans with solutions that are orders of magnitude smaller than previously possible in some domains.
@cite_20: We extend the 0-approximation of sensing actions and incomplete information in Son and Baral (2001) to action theories with static causal laws and prove its soundness with respect to the possible world semantics. We also show that the conditional planning problem with respect to this approximation is NP-complete. We then present an answer set programming based conditional planner, called ASCP, that is capable of generating both conformant plans and conditional plans in the presence of sensing actions, incomplete information about the initial state, and static causal laws. We prove the correctness of our implementation and argue that our planner is sound and complete with respect to the proposed approximation. Finally, we present experimental results comparing ASCP to other planners.
@cite_11: In the last several years the computational complexity of classical planning and HTN planning have been studied. But in both cases it is assumed that the planner has complete knowledge about the initial state. Recently, there has been proposal to use 'sensing' actions to plan in presence of incompleteness. In this paper we study the complexity of planning in such cases. In our study we use the action description language A proposed in 1993 by M. Gelfond and V. Lifschitz and its extensions. The language A allows planning in the situations with complete information. It is known that, if we consider only plans of feasible (polynomial) length, the planning problem for such situations is NP-complete: even checking whether a given objective is attainable from a given initial state is NP-complete. In this paper, we show that the planning problem in presence of incompleteness is indeed harder: it belongs to the next level of complexity hierarchy (in precise terms, it is Σ2P-complete). To overcome the complexity of this problem, C. Baral and T. Son have proposed several approximations. We show that under certain conditions, one of these approximations - O-approximation - makes the problem NP-complete (thus indeed reducing its complexity).
There is a variety of conditional planners, despite the hardness of computing conditional plans: even for polynomially bounded plans with limited number of sensing actions, its complexity is PSPACE-complete @cite_11 . Some of these planners are online, such as CLG @cite_5 , K-Planner @cite_8 , SDR @cite_23 , HCP @cite_33 and CPOR @cite_32 . Since sensing is done online, these solvers do not end up handling many contingencies and thus sometimes do not reach a goal state. Some of the conditional planners are offline, such as Contingent-FF @cite_14 , POND @cite_10 , PKS @cite_18 , @cite_20 , DNFct @cite_13 , PO-PRP @cite_25 , HCplan @cite_16 . These planners construct whole conditional plans with decision points for sensing outcomes, where each execution via a branch of the plan leads to a goal state. Our planner is an offline planner.