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Robotic task planning is computationally challenging. To reduce planning cost and support life-long operation, we must leverage prior planning experience. To this end, we address the problem of extracting reusable and generalizable abstract skills from successful plan executions. In previous work, we introduced a supporting framework, allowing us, theoretically, to extract an abstract skill from a single execution and later automatically adapt it and reuse it in new domains. We also proved that, given a library of such skills, we can significantly reduce the planning effort for new problems. Nevertheless, until now, abstract-skill extraction could only be performed manually. In this paper, we finally close the automation loop and explain how abstract skills can be practically and automatically extracted. We start by analyzing the desired qualities of an abstract skill and formulate skill extraction as an optimization problem. We then develop two extraction algorithms, based on the novel concept of abstraction-critical state detection. As we show experimentally, the approach is independent of any planning domain. 

The problems of verification and realizability are two central themes in the analysis of reactive systems. When multiagent systems are considered, these problems have natural analogues of existence (nonemptiness) of pure-strategy Nash equilibria and verification of pure-strategy Nash equilibria. Recently, this body of work has begun to include finite-horizon temporal goals. With finite-horizon temporal goals, there is a natural hierarchy of goal representation, ranging from deterministic finite automata (DFA), to nondeterministic finite automata (NFA), and to alternating finite automata (AFA), with a worst-case exponential gap between each successive representation. Previous works showed that the realizability problem with DFA goals was PSPACE-complete, while the realizability problem with temporal logic goals is in 2EXPTIME. In this work, we study both the realizability and the verification problems with respect to various goal representations. We first show that the realizability problem with NFA goals is EXPTIME-complete and with AFA goals is 2EXPTIME-complete, thus establishing strict complexity gaps between realizability with respect to DFA, NFA, and AFA goals. We then contrast these complexity gaps with the complexity of the verification problem, where we show that verification with respect to DFAs, NFA, and AFA goals is PSPACE-complete.

 

Reactive synthesis from high-level specifications that combine hard constraints expressed in Linear Temporal Logic (LTL) with soft constraints expressed by discounted sum (DS) rewards has applications in planning and reinforcement learning. An existing approach combines techniques from LTL synthesis with optimization for the DS rewards but has failed to yield a sound algorithm. An alternative approach combining LTL synthesis with satisficing DS rewards (rewards that achieve a threshold) is sound and complete for integer discount factors, but, in practice, a fractional discount factor is desired. This work extends the existing satisficing approach, presenting the first sound algorithm for synthesis from LTL and DS rewards with fractional discount factors. The utility of our algorithm is demonstrated on robotic planning domains. 

Synthesis techniques for temporal logic specifications are typically based on exploiting symbolic techniques, as done in model checking. These symbolic techniques typically use backward fixpoint computation. Planning, which can be seen as a specific form of synthesis, is a witness of the success of forward search approaches. In this paper, we develop a forward-search approach to full-fledged Linear Temporal Logic on finite traces (LTLf) synthesis. We show how to compute the Deterministic Finite Automaton (DFA) of an LTLf formula on-the-fly, while performing an adversarial forward search towards the final states, by considering the DFA as a sort of AND-OR graph. Our approach is characterized by branching on suitable propositional formulas, instead of individual evaluations, hence radically reducing the branching factor of the search space. Specifically, we take advantage of techniques developed for knowledge compilation, such as Sentential Decision Diagrams (SDDs), to implement the approach efficiently.

 

Motivated by applications in boolean-circuit design, boolean synthesis is the process of synthesizing a boolean function with multiple outputs, given a relation between its inputs and outputs. Previous work has attempted to solve boolean functional synthesis by converting a specification formula into a Binary Decision Diagram (BDD) and quantifying existentially the output variables. We make use of the fact that the specification is usually given in the form of a Conjunctive Normal Form (CNF) formula, and we can perform resolution on a symbolic representation of a CNF formula in the form of a Zero-suppressed Binary Decision Diagram (ZDD). We adapt the realizability test to the context of CNF and ZDD, and show that the Cross operation defined in earlier work can be used for witness construction. Experiments show that our approach is complementary to BDD-based Boolean synthesis. 

We consider the problem of synthesizing good-enough (GE)-strategies for linear temporal logic (LTL) over finite traces or LTLf for short.The problem of synthesizing GE-strategies for an LTL formula φ over infinite traces reduces to the problem of synthesizing winning strategies for the formula (∃Oφ)⇒φ where O is the set of propositions controlled by the system.We first prove that this reduction does not work for LTLf formulas.Then we show how to synthesize GE-strategies for LTLf formulas via the Good-Enough (GE)-synthesis of LTL formulas.Unfortunately, this requires to construct deterministic parity automata on infinite words, which is computationally expensive.We then show how to synthesize GE-strategies for LTLf formulas by a reduction to solving games played on deterministic Büchi automata, based on an easier construction of deterministic automata on finite words.We show empirically that our specialized synthesis algorithm for GE-strategies outperforms the algorithms going through GE-synthesis of LTL formulas by orders of magnitude.

 

Robots have begun operating and collaborating with humans in industrial and social settings. This collaboration introduces challenges: the robot must plan while taking the human’s actions into account. In prior work, the problem was posed as a 2-player deterministic game, with a limited number of human moves. The limit on human moves is unintuitive, and in many settings determinism is undesirable. In this paper, we present a novel planning method for collaborative human-robot manipulation tasks via probabilistic synthesis. We introduce a probabilistic manipulation domain that captures the interaction by allowing for both robot and human actions with states that represent the configurations of the objects in the workspace. The task is specified using Linear Temporal Logic over finite traces (LTLf ). We then transform our manipulation domain into a Markov Decision Process (MDP) and synthesize an optimal policy to satisfy the specification on this MDP. We present two novel contributions: a formalization of probabilistic manipulation domains allowing us to apply existing techniques and a comparison of different encodings of these domains. Our framework is validated on a physical UR5 robot.