Partially Punctual Metric Temporal Logic is Decidable

Metric Temporal Logic \mathsf{MTL}[\until_I,\since_I] is one of the most studied real time logics. It exhibits considerable diversity in expressiveness and decidability properties based on the permitted set of modalities and the nature of time interval constraints $I$. Henzinger et al., in their seminal paper showed that the non-punctual fragment of $\mathsf{MTL}$ called $\mathsf{MITL}$ is decidable. In this paper, we sharpen this decidability result by showing that the partially punctual fragment of $\mathsf{MTL}$ (denoted $\mathsf{PMTL}$) is decidable over strictly monotonic finite point wise time. In this fragment, we allow either punctual future modalities, or punctual past modalities, but never both together. We give two satisfiability preserving reductions from $\mathsf{PMTL}$ to the decidable logic \mathsf{MTL}[\until_I]. The first reduction uses simple projections, while the second reduction uses a novel technique of temporal projections with oversampling. We study the trade-off between the two reductions: while the second reduction allows the introduction of extra action points in the underlying model, the equisatisfiable \mathsf{MTL}[\until_I] formula obtained is exponentially succinct than the one obtained via the first reduction, where no oversampling of the underlying model is needed. We also show that $\mathsf{PMTL}$ is strictly more expressive than the fragments \mathsf{MTL}[\until_I,\since] and \mathsf{MTL}[\until,\since_I]

Exploring Convolutional Networks for End-to-End Visual Servoing

Present image based visual servoing approaches rely on extracting hand crafted visual features from an image. Choosing the right set of features is important as it directly affects the performance of any approach. Motivated by recent breakthroughs in performance of data driven methods on recognition and localization tasks, we aim to learn visual feature representations suitable for servoing tasks in unstructured and unknown environments. In this paper, we present an end-to-end learning based approach for visual servoing in diverse scenes where the knowledge of camera parameters and scene geometry is not available a priori. This is achieved by training a convolutional neural network over color images with synchronised camera poses. Through experiments performed in simulation and on a quadrotor, we demonstrate the efficacy and robustness of our approach for a wide range of camera poses in both indoor as well as outdoor environments.Comment: IEEE ICRA 201

Making Metric Temporal Logic Rational

We study an extension of MTL in pointwise time with regular expression guarded modality Reg_I(re) where re is a rational expression over subformulae. We study the decidability and expressiveness of this extension (MTL+Ureg+Reg), called RegMTL, as well as its fragment SfrMTL where only star-free rational expressions are allowed. Using the technique of temporal projections, we show that RegMTL has decidable satisfiability by giving an equisatisfiable reduction to MTL. We also identify a subclass MITL+UReg of RegMTL for which our equisatisfiable reduction gives rise to formulae of MITL, yielding elementary decidability. As our second main result, we show a tight automaton-logic connection between SfrMTL and partially ordered (or very weak) 1-clock alternating timed automata

Logics Meet 1-Clock Alternating Timed Automata

This paper investigates a decidable and highly expressive real time logic QkMSO which is obtained by extending MSO[<] with guarded quantification using block of less than k metric quantifiers. The resulting logic is shown to be expressively equivalent to 1-clock ATA where loops are without clock resets, as well as, RatMTL, a powerful extension of MTL[U_I] with regular expressions. We also establish 4-variable property for QkMSO and characterize the expressive power of its 2-variable fragment. Thus, the paper presents progress towards expressively complete logics for 1-clock ATA

Generalizing Non-Punctuality for Timed Temporal Logic with Freeze Quantifiers

Metric Temporal Logic (MTL) and Timed Propositional Temporal Logic (TPTL) are prominent real-time extensions of Linear Temporal Logic (LTL). In general, the satisfiability checking problem for these extensions is undecidable when both the future U and the past S modalities are used. In a classical result, the satisfiability checking for MITL[U,S], a non punctual fragment of MTL[U,S], is shown to be decidable with EXPSPACE complete complexity. Given that this notion of non punctuality does not recover decidability in the case of TPTL[U,S], we propose a generalization of non punctuality called \emph{non adjacency} for TPTL[U,S], and focus on its 1-variable fragment, 1-TPTL[U,S]. While non adjacent 1-TPTL[U,S] appears to be be a very small fragment, it is strictly more expressive than MITL. As our main result, we show that the satisfiability checking problem for non adjacent 1-TPTL[U,S] is decidable with EXPSPACE complete complexity