Bounded Synthesis of Reactive Programs

Manipulation planning from high-level task specifications, even though highly desirable, is a challenging problem. The large dimensionality of manipulators and complexity of task specifications make the problem computationally intractable. This work introduces a manipulation planning framework with linear temporal logic (LTL) specifications. The use of LTL as the specification language allows the expression of rich and complex manipulation tasks. The framework deals with the state-explosion problem through a novel abstraction technique. Given a robotic system, a workspace consisting of obstacles, manipulable objects, and locations of interest, and a co-safe LTL specification over the objects and locations, the framework computes a motion plan to achieve the task through a synergistic multi-layered planning architecture. The power of the framework is demonstrated through case studies, in which the planner efficiently computes plans for complex tasks. The case studies also illustrate the ability of the framework in intelligently moving away objects that block desired executions without requiring backtracking.

In this paper, we investigate fully-automated controller synthesis of coordination strategies for multi-robot warehouse robotic systems. We consider the scenario where a group of automated guided vehicles (AGVs) deliver goods from starting locations to destinations in a grid-abstracted workspace. We propose a distributed framework with prioritized-based coordination strategy to fulfill the entire planning task. Specifically, the task of each AGV is specified by a Linear Temporal Logic (LTL) specification. The local control strategies are obtained by solving the corresponding LTL reactive synthesis problems. In order to avoid conflicts, we use the prioritized-based coordination strategy to guarantee that the overall systems is safe and live, i.e., AGVs will collide with each other and there is no deadlock and livelock. The proposed design methodology is correct-by-construction with the formal guarantee and is amenable to handle temporal tasks in a flexible manner. Furthermore, the proposed framework is distributed; hence computationally more efficient than the centralized approach. Finally, we demonstrate the proposed distributed framework by simulation examples.

When designing languages for functional reactive programming (FRP) the main challenge is to provide the user with a simple, flexible interface for writing programs on a high level of abstraction while ensuring that all programs can be implemented efficiently in a low-level language. To meet this challenge, a new family of modal FRP languages has been proposed, in which variants of Nakano's guarded fixed point operator are used for writing recursive programs guaranteeing properties such as causality and productivity. As an apparent extension to this it has also been suggested to use Linear Temporal Logic (LTL) as a language for reactive programming through the Curry-Howard isomorphism, allowing properties such as termination, liveness and fairness to be encoded in types. However, these two ideas are in conflict with each other, since the fixed point operator introduces non-termination into the inductive types that are supposed to provide termination guarantees. In this paper we show that by regarding the modal time step operator of LTL a submodality of the one used for guarded recursion (rather than equating them), one can obtain a modal type system capable of expressing liveness properties while retaining the power of the guarded fixed point operator. We introduce the language Lively RaTT, a modal FRP language with a guarded fixed point operator and an `until' type constructor as in LTL, and show how to program with events and fair streams. Using a step-indexed Kripke logical relation we prove operational properties of Lively RaTT including productivity and causality as well as the termination and liveness properties expected of types from LTL. Finally, we prove that the type system of Lively RaTT guarantees the absence of implicit space leaks.

This paper considers robot motion planning under temporal logic constraints in probabilistic maps obtained by semantic simultaneous localization and mapping (SLAM). The uncertainty in a map distribution presents a great challenge for obtaining correctness guarantees with respect to the linear temporal logic (LTL) specification. We show that the problem can be formulated as an optimal control problem in which both the semantic map and the logic formula evaluation are stochastic. Our first contribution is to reduce the stochastic control problem for a subclass of LTL to a deterministic shortest path problem by introducing a confidence parameter $delta$. A robot trajectory obtained from the deterministic problem is guaranteed to have minimum cost and to satisfy the logic specification in the true environment with probability $delta$. Our second contribution is to design an admissible heuristic function that guides the planning in the deterministic problem towards satisfying the temporal logic specification. This allows us to obtain an optimal and very efficient solution using the A* algorithm. The performance and correctness of our approach are demonstrated in a simulated semantic environment using a differential-drive robot.

In this paper, the problem of motion planning for a mobile robot is addressed in which motion planning scenarios such as reachability, invariance, surveillance and sequencing missions are formulated with Linear Temporal Logic (LTL). First, by using the idea of invariant set theory, a novel algorithm is proposed for checking the satisfaction of temporal logic planning specification in the offline phase. Then, an optimal control strategy is designed in the presence of bounded additive disturbances to meet the given temporal logic specification and system constraints. Illustrative case studies for a robot with a double integrator model are presented to demonstrate the applicability of the proposed approach in motion planning tasks.

A formal approach for run-time verification of web applications using scope-extended LTL

This paper presents an approach to checking a running program against Linear Temporal Logic (LTL) specifications. LTL is a widely used logic for expressing properties of programs viewed as sets of executions. Our approach consists of translating LTL formulae to finite-state automata, which are used as observers of the program behavior. The translation algorithm we propose modifies standard LTL to Buchi automata conversion techniques to generate automata that check finite program traces. The algorithm has been implemented in a tool, which has been integrated with the generic JPaX framework for runtime analysis of Java programs.

For human-robot teams that operate in space, safety and robustness are paramount. In situations such as habitat construction, station inspection, or cooperative exploration, incorrect assumptions about the environment or task across the team could lead to mission failure. Thus it is important to resolve any ambiguity about the mission between teammates before embarking on a commanded task. The safeguards guaranteed by formal methods can be used to synthesize correct-by-construction reactive controllers for a robot using Linear Temporal Logic. If a robot fails to synthesize a controller given an instruction, it is clear that there exists a logical inconsistency in the environmental assumptions and/or described interactions. These specifications however are typically crafted in a language unique to the verification framework, requiring the human collaborator to be fluent in the software tool used to construct it. Furthermore, if the controller fails to synthesize, it may prove difficult to easily repair the specification. Language is a natural medium to generate these specifications using modern symbol grounding techniques. Using language empowers non-expert humans to describe tasks to robot teammates while retaining the benefits of formal verification. Additionally, dialogue could be used to inform robots about the environment and/or resolve any ambiguities before mission execution. This paper introduces an architecture for natural language interaction using a symbolic representation that informs the construction of a specification in Linear Temporal Logic. The novel aspect of this approach is that it provides a mechanism for resolving synthesis failure by hypothesizing corrections to the specification that are verified through human-robot dialogue. Experiments involving the proposed architecture are demonstrated using a simulation of an Astrobee robot navigating in the International Space Station.

We present a method to find an optimal policy with respect to a reward function for a discounted Markov decision process under general linear temporal logic (LTL) specifications. Previous work has either focused on maximizing a cumulative reward objective under finite-duration tasks or maximizing an average reward for persistent (e.g., surveillance) tasks. This paper extends and generalizes these results by introducing a pair of occupancy measures to express the LTL satisfaction objective and the expected discounted reward objective, respectively. These occupancy measures are then connected to a single policy via a novel reduction resulting in a mixed integer linear program whose solution provides an optimal policy. Our formulation can also be extended to include additional constraints with respect to secondary reward functions. We illustrate the effectiveness of our approach in the context of robotic motion planning for complex missions under uncertainty and performance objectives.

Functional Reactive Programming (FRP) models reactive systems with events and signals, which have previously been observed to correspond to the "eventually" and "always" modalities of linear temporal logic (LTL). In this paper, we define a constructive variant of LTL with least fixed point and greatest fixed point operators in the spirit of the modal mu-calculus, and give it a proofs-as-programs interpretation as a foundational calculus for reactive programs. Previous work emphasized the propositions-as-types part of the correspondence between LTL and FRP; here we emphasize the proofs-as-programs part by employing structural proof theory. We show that the type system is expressive enough to enforce liveness properties such as the fairness of schedulers and the eventual delivery of results. We illustrate programming in this calculus using (co)iteration operators. We prove type preservation of our operational semantics, which guarantees that our programs are causal. We give also a proof of strong normalization which provides justification that our programs are productive and that they satisfy liveness properties derived from their types.

Automatic synthesis from linear temporal logic (LTL) specifications is widely used in robotic motion planning and control of autonomous systems. A common specification pattern in such applications consists of an LTL formula describing the requirements on the behaviour of the system, together with a set of additional desirable properties. We study the synthesis problem in settings where the overall specification is unrealizable, more precisely, when some of the desirable properties have to be (temporarily) violated in order to satisfy the system’s objective. We provide a quantitative semantics of sets of safety specifications, and use it to formalize the “best-effort” satisfaction of such soft specifications while satisfying the hard LTL specification. We propose an algorithm for synthesizing implementations that are optimal with respect to this quantitative semantics. Our method builds upon the idea of bounded synthesis, and we develop a MaxSAT encoding which allows for maximizing the quantitative satisfaction of the soft specifications. We evaluate our algorithm on scenarios from robotics and power distribution networks.

This paper proposes a novel version of the vehicle routing problem (VRP). Instead of servicing all the customers, feasible solutions of the VRP instance are forced to satisfy a set of complex high-level tasks given as a metric temporal logic (MTL) specification, which allows complex quantitative timing constraints to be incorporated into the problem. For the resulting vehicle routing problem with metric temporal logic specifications (VRPMTL), a mixed-integer linear programming (MILP) based algorithm is provided that solves the problem to optimality. Examples for optimal multi-UAV mission planning are provided where MTL is used as a high level language to specify complex mission tasks.

Dynamic Bayesian networks (DBNs) are compact graphical representations used to model probabilistic systems where interdependent random variables and their distributions evolve over time. In this paper, we study the verification of the evolution of conditional-independence (CI) propositions against temporal logic specifications. To this end, we consider two specification formalisms over CI propositions: linear temporal logic (LTL), and non-deterministic Büchi automata (NBAs). This problem has two variants. Stochastic CI properties take the given concrete probability distributions into account, while structural CI properties are viewed purely in terms of the graphical structure of the DBN. We show that deciding whether a stochastic CI proposition eventually holds is at least as hard as the Skolem problem for linear recurrence sequences, which is a long-standing open problem in number theory. On the other hand, we show that verifying the evolution of structural CI propositions against LTL and NBA specifications is in PSPACE, and is hard for both NP and coNP. We also identify natural restrictions on the graphical structure of the DBN that make the verification of structural CI properties tractable.

We develop a sampling-based motion planning algorithm that combines long-term temporal logic goals with short-term reactive requirements. The mission specification has two parts: (1) a global specification given as a linear temporal logic (LTL) formula over a set of static service requests that occur at the regions of a known environment, and (2) a local specification that requires servicing a set of dynamic requests that can be sensed locally during the execution. The proposed computational framework consists of two main ingredients: (a) an off-line sampling-based algorithm for the construction of a global transition system that contains a path satisfying the LTL formula; and (b) an on-line sampling-based algorithm to generate paths that service the local requests, while making sure that the satisfaction of the global specification is not affected. The off-line algorithm has four main features. First, it is incremental, in the sense that the procedure for finding a satisfying path at each iteration scales only with the number of new samples generated at that iteration. Second, the underlying graph is sparse, which implies low complexity for the overall method. Third, it is probabilistically complete. Fourth, under some mild assumptions, it has the best possible complexity bound. The on-line algorithm leverages ideas from LTL monitoring and potential functions to ensure progress towards the satisfaction of the global specification while servicing locally sensed requests. Examples and experimental trials illustrating the usefulness and the performance of the framework are included.

In this paper, we investigate the design of multirobot warehouse automation systems with complex high-level tasks. We consider a warehouse environment where a group of AGVs move in a grid-partitioned workspace to deliver goods upon requests automatically. The design objective is to synthesize a high-level controller/planner that coordinates the multi-robot system to fulfill the entire task. We use linear temporal logic (LTL) formulas to describe the desired task specifications. Then the controller is generated automatically based on the LTL formula using the theory of reactive synthesis. Compared with most of the existing planning algorithms for warehouse systems, the proposed method is formal in the sense that: (i) the controller is correct-by-construction with provably satisfication guarantees; (ii) it can handle complex temporal tasks in a user-friendly manner; (iii) our framework can also handle the situation of multiple robots with multiple requests. Finally, we implement the proposed synthesis procedure and illustrate our results for multi-robot systems by simulations.