3,036 research outputs found

    An Iterative Abstraction Algorithm for Reactive Correct-by-Construction Controller Synthesis

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    In this paper, we consider the problem of synthesizing correct-by-construction controllers for discrete-time dynamical systems. A commonly adopted approach in the literature is to abstract the dynamical system into a Finite Transition System (FTS) and thus convert the problem into a two player game between the environment and the system on the FTS. The controller design problem can then be solved using synthesis tools for general linear temporal logic or generalized reactivity(1) specifications. In this article, we propose a new abstraction algorithm. Instead of generating a single FTS to represent the system, we generate two FTSs, which are under- and over-approximations of the original dynamical system. We further develop an iterative abstraction scheme by exploiting the concept of winning sets, i.e., the sets of states for which there exists a winning strategy for the system. Finally, the efficiency of the new abstraction algorithm is illustrated by numerical examples.Comment: A shorter version has been accepted for publication in the 54th IEEE Conference on Decision and Control (held Tuesday through Friday, December 15-18, 2015 at the Osaka International Convention Center, Osaka, Japan

    Lazy Abstraction-Based Controller Synthesis

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    We present lazy abstraction-based controller synthesis (ABCS) for continuous-time nonlinear dynamical systems against reach-avoid and safety specifications. State-of-the-art multi-layered ABCS pre-computes multiple finite-state abstractions of varying granularity and applies reactive synthesis to the coarsest abstraction whenever feasible, but adaptively considers finer abstractions when necessary. Lazy ABCS improves this technique by constructing abstractions on demand. Our insight is that the abstract transition relation only needs to be locally computed for a small set of frontier states at the precision currently required by the synthesis algorithm. We show that lazy ABCS can significantly outperform previous multi-layered ABCS algorithms: on standard benchmarks, lazy ABCS is more than 4 times faster

    Iterative Temporal Motion Planning for Hybrid Systems in Partially Unknown Environments

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    This paper considers the problem of motion planning for a hybrid robotic system with complex and nonlinear dynamics in a partially unknown environment given a temporal logic specification. We employ a multi-layered synergistic framework that can deal with general robot dynamics and combine it with an iterative planning strategy. Our work allows us to deal with the unknown environmental restrictions only when they are discovered and without the need to repeat the computation that is related to the temporal logic specification. In addition, we define a metric for satisfaction of a specification. We use this metric to plan a trajectory that satisfies the specification as closely as possible in cases in which the discovered constraint in the environment renders the specification unsatisfiable. We demonstrate the efficacy of our framework on a simulation of a hybrid second-order car-like robot moving in an office environment with unknown obstacles. The results show that our framework is successful in generating a trajectory whose satisfaction measure of the specification is optimal. They also show that, when new obstacles are discovered, the reinitialization of our framework is computationally inexpensive

    Coordinated Robot Navigation via Hierarchical Clustering

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    We introduce the use of hierarchical clustering for relaxed, deterministic coordination and control of multiple robots. Traditionally an unsupervised learning method, hierarchical clustering offers a formalism for identifying and representing spatially cohesive and segregated robot groups at different resolutions by relating the continuous space of configurations to the combinatorial space of trees. We formalize and exploit this relation, developing computationally effective reactive algorithms for navigating through the combinatorial space in concert with geometric realizations for a particular choice of hierarchical clustering method. These constructions yield computationally effective vector field planners for both hierarchically invariant as well as transitional navigation in the configuration space. We apply these methods to the centralized coordination and control of nn perfectly sensed and actuated Euclidean spheres in a dd-dimensional ambient space (for arbitrary nn and dd). Given a desired configuration supporting a desired hierarchy, we construct a hybrid controller which is quadratic in nn and algebraic in dd and prove that its execution brings all but a measure zero set of initial configurations to the desired goal with the guarantee of no collisions along the way.Comment: 29 pages, 13 figures, 8 tables, extended version of a paper in preparation for submission to a journa

    Formal Methods and Safety for Automated Vehicles: Modeling, Abstractions, and Synthesis of Tactical Planners

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    One goal of developing automated road vehicles is to completely free people from driving tasks. Automated vehicles with no human driver must handle all traffic situations that human drivers are expected to handle, possibly more. Though human drivers cause a lot of traffic accidents, they still have a very low accident and failure rate that automated vehicles must match.Tactical planners are responsible for making discrete decisions for the coming seconds or minutes. As with all subsystems in an automated vehicle, these planners need to be supported with a credible and convincing argument of their correctness. The planners interact with other road users in a feedback loop, so their correctness depends on their behavior in relation to other drivers and road users over time. One way to ascertain their correctness is to test the vehicles in real traffic. But to be sufficiently certain that a tactical planner is safe, it has to be tested on 255 million miles with no accidents.Formal methods can, in contrast to testing, mathematically prove that given requirements are fulfilled. Hence, these methods are a promising alternative for making credible arguments for tactical planners’ correctness. The topic of this thesis is the use of formal methods in the automotive industry to design safe tactical planners. What is interesting is both how automotive systems can be modeled in formal frameworks, and how formal methods can be used practically within the automotive development process.The main findings of this thesis are that it is viable to formally express desired properties of tactical planners, and to use formal methods to prove their correctness. However, the difficulty to anticipate and inspect the interaction of several desired properties is found to be an obstacle. Model Checking, Reactive Synthesis, and Supervisory Control Theory have been used in the design and development process of tactical planners, and these methods have their benefits, depending on the application. To be feasible and useful, these methods need to operate on both a high and a low level of abstraction, and this thesis contributes an automatic abstraction method that bridges this divide.It is also found that artifacts from formal methods tools may be used to convincingly argue that a realization of a tactical planner is safe, and that such an argument puts formal requirements on the vehicle’s other subsystems and its surroundings
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