Optimal control of non-deterministic systems for a computationally efficient fragment of temporal logic

Wolff, Eric M.; Topcu, Ufuk; Murray, Richard M.

doi:10.1109/cdc.2013.6760371

Cited by 18 publications

(11 citation statements)

References 26 publications

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“…Informally, the objective of the high level plan is to produce a control policy and find a set of initial PA states such that a goal PA state is eventually reached. To this end, in this section we also develop a Dynamic Programming Principle (DPP) suitable for use on the PA. Because of the two types of non-determinism of the PA, existing algorithms cannot be applied directly [5], [33]. By adapting the algorithm in [5], we obtain two formulations of the DPP, one of which is more computationally efficient as it exploits certain structure in the PA; further details are provided in Remark IV.5.…”

Section: High-level Planmentioning

confidence: 99%

“…We focus on reach-avoid specifications in a priori known environments, in which the system must reach a desired configuration in a safe manner [3], [9], [15], [20]. Reach-avoid offers a fairly rich behavior set so that, for instance, a fragment of linear temporal logic (LTL) can be encoded as a sequence of reach-avoid problems [33], as we also show in our applications.…”

Section: Introductionmentioning

confidence: 99%

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A Modular Framework for Motion Planning Using Safe-by-Design Motion Primitives

et al. 2019

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We present a modular framework for solving a motion planning problem among a group of robots. The proposed framework utilizes a finite set of low level motion primitives to generate motions in a gridded workspace. The constraints on allowable sequences of motion primitives are formalized through a maneuver automaton. At the high level, a control policy determines which motion primitive is executed in each box of the gridded workspace. We state general conditions on motion primitives to obtain provably correct behavior so that a library of safe-by-design motion primitives can be designed. The overall framework yields a highly robust design by utilizing feedback strategies at both the low and high levels. We provide specific designs for motion primitives and control policies suitable for multi-robot motion planning; the modularity of our approach enables one to independently customize the designs of each of these components. Our approach is experimentally validated on a group of quadrocopters.

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Section: High-level Planmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Modular Framework for Motion Planning Using Safe-by-Design Motion Primitives

et al. 2019

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“…During the last few years, several methods have been developed for deterministic, e.g., [1][2] [3], non-deterministic, e.g., [4][5] [6] and stochastic systems, e.g., [7] [8]. These methods specify properties using temporal logics such as linear temporal logic (LTL) and computation tree logic (CTL).…”

Section: Introductionmentioning

confidence: 99%

Sampling-based stochastic optimal control with metric interval temporal logic specifications

Montana

Dodd

2016

2016 IEEE Conference on Control Applications (CCA)

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© 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. Reproduced in accordance with the publisher's self-archiving policy.eprints@whiterose.ac.uk https://eprints.whiterose.ac.uk/ Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version -refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher's website. TakedownIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. Sampling-based Stochastic Optimal Control with Metric Interval Temporal Logic SpecificationsFelipe J. Montana, Jun Liu and Tony J. DoddAbstract-This paper describes a method to find optimal policies for stochastic dynamic systems that maximise the probability of satisfying real-time properties. The method consists of two phases. In the first phase, a coarse abstraction of the original system is created. In each region of the abstraction, a sampling-based algorithm is utilised to compute local policies that allow the system to move between regions. Then, in the second phase, the selection of a policy in each region is obtained by solving a reachability problem on the Cartesian product between the abstraction and a timed automaton representing a real-time specification given as a metric interval temporal logic formula. In contrast to current methods that require a fine abstraction, the proposed method achieves computational tractability by modelling the coarse abstraction of the system as a bounded-parameter Markov decision process (BMDP). Moreover, once the BMDP is created, this can be reused for new specifications assuming the same stochastic system and workspace. The method is demonstrated with an autonomous driving example.

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“…However, these results apply only to certain special classes of hybrid systems. In the work of Karaman, Wolff and others [24], [25], trajectory based optimization is applied for synthesizing optimal control for discrete-time non-linear systems, however, it constrains the class of control strategies considered (to either finite paths or lassos). In contrast, we present a systematic method to explore the class of strategies by considering a sequence of abstract systems from which increasingly better approximations of the optimal cost can be computed.…”

Section: A Related Workmentioning

confidence: 99%

Optimal control with regular objectives using an abstraction-refinement approach

Leong

Prabhakar

2016

2016 American Control Conference (ACC)

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Abstract-This paper presents a method to synthesize a sequence of control inputs for a discrete-time switched linear system equipped with a cost function, such that the controlled system behavior satisfies a linear-time temporal objective with minimal cost. An abstract finite state weighted transition system is constructed, such that the cost of the optimal control on the abstract system provides an upper bound on the cost of the optimal control for the original system. Specifically, the abstract system is constructed from finite partitions of the state and input spaces by solving certain optimization problems, and a sequence of controllers is obtained by considering a sequence of uniformly refined partitions. Under mild assumptions on the optimal control for the switched system, the costs of the sequence of controllers constructed converges to the cost of the optimal control for the switched system. The abstraction refinement algorithm is implemented in the tool OptCAR. The feasibility of this approach is illustrated on two different examples, by constructing automatically, sub-optimal controllers with improving optimal costs.

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Optimal control of non-deterministic systems for a computationally efficient fragment of temporal logic

Cited by 18 publications

References 26 publications

A Modular Framework for Motion Planning Using Safe-by-Design Motion Primitives

A Modular Framework for Motion Planning Using Safe-by-Design Motion Primitives

Sampling-based stochastic optimal control with metric interval temporal logic specifications

Optimal control with regular objectives using an abstraction-refinement approach

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