303 research outputs found
Certified Universal Gathering in for Oblivious Mobile Robots
We present a unified formal framework for expressing mobile robots models,
protocols, and proofs, and devise a protocol design/proof methodology dedicated
to mobile robots that takes advantage of this formal framework. As a case
study, we present the first formally certified protocol for oblivious mobile
robots evolving in a two-dimensional Euclidean space. In more details, we
provide a new algorithm for the problem of universal gathering mobile oblivious
robots (that is, starting from any initial configuration that is not bivalent,
using any number of robots, the robots reach in a finite number of steps the
same position, not known beforehand) without relying on a common orientation
nor chirality. We give very strong guaranties on the correctness of our
algorithm by proving formally that it is correct, using the COQ proof
assistant. This result demonstrates both the effectiveness of the approach to
obtain new algorithms that use as few assumptions as necessary, and its
manageability since the amount of developed code remains human readable.Comment: arXiv admin note: substantial text overlap with arXiv:1506.0160
A Certified Universal Gathering Algorithm for Oblivious Mobile Robots
We present a new algorithm for the problem of universal gathering mobile
oblivious robots (that is, starting from any initial configuration that is not
bivalent, using any number of robots, the robots reach in a finite number of
steps the same position, not known beforehand) without relying on a common
chirality. We give very strong guaranties on the correctness of our algorithm
by proving formally that it is correct, using the COQ proof assistant. To our
knowledge, this is the first certified positive (and constructive) result in
the context of oblivious mobile robots. It demonstrates both the effectiveness
of the approach to obtain new algorithms that are truly generic, and its
managability since the amount of developped code remains human readable
TuringMobile: A Turing Machine of Oblivious Mobile Robots with Limited Visibility and Its Applications
In this paper we investigate the computational power of a set of mobile robots with limited visibility. At each iteration, a robot takes a snapshot of its surroundings, uses the snapshot to compute a destination point, and it moves toward its destination. Each robot is punctiform and memoryless, it operates in R^m, it has a local reference system independent of the other robots\u27 ones, and is activated asynchronously by an adversarial scheduler. Moreover, the robots are non-rigid, in that they may be stopped by the scheduler at each move before reaching their destination (but are guaranteed to travel at least a fixed unknown distance before being stopped).
We show that despite these strong limitations, it is possible to arrange 3m+3k of these weak entities in R^m to simulate the behavior of a stronger robot that is rigid (i.e., it always reaches its destination) and is endowed with k registers of persistent memory, each of which can store a real number. We call this arrangement a TuringMobile. In its simplest form, a TuringMobile consisting of only three robots can travel in the plane and store and update a single real number. We also prove that this task is impossible with fewer than three robots.
Among the applications of the TuringMobile, we focused on Near-Gathering (all robots have to gather in a small-enough disk) and Pattern Formation (of which Gathering is a special case) with limited visibility. Interestingly, our investigation implies that both problems are solvable in Euclidean spaces of any dimension, even if the visibility graph of the robots is initially disconnected, provided that a small amount of these robots are arranged to form a TuringMobile. In the special case of the plane, a basic TuringMobile of only three robots is sufficient
Parameterized Verification of Algorithms for Oblivious Robots on a Ring
We study verification problems for autonomous swarms of mobile robots that
self-organize and cooperate to solve global objectives. In particular, we focus
in this paper on the model proposed by Suzuki and Yamashita of anonymous robots
evolving in a discrete space with a finite number of locations (here, a ring).
A large number of algorithms have been proposed working for rings whose size is
not a priori fixed and can be hence considered as a parameter. Handmade
correctness proofs of these algorithms have been shown to be error-prone, and
recent attention had been given to the application of formal methods to
automatically prove those. Our work is the first to study the verification
problem of such algorithms in the parameter-ized case. We show that safety and
reachability problems are undecidable for robots evolving asynchronously. On
the positive side, we show that safety properties are decidable in the
synchronous case, as well as in the asynchronous case for a particular class of
algorithms. Several properties on the protocol can be decided as well. Decision
procedures rely on an encoding in Presburger arithmetics formulae that can be
verified by an SMT-solver. Feasibility of our approach is demonstrated by the
encoding of several case studies
Certified Impossibility Results for Byzantine-Tolerant Mobile Robots
We propose a framework to build formal developments for robot networks using
the COQ proof assistant, to state and to prove formally various properties. We
focus in this paper on impossibility proofs, as it is natural to take advantage
of the COQ higher order calculus to reason about algorithms as abstract
objects. We present in particular formal proofs of two impossibility results
forconvergence of oblivious mobile robots if respectively more than one half
and more than one third of the robots exhibit Byzantine failures, starting from
the original theorems by Bouzid et al.. Thanks to our formalization, the
corresponding COQ developments are quite compact. To our knowledge, these are
the first certified (in the sense of formally proved) impossibility results for
robot networks
Model Checking of Robot Gathering
Recent advances in distributed computing highlight models and algorithms for autonomous mo- bile robots that self-organize and cooperate together in order to solve a global objective. As results, a large number of algorithms have been proposed. These algorithms are given together with proofs to assess their correctness. However, those proofs are informal, which are error prone. This paper presents our study on formal verification of mobile robot algorithms. We first propose a formal model for mobile robot algorithms on anonymous ring shape network under multiplicity and asynchrony assumptions. We specify this formal model in Maude, a specification and pro- gramming language based on rewriting logic. We then use its model checker to formally verify an algorithm for robot gathering problem on ring enjoys some desired properties. As the result of the model checking, counterexamples have been found. We detect the sources of some unforeseen design errors. We, furthermore, give our interpretations of these errors
Certified Impossibility Results for Byzantine-Tolerant Mobile Robots
We propose a framework to build formal developments for robot networks using the COQ proof assistant, to state and to prove formally various properties. We focus in this paper on impossibility proofs, as it is natural to take advantage of the COQ higher order calculus to reason about algorithms as abstract objects. We present in particular formal proofs of two impossibility results forconvergence of oblivious mobile robots if respectively more than one half and more than one third of the robots exhibit Byzantine failures, starting from the original theorems by Bouzid et al.. Thanks to our formalization, the corresponding COQ developments are quite compact. To our knowledge, these are the first certified (in the sense of formally proved) impossibility results for robot networks
Formal Foundations of 3D Geometry to Model Robot Manipulators
International audienceWe are interested in the formal specification of safety properties of robot manipulators down to the mathematical physics. To this end, we have been developing a formalization of the mathematics of rigid body transformations in the COQ proof-assistant. It can be used to address the forward kinematics problem, i.e., the computation of the position and orientation of the end-effector of a robot manipulator in terms of the link and joint parameters. Our formalization starts by extending the Mathematical Components library with a new theory for angles and by developing three-dimensional geometry. We use these theories to formalize the foundations of robotics. First, we formalize a comprehensive theory of three-dimensional rotations, including exponentials of skew-symmetric matrices and quaternions. Then, we provide a formalization of the various representations of rigid body transformations: isometries, homogeneous representation, the Denavit-Hartenberg convention, and screw motions. These ingredients make it possible to formalize robot manipulators: we illustrate this aspect by an application to the SCARA robot manipulator
Cyber-Human Systems, Space Technologies, and Threats
CYBER-HUMAN SYSTEMS, SPACE TECHNOLOGIES, AND THREATS is our eighth textbook in a series covering the world of UASs / CUAS/ UUVs / SPACE. Other textbooks in our series are Space Systems Emerging Technologies and Operations; Drone Delivery of CBNRECy – DEW Weapons: Emerging Threats of Mini-Weapons of Mass Destruction and Disruption (WMDD); Disruptive Technologies with applications in Airline, Marine, Defense Industries; Unmanned Vehicle Systems & Operations On Air, Sea, Land; Counter Unmanned Aircraft Systems Technologies and Operations; Unmanned Aircraft Systems in the Cyber Domain: Protecting USA’s Advanced Air Assets, 2nd edition; and Unmanned Aircraft Systems (UAS) in the Cyber Domain Protecting USA’s Advanced Air Assets, 1st edition. Our previous seven titles have received considerable global recognition in the field. (Nichols & Carter, 2022) (Nichols, et al., 2021) (Nichols R. K., et al., 2020) (Nichols R. , et al., 2020) (Nichols R. , et al., 2019) (Nichols R. K., 2018) (Nichols R. K., et al., 2022)https://newprairiepress.org/ebooks/1052/thumbnail.jp
RDA: A Coq Library to Reason about Randomised Distributed Algorithms in the Message Passing Model
Distributed algorithms have received considerable attention and were studied intensively in the past few decades. Under some hypotheses on the distributed system, there is no deterministic solution to certain classical problems. Randomised solutions are then needed to solve those problems. Probabilistic algorithms are generally simple to formulate. However, their analysis can become very complex, especially in the field of distributed computing.
In this paper, we formally model in Coq a class of randomised distributed algorithms. We develop some tools to help proving impossibility results about classical problems and analysing this class of algorithms. As case studies, we examine the handshake and maximal matching problems. We show how to use our tools to formally prove properties about algorithms solving those problems
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