Complete Heterogeneous Self-Reconfiguration: Deadlock Avoidance Using Hole-Free Assemblies

Pickem, Daniel; Egerstedt, Magnus; Shamma, Jeff S.

doi:10.3182/20130925-2-de-4044.00059

Cited by 3 publications

(4 citation statements)

References 9 publications

(10 reference statements)

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“…A collection of agents is furthermore called a configuration. Therefore, a configuration C composed of N agents is a subset of the representable space Z dN (see [18]). Moreover, we will deal with homogeneous configurations, in which all agents have the same properties and are completely interchangeable.…”

Section: Problem Formulationmentioning

confidence: 99%

“…a) 2D reconfiguration: In the two-dimensional case agents are restricted to motions on the xy-plane. Unlike in previous work (see [17] and [18]) where we required a configuration to remain connected at all times, in this work, agents are allowed to disconnect from all (or a subset of) other agents. This approach enables agents to separate from and merge with other agents at a later time.…”

Section: Action Set Computationmentioning

confidence: 99%

“…In the sliding cube model (see [4], [5], [17], [18], [19]), a cube is able to perform two primitive motions -a sliding and a corner motion. In general, a motion specifies a translation along coordinate axes and is represented by an element m ∈ Z d .…”

Section: A Motion Modelmentioning

confidence: 99%

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A game-theoretic formulation of the homogeneous self-reconfiguration problem

Pickem

Egerstedt

Shamma

2015

2015 54th IEEE Conference on Decision and Control (CDC)

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In this paper we formulate the homogeneous two-and three-dimensional self-reconfiguration problem over discrete grids as a constrained potential game. We develop a game-theoretic learning algorithm based on the Metropolis-Hastings algorithm that solves the self-reconfiguration problem in a globally optimal fashion. Both a centralized and a fully distributed algorithm are presented and we show that the only stochastically stable state is the potential function maximizer, i.e. the desired target configuration. These algorithms compute transition probabilities in such a way that even though each agent acts in a self-interested way, the overall collective goal of self-reconfiguration is achieved. Simulation results confirm the feasibility of our approach and show convergence to desired target configurations.

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Section: Problem Formulationmentioning

confidence: 99%

Section: Action Set Computationmentioning

confidence: 99%

See 1 more Smart Citation

A game-theoretic formulation of the homogeneous self-reconfiguration problem

Pickem

Egerstedt

Shamma

2015

2015 54th IEEE Conference on Decision and Control (CDC)

Self Cite

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“…When strong connectivity is enforced, reconfiguration for 2-D shapes can be completed in O(n 2 ) moves [11]- [13], or in O(n) rounds for synchronous distributed settings [14]. 3-D versions of the problem have also been studied under the restriction that the initial and final configurations have no holes [15]. In [16], the 3-D sliding cube model enabled locomotion over arbitrary obstacles.…”

mentioning

confidence: 99%

Reconfiguration planning for pivoting cube modular robots

Sung

Bern

Romanishin

et al. 2015

2015 IEEE International Conference on Robotics and Automation (ICRA)

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Abstract-In this paper, we present algorithms for selfreconfiguration of modular robots that move by pivoting. The modules are cubes that can pivot about their edges along thê x,ŷ, orẑ axes to move on a 3-dimensional substrate. This is a different model from prior work, which usually considers modules that slide along their faces. We analyze the pivoting cube model and give sufficient conditions for reconfiguration to be feasible. In particular, we show that if an initial configuration does not contain any of three subconfigurations, which we call rules, then it can reconfigure into a line. We provide provably correct algorithms for reconfiguration for both 2-D and 3-D systems, and we verify our algorithms via simulation on randomly generated 2-D and 3-D configurations.I. INTRODUCTION Modular robots consist of multiple connected modules, each with limited capabilities, that can be reconfigured to produce complex functionality as required by a task. Among the self-reconfigurable modular systems that have been developed [1]- [7], pivoting has emerged as a simple but powerful motion predicate [7]. In this paper, we describe a model for pivoting cubes in 3-D. We consider reconfiguration in both 2-D and 3-D settings and demonstrate that barring certain subconfigurations allows us to guarantee reconfiguration in O(n 2 ) moves. We provide provably correct algorithms for performing such reconfiguration. These are not optimal but are the first correct algorithms for the 3-D pivoting cube model. We perform simulations on random 2-D and 3-D configurations and show that in many cases, reconfiguration does not require the upper bound of n 2 moves. Pivoting modules, although prevalent in hardware [5], [7], are not well-studied. Pivoting modules sweep out a volume that extends past their initial and final positions, and any reconfiguration algorithm must take this motion constraint into account. An O(n 2 ) algorithm for 2-D pivoting modules was given in [8] but the model relaxed connectivity constraints compared to what many modular robots require and allowed movements that are often not physically realizable. Nguyen et al. [9] considered 2-D pivoting hexagons while requiring strong connectivity (connectivity through faces) and provided sufficient conditions for reconfiguration in O(n 5/2 ) moves. In [10], pivoting squares were reconfigured using a stochastic approach, and work in [5] analyzed the same system using meta-modules. A model for pivoting cubes in 3-D was introduced in [7], but the planning problem was not addressed. To our knowledge, there have been no studies of reconfiguration for pivoting cubes in 3-D.

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