The Computational Complexity of Controller-Environment Co-design Using Library Selection for Distributed Construction

Abstract

Creating specified structures through the coordinated efforts of teams of simple autonomous robots is a significant problem in distributed robotics. All previous effort, both empirical and theoretical, has focused on the problems of designing either controllers or environments which, in tandem with given environments or controllers, built the specified structures. In this paper, we give the results of the first computational and parameterized complexity analyses of the controller-environment co-design problem in the simple case where teams of finite-state robots are designed by selecting controllers from a given library. We show that this problem cannot be solved efficiently in general or under a number of restrictions, and give the first restrictions under which this problem is efficiently solvable.We also consider two elaborations on this problem. First, we analyze the controllerenvironment co-design problem under a new architecture in which robots have a transient memory. Second, we give the first definitions of and derive computational complexity results for stigmergy-related parameters for the controller-environment co-design problem. ii Acknowledgements I would like to express my profound gratitude to Dr. Todd Wareham, my research supervisor, for his academic guidance, untiring support, research grant and his valuable and constructive feedback of this research work. His readiness to accommodate me whenever possible and to help me throughout my research work is much appreciated.

Creating Teams of Simple Agents for Specified Tasks: A Computational Complexity Perspective

“…Such research could initially focus on more fully characterizing those combinations of restrictions that do and do not render team verification and design tractable. Such work has already been started [8,9,10,12,11,13] for team verification and design in swarm robotics relative a variety of restrictions using more advanced analysis techniques (e.g., parameterized complexity analysis [27]). Additional restrictions of particular interest here are those that "break" the reductions underlying our intractability results, e.g., restrictions on the degree and type of structure encountered by agents in their environments (including the presences of other agents).…”

“…Though this is a basic model in which robots sense and move without uncertainty in a discrete and synchronous manner in a 2D grid-based environment, it is flexible enough to allow investigations along the three team and agent architectural dimensions listed in the introduction. In the interests of concision, most of this review is the "short form" given in [8,10]; readers wishing more details should consult [9,11]. This will be followed by formalization of computational problems within this model corresponding to various types of robot team verification and design.…”

“…We use the notions of deterministic robot and team operation proposed in [8,11] (i.e., requiring that at any time as the team operates in an environment, all transitions enabled in a robot relative to the current state of that robot perform the same environment modifications and progress to the same next state). Given this, an individual FSR is not itself deterministic but rather the operation of that FSR is deterministic in the context of a particular FSR team operating in a particular environment.…”

“…A natural question at this point is what algorithmic options are and are not available for the efficient verification and design of teams relative to the three dimensions listed above. In this paper, we give some initial answers to this question, building on recent work [8,9,10,11,12,13] addressing related questions in swarm robotics for distributed construction. 1 In particular, we give proofs (modified from several given previously in [9,10,11] 2 ) which demonstrate that the problems of team verification and design are by large both exact and approximate polynomial-time intractable in general relative to the most basic types of homogeneous and heterogeneous teams consisting of simple reflex agents that do not use stigmergy.…”