A Parallel Distributed Strategy for Arraying a Scattered Robot Swarm

We consider the problem of organizing a scattered group of $n$ robots in two-dimensional space, with geometric maximum distance $D$ between robots. The communication graph of the swarm is connected, but there is no central authority for organizing it. We want to arrange them into a sorted and equally-spaced array between the robots with lowest and highest label, while maintaining a connected communication network. In this paper, we describe a distributed method to accomplish these goals, without using central control, while also keeping time, travel distance and communication cost at a minimum. We proceed in a number of stages (leader election, initial path construction, subtree contraction, geometric straightening, and distributed sorting), none of which requires a central authority, but still accomplishes best possible parallelization. The overall arraying is performed in $O(n)$ time, $O(n^2)$ individual messages, and $O(nD)$ travel distance. Implementation of the sorting and navigation use communication messages of fixed size, and are a practical solution for large populations of low-cost robots

Finding a needle in an exponential haystack: Discrete RRT for exploration of implicit roadmaps in multi-robot motion planning

We present a sampling-based framework for multi-robot motion planning which combines an implicit representation of a roadmap with a novel approach for pathfinding in geometrically embedded graphs tailored for our setting. Our pathfinding algorithm, discrete-RRT (dRRT), is an adaptation of the celebrated RRT algorithm for the discrete case of a graph, and it enables a rapid exploration of the high-dimensional configuration space by carefully walking through an implicit representation of a tensor product of roadmaps for the individual robots. We demonstrate our approach experimentally on scenarios of up to 60 degrees of freedom where our algorithm is faster by a factor of at least ten when compared to existing algorithms that we are aware of.Comment: Kiril Solovey and Oren Salzman contributed equally to this pape

Motion Planning for Unlabeled Discs with Optimality Guarantees

We study the problem of path planning for unlabeled (indistinguishable) unit-disc robots in a planar environment cluttered with polygonal obstacles. We introduce an algorithm which minimizes the total path length, i.e., the sum of lengths of the individual paths. Our algorithm is guaranteed to find a solution if one exists, or report that none exists otherwise. It runs in time $\tilde{O}(m^4+m^2n^2)$, where $m$ is the number of robots and $n$ is the total complexity of the workspace. Moreover, the total length of the returned solution is at most $\text{OPT}+4m$, where OPT is the optimal solution cost. To the best of our knowledge this is the first algorithm for the problem that has such guarantees. The algorithm has been implemented in an exact manner and we present experimental results that attest to its efficiency