Abstract-This paper presents Meld, a programming language for modular robots, i.e., for independently executing robots where inter-robot communication is limited to immediate neighbors. Meld is a declarative language, based on P2, a logicprogramming language originally designed for programming overlay networks. By using logic programming, the code for an ensemble of robots can be written from a global perspective, as opposed to a large collection of independent robot views. This greatly simplifies the thought process needed for programming large ensembles. Initial experience shows that this also leads to a considerable reduction in code size and complexity.An initial implementation of Meld has been completed and has been used to demonstrate its effectiveness in the Claytronics simulator. Early results indicate that Meld programs are considerably more concise (more than 20x shorter) than programs written in C++, while running nearly as efficiently.

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Abstract. We address how to write programs for distributed computing systems in which the network topology can change dynamically. Examples of such systems, which we call ensembles, include programmable sensor networks (where the network topology can change due to failures in the nodes or links) and modular robotics systems (whose physical configuration can be rearranged under program control). We extend Meld [1], a logic programming language that allows an ensemble to be viewed as a single computing system. In addition to proving some key properties of the language, we have also implemented a complete compiler for Meld. It generates code for TinyOS [14] and for a Claytronics simulator [12]. We have successfully written correct, efficient, and complex programs for ensembles containing over one million nodes.

Abstract-Internal localization, the problem of estimating relative pose for each module (part) of a modular robot is a prerequisite for many shape control, locomotion, and actuation algorithms. In this paper, we propose a robust hierarchical approach that uses normalized cut to identify dense subregions with small mutual localization error, then progressively merges those subregions to localize the entire ensemble. Our method works well in both 2D and 3D, and requires neither exact measurements nor rigid inter-module connectors. Most of the computations in our method can be effectively distributed. The result is a robust algorithm that scales to large, non-homogeneous ensembles. We evaluate our algorithm in accurate 2D and 3D simulations of scenarios with up to 10,000 modules.

In this article we describe a concept for a new type of material, which we call claytronics , made out of very large numbers-potentially millionsof submillimeter-sized spherical robots. While still only a concept, we have completed a considerable amount of initial design and experimentation work, enough at this point to allow us to understand what is readily achievable within a short time frame (less than a decade) and also to identify some of the most significant technical challenges yet to be overcome. To date, we have developed and analyzed several promising engineering designs, conducted numerous large-scale experiments on a high-fidelity physics-based simulator, and successfully carried out several prototype three-dimensional (3D) microelectromechanical systems (MEMS) manufacturing runs. These experiences lead us to believe that there are no fundamental software or hardware barriers to realizing claytronics on a large scale and within a few years.While the most fundamental purpose of our research on claytronics is to understand manufacturing and programming of very large ensembles of independently actuated computing devices, it is also clear that such a material would have numerous practical applications, ranging from shape-shifting radio antennas (important for software-defined radios) to 3D fax machines. Perhaps our most fanciful-sounding application, however, is motivated by one of the most basic of human needs: to communicate and interact with others. Two centuries ago, the only practical way to carry on a real-time conversation with