Coordinated multi-agent robotic construction provides a means to build infrastructure in extreme environments and improve efficiency in high performance applications. Planning methods are key to understanding and achieving the scope of such applications, and are typically tailored to specific models of construction material and a consideration of passivity or activity thereof. Here, we focus on the NASA Automated Reconfigurable Mission Adaptive Digital Assembly Systems (ARMADAS) model, which includes passive lightweight structural modules and small robots that traverse the structure. We present an algorithm for calculating a build plan for robots under the constraints of this type of system. We then evaluate the quality of this plan experimentally. Many of the techniques we use can be applied to any robotic assembly system whose robots perform locomotion over the structure that they are building.

The sliding cubes model is a well-established theoretical framework that supports the analysis of reconfiguration algorithms for modular robots consisting of face-connected cubes. The best algorithm currently known for the reconfiguration problem, by Abel and Kominers [arXiv, 2011], uses O(n3) moves to transform any n-cube configuration into any other n-cube configuration. As is common in the literature, this algorithm reconfigures the input into an intermediate canonical shape. In this paper we present an in-place algorithm that reconfigures any n-cube configuration into a compact canonical shape using a number of moves proportional to the sum of coordinates of the input cubes. This result is asymptotically optimal. Furthermore, our algorithm directly extends to dimensions higher than three.

Given two sets $R$ and $B$ of $n$ points in the plane, we present efficient algorithms to find a two-line linear classifier that best separates the "red" points in $R$ from the "blue" points in $B$ and is robust to outliers. More precisely, we find a region $\mathcal{W}_B$ bounded by two lines, so either a halfplane, strip, wedge, or double wedge, containing (most of) the blue points $B$, and few red points. Our running times vary between optimal $O(n\log n)$ and around $O(n^3)$, depending on the type of region $\mathcal{W}_B$ and whether we wish to minimize only red outliers, only blue outliers, or both.

The concept of programmable matter envisions a very large number of tiny and simple robot particles forming a smart material. Even though the particles are restricted to local communication, local movement, and simple computation, their actions can nevertheless result in the global change of the material's physical properties and geometry. A fundamental algorithmic task for programmable matter is to achieve global shape reconfiguration by specifying local behavior of the particles. In this paper we describe a new approach for shape reconfiguration in the \emph{amoebot} model. The amoebot model is a distributed model which significantly restricts memory, computing, and communication capacity of the individual particles. Thus the challenge lies in coordinating the actions of particles to produce the desired behavior of the global system. Our reconfiguration algorithm is the first algorithm that does not use a canonical intermediate configuration when transforming between arbitrary shapes. We introduce new geometric primitives for amoebots and show how to reconfigure particle systems, using these primitives, in a linear number of activation rounds in the worst case. In practice, our method exploits the geometry of the symmetric difference between input and output shape: it minimizes unnecessary disassembly and reassembly of the particle system when the symmetric difference between the initial and the target shapes is small. Furthermore, our reconfiguration algorithm moves the particles over as many parallel shortest paths as the problem instance allows.