Universal Reconfiguration of Facet-Connected Modular Robots by Pivots: The O(1) Musketeers

We present the first universal reconfiguration algorithm for transforming a modular robot between any two facet-connected square-grid configurations using pivot moves. More precisely, we show that five extra "helper" modules ("musketeers") suffice to reconfigure the remaining n modules between any two given configurations. Our algorithm uses O(n^2) pivot moves, which is worst-case optimal. Previous reconfiguration algorithms either require less restrictive "sliding" moves, do not preserve facet-connectivity, or for the setting we consider, could only handle a small subset of configurations defined by a local forbidden pattern. Configurations with the forbidden pattern do have disconnected reconfiguration graphs (discrete configuration spaces), and indeed we show that they can have an exponential number of connected components. But forbidding the local pattern throughout the configuration is far from necessary, as we show that just a constant number of added modules (placed to be freely reconfigurable) suffice for universal reconfigurability. We also classify three different models of natural pivot moves that preserve facet-connectivity, and show separations between these models

Force-Guiding Particle Chains for Shape-Shifting Displays

We present design and implementation of a chain of particles that can be programmed to fold the chain into a given curve. The particles guide an external force to fold, therefore the particles are simple and amenable for miniaturization. A chain can consist of a large number of such particles. Using multiple of these chains, a shape-shifting display can be constructed that folds its initially flat surface to approximate a given 3D shape that can be touched and modified by users, for example, enabling architects to interactively view, touch, and modify a 3D model of a building.Comment: 6 pages, 5 figure, submitted to IROS 201

Robotic metamorphosis by origami exoskeletons

Changing the inherent physical capabilities of robots by metamorphosis has been a long-standing goal of engineers. However, this task is challenging because of physical constraints in the robot body, each component of which has a defined functionality. To date, self-reconfiguring robots have limitations in their on-site extensibility because of the large scale of today’s unit modules and the complex administration of their coordination, which relies heavily on on-board electronic components. We present an approach to extending and changing the capabilities of a robot by enabling metamorphosis using self-folding origami “exoskeletons.” We show how a cubical magnet “robot” can be remotely moved using a controllable magnetic field and hierarchically develop different morphologies by interfacing with different origami exoskeletons. Activated by heat, each exoskeleton is self-folded from a rectangular sheet, extending the capabilities of the initial robot, such as enabling the manipulation of objects or locomotion on the ground, water, or air. Activated by water, the exoskeletons can be removed and are interchangeable. Thus, the system represents an end-to-end (re)cycle. We also present several robot and exoskeleton designs, devices, and experiments with robot metamorphosis using exoskeletons

A Stochastic Approach to Shortcut Bridging in Programmable Matter

In a self-organizing particle system, an abstraction of programmable matter, simple computational elements called particles with limited memory and communication self-organize to solve system-wide problems of movement, coordination, and configuration. In this paper, we consider a stochastic, distributed, local, asynchronous algorithm for "shortcut bridging", in which particles self-assemble bridges over gaps that simultaneously balance minimizing the length and cost of the bridge. Army ants of the genus Eciton have been observed exhibiting a similar behavior in their foraging trails, dynamically adjusting their bridges to satisfy an efficiency trade-off using local interactions. Using techniques from Markov chain analysis, we rigorously analyze our algorithm, show it achieves a near-optimal balance between the competing factors of path length and bridge cost, and prove that it exhibits a dependence on the angle of the gap being "shortcut" similar to that of the ant bridges. We also present simulation results that qualitatively compare our algorithm with the army ant bridging behavior. Our work gives a plausible explanation of how convergence to globally optimal configurations can be achieved via local interactions by simple organisms (e.g., ants) with some limited computational power and access to random bits. The proposed algorithm also demonstrates the robustness of the stochastic approach to algorithms for programmable matter, as it is a surprisingly simple extension of our previous stochastic algorithm for compression.Comment: Published in Proc. of DNA23: DNA Computing and Molecular Programming - 23rd International Conference, 2017. An updated journal version will appear in the DNA23 Special Issue of Natural Computin

Reconfiguring Non-Convex Holes in Pivoting Modular Cube Robots

We present an algorithm for self-reconfiguration of admissible 3D configurations of pivoting modular cube robots with holes of arbitrary shape and number. Cube modules move across the surface of configurations by pivoting about shared edges, enabling configurations to reshape themselves. Previous work provides a reconfiguration algorithm for admissible 3D configurations containing no non-convex holes; we improve upon this by handling arbitrary admissible 3D configurations. The key insight specifies a point in the deconstruction of layers enclosing non-convex holes at which we can pause and move inner modules out of the hole. We prove this happens early enough to maintain connectivity, but late enough to open enough room in the enclosing layer for modules to escape the hole. Our algorithm gives reconfiguration plans with O(n^2) moves for n modules

Particle Computation: Complexity, Algorithms, and Logic

We investigate algorithmic control of a large swarm of mobile particles (such as robots, sensors, or building material) that move in a 2D workspace using a global input signal (such as gravity or a magnetic field). We show that a maze of obstacles to the environment can be used to create complex systems. We provide a wide range of results for a wide range of questions. These can be subdivided into external algorithmic problems, in which particle configurations serve as input for computations that are performed elsewhere, and internal logic problems, in which the particle configurations themselves are used for carrying out computations. For external algorithms, we give both negative and positive results. If we are given a set of stationary obstacles, we prove that it is NP-hard to decide whether a given initial configuration of unit-sized particles can be transformed into a desired target configuration. Moreover, we show that finding a control sequence of minimum length is PSPACE-complete. We also work on the inverse problem, providing constructive algorithms to design workspaces that efficiently implement arbitrary permutations between different configurations. For internal logic, we investigate how arbitrary computations can be implemented. We demonstrate how to encode dual-rail logic to build a universal logic gate that concurrently evaluates and, nand, nor, and or operations. Using many of these gates and appropriate interconnects, we can evaluate any logical expression. However, we establish that simulating the full range of complex interactions present in arbitrary digital circuits encounters a fundamental difficulty: a fan-out gate cannot be generated. We resolve this missing component with the help of 2x1 particles, which can create fan-out gates that produce multiple copies of the inputs. Using these gates we provide rules for replicating arbitrary digital circuits.Comment: 27 pages, 19 figures, full version that combines three previous conference article