In many cutting-edge applications, high-fidelity computational models prove to be too slow for practical use and are therefore replaced by much faster surrogate models. Recently, deep learning techniques have increasingly been utilized to accelerate such predictions. To enable learning on large-dimensional and complex data, specific neural network architectures have been developed, including convolutional and graph neural networks. In this work, we present a novel encoder–decoder geometric deep learning framework called MAgNET, which extends the well-known convolutional neural networks to accommodate arbitrary graph-structured data. MAgNET consists of innovative Multichannel Aggregation (MAg) layers and graph pooling/unpooling layers, forming a graph U-Net architecture that is analogous to convolutional U-Nets. We demonstrate the predictive capabilities of MAgNET in surrogate modeling for non-linear finite element simulations in the mechanics of solids.

We present a distributed framework for predicting whether a planned reconfiguration step of a modular robot will mechanically overload the structure, causing it to break or lose stability under its own weight. The algorithm is executed by the modular robot itself and based on a distributed iterative solution of mechanical equilibrium equations derived from a simplified model of the robot. The model treats intermodular connections as beams and assumes no-sliding contact between the modules and the ground. We also provide a procedure for simplified instability detection. The algorithm is verified in the Programmable Matter simulatorVisibleSim, and in real-life experiments on the modular robotic systemBlinky Blocks.

Large-scale 3D autonomous self-reconfigurable modular robots are made of numerous interconnected robotic modules that operate in a close packing. The modules are assumed to have their own CPU and memory, and are only able to communicate with their direct neighbors. As such, the robots embody a special computing architecture: a distributed memory and distributed CPU system with a local message-passing interface. The modules can move and rearrange themselves changing the robot's connection topology. This may potentially cause mechanical failures (e.g., overloading of some inter-modular connections), which are irreversible and need to be detected in advance. In the present contribution, we further develop the idea of performing model-based detection of mechanical failures, posed in the form of balance equations solved by the modular robot itself in a distributed manner. A special implementation of the Conjugate Gradient iterative solution method is proposed and shown to greatly reduce the required number of iterations compared with the weighted Jacobi method used previously. The algorithm is verified in a virtual test bed-the VisibleSim emulator of the modular robot. The assessments of time-, CPU-, communication- and memory complexities of the proposed scheme are provided.

We discuss selected mechanical aspects of self-reconfiguration of densely-packed modular robots. The change of connection topology and transport of modules are fundamental mechanisms for these systems, which determine their desired emergent behavior, e.g., movement, shape change or interaction with their surroundings. At the same time, reconfiguration affects the forces between modules. We present a distributed procedure by which a robot can predict if the next planned reconfiguration step will overstress intermodular connections. We use a Finite Element model of a modular robot, with one-node-per-module discretization and beam elements representing intermodular connections. The analysis is restricted to static loads and linear elasticity. We present a distributed procedure of aggregation of the stiffness matrix and iterative solution of the resulting equations of elasticity. The procedure is illustrated with numerical examples and analyzed in terms of its efficiency.

Module localization is an important aspect of the operation of self-reconfigurable robots. The knowledge of spatial positions of modules, or at least of the overall shape which the modules form, is the usual prerequisite for reconfiguration planning. We present a general, decentralized algorithm for determining the positions of modules placed on a cubic grid from local sensor information. The connection topology of the robot is arbitrary. We assume that a module can sense the presence of its immediate neighbors on the grid and determine their positions in its own local coordinate system, but cannot sense the orientations of the coordinate systems of its neighbors. Since orientation cannot be directly communicated between modules, the modules can only exchange information about the relative positions of their neighbors. The algorithm aggregates this information over the entire network of modules and narrows down the set of valid positions for each module as far as possible. If there exists a unique locally-consistent assignment of coordinates to all modules then it is found.

A collective actuator is a self-reconfigurable modular-robotic structure which produces useful mechanical work through simultaneous reconfiguration of its constituent units. An actuator is additionally called scalable if its force-to-weight ratio does not depend on the number of its member modules. In this work, we consider scalable collective actuators built from spherical catoms with two connection types: strong but fixed and weak but mobile. We investigate how to construct these actuators in such a way, as to maximize their force-to-weight ratio. We present a number of designs of high strength, whose force capacities significantly exceed those of similar actuators reported previously.

The term Programmable Matter (PM) describes the class of future meta-materials of programmable and controllable properties and behavior, e.g., able to autonomously transform into an arbitrary shape. The robotic approaches towards PM are based on the concept of cooperation of millions of micro-robots (modules), acting at a very fine length-scale and collectively imitating deformation of a macroscopically continuous material. Recent ideas about reconfiguration of a collective of modules to obtain a desired overall mechanical response are promising. However, they are limited by the strength of individual connections between modules. In the present work, we propose a way of arranging spherical modules into microstructures, in which some connections are fixed and mechanically stronger, and the rest are active (reconfigurable) but weaker. If the fixed connections are sufficiently strong, the proposed microstructures perform the function of collective actuation by exerting forces proportional to their volumes. Two variants of a linear-actuator microstructure are presented and studied in more detail. A rotary-actuator microstructure is also introduced.