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We propose the concept of a Force-Amplifying N-robot Transport System (Force-ANTS) to coordinate the manipulation forces from a group of robots in order to transport a heavy object in a planar environment. Our approach requires no explicit communication among robots. Instead, we prove that robots can use local measurements of the object’s motion at their attachment points as implicit information for force coordination. A leader (either a robot or human) can guide the whole group towards the destination by applying a relatively small force, whose effect is amplified by the follower robots as they align their forces with the leader’s. Two Force-ANTS implementations are introduced and analyzed, accounting for two different classes of object dynamics: small objects where kinetic friction dominates, and large objects where inertia and viscous friction dominate. Our approach can be used as a modular system for transporting heavy objects of various sizes in many real-life applications. Simulations with up to 1000 robots and experiments using four custom-built robots are conducted to validate our approach. We also conduct human–robot cooperation experiments where the human force is amplified by three follower robots.

As additive manufacturing of mechanical parts gains broad acceptance, efforts to embed electronic or electromechanical components in these parts are intensifying. We discuss recent work in printable electronics and introduce an alternative, which we call Bitblox. Bitblox are small, modular, interconnecting blocks that embed simple electromechanical connectivity and functionality. Not all blocks are identical; instead the unique combinations and positions of Bitblox within an assembly determine the mechanical and electrical properties of the assembly. We describe the design details of Bitblox, compare them to similar materials, and demonstrate their use in a working three-dimensional printer through several examples.

This paper proposes a self-assembling soft modular matter, called SoftCubes, where soft-bodied modules are disassembled into a flexible string by an external tension and self-assemble into the preprogrammed three-dimensional (3D) shape. The developed soft modular matter has three main design features. Firstly, entire modules of the 3D shape are serially connected. Such a structure allows all the modules to be disassembled by external tension. Secondly, the outer body of the modules and the connecting parts are made of soft stretchable elastomer. Due to the soft body of the modules, after disassembling, the serially connected modules become a highly flexible and soft string, and have an extreme shape adaptation capability. Also, if the external tension is removed, the preprogrammed 3D shape is recovered by the elastic restoring force of soft-bodied modules. Finally, embedded small permanent magnets induce magnetic self-assembling forces and maintain a mechanical robustness of the 3D shape of module assembly. Due to the magnetic self-assembly, the soft modules are precisely aligned with neighboring modules in a lattice structure. The paper also presents an algorithm to generate the serial connection path of modules for creating a given 3D shape. Various physical interactions between self-assembling module prototypes are visualized in two-dimensional motion tracking experiments. Finally, the shape reconfiguration ability of soft modular matter is demonstrated. SoftCubes is a new class of programmable modular matter where shape memory ability is embedded in the structure, and shows a physical implementation of various 3D shapes with a high resolution and a high scalability.

External actuation in self-reconfigurable modular robots promises to allow modules to shrink down in size. Synchronous external motions promise to allow fast convergence and assembly times. XBot is a modular system that uses synchronous external actuation, but has a limited range of reachable configurations stemming from a single motion primitive of a module rotating about another. This paper proposes to extend the motion primitives by using moves with two modules swinging in a dynamic chain. The feasibility of these motion primitives is proven experimentally. A parameterization of the external actuation motion profiles is explored to define a space of physically valid motion profiles. The larger the space, the more robust the motion primitives will be to inexact initial conditions and to imprecision in the external actuation mechanisms. In addition, this paper proves that a configuration of XBot meta-modules can reach any configuration using just these motion primitives.

Reconfigurable modular robots have the ability to use different gaits and configurations to perform various tasks. A rolling gait is the fastest currently implemented gait available for traversal over level ground and shows dramatic improvements in efficiency. In this work, we analyze and implement a sensor-based feedback controller to achieve dynamic rolling for a loop robot. The robot senses its position relative to the ground and changes its shape as it rolls. This shape is such that its center of gravity is maintained to be in front of its contact point with the ground, so in effect the robot is continuously falling and thus accelerates forward. Using simulation and experimental results, we show how the desired shape can be varied to achieve higher terminal velocities. The highest velocity achieved in this work is 26 module lengths per second (1.6 m/s) which is believed to be the fastest gait yet implemented for an untethered modular robot. One of the major findings is that more elongated shapes achieve higher terminal velocities than rounder shapes. We demonstrate that this trend holds going up inclines as well as down. We show that rounder shapes have lower specific resistance and are thus more energy efficient. The control scheme is scalable to an arbitrary number of modules, shown here using eight to 14 modules.

In this paper we define a complexity ratio that measures the degree to which a robot is self-replicating based on the number and complexity of subsystems that it can assemble to form a functional replica. We also quantify how structured the environment must be in order for a robot to function. This calculation uses Sanderson's concept of parts entropy. Together, the complexity measure of the robot and environmental entropy provide quantitative benchmarks to assess the state of the art in the subfield of self-replicating robotic systems, and provide goals for the design of future systems. We demonstrate these principles with three prototype systems that show different degrees of robotic self-replication. The first robot is controlled by a microprocessor and consists of five subsystems. The second has no microprocessor and is implemented as a finite-state machine consisting of discrete logic chips that are distributed over five subsystems. The third design consists of six subsystems and is able to handle greater environmental entropy. These systems demonstrate the desired progression towards self-replicating robots consisting of greater numbers of subsystems, each of lower complexity, and which are able to function in environments with increasing levels of disorder.

In recent years self-reconfigurable modular robots have gained increasing interest from part of the international robotic community. Although recent robots of this type are characterized by advanced electro-mechanical designs, the development of their supporting control techniques have only registered strong results in the field of locomotion problems, while the manipulation capabilities of existing systems still appear to be quite limited. Aiming to provide a contribution along this latter direction, in this paper we propose a computationally distributed technique for controlling the motion of any tree-structured chain resulting from reconfiguration in its operational space. The presented strategy, which could actually be adopted when dealing with any kind of chain-based modular robotic system, turns out to be particularly well suited to self-reconfigurable structures for three main reasons: (i) it is not based on any explicit role assignment; all of the modules can be added, removed or exchanged online as required, with no impact on the overall control architecture; (ii) each module has only a very limited set of local information that must be known a priori and can be totally unaware of the remaining part of the chain; (iii) no external centralized controller is necessary; basic local processing and communication units onboard every module and a simple man—machine interface providing high-level commands are enough. A global self-coordinating behavior is automatically exhibited by the proposed technique at power-on or immediately after any configuration change as the result of a number of repeated data exchanges, performed online along the chain at every sampling interval. Although achievable performances depend on the available communication bandwidth, the convergence towards a final position error of zero is, however, always guaranteed. Moreover, because the computational burden required by every module is extremely light, the proposed technique represents an effective control solution that can be easily implemented onboard many of the low-cost and small control platforms available on existing self-reconfigurable robots.

We present a decentralized algorithmic approach to automatically building user-specified three-dimensional structures from modular units. Our bipartite system comprises passive units (blocks), responsible for embodying the structure and determining where further units can legally be attached, and active units (robots), responsible for transporting passive units. The algorithmic issues are correspondingly decomposed into two parts: (1) deciding where passive units may be attached; and (2) getting them to those locations. For the first part, we give simple, scalable rules for attachment and prove that they will reliably lead to the construction of any desired structure from a large class of three-dimensional shapes. For the second part, we compare three approaches: random movement, systematic search and gradient-following; each approach is successively faster but requires more communication overhead and/or unit capabilities. The system we describe enables guaranteed construction of desired structures using very simple agent algorithms, taking a high-level specification as the only required input. The topic of collective construction is related to the problems of programmed self-assembly and self-reconfiguration in modular robots, and the rules governing block attachment presented here may be usefully applied to such systems.

Designing distributed controllers for self-reconfiguring modular robots has been consistently challenging. We have developed a reinforcement learning approach which can be used both to automate controller design and to adapt robot behavior on-line. In this paper, we report on our study of reinforcement learning in the domain of self-reconfigurable modular robots: the underlying assumptions, the applicable algorithms and the issues of partial observability, large search spaces and local optima. We propose and validate experimentally in simulation a number of techniques designed to address these and other scalability issues that arise in applying machine learning to distributed systems such as modular robots. We discuss ways to make learning faster, more robust and amenable to on-line application by giving scaffolding to the learning agents in the form of policy representation, structured experience and additional information. With enough structure modular robots can run learning algorithms to both automate the generation of distributed controllers, and adapt to the changing environment and deliver on the self-organization promise with less interference from human designers, programmers and operators.

Distributed systems frequently exhibit properties of interest which span multiple entities. These properties cannot easily be recognized from any single entity, but can be readily detected by combining the knowledge of multiple entities. Testing for distributed properties is especially important in debugging or verifying software for modular robots. We have developed a technique we call distributed watchpoint triggers which can efficiently recognize distributed conditions. Our watchpoint description language can handle a variety of temporal, spatial and logical properties spanning multiple robots. In this paper we present the specification language, describe the distributed online mechanism for detecting distributed conditions in a running system and evaluate the performance of our implementation.

Posture sensing techniques for Compliant Framed Modular Mobile Robots (CFMMR) are presented in this paper using a new Relative Posture Sensor (RPS) combined with standard sensors in a tiered fusion algorithm. The RPS consists of a compliant frame member instrumented with strain gauges and associated algorithms such that the RPS can predict relative posture. The first tier of the fusion algorithm uses traditional Kalman filters and rigid axle kinematic models to predict the global posture of each axle. In the second tier, a Relative Measurement Stochastic Posture Error Correction (RMSPEC) algorithm is introduced to fuse disparate axle data using the RPS. Experimental results are derived from over 60 trials operating the robot on high traction carpet, low traction sand, and sand with rugged rocky terrain. Results comparing the proposed sensory system with standard sensory systems demonstrate that the proposed techniques yield accurate relative posture estimates and posture regulation even on rugged terrain, which is a vast improvement over previous results.

Previous work on self-reconfiguring modular robots has concentrated primarily on designing hardware and developing reconfiguration algorithms tied to specific hardware systems. In this paper, we introduce a generic model for lattice-based self-reconfigurable robots and present several generic locomotion algorithms that use this model. The algorithms presented here are inspired by cellular automata, using geometric rules to control module actions. The actuation model used is a general one, assuming only that modules can generally move over the surface of a group of modules. These algorithms can then be instantiated onto a variety of particular systems. Correctness proofs of many of the rule sets are also given for the generic geometry; this analysis can carry over to the instantiated algorithms to provide different systems with correct locomotion algorithms. We also present techniques for automated analysis that can be used for algorithms that are too complex to be easily analyzed by hand.

Self-reconfigurable robots are versatile systems consisting of large numbers of independent modules. Effective use of these systems requires parallel actuation and planning, both for efficiency and independence from a central controller. In this paper we present the PacMan algorithm, a technique for distributed actuation and planning for systems with two- or three-dimensional unit-compressible modules. We give two versions of the algorithm along with correctness analysis. We also analyze the parallel actuation capability of the algorithm, showing that it will not deadlock and will avoid disconnecting the robot. We have implemented PacMan on the Crystal robot, a hardware system developed in our lab, and we present experiments and discuss the feasibility of large-scale implementation.

In this paper we address a reconfiguration planning method for locomotion of a homogeneous modular robotic system and we conduct an experiment to verify that the planned locomotion can be realized by hardware. Our recently developed module is self-reconfigurable. A group of the modules can thus generate various three-dimensional robotic structures and motions. Although the module itself is a simple mechanism, self-reconfiguration planning for locomotion presents a computationally difficult problem due to the many combinatorial possibilities of modular configurations. In this paper, we develop a two-layered planning method for locomotion of a class of regular structures. This locomotion mode is based on multi-module blocks. The upper layer plans the overall cluster motion called flow to realize locomotion along a given desired trajectory; the lower layer determines locally cooperative module motions, called motion schemes, based on a rule database. A planning simulation demonstrates that this approach effectively solves the complicated planning problem. Besides the fundamental motion capacity of the module, the hardware feasibility of the planning locomotion is verified through a self-reconfiguration experiment using the prototype modules we have developed.

A modular robotic system consists of standardized joint and link units that can be assembled into various kinematic configurations for different types of tasks. For the control and simulation of such a system, manual derivation of the kinematic and dynamic models, as well as the error model for kinematic calibration, require tremendous effort, because the models constantly change as the robot geometry is altered after module reconfiguration. This paper presents a framework to facilitate the model-generation procedure for the control and simulation of the modular robot system. A graph technique, termed kinematic graphs and realized through assembly incidence matrices (AIM), is introduced to represent the module-assembly sequence and robot geometry. The kinematics and dynamics are formulated based on a local representation of the theory of Lie groups and Lie algebras. The automatic model-generation procedure starts with a given assembly graph of the modular robot. Kinematic, dynamic, and error models of the robot are then established, based on the local representations and iterative graph-traversing algorithms. This approach can be applied to a modular robot with both serial and branch-type geometries, and arbitrary degrees of freedom. Furthermore, the AIM of the robot naturally leads to solving the task-oriented optimal configuration problem in modular robots. There is no need to maintain a huge library of robot models, and the footprint of the overall software system can be reduced.

This Special Issue contains 13 papers that cover the most recent advances in the area of self-reconfiguring modular robots. Self-reconfiguring robots are modular robots that can change their morphology and topology. Each module is a robot by itself. These systems promise great flexibility compared to fixed-shape robots. By keeping the design of each individual module relatively simple and through mass production, selfreconfiguring robots can offer an affordable platform to perform a variety of tasks. They have the potential to perform self-diagnosis and self-repair. Moreover, a simple design lends itself well to miniaturization. Potential applications included reconnaissance missions in search and rescue operations, self-assembly (both in space and at the micro-scale), and self-replication on other planets or moons. However, the design, control, communication, and planning for such systems give rise to many challenges. Most of the papers in this issue were presented at the Workshop on Self-Reconfiguring Modular Robots held at the 2006 “Robotics: Science & Systems” conference in Philadelphia, PA. Submissions for the workshop were reviewed by the Program Committee for this workshop, which consisted of Greg Chirikjian (Johns Hopkins), Eric Klavins (University of Washington), Hod Lipson (Cornell), Mark Moll (Rice), Daniela Rus (MIT), Behnam Salemi (ISI/USC), Wei-Min Shen (ISI/USC), and Mark Yim (University of Pennsylvania). After the workshop, workshop participants and the wider robotics community were invited to submit journallength papers, which were submitted to another round of reviews. As part of the workshop, a panel discussion was held to discuss the Grand Challenges for the field. The key technical difficulties that were identified were: Scaling up: Typically, experiments are performed only on a small number of modules. As the number of modules increases, new challenges arise such as power distribution, efficient communication, and fault / noise tolerance. Self-repairing systems: Self-repair requires modules to identify what the global arrangement of modules should be and what each individual module’s role is. Even deciding whether a system requires repair is already a challenging problem. Self-assembly can be seen as the most extreme form of self-repair. Self-replication: Although simple self-replicating systems exist, it remains a formidable challenge to design a modular robot that can assemble copies of itself from elementary parts. Miniaturization: At the micro-/nano-scale, biological processes efficiently use stochastic motions that are robust to intrinsic noise. Most of the current robotic systems overcome uncertainty through brute force. Bridging this gap, and coming up with efficient algorithms at the nanoscale is a big challenge. In this issue, Brener et al. analyze current designs for modular robots using results from crystallography. Campbell and Pillai describe a method for collective actuation of modules, thereby forming more powerful meta-modules. De Rosa et al. bring tools for debugging and verification for distributed software systems to the domain of modular robots. Fitch and Butler introduce a new locomotion algorithm for lattice-type modular robots that scales up to millions of modules. Gilpin et al. describe a novel approach to shape formation through self-disassembly. Kurokawa et al. describe recent advances in distributed self-reconfiguration. Lee et al. introduce a formal framework to analyze the complexity of self-replicating systems and present several