Despite their growing popularity, swarms of robots remain limited by the operating time of each individual. We present algorithms that allow a human to sculpt a swarm of robots into a shape that persists in space perpetually, independent of onboard energy constraints, such as batteries. Robots generate a path through a shape such that robots cycle in and out of the shape. Robots inside the shape react to human initiated changes and adapt the path through the shape accordingly. Robots outside the shape recharge and return to the shape so that the shape can persist indefinitely. The presented algorithms communicate shape changes throughout the swarm using message passing and robot motion. These algorithms enable the swarm to persist through any arbitrary changes to the shape. We describe these algorithms in detail and present their performance in simulation and on a swarm of mobile robots. The result is a swarm behavior more suitable for extended duration, dynamic shape-based tasks in applications, such as entertainment, agriculture, and emergency response.

Complexity, cost, and power requirements for the actuation of individual robots can play a large factor in limiting the size of robotic swarms. Here we present PCBot, a minimalist robot that can precisely move on an orbital shake table using a bi-stable solenoid actuator built directly into its PCB. This allows the actuator to be built as part of the automated PCB manufacturing process, greatly reducing the impact it has on manual assembly. Thanks to this novel actuator design, PCBot has merely five major components and can be assembled in under 20 seconds, potentially enabling them to be easily mass-manufactured. Here we present the electro-magnetic and mechanical design of PCBot. Additionally, a prototype robot is used to demonstrate its ability to move in a straight line as well as follow given paths.

This paper describes a distributed algorithm for computing the number of robots in a swarm, only requiring communication with neighboring robots. The algorithm can adjust the estimated count when the number of robots in the swarm changes, such as the addition or removal of robots. Probabilistic guarantees are given, which show the accuracy of this method, and the trade-off between accuracy, speed, and adaptability to changing numbers. The proposed approach is demonstrated in simulation as well as a real swarm of robots.

In this paper, we propose an abstraction that captures high-level formation and location-based swarm behaviors, and an automated control synthesis framework to generate correct-by-construction behaviors. Our abstraction includes symbols representing both possible formations and physical locations in the workspace. We allow users to write linear temporal logic (LTL) specifications over the symbols to specify high-level tasks for the swarm. To satisfy a specification, we automatically synthesize a centralized symbolic plan, and environment and swarm-size-dependent motion controllers that are guaranteed to implement the symbolic transitions. In addition, using integer programming (IP), we assign robots to different sub-swarms to execute the synthesized symbolic plan. Our framework gives insights into controlling a large fleet of autonomous robots to achieve complex tasks which require composition of behaviors at different locations and coordination among different groups of robots in a correct-by-construction way. We demonstrate the proposed framework in simulation with 16 UAVs and 8 ground vehicles, and on a physical platform with 20 ground robots, showcasing the generality of the approach and discussing the implications of controlling constrained physical hardware.

Robotic self-assembly allows robots to join to form useful, on-demand structures. Unfortunately, the methods employed by most self-assembling robotic swarms compromise this promise of adaptability through their use of fixed docking locations, which impair a swarm's ability to handle imperfections in the structural lattice resulting from load deflection or imperfect robot manufacture; these concerns worsen as swarm size increases. Inspired by the amorphous structures built by cells and social insects, FireAnt3D uses a novel docking mechanism, the 3D continuous dock, to attach to like robots regardless of alignment. FireAnt3D demonstrates the use of the 3D continuous docks, as well as how a robot can use such docks to connect to like robots and locomote over arbitrary 3D arrangements of its peers. The research outlined in this paper presents a profoundly different approach to docking and locomotion during self-assembly and addresses longstanding challenges in the field of robotic self-assembly.

In this article, we consider the problem of planar graph-based simultaneous localization and mapping (SLAM) that involves both poses of the autonomous agent and positions of observed landmarks. We present complex (CPL)-SLAM, an efficient and certifiably correct algorithm to solve planar graph-based SLAM using the complex number representation. We formulate and simplify planar graph-based SLAM as the maximum likelihood estimation on the product of unit complex numbers, and relax this nonconvex quadratic complex optimization problem to convex complex semidefinite programming (SDP). Furthermore, we simplify the corresponding complex SDP to Riemannian staircase optimization (RSO) on the complex oblique manifold that can be solved with the Riemannian trust region method. In addition, we prove that the SDP relaxation and RSO simplification are tight as long as the noise magnitude is below a certain threshold. The efficacy of this work is validated through applications of CPL-SLAM and comparisons with existing state-of-the-art methods on planar graph-based SLAM, which indicates that our proposed algorithm is capable of solving planar graph-based SLAM certifiably, and is more efficient in numerical computation and more robust to measurement noise than existing state-of-the-art methods. The C++ code for CPL-SLAM is available at https://github.com/MurpheyLab/CPL-SLAM.

The task of shape formation in robot swarms can often be reduced to two tasks - assigning goal locations to each robot and creating a collision-free path to that goal. In this article, we present a distributed algorithm that solves these tasks concurrently, enabling a swarm of robots to move and form a shape quickly and without collision. A user can specify a desired shape as an image, send that to a swarm of identically programmed robots, and the swarm will move all robots to goal locations within the desired shape. This algorithm was executed on a swarm of up to 1024 simulated robots and a swarm of 100 real robots, showing that it reliably converges to all robots forming the shape.

In this paper, we present CPL-Sync, a certifiably correct algorithm to solve planar pose graph optimization (PGO) using the complex number representation. We formulate planar PGO as the maximum likelihood estimation (MLE) on the product of unit complex numbers, and relax this nonconvex quadratic complex optimization problem to complex semidefinite programming (SDP). Furthermore, we simplify the corresponding semidefinite programming to Riemannian staircase optimization (RSO) on complex oblique manifolds that can be solved with the Riemannian trust region (RTR) method. In addition, we prove that the SDP relaxation and RSO simplification are tight as long as the noise magnitude is below a certain threshold. The efficacy of this work is validated through comparisons with existing methods as well as applications on planar PGO in simultaneous localization and mapping (SLAM), which indicates that the proposed algorithm is capable of solving planar PGO certifiably, and is more efficient in numerical computation and more robust to measurement noises than existing state-of-the-art methods. The C++ code for CPL-Sync is available at https://github.com/fantaosha/CPL-Sync.

Specialization has always been a tool for work distribution and simplification in nature and in distributed robotics. We present a novel approach to use hardware specialization hierarchically to enhance the capabilities of a swarm without increasing complexity, allowing a numerous group of robots to benefit from the extended features of a few to complete a task that was impossible for them before. We tested the concept under a simulated environment with a classical distributed robotics problem, shape formation, and validated the simulated results against a real experiment.

Nature offers many examples of organisms coming together to form self-assembling structures. The attachment methods these organisms employ allow them to grab onto others' bodies, often without need for specific alignment or orientation, an ability absent from most existing robotic self-assembling structures, which require complicated sensing and specific alignment. This paper presents FireAnt, a modular 2D robot that demonstrates full-body continuous docks, an attachment mechanism able to attach anywhere onto other robots at any orientation, eliminating the need for alignment mechanisms and complex sensors. Such docks allow FireAnt to climb over copies of itself, something critical to self-assembling structures. This paper first discusses the design of FireAnt before presenting test results that show the strength and reliability of the continuous docks and demonstrate FireAnt's ability to traverse an environment consisting of inert FireAnt robots. The work presented in this paper provides a docking mechanism that can minimize the mechanical complexity of modular robots and will allow the creation of swarms of rigid and adaptable self-assembling structures.

Local communication and sensing between individuals are frequently used for control in multi-robot systems. However, in current flying multi-robot systems, such as swarms of quadrotors, these abilities are often only emulated using global communication and global position sensing. This is mainly due to the complexity, cost, weight, or power requirements for such sensors. Here we present a system that can allow for more natural swarming behaviors by enabling direct bearing and elevation sensing, as well as communication between nearby rotor-craft. This system takes advantage of the existing motion of the vehicles propellers, is low power, and can be adapted to existing vehicles with only simple modifications. We describe the system, present a working prototype, show performance of this prototype, and conclude by describing future work integrating the system into a rotor-craft swarm.

Climbing robots have many potential applications including maintenance, monitoring, search and rescue, and self-assembly. While numerous climbing designs have been investigated, most are limited to stiff components. Flippy (Fig. 1) is a small, flipping biped robot with a soft, flexible body and on-board power and control. Due to its built-in compliance, flipping gait, and corkscrew gripper, it can autonomously climb up and down surfaces held at any angle relative to gravity and transition from one surface to another, without complex sensing or control. In this paper, we demonstrate the robot's ability to flip consistently over a flat Velcro surface and 2D Velcro track, where it reliably climbs vertically, upside down and back to a flat surface, completing all the interior transitions in-between.

Self-folding provides an efficient way of creating complex 3D geometries from 2D composites. However, the precision of self-folding structures is often limited by the use of open-loop folding mechanisms. In this paper we demonstrate feedback-controlled self-folding using a shape memory polymer and optical sensors to accurately control folding angles. We present a method of quickly and inexpensively fabricating large collectives of self-folding autonomous robots that can be transported in flat configurations prior to autonomous deployment at target destinations. To demonstrate this, we build a collective of robots that is manufactured in one continuous laminar composite. Individual robots in the collective detach from one other, self-fold into pre-programmed configurations and navigate by phototaxis. This method could be applied to a broad range of applications where logistics necessitate compact transport and where external manipulation is difficult or expensive, such as in space applications or delivering search-and-rescue robots in cluttered environments.

Complexity, cost, and power requirements for actuation of individual robots are large factors in limiting the size of robotic swarms. Here we present a prototype robotic system that allows for externally powered motion in 2D without sacrificing individual autonomy, which simplifies the robot hardware, possibly enabling larger swarm sizes. This is accomplished using a table surface that is moving in an orbital fashion, and where robots can move to any point on the table surface simply through a series of carefully timed attachment and detachment steps. We present a model for the robot's motion, and use this model to create a motion controller that allows the robot to move from its current position to any other position on the table in approximately a straight line. We show this controller working in simulation as well as on an experimental hardware system.

Social insects have evolved to self-assemble ad-hoc structures from their bodies to quickly adapt to unexpected obstacles and situations. Inspired by these natural systems, we present an autonomous tread-based robot which is capable of using its own body as a building block for assembling structures. We analytically assess the optimality of the robot design, and experimentally test its ability to climb over like robots under varying conditions. Finally, using a simple self-assembly algorithm relying on only local sensing, robot prototypes are used to demonstrate the self-assembly of a 2D pyramid structure.

There is a widely recognized need for improved STEM education and increased technological literacy. Robots represent a promising educational tool with potentially large impact, due to their broad appeal and wide relevance; however, many existing educational robot platforms have cost as a barrier to widespread use. Here we present AERobot, a simple low-cost robot that can be easily used for introductory programming and robotics teaching, starting from a primary or middle school level. The hardware is open-source and can be built for ~$10 per robot, making it possible for each student to have (and keep) their own robot, while still encompassing a rich sensor suite enabling a variety of activities. A free, open-source graphical programming environment allows students without previous programming experience to command the robot. We report on the results of three sessions of a one-week pilot course held in the summer of 2014 by STEM summer camp i2 Camp.

Roboticists, biologists, and chemists are now producing large populations of simple robots, but controlling large populations of robots with limited capabilities is difficult, due to communication and onboard-computation constraints. Direct human control of large populations seems even more challenging. In this paper we investigate control of mobile robots that move in a 2D workspace using three different system models. We focus on a model that uses broadcast control inputs specified in the global reference frame. In an obstacle-free workspace this system model is uncontrollable because it has only two controllable degrees of freedom - all robots receive the same inputs and move uniformly. We prove that adding a single obstacle can make the system controllable, for any number of robots. We provide a position control algorithm, and demonstrate through extensive testing with human subjects that many manipulation tasks can be reliably completed, even by novice users, under this system model, with performance benefits compared to the alternate models. We compare the sensing, computation, communication, time, and bandwidth costs for all three system models. Results are validated with extensive simulations and hardware experiments using over 100 robots.

In current robotics research there is a vast body of work on algorithms and control methods for groups of decentralized cooperating robots, called a swarm or collective. These algorithms are generally meant to control collectives of hundreds or even thousands of robots; however, for reasons of cost, time, or complexity, they are generally validated in simulation only, or on a group of a few tens of robots. To address this issue, this paper presents Kilobot, a low-cost robot designed to make testing collective algorithms on hundreds or thousands of robots accessible to robotics researchers. To enable the possibility of large Kilobot collectives where the number of robots is an order of magnitude larger than the largest that exist today, each robot is made with only $14 worth of parts and takes 5 minutes to assemble. Furthermore, the robot design allows a single user to easily operate a large Kilobot collective, such as programming, powering on, and charging all robots, which would be difficult or impossible to do with many existing robotic systems.

A collective of robots can together complete a task that is beyond the capabilities of any of its individual robots. One property of a robotic collective that allows it to complete such a task is the shape of the collective. One method to form that shape is to form it at a size proportional to the number of robots in that collective, i.e. scalably. In our previous work, scalably forming the shape of the collective required that each robot know the total number of robots in the collective. In this work we present a method called S-DASH, which now allows a collective to scalably form a shape without knowing how many robots are in the collective. Furthermore, S-DASH will change the size of the shape to reflect the addition or removal of robots from the collective. This paper also provides demonstrations of S-DASH running on a simulated collective of robots.

Flexible and reliable connection is critical for self-reconfiguration, self-assembly, or self-healing. However, most existing connection mechanisms suffer from a deficiency that a connection would seize itself if one end malfunctions or is out of service. To mitigate this limitation on self-healing, this paper presents a new SINGO connector that can establish or disengage a connection even if one end of the connection is not operational. We describe the design and the prototype of the connector and demonstrate its performance by both theoretical analysis and physical experimentations.

This paper presents a bio-inspired, distributed control algorithm calledTENTACLESfor a group of radio robots to move, self-configure and maintain communication between some critical entities (such as humans, command centers, or other systems) in an unknown environment. The basic idea is to direct robots' explorative movements to grow ¿tentacles¿ from entities and establish links when tentacles meet. This approach can self-heal failures of robots and improve communication coverage and quality over time. Experiments in simulations and real robots have shown positive results.

A collective of robots can together complete a task that is beyond the capabilities of any of its individual robots. One property of a robotic collective that allows it to complete such a task is the shape of the collective. In this paper, we present a distributed control method, called DASH, to enable a collective of robots to robustly and consistently form and maintain a pre-defined shape. This control method allows the shape that is formed to be at a scale proportional to the number of robots in the collective. If this collective shape is damaged through the un-controlled movement, removal, or addition of some members of the collective, the existing members will recover the desired shape, proportional to the new number of robots in the collective. We also analyze this control method in terms of class of acceptable shapes and discuss the convergence to the desired shape.

As the ability to produce a large number of small, simple robotic agents improves, it becomes essential to control the behavior of these robots in such a way that the sum of their actions gives rise to the desired overall result. These robots are modeled as homogeneous, distributed robots, with only one simple short range sensor. Our simple robots are tasked to form and hold a desired swarm shape, independent of the total number of agents. If this shape is damaged by the removal of some of the robots, the remaining agents will recover the former shape, but on a smaller scale. These shapes can also have a pattern such as a picture or drawing displayed on them by controlling the individual robots color, symbolically representing the differentiation of agents within the swarm. This pattern will resize to fit the existing swarm. With the ability to synchronize in time, the swarm gains the ability to change the pattern displayed, resulting in a moving image.

Superbot consists of Lego-like but autonomous robotic modules that can reconfigure into different systems for different tasks. Examples of configurable systems include rolling tracks or wheels (for efficient travel), spiders or centipedes (for climbing), snakes (for burrowing in ground), and climbers (for inspection and repair in space). This video shows several configurations and behaviors that are new for modular and reconfigurable robots. Each SuperBot module is a complete robotic system and has a power supply, micro- controllers, sensors, communication, three degrees of freedom, and six connecting faces (front, back, left, right, up and down) to dynamically connect to other modules. This design allows flexible bending, docking, and continuous rotation. A single module can move forward, back, left, right, flip-over, and rotate as a wheel. Modules can communication with each other for totally distributed control and can support arbitrary module reshuffling during their operation. The modules have both internal and external sensors for monitoring self-status and environmental parameters. They can form arbitrary configurations (graphs) and can control these configurations for different functionality such as locomotion, manipulation, and self-repair. This video shows the latest status the SuperBot modules and all these behaviors were made in just one week. The fact that SuperBot can achieve so much in so short a time demonstrates the unique value of modular, multifunctional and self-reconfigurable robots.

This paper presents a modular and reconfigurable robot for multiple locomotion modes based on reconfigurable modules. Each mode consists of characteristics for the environment type, speed, turning-ability, energy-efficiency, and recover ability from failures. The paper demonstrates this solution by the Superbot robot that combines advantages from MTRAN, CONRO and others. Experimental results, both in real robots and in simulation, have shown the validity of the approach and demonstrated the movements of forward, backward, turn, sidewinder, maneuver, and travel on batteries up to 500 meters on a flat terrain. In physics-based simulation, Superbot can perform as snake, caterpillar, insect, spider, rolling track, H-walker, etc., and move 1.0 meter/second on flat terrain with less than 6 W/module, and climb slopes of no less 40 degrees

Docking between independent groups of self-reconfigurable robotic modules enables the merger of two or more independent self-reconfigurable robots. This ability allows independent reconfigurable robots in the same environment to join together to complete a task that would otherwise not be possible with the individual robots prior to merging. The challenges for this task include: (1) coordinate and align two independent self-reconfigurable robots using the docking guidance system available only at the connectors of the docking modules; (2) overcome the inevitable errors in the alignment by a novel and coordinated movements from both docking ends; (3) ensure the secure connection at the end of docking; (4) switch configuration and let modules to discover the changes and new connections so that the two docked robots will move as a single coherent robot. We have developed methods for overcome these challenging problems and accomplished for the first time an actual docking between two independent CONRO robots each with multiple modules.

In this paper, we introduce and describe the notion of a robotic enzyme, and how it can use properties that are similar to biological enzymes to autonomously self-replicate. We test the idea of robotic enzymes using a virtual environment that simulates the currently existing modular robots in a physically accurate way. We describe the self-replicating features of robotic enzymes, and how they could be used to autonomously self-replicate for multiple generations, limited only by the amount of modules in the environment.