In this paper, we present a time-discrete, incremental methodology for modeling, at the microscopic and macroscopic level, the dynamics of distributed manipulation experiments using swarms of autonomous robots endowed with reactive controllers. The methodology is well-suited for nonspatial metrics since it does not take into account robots ’ trajectories or the spatial distribution of objects in the environment. The strength of the methodology lies in the fact that it has been generated by considering incremental abstraction steps, from real robots to macroscopic models, each with well-defined mappings between successive implementation levels. Precise heuristic criteria based on geometrical considerations and systematic tests with one or two real robots prevent the introduction of free parameters in the calibration procedure of models. As a consequence, we are able to generate highly abstracted macroscopic models that can capture the dynamics of a swarm of robots at the behavioral level while still being closely anchored to the characteristics of the physical set-up. Although this methodology has been and can be applied to other experiments in distributed manipulation (e.g., object aggregation and

Abstract — The problem is studied of achieving a specified formation among a group of mobile autonomous agents by distributed control. If convergence to a point is feasible, then more general formations are achievable too, so the focus is on convergence to a point (the agreement problem). Three formation strategies are studied and convergence is proved under certain conditions. Also, motivated by the question of whether collisions occur, formation evolution is studied. I.

We introduce a framework, called "physicomimetics," that provides distributed control of large collections of mobile physical agents in sensor networks. The agents sense and react to virtual forces, which are motivated by natural physics laws. Thus, physicomimetics is founded upon solid scientific principles. Furthermore, this framework provides an effective basis for self-organization, fault-tolerance, and self-repair. Three primary factors distinguish our framework from others that are related: an emphasis on minimality (e.g., cost effectiveness of large numbers of agents implies a need for expendable platforms with few sensors), ease of implementation, and run-time efficiency. Examples are shown of how this framework has been applied to construct various regular geometric lattice configurations (distributed sensing grids), as well as dynamic behavior for perimeter defense and surveillance. Analyses are provided that facilitate system understanding and predictability, including both qualitative and quantitative analyses of potential energy and a system phase transition. Physicomimetics has been implemented both in simulation and on a team of seven mobile robots. Specifics of the robotic embodiment are presented in the paper.

We present a decentralized, behavior-based approach to assembling and maintaining robot formations. Our approach dynamically grows formations from single robots into line segments and ultimately larger and more complex formations. Formation growth

Abstract — Real life deployment of robot formation cannot assume that robots are going to be correctly positioned to move in a particular configuration. To do so, we propose an approach that allows the group to determine autonomously the most appropriate assignment of positions in the formation. Our approach is distributed and uses directional visual perception to localize robots. Inter-robot communication allows them to share information on which robots are nearby, so that each can evaluate it ability to be the conductor of the group and assign formation positions to the other robots by minimizing repositioning. The assignment search is done using a distributed bounded depth-first with pruning search. The robot with the best score is selected as the conductor, and the other robots received from the conductor their assignment in the formation. Validation of our work is done in simulation and with Pioneer 2 robots. I.

Abstract — This paper studies the effects of the geometry of a mobile robot formation on the accuracy of the robots’ localization. The general case of heterogeneous (in terms of sensor accuracy) robot teams performing Cooperative Localization is considered. An analysis of the time evolution of the covariance matrix of the position estimates allows us to express the steady-state positioning uncertainty of the robots as an analytic function of the relative positions of the robots in the formation. This metric encapsulates the effect of formation geometry on the information content of the exteroceptive measurements, as well as the effect of the influx of uncertainty due to the errors in the robots ’ odometry. Thus, by minimizing the trace of the steady state covariance matrix with respect to the positions of the robots, the optimal robot configuration can be determined. Numerical experiments are presented, which indicate that it is possible to derive a practical rule for determining optimal formations, without the need to resort to extensive simulations, or experimentation. I.

From an engineering point of view, the problem of coordinating a set of autonomous, mobile robots for the purpose of cooperatively performing a task has been studied extensively over the past decade. In contrast, in this paper we aim at an understanding of the fundamental algorithmic limitations on what a set of autonomous mobile robots can or cannot achieve. We therefore study a hard task for a set of weak robots. The task is for the robots in the plane to form any arbitrary pattern that is given in advance. This task is fundamental in the sense that if the robots can form any pattern, they can agree on their respective roles in a subsequent, coordinated action. The robots are weak in several aspects. They are anonymous; they cannot explicitly communicate with each other, but only observe the positions of the others; they cannot remember the past; they operate in a very strong form of asynchronicity. We show that the tasks that such a system of robots can perform depend strongly on their common agreement about their environment, i.e., the readings of their environment sensors. If the robots have no common agreement about their environment, they cannot form an arbitrary pattern. If each robot has a compass needle that indicates North (the robot world is a flat surface, and compass needles are parallel), then any odd number of robots can form an arbitrary pattern, but an even number cannot (in the worst case). If each robot has two independent compass needles, say North and East, then any set of robots can form any pattern.

In many multi-robot applications, the specific assignment of goal configurations to robots is less important than the overall behavior of the robot formation. In such cases, it is convenient to define a permutation-invariant multi-robot formation as a set of robot configurations, without assigning specific configurations to specific robots. For the case of robots that translate in the plane, we can represent such a formation by the coefficients of a complex polynomial whose roots represent the robot configurations. Since these coefficients are invariant with respect to permutation of the roots of the polynomial, they provide an effective representation for permutation-invariant formations. In this paper, we extend this idea to build a full representation of a permutation-invariant formation space. We describe the properties of the representation, and show how it can be used to construct collision-free paths for permutationinvariant formations.

Abstract—In formation-maintenance (formation control) tasks, robots maintain their relative position with respect to their peers, according to a desired geometric shape. Previous work has examined formation-maintenance algorithms, based on formation control graphs, that ensure the theoretical stability of the formation. However, an exponential number of stable controllers exists. Thus a key question is how to select (construct) a formation controller that optimizes desired properties, such as sensor usage. We present a novel representation of the sensing capabilities of robots in formations, using a monitoring multigraph. We first show that graphtheoretic techniques can then be used to efficiently compute optimal sensing policies that maintain a given formation, while minimizing sensing costs. In particular, separation-bearing (distance-angle) control targets are automatically constructed for each individual robot in the formation, taking into account its specific sensor morphology. Then, we present a protocol allowing control graphs to be switched on line, to allow robots to adjust to sensory failures. We report on results from comprehensive experiments with physical and simulated robots. The results show that the use of the dynamic protocol allows formations of real robots to move significantly faster and with greater precision, while reducing the number of formation failures, due to sensor limitations. We also evaluate the sensitivity of our approach to communication reliability, and discuss opportunities and challenges raised by our approach. Index Terms—Coordinated movement, mobile robots, multirobot formations, multirobot systems. I.

We present an on-board robotic module which can determine relative positions among miniature robots. The module uses high-frequency modulated infrared emissions to enable nearby robots to determine the range, bearing, and message of the sender with a rapid update rate. A CSMA protocol is employed for scalable operation. We describe a technique for calculating the range and bearing between robots, which can be generalized for use with more sophisticated relative positioning systems. Using this method, we characterize the accuracy of positioning between robots and identify different sources of imprecision. Finally, the utility of this module is clearly demonstrated with several robotic formation experiments, where precise multi-robot formations are maintained throughout difficult maneuvers.