We review existing approaches to mathematical modeling and analysis of multi-agent systems in which complex collective behavior arises out of local interactions between many simple agents. Though the behavior of an individual agent can be considered to be stochastic and unpredictable, the collective behavior of such systems can have a simple probabilistic description. We show that a class of mathematical models that describe the dynamics of collective behavior of multi-agent systems can be written down from the details of the individual agent controller. The models are valid for Markov or memoryless agents, in which each agents future state depends only on its present state and not any of the past states. We illustrate the approach by analyzing in detail applications from the robotics domain: collaboration and foraging in groups of robots.
In the robotics domain, Sugawara and coworkers @cite_62 @cite_26 developed simple state-based analytical models of cooperative foraging in groups of communicating and non-co -mmu -ni -cating robots and studied them quantitatively. Although these models are similar to ours, they are overly simplified and fail to take crucial interactions among robots into account. In separate papers, we have analyzed collaborative @cite_46 and foraging @cite_29 behavior in groups of robots. The focus of that work is on realistic models and the comparison of the models' predictions to experimental and simulations results. For example, in @cite_46 , we considered the same model of collaborative stick-pulling presented here, but studied it under the same conditions as the experiments. In @cite_29 , we found that we had to include avoiding-while-searching and wall-avoiding states in the model in order to obtain good quantitative agreement between the model and results of sensor-based simulations. The focus of this paper, on the other hand, is to show that there is a principled way to construct a macroscopic model of collective dynamics of a MAS, and, more importantly, a practical recipe'' for creating such a model from the details of the microscopic controller.
@cite_29 @cite_46 @cite_62 @cite_26
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In multi-robot applications, such as foraging or collection tasks, interference, which results from competition for space between spatially extended robots, can significantly affect the performance of the group. We present a mathematical model of foraging in a homogeneous multi-robot system, with the goal of understanding quantitatively the effects of interference. We examine two foraging scenarios: a simplified collection task where the robots only collect objects, and a foraging task, where they find objects and deliver them to some pre-specified “home” location. In the first case we find that the overall group performance improves as the system size growss however, interference causes this improvement to be sublinear, and as a result, each robot's individual performance decreases as the group size increases. We also examine the full foraging task where robots collect objects and deliver them home. We find an optimal group size that maximizes group performance. For larger group sizes, the group performance declines. However, again due to the effects of interference, the individual robot's performance is a monotonically decreasing function of the group size. We validate both models by comparing their predictions to results of sensor-based simulations in a multi-robot system and find good agreement between theory and simulations data. In this article, we present a macroscopic analytical model of collaboration in a group of reactive robots. The model consists of a series of coupled differential equations that describe the dynamics of group behavior. After presenting the general model, we analyze in detail a case study of collaboration, the stick-pulling experiment, studied experimentally and in simulation by (Autonomous Robots, 11, 149-171). The robots' task is to pull sticks out of their holes, and it can be successfully achieved only through the collaboration of two robots. There is no explicit communication or coordination between the robots. Unlike microscopic simulations (sensor-based or using a probabilistic numerical model), in which computational time scales with the robot group size, the macroscopic model is computationally efficient, because its solutions are independent of robot group size. Analysis reproduces several qualitative conclusions of : namely, the different dynamical regimes for different values of the ratio of robots to sticks, the existence of optimal control parameters that maximize system performance as a function of group size, and the transition from superlinear to sublinear performance as the number of robots is increased. We study the efficiency of cooperative behavior in a society of interacting agents. After reviewing the problem and defining the concept of swarm intelligence, we examine the collective behavior of many-body active clusters through the task of gathering pucks in a field. We used a simple robot with a drive system and the simplest means of interaction; a light and some sensors. The effectiveness of group behavior was studied for various (homogeneous, localized) puck distributions in a real experiment, simulations, and analysis. To evaluate the efficiency of group behavior, we examined the scaling relation between the task completion time and the number of robots, and the relation between the interaction duration and the efficiency of the group. We also found that a critical density for efficiency when the interaction distance is finite. These results show that cooperation between elements using a simple interaction strongly enhances the performance of the group compared to independent individuals. We have researched the efficiency of cooperative behavior of interacting multirobots. In this paper, we generalize the definition of swarm intelligence and examine the emergence of the generalized swarm intelligence (here we call it “swarm function”) through the task of gathering pucks in a field by interacting simple robots. This robot has a drive system and the simplest means of interaction. The effectiveness of group behavior was studied for various (homogeneous, localized) puck distributions. To evaluate the efficiency of group behavior, we proposed a scaling relation between the task completion time and the number of robots, and examined the relation between the interaction duration and the efficiency of the group. We also proposed a simplified state transition diagram of the group and analysed their characteristics using it.