The work described is part of a long term program of introducing institutional robotics, a novel framework for the coordination of robot teams that stems from institutional economics concepts. Under the framework, institutions are cumulative sets of persistent artificial modifications made to the environment or to the internal mechanisms of a subset of agents, thought to be functional for the collective order. In this article we introduce a formal model of institutional controllers based on Petri nets. We define executable Petri nets—an extension of Petri nets that takes into account robot actions and sensing—to design, program, and execute institutional controllers. We use a generalized stochastic Petri net view of the robot team controlled by the institutional controllers to model and analyze the stochastic performance of the resulting distributed robotic system. The ability of our formalism to replicate results obtained using other approaches is assessed through realistic simulations of up to 40 e-puck robots. In particular, we model a robot swarm and its institutional controller with the goal of maintaining wireless connectivity, and successfully compare our model predictions and simulation results with previously reported results, obtained by using finite state automaton models and controllers.

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 Ijspeert et al. [ 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 Ijspeert et al.: 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.