15,072 research outputs found
A macroscopic analytical model of collaboration in distributed robotic systems
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
Stochastic differential equations for evolutionary dynamics with demographic noise and mutations
We present a general framework to describe the evolutionary dynamics of an
arbitrary number of types in finite populations based on stochastic
differential equations (SDE). For large, but finite populations this allows to
include demographic noise without requiring explicit simulations. Instead, the
population size only rescales the amplitude of the noise. Moreover, this
framework admits the inclusion of mutations between different types, provided
that mutation rates, , are not too small compared to the inverse
population size 1/N. This ensures that all types are almost always represented
in the population and that the occasional extinction of one type does not
result in an extended absence of that type. For this limits the use
of SDE's, but in this case there are well established alternative
approximations based on time scale separation. We illustrate our approach by a
Rock-Scissors-Paper game with mutations, where we demonstrate excellent
agreement with simulation based results for sufficiently large populations. In
the absence of mutations the excellent agreement extends to small population
sizes.Comment: 8 pages, 2 figures, accepted for publication in Physical Review
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