Abstract:
In recent years, simulation and analysis methods from chemical reaction
network theory have been adopted by engineers designing swarms
consisting of possibly thousands of individually inexpensive robots
that together form teams that achieve global performance objectives
with minimal explicit coordination. In these large numbers, the design
and analysis of robot teams that each operate by deterministic automata
is intractable. Stochastic robotics provides one approach to combating
this problem. In this framework, individual robot behaviors are driven
by stochastic control policies, and so the individuals interact with
each other and their environment in much the same way as entities of a
gas. Thus, the set of transition rates deployed across robots become a
lower-order subspace on which to design control strategies that achieve
statistical performance metrics. Moreover, the motion of mobile robots
in such a framework are well characterized by advection--diffusion
processes that are controlled in a similar fashion. In this talk, I
briefly survey several recently proposed methods for designing such
systems of stochastic robots. Additionally, I describe how these
chemical reaction networks have been augmented with the continuous
dynamics of the background environment to form stochastic hybrid
systems amenable to use of extended generators from the theory of
piecewise deterministic processes. For this latter case, I will present
recent results on the application of these methods in describing
collective transport of objects by teams of Aphaenogaster cockerelli
ants, where the study was conducted with bio-inspired robotics in mind.
If time permits, recent results will be summarized on other approaches
to decentralized control of task-processing agents, including one
strategy that optimizes stochastic volunteering policies on networks of
selfish task processing agents that nonetheless converge to
self-sacrificing Nash equilibria that approximate the ideal
Pareto-optimal solution. |