Kinetic theory for the emergence of complex behavior in social and economic systems

Stochastic Robotics: Complexity, Compositionality, and Scalability

Theodore Pavlic

Arizona State University


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.