Collaborative Research: Modeling, Analysis, and Control of the Spatio-temporal Dynamics of Swarm Robotic Systems

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Massive populations, or swarms, of low-cost autonomous robots have the potential to collectively perform tasks over very large domains and time scales, succeeding even in the presence of failures, errors, and disturbances. It is becoming feasible to create robotic swarms in practice due to ongoing advances in computing, sensing, actuation, power, control, and 3D printing technologies. In recent years, the miniaturization of these technologies has led to many novel robot platforms for swarm applications, including micro aerial vehicles. However, it remains a challenge to reliably control arbitrary numbers of such resource-constrained robots in unknown environments where global information and communication are limited or undependable. This research project aims to overcome this challenge by developing a rigorous framework for the scalable control of robotic swarms in realistic environments. The framework combines techniques from the fields of fluid dynamics, signal reconstruction, control theory, and optimization. This work provides a theoretically grounded approach for automatically programming robotic swarms to perform a diverse set of tasks of wide benefit to society, including environmental monitoring and exploration, disaster recovery, security operations, and even biomedical imaging and targeted cancer therapies at the nanoscale. This project develops a formal methodology for analyzing and controlling the spatiotemporal dynamics of robotic swarms that are to be deployed in complex unknown environments. The designed robot control policies incorporate stochastic behaviors such as random encounters with environmental features and produce target collective behaviors within a specified degree of confidence. The confidence estimates are computed using a novel application of vortex methods, originally derived for fluid dynamic models and recently adapted to obtain continuum limits of discrete swarm models that incorporate pairwise interaction rules for maintenance of group structure. The control approach uses new computational algorithms for compressive sensing to reconstruct scalar environmental fields from sparse robot sensor data and to design efficient strategies for robot data collection. The methodology is demonstrated with a case study on designing control policies for micro aerial vehicles that are tasked to pollinate a crop field. Both computer models and testbed field experiments are used to validate theoretical predictions for the confidence estimates on system performance. Beyond robotics, the project provides analytical tools for a deeper understanding of the complex macroscopic behaviors of systems that can be represented with similar models, including non-well-mixed chemical reaction networks and natural swarms such as social insect colonies.