Distributed Protocols, Nonlinear State-Dependent Networks, and Human-Swarm Interactions

Abstract

This dissertation aims to explore intuitive control mechanisms for distributed protocols over networks with a goal of understanding state-dependent networks and attaining high-level human-swarm interactions. Two canonical models for network dynamics are examined from the perspective of intuitive coarse input control, namely, the linear advection dynamics with applications including formation control and load balancing; and a pair of nonlinear complex-valued dynamics which describes phase locking in coupled oscillators. Dynamic invariance properties and the topology of the basins of attraction are shown to relate to the underlying network topology which can then be exploited for coarse control. A novel bearing-compass protocol for formation control, relying only on bearing measurements between agents, is introduced which is particularly suitable for manipulation due to its translation and scaling invariance features. This formation control dynamics can be framed as a state-dependent network, with weighted edges in the network dependent on relative measurements between the pairs of nodes incident to each edge. Formulating measures that quantify the effective access points within the network, leader selection algorithms are provided relying on submodular optimization theory. Key to understanding the bearing-compass dynamics is bearing rigidity theory which is used to describe the information content of the bearing measurements within the network. Optimizing the graph topology and access point selection with respect to rigidity measures, performant bearing-compass dynamics is generated which is well suited to external manipulation by coarse control. Generalized notions of rigidity formed from different measurements are derived and give rise to generalized measurement-based distributed protocols - a family of state-dependent network dynamics. Supporting the theory developed in this dissertation, a distributed unicycle ground vehicles platform was developed and exercised with a subset of the aforementioned distributed protocols.