Density-Based Guidance and Control for Decentralized Autonomous Swarms

Abstract

Autonomous swarms are an ensemble of thousands of expendable, ideally low-cost, systemsor robots working collaboratively to accomplish missions in harsh environments, where a single monolithic system is either too risky or impractical for successful completion of the collective objective. Due to their distinguishing advantages in redundancy, reconfigurability, and robustness, guidance and control of autonomous swarms have become a rapidly emerging research area, with particularly strong interest in future space missions. This dissertation addresses both the guidance and control problems in a hierarchically decomposed framework in order to keep each level tractable while ensuring mathematical guarantees such as stability and convergence at each level of the hierarchy. As a result, the proposed solutions at each level employ different mathematical tools and methods, while the overall framework is unified through the notion of spatial density. The first part of the dissertation addresses the guidance level of the proposed hierarchicalframework by focusing on high-level density sequence design that interfaces with lower-level swarm control. It presents additional results extending prior work on Markov chain-based synthesis of desired density sequences. New constraints are introduced into the Markov chain synthesis optimization problem to provide additional control over the transitional behavior of target density sequences, particularly with respect to the spatial trajectory probabilities of individual agents. The second and core part of the dissertation addresses the control level of the hierar-chical framework by developing a decentralized, density-based swarm control algorithm for tracking desired spatial density distributions. The proposed control algorithm assumes heat equation-based transition dynamics for the swarm and employs a density feedback control law based on nonparametric local density estimation from local agent measurements. Sta- bility and convergence of the resulting closed-loop system are established in the continuum limit, yielding asymptotic guarantees with increasing numbers of agents. In addition, formal collision avoidance guarantees are derived for a class of kernel functions used in the local density estimation process. Finally, the control framework is extended with an adaptive mechanism that enables decentralized, online optimization of the density estimation param- eters, allowing each agent to adjust its estimation strategy in real time using only local information.