Safe Affine Transformation-Based Guidance of a Large-Scale Multi-Quadcopter System (MQS)

Abstract

This paper studies the problem of affine transformation-based guidance of a multi-quadcopter system (MQS) in an obstacle-laden environment. Such MQSs can perform a variety of cooperative tasks including information collection, inspection mapping, disinfection, and firefighting. The MQS affine transformation is an approach to a decentralized leaderfollower coordination guided by 𝑛 + 1 leaders, where leaders are located at vertices of an 𝑛-D simplex, called leading simplex, at any time 𝑡. The remaining agents are followers acquiring the desired affine transformation via local communication. Followers are contained in a rigid-size ball at any time 𝑡 but they can be distributed either inside or outside the leading simplex. By eigendecomposition of the affine transformation coordination, safety in a large-scale MQS coordination can be ensured by constraining eigenvalues of the affine transformation. Given the initial and final configurations of the MQS, A* search is applied to optimally plan safe coordination of a large-scale MQS minimizing the travel distance between the the initial and final configuration. The paper also proposes a proximity-based communication topology for followers to assign communication weights with their inneighbors and acquire the desired coordination with minimal computation cost.