  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 leader-follower 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
eigen-decomposition 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-star 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 in-neighbors and
acquire the desired coordination with minimal computation cost.
