Safe Multiquadcopter System Continuum Deformation Over Moving Frames

This paper proposes a new scalable model for coordination of multiple quadcopter systems by treating collective motion as continuum deformation over a moving frame. The quadcopters are considered as particles in a 2-D deformable body evolving in a 3-D motion space. The 2-D continuum reference frame (CRF) can arbitrarily translate and rotate in a 3-D motion space for maneuverability. Furthermore, a quadcopter team can significantly deform over the CRF presenting risk of interagent collisions. The formulation is therefore proven in this paper to guarantee interagent collision avoidance and quadcopter containment. Quadcopter team deformation is guided by N
_L
≥ 3 leader quadcopters initially placed at the vertices of a convex polygon denoted as a leading convex polygon. The CRF is then assigned based on independent leader quadcopters' 3-D positions defined by a homogeneous deformation, which, in turn, dictates follower motions. A local communication protocol is defined for the followers to acquire the desired continuum deformation. By formal characterization of the leading convex polygon deformation, both interagent collision avoidance and quadcopter containment are guaranteed in a large-scale continuum deformation coordination. A quadcopter team with 40 agents is simulated to illustrate a large-scale collective descent defined by continuum deformation coordination over a reference frame moving in the longitudinal plane.