This presentation discusses continuum deformation modeling of coordination of a large number of aerial vehicles treated as particles of deformable bodies (or continuum). Assuming desired coordination of an unmanned aerial system (UAS) team is the solution of Laplace equation, Lagrangian and Eulerian continuum mechanics will be applied to safely plan UAS coordination in a finite airspace. The Lagrangian continuum mechanics is used to manage large-scale coordination of a UAS team in a cluttered environment when the total number of agents is fixed. In this context, we optimize a large-scale continuum deformation coordination, and formally specify and verify collision-free collective motion with minimal communication and computation overhead, enabling distance between individual UAVs to significantly change while assuring the vehicles do not collide. Furthermore, the Eulerian continuum mechanics can be applied to achieve freely scalable coordination and manage traffic coordination in a finite airspace. Using the Eulerian description of continuum mechanics, the space and time allocated to an individual UAS can be effectively managed and the airspace capacity can be maximized through controlling UAS inflow and outflow at the airspace boundaries with minimum computation overhead. In particular, the airspace can be classified into planned and unplanned spaces by dynamically updating planned-unplanned airspace boundaries while nominal coordination is obtained as the solution of a governing PDE with spatiotemporal cyber-physical parameters.
Dr. Hossein Rastgoftar is currently an assistant professor in the Aerospace and Mechanical Engineering Department at the University of Arizona. Prior to this, he was an assistant professor of Mechanical Engineering at Villanova University and an adjunct assistant professor at the University of Michigan from 2020 to 2021. He was also an assistant research scientist (2017 to 2020) and a postdoctoral researcher (2015 to 2017) in the Aerospace Engineering Department at the University of Michigan. He received his Ph.D. in Mechanical Engineering from Drexel University in 2015. Rastgoftar’s areas of interest span decision-making under uncertainty, human-robotic interaction, swarm robotics, system autonomy, UAS traffic management, intelligent transportation, formal specification and verification, and finite-state abstraction of dynamical systems. He is the sole author of the book “Continuum Deformation of Multi-Agent System” published by Springer, springer.com/gp/book/9783319415932.