| We study the problem of optimal multi-agent, coordination and related applications. The dissertation consists of three parts. In the first part, the problem of optimal coordinated motions for multiple agents moving on a plane is studied. In the second part, we study the optimal resolution maneuvers for multiple aircraft flying in three dimensional airspace. In the last part, the problem of optimal collision avoidance and formation switching on Riemannian manifold is studied. In all three parts, the motions of the participating agents need to satisfy some separation constraints, while the underlying space that the agents move on is two dimensional Euclidean space, three dimensional Euclidean space, and general Riemannian manifolds, respectively. We try to find the optimal coordinated motions that minimize a certain energy cost function. Various necessary conditions for the optimal solutions are obtained and numerical algorithms are proposed to compute them. |
