Aircraft conflict resolution: Lie-Poisson reduction for game on SE(2)
J. Zhang, S. S. Sastry · Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228) · 2002
In this paper, the problem of conflict resolution for two non-cooperative aircraft at a fixed altitude is considered. We formulate the problem into a differential game, and then apply the Lie-Poisson reduction on the dual of the Lie algebra of the special Euclidean group. The reduced Hamiltonian dynamics is thus derived and can be integrated explicitly, backwards in time. We use hybrid automata to describe the solution to the reduced dynamics as well as the aircraft maneuvers in the game. The safe portion of the target-set frontier is calculated, and the solution to the boundary of the safe portion is also derived.