Aircraft conflict resolution: Lie-Poisson reduction for game on SE(2)

Author

Zhang, Jun ; Sastry, Shankar

Author_Institution

Dept. of Electr. Eng. & Comput. Sci., California Univ., Berkeley, CA, USA

Volume

2

fYear

2001

fDate

2001

Firstpage

1663

Abstract

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

Keywords

Lie algebras; Lie groups; air traffic control; aircraft; automata theory; collision avoidance; differential games; duality (mathematics); dynamics; integration; optimal control; safety; stochastic processes; Euclidean group; Lie algebra dual; Lie-Poisson reduction; SE(2) differential game; aircraft conflict resolution; aircraft maneuvers; backwards integration; boundary; fixed altitude; hybrid automata; noncooperative aircraft; reduced Hamiltonian dynamics; safe portion; target set frontier; Aerospace control; Aerospace materials; Aerospace safety; Air safety; Air traffic control; Aircraft propulsion; Algebra; Automata; Fuel economy; Game theory;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2001. Proceedings of the 40th IEEE Conference on

Conference_Location

Orlando, FL

Print_ISBN

0-7803-7061-9

Type

conf

DOI

10.1109/.2001.981140

Filename

981140