Considers the problem of resolving conflicts involving multiple aircraft. First a framework is formulated where conflicts may be solved efficiently. Within this framework, the conflict resolution problem is shown to be a non-convex, quadratically constrained quadratic program. Cheap lower bounds to this problem are developed based on positive semidefinite relaxations of the dual of this program. A unique method is proposed to systematically determine the regions of the state-space where the conflict resolution algorithm is guaranteed to perform well within the proposed framework.
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