Three-Dimensional Aircraft Conflict Resolution Based on Smoothing Methods

Abstract

The development of an automated and optimal conflict predicting and resolution strategy is one of the most important components in successfully implementing the Next Generation Air Transportation System concept. The conflict resolution problem, which occurs between multiple aircraft described by a three-degree-of-freedom nonlinear point-mass model, is the focus of this study. A novel method for handling nondifferentiable disjunctive conflict avoidance constraints is developed by using smoothing functions, which are constructed by integrating a probability density function. Thus, the conflict resolution problem is posed as an optimal control problem and discretized into a nonlinear programming problem via the direct transcription approach with a Radau collocation point. The approximation error obtained using the smoothing functions is examined through sensitivity analysis. An estimable linear relationship is established between the approximation error and the smoothing parameter, which indicates that the approximation error is controllable. Numerical results show that the proposed approach efficiently produces conflict-free and feasible maneuvers. The approximation errors are also evaluated and found to be minimal and negligible.