Study on trajectory optimization of multiple aircraft using homotopy method

Due to the continuous economic growth and globalization, the demand of the commercial air traffic is increasing continuously. Along with that, the congestion in airspaces near airports is a serious problem. To solve the problem, Air Traffic Management is gathering attention. One of the most difficult situations for air traffic controlers is to control multiple aircrafts in congested areas. This paper focuses on guidance of two aircrafts merging problem. Currently, air traffic controlers judge it by their knowledge coming from experience or by using their intuition. In this paper, simultaneous optimization method for trajectory and sequence is proposed. The biggest characteristic of the proposed method is that initial assumption is defined with the condition that two aircrafts interferes at a merging point. And at the end of a numerical caluculation, an optimal solution is given and interfere avoidance will be performed without selecting the sequence by hand. An unique coordinate system called Space-Time coordinate system was applied to construct a model. Homotopy method is used as a non-linear simultaneous equation solver. The interference avoidance is conducted by using terminal time constraint.