Trajectory optimization for n-vehicles using a reduced order formulation

Different methods of optimizing terrain following and terrain masking trajectories have been investigated as an extension of earlier reduced order formulations. This paper examines simultaneous optimal path planning for multiple aircraft maneuvering in the same terrain section, where both vehicles are flying at a constant velocity. First, equations are derived for the simultaneous optimal path planning of two vehicles. Next, those equations are expanded to include an n-number of vehicles. Two forms of the 2D equations of notion are investigated - a simplified form and a local tangent plane set. In addition, the trajectories can be optimized with respect to two different criteria - a minimum time case and a terrain masking case.