Multiresolution Aircraft Guidance in a Spatiotemporally-varying Threat Field

We consider the problem of generating an optimal aircraft reference trajectory in a horizontal plane, where the objective is to minimize exposure to a spatiotemporally varying scalar field. We consider a special case, where this field is timeinvariant, and we discuss optimal trajectory generation for an aircraft kinematic model based on firstand second-order necessary conditions of optimal control. Next, we consider the general case, with the additional assumption that the knowledge of this field is available in vehicle-centric multiresolution detail. For this general problem, we propose a hybrid algorithm that combines (continuous) trajectory optimization with a (discrete) geometric path-planning method. This path-planning method uses wavelet-based multiresolution cell decompositions to find a path to the destination through regions where the field intensity is known with lesser detail. The results of this geometric path-planning algorithm provide a terminal penalty function for the trajectory optimization problem. We provide illustrative numerical simulation results for the proposed algorithm.