Finite-Burn Linear Targeting Algorithm for Autonomous Path Planning and Guidance

In path planning and guidance applications, linear targeting through differential corrections is a classical approach for identifying feasible solutions that meet specified mission and trajectory constraints. However, to date, these methods relied on the assumption that the associated correction maneuvers were impulsive in nature. This impulsive assumption is generally reasonable when the duration of the engine burn is small. However, this approximation breaks down when lower thrust engines are employed as the duration of the burn becomes more significant. In these cases, an impulsive linear targeting algorithm is inadequate. Often times, low-thrust problems of this type are solved from the perspective of optimal trajectory design and depend on numerical methods like nonlinear programming. These methods, however, are generally considered prohibitive for autonomous flight applications, where computational resources are limited and optimality is not always as important as feasibility. The present study focuses on the theoretical development and numerical validation of a linear targeting algorithm capable of accommodating finite burn maneuvers. Examples are presented to contrast the performance of this new targeting process against more classical impulsive targeting methods. The examples presented focus largely on precision entry applications, but the finite burn targeting process itself is applicable across a broad set of scenarios and fields.