In this paper, we provide a survey on available numerical approaches for solving low-thrust trajectory optimization problems. First, a general mathematical framework based on hybrid optimal control will be presented. This formulation and their elements, namely objective function, continuous and discrete state and controls, and discrete and continuous dynamics, will serve as a basis for discussion throughout the whole manuscript. Thereafter, solution approaches for classical continuous optimal control problems will be briefly introduced and their application to low-thrust trajectory optimization will be discussed. A special emphasis will be placed on the extension of the classical techniques to solve hybrid optimal control problems. Finally, an extensive review of traditional and state-of-the art methodologies and tools will be presented. They will be categorized regarding their solution approach, the objective function, the state variables, the dynamical model, and their application to planetocentric or interplanetary transfers.

Uncertainty in aircraft trajectory planning and prediction generates major challenges for the future air traffic management system. Therefore, understanding and managing uncertainty will be necessary to realize improvements in air traffic capacity, safety, efficiency, and environmental impact. Meteorology (in particular, winds) represents one of the most relevant sources of uncertainty. In the present work, a framework based on optimal control is introduced to address the problem of robust and efficient trajectory planning under wind forecast uncertainty, which is modeled with probabilistic forecasts generated by ensemble prediction systems. The proposed methodology is applied to a flight planning scenario under a free-routing operational paradigm and employed to compute trajectories for different sets of user preferences, exploring the trade-off between average flight cost and predictability. Results show how the impact of wind forecast uncertainty in trajectory predictability at a pretactical planning horizon can be not only quantified, but also reduced through the application of the proposed approach.

Maneuver detection and estimation is deemed crucial for maintaining catalogs of Resident Space Objects (RSOs) as it helps to avoid sets of duplicated objects and track correlation issues. In fact, maneuvers, along with launches and break-up events, are the main source of potential new object detections during RSOs cataloging activities. For the continuous and reliable provision of Space Situational Awareness (SSA) and Space Traffic Management (STM) services, a challenging trade-off between detection time and characterization accuracy of maneuvers needs to be performed. In this paper, two novel and operationally feasible methodologies are proposed for maneuver detection and estimation. The first, a track-to-orbit methodology, uses a pre-maneuver orbit to linearize the dynamics and estimate the single burn that minimizes the residuals of the post-maneuver tracks. The second, an orbit-to-orbit methodology, estimates the double burn that solves a minimization problem between the pre-maneuver and post-maneuver orbits. Both methods, based on an optimal control approach, are not only proposed to tackle the maneuver estimation problem but also to be integrated on operational and robust association frameworks. Results are presented for optical scenarios with both simulated and real data, providing insightful conclusions on the capabilities, performance and limitations of the proposed methods. Particular emphasis is given to the importance of the track association, since a single track is usually not enough to perform a reliable estimation of the maneuver. Besides, the capability of the methods to provide a solution to the association problem, even when not perfectly characterizing the true maneuver, is discussed.