Sensitivity Methods Applied to Orbital Pursuit-Evasion
In this work, sensitivity methods are examined as a means to solve and analyze the problem of orbital pursuit-evasion (PE). Orbital PE is a two-sided spacecraft trajectory optimization problem characterized by high dimensionality and nonlinearity. Modern methods for solving problems of this sort employ generic, computationally intensive techniques, including random search methods such as the genetic algorithm; collocation methods based on discrete approximation; or combinations of these methods. The advantages of these methods are relatively high degrees of robustness, straightforward implementation, and ease of handling state and control constraints. Yet we note the disadvantages: chiefly high computation load, as well as absence of insight into the problem, and accuracy of the result. Sensitivity methods provide corresponding strengths in each of these areas. We present novel sensitivity analysis techniques that may be useful in other optimization problems featuring high dimensionality, nonlinearity, and/or state and control constraints. The techniques shown include a novel solution method; a computationally efficient feedback control technique; a means of sketching barrier surfaces; and the use of hybrid one-sided/two-sided controllers for sophisticated emergent behavior. We also introduce a new formulation of the problem incorporating a minimum-altitude constraint, and we make an initial investigation of a sensitivity-based method of handling state constraints. Overall, our results suggest that sensitivity methods can provide useful augmentation to techniques that rely more heavily upon computational power, and may be particularly valuable for implementation in an onboard control algorithm.