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The space mission planning process is considered as a hybrid optimal control problem. Hybrid optimal control problems are problems that include categorical variables in the problem formulation. For example, an interplanetary trajectory may consist of a sequence of low thrust arcs, impulses and planetary flybys. However, for each choice of the structure of the mission, for example, for a particular choice of the number of planetary flybys to be used, there is a corresponding optimal trajectory. It is not a priori clear which structure will yield the most efficient mission. In this work we present a mathematical framework for describing such problems and solution methods for the hybrid optimal control problem based on evolutionary principles that have the potential for being a robust solver of such problems. As an example, the methods are used to find the optimal choice of three asteroids to visit in sequence, out of a set of eight candidate asteroids, in order to minimize the fuel required.

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In this paper, we develop a novel algorithm for spacecraft trajectory planning in an environment cluttered with many geometrically-fixed obstacles. The Spherical Expansion and Sequential Convex Programming (SE-SCP) algorithm first uses a spherical-expansionbased sampling algorithm to explore the workspace. Once a path is found from the start position to the goal position, the algorithm generates a locally optimal trajectory within the homotopy class using sequential convex programming. If the number of samples tends to infinity, then the SE-SCP trajectory converges to the globally optimal trajectory in the workspace. The SE-SCP algorithm is computationally efficient, therefore it can be used for real-time applications on resource-constrained systems. We also present results of numerical simulations and comparisons with existing algorithms.

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