Multi-arc Spacecraft Trajectory Optimization

Multi-arc optimal control problems regard dynamical systems subject to interior discontinuities or constraints. The related necessary conditions for an extremal include a set of multipoint corner conditions, to enforce in the numerical solution process. This research shows that a judicious choice of the state variables useful to describe the system dynamics leads to identifying closed-form jump relations for the costate variables, starting from the previously mentioned corner conditions. This allows the sequential solution of the multi-arc optimal control problem of interest, with two apparent advantages: (a) the parameter set for an indirect-type solution methodology retains the same size of the one defined for a single-arc problem and (b) the multipoint conditions are satisfied in the sequential solution process. The multi-arc formulation is applicable to a variety of space mission scenarios, and two challenging problems are addressed as illustrative examples, i.e., (1) low-thrust Earth orbit transfer with eclipse constraints on the available thrust, and (2) low-thrust Earth-Moon orbit transfer in a high-fidelity dynamical framework. For problem (1), the multi-arc formulation avoids regularization and averaging, which were extensively used in preceding works, while for problem (2) the multi-arc formulation allows a high-fidelity description of orbital motion. In both cases, all the necessary conditions for optimality can be satisfied to a great accuracy in the numerical solution process.