The objective of this dissertation is to use second-order cone programming (SOCP) for autonomous trajectory planning of optimal control problems arisen from aerospace applications. Rendezvous and proximity operations (RPO) of spacecraft in any general orbit include various constraints on acquisition of docking axis point, approach corridor, plume impingement inhibition, relative velocity, and rate of change of thrust. By a lossless relaxation technique, this highly constrained RPO problem (non-convex) is transformed into a relaxed problem the solution of which is proven to be the same as that of the original problem. Then a novel successive approximation method, forming a sequence of subproblems with linear and time-varying dynamics, is applied to solve the relaxed problem. Each subproblem is a SOCP problem which can be solved by state-of-the-art primal-dual interior point method. Constraints on collision avoidance, or more generally concave inequality state constraints, from any aerospace application also make a problem non-convex. A successive linearization method is employed to linearize the concave inequality constraints. It is proven that the successive solutions from this method globally converge to the solution of the original problem and the converged solution has no conservativeness. Further non-convex constraints include nonlinear terminal constraints which are handled by first approximated with first-order expansions, and then compensated with second-order corrections to improve the robustness of the approach. The effectiveness of the methodology proposed in this dissertation is supported by various applications in highly constrained RPO, finite-thrust orbital transfers, and optimal launch ascent.
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