Autonomous rendezvous and proximity operations (RPO) of spacecraft require the capability of on-board planning and executing highly constrained trajectories without ground support. This paper presents a general and rigorous methodology and algorithmic procedure toward this goal with the target vehicle that can be in an arbitrary orbit. The RPO problem is formulated as a nonlinear optimal control problem, subject to various state and control inequality constraints and equality constraints on interior points and terminal conditions. By a lossless relaxation technique, a relaxed problem is formed the solution of which is proven to be equivalent to that of the original RPO problem.The relaxed problem is then solved by a novel successive solution process, in which the solutions of a sequence of constrained subproblems with linear, time-varying dynamics are sought. After discretization, each of these problems becomes a second-order cone programming problem. Their solutions, if exist, are guaranteed to be found by a primal-dual interior-point algorithm. The efficacy of the proposed methodology is strongly supported by numerical experiments.
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