Autonomous Trajectory Planning for Rendezvous and Proximity Operations by Conic Optimization

Abstract

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.

Survey of convex optimization for aerospace applications

“…[18,19]. Spacecraft rendezvous and proximity operations with the target spacecraft in any Keplerian orbit, which corresponds to a highly nonlinear optimal control problem, were solved by successive second-order cone programming (SOCP) [20][21][22][23]. The application of convex optimization in the spacecraft rendezvous guidance problem can also be found in Refs.…”

“…Nevertheless, in some special cases convergence can be proved. For instance, when concave constraints are successively linearized within the framework of SOCP, the corresponding successive solution procedure is theoretically proved to converge [20]. Another representative example is that convergence is proved when an iterative rank minimizing approach is used to approximate the nonconvex rank-one constraint [31,54].…”

Docking algorithm for flexible microsatellite mock-ups on planar air-bearing test-bench

“…Its computation requires the use of convex linear and quadratic programming. In the papers [14,15] proposed a second-order coneprogramming-based methodology to solve the rendezvous and proximity operations problem. Another approach is to apply the inverse dynamics in the virtual domain method for rapid sub-optimal docking trajectory generation.…”

Autonomous Trajectory Planning by Convex Optimization

“…Nevertheless, the gap in the knowledge is that those methods are all based on the linearized model which becomes inaccurate or even invalid when the relative distance is not sufficient small. More importantly, they are not able to incorporate various kinds of constraints that are necessary in practice [9], such as those on approach corridor, hold points, plume impingement inhibition and relative velocity [10].…”

“…Refs. [21,25,26] successfully applied the SOCP-based approach to solve powered descent guidance for Mars landing, which inspired the work of applying it to the RPO problem in this chapter [9].…”