Autonomous attitude planning for gravity wave detection using hybrid convex optimization

The autonomous attitude planning in the gravity wave detection tasks poses great technical challenges because of its highly nonlinear time-varying terminal constraints, free-time problem structure, nonlinear dynamical constraints, and other path constraints. To solve this problem efficiently and robustly, this paper combines the idea of semi-definite programming (SDP) and second-order cone programming (SOCP). A successive penalization procedure is employed in the basic framework of SDP to ensure the iterative feasibility and convergence from each random initial guess toward the true solution. Focusing on the commonly encountered slow computational speed of the conventional SDP, a block-division strategy is proposed to decrease the dimensions of the design variable. Additionally, a strengthened SOCP reformulation constraint is introduced in the iterative problem to obtain the concave-convergence property to speed up the convergence. Theoretical Analyses are presented to verify the convergence of the method. A large number of numerical simulations are performed to validate the effectiveness, efficiency, and robustness of the proposed method compared to the advanced convex optimization-based method, iterative rank minimization (IRM), and nonlinear programming solver, GPOPS-II (SNOPT). Results show that the proposed SPCR method could improve the 20%∼70% solving success rate and reduce 80%∼90% of necessary computational time.