Quasi-spectral predictive guidance for autonomous rendezvous and docking with state triggered phase transition and non-convex path constraint

This article presents a predictive guidance architecture for autonomous low thrust spacecraft rendezvous and docking (RVD) using robust Quasi-Spectral Model Predictive Static Programming. This work parametrizes the control history as a truncated set of basis function coefficients, thereby reducing the number of optimising variables by over 300 fold when compared to complete grid transcription method while preserving the quality of the solution within a margin of 0.4% of optimum. The robustness of the architecture is enhanced through safeguarded backtracking line search and adaptive trust region through iterative refinement. The non-convex Keep out Zone (KOZ) is convexified through successive linearisation using the rotating hyperplanes and embedding them directly into the sensitivity formulation of QS-MPSP. This enables the pure quadratic formulation of constraints at each iteration. The state-triggered constraints are employed with smooth tangent blending enabling autonomous transition between the approach and docking phase without any discontinuity in the constraint Jacobian. The proposed architecture is validated across two different mission scenario of Keep out Zone avoidance and line of sight (LOS) docking achieving a mean solve time of 1.494 s and 0.419 s respective on a standard computing platform. A 500 run open loop Monte carlo campaign also validated the robustness of the proposed method with 100% convergence within millimeter level terminal error. The closed loop validation of the guidance model is performed with non linear equations of motion considering Earth’s Oblateness (J 2 ) as perturbation and the solver converges with 100% across 100 randomized samples within the mission tolerances for each mission phase.