Robust Approach Planning for Tumbling Targets with Uncertain Inertia via Koopman Prediction and Spherical Cap Coverage

This research addresses robust trajectory planning for a freely tumbling non-cooperative target with uncertain inertia estimates, accounting for both approach geometry under random attitudes and navigation error. Inertia errors propagate through nonlinear attitude dynamics to produce non-Gaussian docking-axis distributions, making prediction errors in obstacle and docking-corridor geometry difficult to incorporate accurately into trajectory optimization. A planning framework is, therefore, developed that combines Koopman-based sample prediction, optimal terminal docking-axis selection, and risk-constrained covariance control. A normalized Koopman–Galerkin model rapidly propagates inertia uncertainty, while coordinate transformations convert attitude uncertainty into trajectory-ensemble constraints under static geometry. A maximum-coverage spherical cap with a fixed angular radius is determined from the conical-corridor dimensions to select the optimal terminal docking-axis direction. Boundary-sample extraction and chance-constraint convexification are combined within sequential convex programming to jointly design the reference trajectory and feedback control law. In an existing attitude-propagation case, Koopman propagation of 1000 trajectories over 200 s achieved an approximately 245.7-fold speedup over the reference Runge–Kutta implementation. In a separate 150 s closed-loop approach comparison using shared feedback and disturbances, robust planning increased the geometric-criterion pass rate for the same 1000 translation–attitude combinations from 55.6% to 82.8%. Among the 1000 translational simulation runs in each group, 92.9% of the deterministic trajectories exceeded the control limit at least once, whereas no exceedance was observed in the robust group; mean cumulative control expenditure increased by 26.32%. These results support using inertia-distribution characteristics to improve approach geometry and control-constraint satisfaction under the specified conditions, while indicating that these improvements require additional maneuvering effort.