Transcription-Induced Failure Modes in 6-DOF Rocket Landing Trajectory Optimization
For practitioners of trajectory optimization, this work exposes hidden failure modes in common transcription methods and provides guidance on selecting robust discretizations.
The paper reveals that transcription errors in discretizing continuous dynamics for rocket landing trajectory optimization can cause NLP solvers to produce infeasible or suboptimal trajectories. Among fourteen transcription methods tested on a 6-DOF problem, only three passed rigorous validation, and a fourth-order implicit scheme (GL2) unexpectedly matched or outperformed a sixth-order explicit method (RK6) in both accuracy and solve speed.
Solving optimal control problems via large-scale NLP solvers depends on discretizing continuous dynamics. Yet, this transcription step hides critical vulnerabilities-most notably truncation error and invariant drift-that can drive solvers toward dynamically infeasible or suboptimal trajectories. To expose these hidden failures, we introduce a problem- and transcription-agnostic adversarial objective that leverages the structure of local truncation-error bounds to aggressively amplify such defects. When applied to a 6-DOF rocket-landing problem, we reveal a stark reliability gap: of fourteen transcription methods tested, only three satisfy rigorous validation criteria. These results also expose a striking performance inversion: even in the absence of classical stiffness, a fourth-order implicit scheme (GL2) matches the fidelity of a sixth-order explicit method (RK6). Using B-series expansions and symplectic Runge-Kutta theorems, we isolate the specific truncation errors and quaternion-invariant drift responsible for these failures. Crucially, these theoretical vulnerabilities dictate operational performance: in practical lateral-divert scenarios, the implicit GL2 consistently outperforms the explicit RK6 in both end-to-end solve speed and robustness.