Transcription-Induced Failure Modes in 6-DOF Rocket Landing Trajectory Optimization

TL;DR

This paper uncovers hidden vulnerabilities in trajectory optimization for rocket landing caused by discretization errors, revealing that certain transcription methods are unreliable and that implicit schemes can outperform explicit ones in practice.

Contribution

It introduces an adversarial objective to expose transcription failures and provides theoretical analysis explaining why some methods are more reliable in rocket landing trajectory optimization.

Findings

Only 3 out of 14 transcription methods meet validation criteria.

Implicit GL2 scheme matches RK6 in fidelity despite lower order.

Implicit GL2 outperforms RK6 in speed and robustness in lateral-divert scenarios.

Abstract

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.