Direct Collocation for Numerical Optimal Control of Second-Order ODE

Léo Simpson, Armin Nurkanović, Moritz Diehl

correcthigh confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper’s SC/PC formulations, complexity counts (variables, constraints, and Jacobian nonzeros), and accuracy claims match the candidate solution. Both rely on the same stage-wise polynomial parameterizations (paper’s semi-Hermite basis; model’s Hermite–Lagrange) and arrive at identical formulas (Table I in the paper). The paper emphasizes the q̇-independence assumption for the sparsity benefit and the equal global order (between d and 2d), which the model also assumes; a minor nuance in the paper about PC’s higher local accuracy in q (but not in q̇) was omitted in the model but does not affect the main claims.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The paper delivers a clear and practically meaningful comparison between SC and PC for second-order ODE OCPs, formalizing the sparsity/complexity advantages of PC under a natural \$\dot q\$-independence assumption and confirming equal accuracy. The semi-Hermite parameterization is well motivated and leads to the claimed sparsity metrics. The main results align with standard collocation theory and are numerically corroborated. Minor additions (explicit nonzero-count derivations and crisper statement of assumptions) would improve completeness and reproducibility.