A practical direct optimal control formulation for interplanetary trajectory design must balance modeling fidelity, numerical robustness, and implementation simplicity. This paper revisits zero?order?hold (ZOH) transcriptions with that balance in mind, focusing on three deliberate departures from standard practice: a) the use of variable time grids, b) smooth overparameterized encodings for vector controls and boundary conditions, and c) systematic cross?benchmarks on multiple dynamical models, including low?thrust, solar sailing, equinoctial elements, and the CR3BP. The emphasis is on a practically useful and generic recipe that can be implemented in standard nonlinear programming environments and retaining favorable smoothness and convergence properties for gradient?based solvers.

The first contribution is a variable time?grid ZOH transcription. Instead of adopting a uniform time discretization, the proposed approach treats segment durations as decision variables, enabling the optimizer to allocate temporal resolution where dynamics or control activity are most demanding. The time grid is parametrized via a differentiable mapping onto the simplex, ensuring strictly increasing nodes and smooth dependence on optimization variables. An unconstrained vector of parameters is mapped to positive segment lengths that sum to the total transfer time through a softmax?type transformation, and the time nodes are obtained as cumulative sums of these lengths. This construction embeds the time discretization directly into the optimization variables while guaranteeing a well?ordered grid without explicit inequality constraints. The resulting differentiable simplex parametrization enables controlled non?uniformity of the time mesh while preserving good gradient properties, which is particularly relevant for eccentric orbits and bang–bang control structures that are poorly represented by uniform grids.

The second contribution is a smooth four?parameter encoding of control vectors, designed to provide well?behaved gradients across the entire feasible set. Classical parameterizations often suffer from singularities or poorly scaled derivatives, which can slow convergence and cause failures in gradient?based methods. The proposed encoding decouples magnitude from direction at the cost of a four?dimensional representation and additional equality constraints, but yields smooth first? and second?order derivatives, improves numerical conditioning, and reduces the need for ad hoc regularization. This is especially important for ballistic phases, where singularities arise around the zero?thrust manifold.

The third contribution is a systematic performance evaluation across diverse, representative dynamical settings: two?body Keplerian dynamics, equinoctial formulations suited to low?thrust spirals, solar?sail dynamics, and the circular restricted three?body problem. For each model, the paper benchmarks multiple combinations of time?grid strategies (uniform vs non?uniform) and control encodings (classical vs four?parameter) on time?optimal and fuel?optimal transfers. Performance metrics include convergence rate, success ratio, objective value, constraint violation, and sensitivity to initialization.

The results show how the proposed general implemention provide substantial gains over uniform discretizations, as well as highlight how the proposed encoding significantly improves optimization robustness and speed relative to standard parameterizations.

Taken together, these elements yield a practical guide to constructing direct ZOH optimal control formulations for interplanetary missions. The paper places particular emphasis on reproducibility and implementation details, including scaling choices, constraint handling, and initialization strategies that have proven effective in practice. The goal is not to introduce an entirely new class of methods, but to consolidate and extend existing ideas into a coherent, implementable framework that can serve both as a baseline for research comparisons and as a starting point for mission design applications.