<![CDATA[Nonlinear model predictive control (NMPC) is widely adopted for mobile robot trajectory tracking, yet the interaction between transcription methods and learning-based enhancements remains unstudied for differential-drive platforms. This paper presents a unified CasADi/Interior Point OPTimizer (IPOPT) evaluation of fourth-order Runge-Kutta (RK4) multiple shooting (MS) and Hermite-Simpson (HS) direct collocation on a TurtleBot3 Burger across ten scenarios spanning five trajectory families, model mismatch, and sensor noise. A ?-ambiguity in the standard ???2 (??) heading cost is identified and corrected, reducing figure-eight tracking error by approximately 95%. RK4 MS achieves superior baseline accuracy in 9 of 10 experiments (? < 0.01). Three hybrid neural approaches are evaluated: warm-starting reduces solve time by 16% with no accuracy loss; adaptive transcription selection outperforms the baseline in 3 of 10 experiments; and neural approximate control achieves sub-millisecond inference but degrades on unseen trajectories (51%-64% fallback rate). A generalization hierarchy emerges: solver-in-the-loop methods generalize without measurable degradation, whereas solver-replacement methods require trajectory-specific training. These findings suggest that solver involvement is a key factor influencing generalization in learning-augmented predictive control. All results are statistically validated across 500 simulations.]]>
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