We study the problem of Trajectory Optimization (TO) for a general class of stiff and constrained dynamic systems. We establish a set of mild assumptions, under which we show that TO converges numerically stably to a locally optimal and feasible solution up to arbitrary user-specified error tolerance. Our key observation is that all prior works use SQP as a black-box solver, where a TO problem is formulated as a Nonlinear Program (NLP) and the underlying SQP solver is not allowed to modify the NLP. Instead, we propose a white-box TO solver, where the SQP solver is informed with characteristics of the objective function and the dynamic system. It then uses these characteristics to derive approximate dynamic systems and customize the discretization schemes.

翻译：本文研究针对一类通用的刚性与约束动态系统的轨迹优化问题。我们建立了一组温和假设条件，并证明在此条件下轨迹优化能够数值稳定地收敛至局部最优且可行的解，且误差不超过用户指定的任意容限。我们的核心发现是：现有研究均将序列二次规划作为黑盒求解器使用，即轨迹优化问题被表述为非线性规划问题，而底层的序列二次规划求解器不允许修改该非线性规划。与之相反，我们提出一种白盒轨迹优化求解器，该求解器将目标函数与动态系统的特性告知序列二次规划算法，进而利用这些特性推导近似动态系统并定制离散化方案。