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：本文研究适用于一类普遍存在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，并证明在该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，且收敛精度可达用户指定的任意误差容限。我们发现，现有研究均将序列二次规划作为黑盒求解器使用，即将轨迹优化问题表述为非线性规划问题，且不允许底层序列二次规划求解器修改该非线性规划。与之相反，我们提出一种白盒轨迹优化求解器，该求解器使序列二次规划算法能够获取目标函数与动态系统的特征信息，进而利用这些特征推导近似动态系统并定制离散化方案。