Dynamic polarization control (DPC) is beneficial for many optical applications. It is often realized via tunable waveplates to perform automatic polarization tracking and manipulation. Efficient algorithms are essential to realize an endless polarization control process at high speed. However, the standard gradient-based algorithm is not well analyzed. Here, we model the DPC with a Jacobian-based control theory framework that finds a lot in common with robot kinematics. We then give a detailed analysis of the condition of the Stokes vector gradient as a Jacobian matrix. We identify the multi-stage DPC as a redundant system enabling control algorithms with null-space operations. An efficient, reset-free algorithm can be found. We anticipate more customized DPC algorithms to follow the same framework in various optical systems.