让机械臂沿预定路径运动时可实时调整，兼顾规划效率与灵活性。

Traditional offline redundancy resolution of trajectories for redundant manipulators involves computing inverse kinematic solutions for Cartesian space paths, constraining the manipulator to a fixed path without real-time adjustments. Online redundancy resolution can achieve real-time adjustment of paths, but it cannot consider subsequent path points, leading to the possibility of the manipulator being forced to stop mid-motion due to joint constraints. To address this, this paper introduces a dynamic programming-based offline redundancy resolution for redundant manipulators along prescribed paths with real-time adjustment. The proposed method allows the manipulator to move along a prescribed path while implementing real-time adjustment along the normal to the path. Using Dynamic Programming, the proposed approach computes a global maximum for the variation of adjustment coefficients. As long as the coefficient variation between adjacent sampling path points does not exceed this limit, the algorithm provides the next path point's joint angles based on the current joint angles, enabling the end-effector to achieve the adjusted Cartesian pose. The main innovation of this paper lies in augmenting traditional offline optimal planning with real-time adjustment capabilities, achieving a fusion of offline planning and online planning.