Redundancy Optimization for Robotic Grinding on Complex Surfaces via Hierarchical Dynamic Programming

In robotic grinding of complex curved surfaces, the low stiffness of serial robots causes tool tip deflection and degrades surface quality. The axial symmetry of grinding discs introduces a free rotational parameter at each waypoint, converting a standard 6-DOF robot into a functionally redundant system. However, this redundancy has not been systematically exploited for stiffness optimization along the trajectory. This paper proposes a hierarchical dynamic programming framework to optimize the redundancy angle sequence over the entire grinding trajectory. A kinematic transformation parameterizes the flange target by the redundancy angle, enabling enumeration of feasible candidate configurations over a discretized grid. A composite stiffness index that accounts for the normal, feed, and cross-feed grinding force components is formulated at the contact point. Hierarchical constraint filtering removes configurations that violate posture, singularity, velocity, acceleration, and stiffness constraints. The Viterbi algorithm then recovers the minimum-cost path that balances stiffness performance and joint motion smoothness. Finally, a post-processing step based on a cubic smoothing spline generates C2-continuous joint trajectories. Simulations on a UR5 robot grinding a curved surface evaluate the proposed framework against fixed-angle, greedy, and flange-stiffness baselines. The proposed method improves the mean composite stiffness by 31.7% and 17.9% over the fixed-angle and flange-stiffness baselines, respectively, and reduces the maximum joint jump by two orders of magnitude compared with the greedy strategy. Experimental validation on a UR5 robot confirms that the smoothed trajectory is accurately tracked while the stiffness threshold is preserved. A multi-trajectory analysis further shows that the stiffness threshold is maintained across all grinding trajectories. These results demonstrate the effectiveness of the proposed framework for redundancy optimization in robotic grinding with tool spin symmetry.