Direct velocity planning on parameterized tool path for deterministic polishing with robust dynamic limitation

In deterministic polishing, optimizing dwell time should meet polishing accuracy with machine dynamic limitations. Directly constraining and optimizing numerous discrete dwell times not only reduces computational efficiency but also complicates balancing polishing accuracy and acceleration constraints. This study employs shared parameter B-splines to continuously describe the polishing path and velocity curve, inherently incorporating both dwell time and acceleration into these splines. By leveraging the properties of B-splines, velocity boundaries can be flexibly limited on each spline segment, facilitating the management of issues at path corners and edges. Local velocity constraint, knot elimination, and piston adjustment are combined to ensure robust dynamic constraints on the XY axes for different tool paths while maintaining computational accuracy. With the complete polishing motion optimized, the matrix replacement method effectively reveals differences in polishing errors between discrete dwell time optimization and continuous polishing motion. The cPVT interpolation is utilized to accurately approximate the planned motion through dense resampling. Simulation on both raster and random paths shows that the proposed method can provide a more practical and feasible polishing motion. Bonnet polishing experiments demonstrate that the proposed method achieves a 43% improvement in PV compared to the LSQR algorithm.