A Novel Contouring Control Method Based on Optimal Vector-Referenced Moving Frame for 3D Trajectory With Zero Curvature

Contouring control of 3D trajectory is critical in multi-axial machine tool, scanning stage and other precision automation systems. Currently, most contouring controllers are based on Frenet frames, thus their limited applicability to nonzero-curvature 3D trajectories rather than zero-curvature ones which exist ubiquitously in multi-axial motion systems. This paper proposes an optimal vector-referenced moving frame based contouring controller (OVRMFCC) suitable for contouring control of 3D zero-curvature trajectories. Firstly, the optimal vector-referenced moving frame (OVRMF) capable of framing arbitrary finite-length smooth 3D trajectory regardless of its curvature was proposed. Then, a contouring controller (OVRMFCC) based on OVRMF was designed, followed by derivation of its analytical form and proof of its convergence. Finally, this controller was deployed to an FPGA-based controller target with comprehensive comparison experiments on a triaxial system. Experimental results indicates that OVRMFCC reduces at least 46.6% maximum contour error, and 25.0% root-mean-square contour error compared to cross-coupled controller. Besides, OVRMFCC achieves almost the same precision on trajectories with nonzero curvature or curvature singularities compared to TCF. It still maintains high-precision contour tracking on trajectories with continuous zero-curvature segments or planned discrete trajectories with sharp curvature changes, while TCF crashes or leads to several times larger contour error.