A Chord Error-Priority Bilevel Interpolation Optimization Method for Complex Path Planning

To address path deviation and efficiency reduction issues in traditional interpolation optimization algorithms for complex path machining, this paper proposes a chord error-priority bilevel interpolation optimization method (CPBI). First, arc length parametric modeling of the machining path is performed within the Frenet–Serret framework, yielding curvature and torsion information. After introducing geometric-based multi-machining constraints in the outer layer, the velocity upper limit is established by controlling chord error to dynamically adjust regions with curvature mutation. In the inner layer, combining the velocity limit with bidirectional scanning achieves adaptive optimization of interpolation step size and optimal velocity planning that balances precision and smoothness. Simulation results demonstrate that CPBI effectively reduces the number of interpolation points by 30–50% while ensuring the chord error. Compared with the reference method, the CPBI improved efficiency by 14.31% and 34.72% in machining experiments on S-shaped and wave-shaped paths, respectively. The results validated the CPBI’s high precision and efficiency advantages in complex path machining, providing an effective solution for CNC path optimization in high-end manufacturing.