NURBS Function Closed-Loop Mapping Trajectory Planning of Serial Robotic Plasma Cladding for Complex Surface Coatings

Abstract

In order to solve the problem of the trajectory planning of robotic plasma cladding for complex surface coating, the concept of NURBS function open/closed-loop mapping is proposed in this work to explore the new approach of the trajectory planning for complex NURBS surfaces. The trajectory planning is carried out by a 2D-NURBS curve C(u) on a 2D plane, which is mapped on a predefined 3D-NURBS surface S(u,v) using the NURBS surface function to form a 3D mapping curve named NURBS function mapping (NURBS-FM) curve. Using the fixed step (FS) interpolation, the equal chord length (ECL) interpolation, the equal arc length (EAL) interpolation and the equal bow height (EBH) interpolation, etc., a complex curve can be interpolated. The FS/ECL/EAL/EBH can be defined as constraint. Depending on where the constraint is applied, the NURBS-FM can be divided into open-loop mapping and closed-loop mapping. The NURBS function open-loop mapping (NURBS-FOLM) is carried out along the route of u→C(u)→S(u,v), while the NURBS function closed-loop mapping (NURBS-FCLM) along the route of u→C(u)→S(u,v) →u →…. The constraint is applied to the 2D-NURBS curve in NURBS-FOLM, while to the 3D NURBS-FM curve in NURBS-FCLM. The NURBS-FOLM and NURBS-FCLM can ensure that the interpolation points on the 2D-NURBS curve and 3D NURBS-FM curve have the ECL/EAL/EBH characteristics, respectively. When the 3D NURBS-FM curve is regarded as plasma cladding trajectory, the NURBS-FCLM can provide engineers with a new ECL/EAL/EBH interpolation method for cladding trajectory. The simulation and experiment verify the NURBS-FCLM is feasible and effective. With the increasing application of complex surface protective coatings prepared by plasma cladding, the NURBS-FCLM has broad application prospects inevitably.