A one-step corner smoothing method of industrial robots for the mixed toolpath of lines and NURBS

The smoothness of corners in discrete toolpaths is of crucial importance for improving machining quality. Corner smoothing methods for discrete toolpaths composed of linear and arc segments have been extensively investigated. However, existing corner smoothing methods rely on complicated vector derivations and cannot be directly applied to the mixed toolpath of lines and NURBS, due to the lack of an analytical relationship between the NURBS parameter and its arc length. This paper proposes a one-step corner smoothing method of industrial robots for the mixed toolpath of lines and NURBS, aiming to balance the machining efficiency and accuracy of robots. This method first performs feedrate planning for each path segment. Overlapping time and adjustment angles are selected as optimization variables, which are used to adjust the motion time of the corner trajectory and the convex-concave degree of the corner, respectively. With the corner error as a constraint and the maximization of overlapping time as the objective, the corner smoothing problem is thus transformed into a mixed-integer optimization problem. This optimization problem can be solved by mature global optimization solvers and is currently applicable for offline implementation. Meanwhile, considering the nonlinearity of robot motion, traditional corner error definitions fail to fully describe the deviation at corners. This method redefines the corner error, thereby enabling more precise constraint of the corner error. Simulations and experiments on industrial robots demonstrate that the proposed method can improve command trajectory smoothness and machining efficiency while reducing contour error, showing its industrial relevance and practical value for real machining applications.