Definition and estimation of joint-space contour error based on generalized curve for five-axis contour following control

Five-axis contour following is one of the main tasks for five-axis CNC machine tools. The contour following accuracy directly determines the final machining precision. Therefore, control of the five-axis contour error is significant. Currently, most existing definitions of five-axis contour error are in the Cartesian task space, and this inevitably requires direct and inverse Jacobian transformations between the task-space contour-error computation and the joint-space contour-error control. Different from them, this paper defines the five-axis contour error in the R-5 joint space through adjusting uniform units of five joints, and accordingly proposes a third-order estimation algorithm for the defined joint-space contour error, with the help of the concept of generalized curve. Based on the joint-space contour-error definition and estimation, a joint-space five-axis cross-coupling control scheme is finally provided. Simulation and experimental results demonstrate that the presented third-order joint-space contour-error estimation algorithm has a satisfactory estimation accuracy, and the presented joint-space five-axis contour control method can decrease both of the joint-space and the task-space five-axis contour errors by more than 49%. It is also analyzed and verified that comparing with routine task-space five-axis contour control method, the presented joint-space method not only needs not the direct and inverse Jacobian transformations during error estimation, which saves the computational burden, but also generates minimum axial contour-control commands, which enhances the control stability, thus resulting in better contour-following performances.