Real time tool path smoothing of short linear commands for robot manipulator by constructing asymmetrical Pythagoran-hodograph (PH) splines

Tool path smoothing of linear commands is important to guarantee the high-order motion continuity of multi-axis motion control systems. The existing local tool path smoothing methods mainly construct symmetrical splines at transition corners of linear segments. When the linear segments are short, the symmetrical splines must be shrunk to avoid overlapping, which gives rise to relatively high curvature and low machining efficiency. This paper proposes a tool-path smoothing algorithm for serial industrial robots with 6 rotary (6R) joints by constructing asymmetrical Pythagorean-hodograph (PH) splines. Firstly, symmetrical PH splines are initially constructed at transition corners to realize the third-order differential continuity of tool path position and tool orientation. Tool tip position smoothing errors are constrained by directly evaluating the control polygon length of spline according to the error tolerance in the workpiece coordinate system, while the tool orientation smoothing errors are constrained by adjusting control polygon length after converting tool orientation error to Euler angles using Jacobian matrix. Then asymmetrical splines are constructed by dealing with the spline overlapping problem, while guarantying the fully utilization of error tolerance to reduce spline curvature. The position and orientation are synchronized to the arc-length of the tool tip position to ensure the continuity of acceleration and jerk commands. The control points and arc-length of the constructed asymmetrical splines can all be solved analytically, which makes it suitable for on-line tool path smoothing. Experiments demonstrate that the proposed method achieves higher motion efficiency and lower tracking error than the existing symmetrical and asymmetrical tool path smoothing methods, which validates the advantages of the proposed method in high speed machining.