An analytical C3 continuous tool path corner smoothing algorithm for 6R robot manipulator

Tool path smoothness is important to guarantee good dynamic and tracking performance of robot manipulators. An analytical C3 continuous tool path corner smoothing algorithm is proposed for robot manipulators with 6 rotational (6R) joints. The tool tip position is smoothed directly in the workpiece coordinate system (WCS). The tool orientation is smoothed after transferring the tool orientation matrix as three rotary angles. Micro-splines of the tool tip position and tool orientation are constructed under the constraints of the maximum deviation error tolerances in the WCS. Then the tool orientation and tool tip position are synchronized to the tool tip displacement with C3 continuity by replacing the remaining linear segments using specially constructed B-splines. Control points of the locally inserted micro-splines are all evaluated analytically without any iterative calculations. Simulation and experimental results show that the proposed algorithm satisfies constraints of the preset tool tip position and the tool orientation tolerances. The proposed corner smoothing algorithm achieves smoother and lower jerks than C2 continuous corner smoothing algorithm. Experimental results show that the tracking errors associated to the execution of the C3 continuous tool path are up to 10% smaller than C2 continuous path errors.