Research On Path Smoothing Technology Based On Cubic Non-uniform B-spline Curve

Piecewise-linear path is the most common format for complex applications of robots and machine tools to approximate the curve contour of complex motion trajectory,but lacks the geometrical continuity at the corner.The discontinuity of linear path leads to vibration and impact during execution,affect service life,reduce quality and efficiency.A global corner smoothing method based on cubic non-uniform B-spline curve is proposed.the proposed method realizes globally smoothing of tool path,achieve stable motion and controllable contour error.Firstly,According to the strong convex packet property of B-sample curve theory,combined with geometric constraints such as straight line angle,maximum contour error,obtained the control vertices.Then,the improved accumulated chord length method is used to parameterize the control vertex,calculate the node vector corresponding to the control vertex,establish the mapping relationship between the node vector and the control vertex,obtain the node vector sequence that reflects the degree to which the B-sample curve approximates the path points,generate the global corner smooth trajectory on the continuous linear trajectory,and establish its geometric smoothing model.In the motion planning stage,according to the geometric characteristics of the global corner geometric smooth trajectory and the system kinematics constraints,and according to the look-ahead planning,find the speed mutation point,the trajectory is segmented according to the sudden change point,and use the adaptive Simpson integral to calculate the length of the segmented trajectory.Then,a seven-stage S-shaped acceleration/deceleration control algorithm is used for segmented speed planning to achieve stable motion.During the interpolation phase,the second-order Taylor expansion method is used to calculate the interpolation parameters,which not only meets the calculation accuracy,but also ensures the constraint requirements of pantograph height error in interpolation.Simulation results show that compared with the existing methods the proposed global corner smoothing method has higher accuracy and achieve high order continuity of machining trajectory.It can effectively shorten the processing time,improve the smoothness of motion.Moreover,it can greatly improve the processing quality,and meet the preset interpolation error requirements.