Smooth time-optimal tool trajectory generation for CNC manufacturing systems

An optimization approach is proposed in this paper for generating smooth and time-optimal path constrained tool trajectory for Cartesian computer numerical control (CNC) manufacturing systems. The desired smooth time-optimal trajectory generation (STOTG) problem is formulated as a general optimal control problem. And axis jerk (derivative of acceleration with respect to time) constraints are introduced into this problem to remove discontinuities of the acceleration profiles. The desired smoothness of the trajectory can be accomplished by adjusting the values of jerk constraints. A control vector parameterization (CVP) method is applied to convert the optimal control problem into a nonlinear programming (NLP) problem which can be solved conveniently and effectively. The third derivative of the path parameter with respect to time (pseudo-jerk) and jerk act as optimization variables. The pseudo-jerk is approximated as piecewise constant, thus for at least second-order continuous parametric path, the resulted optimized trajectory with respect to time is also at least second-order continuous. Sequential quadratic programming (SQP) method is used to solve the NLP problem, through which numerical solution is obtained. Non-smooth (i.e. without considering jerk constraints) time-optimal trajectory generation (non-STOTG) problem is also considered in this paper for the purpose of comparison. Solutions of time-optimal trajectory generation (TOTG) problems for two test paths are performed to verify the effectiveness of the proposed approach. (C) 2012 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.