Abstract: A Newton-CG(conjugate gradient) augmented Lagrangian approach was proposed for solving the time optimal trajectory planning problem of computer numerical control (CNC) systems. By using nonlinear variable substitution, time optimal trajectory planning problem is formulated as a time-independent convex optimal control problem. Then based on the extended Pontryagin maximum principle, detailed proofs are provided to show that the optimal control of the chord error and axis acceleration constrained problem has “bangbang” structure. Based on control vector parameterization (CVP) method, the resulted optimal control problem is further converted into a semi-infinite programming problem with infinite dimension constraints. Augmented Lagrangian functions are constructed to convert the constrained optimization problem into a series of non constrained optimization subproblems. An iteration process is performed by using the linear search Newton-CG method. The results of the time optimal trajectory planning for test paths demonstrate the effectiveness of the approach.  

Key words: augmented Lagrangian function, Newton-conjugate gradient method, time optimal trajectory, semi-infinite programming