Smooth and time-optimal trajectory planning for computer numerical control systems

On the basis of the control vector parameterization(CVP) method,we investigate the numerical approach for solving the smooth and time-optimal trajectory planning problem of computer numerical control(CNC) systems.The jerk constraints are considered in the problem to realize the smooth feeding-rate of the trajectory.By using a time normalization factor,we reformulate the original jerk constrained time-optimal trajectory planning problem as a time-independent optimal control problem.The third derivative of the path parameter with respect to time,also known as pseudo-jerk,and the terminal time are taken as optimization variables.The piece-wise constant approximation method is used to approach the pseudojerk,and the optimal control problem is converted into a general nonlinear programming(NLP) problem.Constraint aggregation functions are introduced to approximate the process constraints(i.e.,jerk and acceleration constraints) as final time constraints,and the computation load of constraints can be reduced significantly.By constructing the Hamiltonian functions of objective and constraint functions,and employing the adjoint approach,we obtain the gradients which are required in the process of NLP solution.