Optimal feedrate planning on a five-axis parametric tool path with global geometric and kinematic constraints

The optimal feedrate planning problem for the five-axis parametric tool path remains challenging due to the nonlinear relationships between the joint space and the Cartesian space. We present a novel and complete optimal feedrate planning method for a five-axis parametric tool path by constraining the velocity, acceleration, jerk in the joint space, and the chord error in the Cartesian space. Our method formulates the problem as an optimal control problem, and we propose an iteration control vector parametrization method to compute the optimal solution. Compared with the new development five-axis feedrate planning methods, our solution satisfies "bang-bang" optimal control, and each constraint is strictly under the limits globally. Examples and comparisons with two other methods are demonstrated to show the effectiveness of the algorithm.