Minimum Time Trajectory Planning for Five-Axis Machining with General Kinematic Constraints

Abstract. In this paper, the minimum time feedrate trajectory planning problem for five-axis computer numerical control (CNC) machining is studied. A more accurate model for the feedrate trajectory planning problem is proposed by constraining the velocity, acceleration, and jerk for all five axes in the joint space and constraining the chord error in the workpiece coordinate system. For the newly introduced minimum time trajectory planning problem, we prove that a necessary condition for a solution to be optimal is “bang-bang” in the sense at least one of the velocity, acceleration, jerk, or chord error reaches its limits at anytime. Finally, an efficient numerical algorithm based on control vector parametrization is given to solve the planning problem and an example on five-axis milling of a jet engine impeller is given.