Feedrate optimization for smooth minimum-time trajectory generation with higher order constraints

The generation of a time-optimal feedrate trajectory under various machine and process-related constraints has received significant attention in CNC machining and robotics applications. While most of the existing feedrate planning algorithms take velocity and acceleration into the consideration as capability constraints, the introduction of higher order dynamic states, such as jerk and/or jounce, makes the feedrate planning and optimization extremely challenging, as the dimension of the planning problem is increased accordingly. This paper proposes a heuristic trajectory planning algorithm that can provide a near-optimal minimum time trajectory for problems with higher order dynamic states. The algorithm starts with a non-time-optimal but feasible velocity trajectory, which is interpolated from a number of knot points by piecewise spline interpolation with high-order continuity. Then, the trajectory is improved by scanning and increasing the velocity at each knot points while maintaining the feasibility of the resulting trajectory. A near-optimal trajectory is achieved when the improvement in travel time from the last scan iteration is smaller than a given value. The algorithm supports the incorporation of higher order dynamic states (up to the fifth derivative of displacement) in constraints for optimization without sacrificing the computational efficiency. Examples including linear and curved toolpath are presented to illustrate the effectiveness of this algorithm for high-speed contouring.