Two-Stage Feedrate Optimization for Freeform Toolpath Contouring

This paper presents a feedrate optimization for spline toolpaths, performed via two steps: Linear Programming (LP) to obtain a fast and approximate solution followed by Sequential Quadratic Programming (SQP) based refinement of the feed profile. The LP algorithm is proven to be robust and computationally efficient. It can process long look-ahead windows (>1000 points), but does not allow the incorporation nonlinear constraints, like true axis level jerk, motor torque, of servo error. The result of the LP solution can also be conservative in jerk-limited problems. SQP allows nonlinear constraints, but is typically restricted to smaller problem size (<100 free variables, i.e. control points). The proposed algorithm, by utilizing the solution of LP as an initial guess for SQP, and using a dual look-ahead buffer (long range for LP and short range for SQP) takes advantage of the strengths of both approaches. The results are demonstrated in simulation results, which are currently being adopted for machining experiments as well.