Accurate and computationally efficient approach for simultaneous feedrate optimization and servo error pre-compensation of long toolpaths—with application to a 3D printer

Abstract

Feedrate optimization (FO) and servo error pre-compensation (SEP) are often performed independently to improve the accuracy and speed, respectively, of computer-controlled manufacturing machines. However, this independent approach leads to excessive tradeoff between speed and accuracy. To address this issue, the authors have proposed a new concept of simultaneous FO and SEP (or FOSEP) where SEP is integrated into FO, yielding large reductions in motion time without sacrificing positioning accuracy relative to independent FO and SEP. However, in their prior work, the authors used linear programming to achieve FOSEP resulting in the following: (i) inaccuracy in enforcing nonlinear constraints and (ii) poor computational efficiency for long toolpaths. To address these two problems, this paper proposes a new approach for FOSEP using windowed sequential linear programming (SLP). The use of SLP improves the accuracy of FOSEP in enforcing nonlinear constraints; however, it lowers the computational efficiency of FOSEP. Windowing addresses the problem of low computational efficiency by applying SLP to FOSEP in small overlapping batches. A downside of windowed SLP is that it may lead to infeasibility in the optimization. This problem is resolved by smoothly switching between the optimal solution obtained using windowed SLP and a backup conservative solution in case of impending infeasibility. The proposed windowed SLP with smooth switching approach for FOSEP is validated in simulations where it significantly improves the accuracy and computational efficiency of FOSEP while guaranteeing feasibility. The practical benefits of the proposed approach for FOSEP is demonstrated in experiments on a 3D printer where it achieves up to 25% reduction in cycle time without sacrificing printing quality relative to the conventional approach of independent FO then SEP, both applied to a long toolpath.