## Abstract and Applied Analysis

### Minimum Time Trajectory Optimization of CNC Machining with Tracking Error Constraints

#### Abstract

An off-line optimization approach of high precision minimum time feedrate for CNC machining is proposed. Besides the ordinary considered velocity, acceleration, and jerk constraints, dynamic performance constraint of each servo drive is also considered in this optimization problem to improve the tracking precision along the optimized feedrate trajectory. Tracking error is applied to indicate the servo dynamic performance of each axis. By using variable substitution, the tracking error constrained minimum time trajectory planning problem is formulated as a nonlinear path constrained optimal control problem. Bang-bang constraints structure of the optimal trajectory is proved in this paper; then a novel constraint handling method is proposed to realize a convex optimization based solution of the nonlinear constrained optimal control problem. A simple ellipse feedrate planning test is presented to demonstrate the effectiveness of the approach. Then the practicability and robustness of the trajectory generated by the proposed approach are demonstrated by a butterfly contour machining example.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 835098, 15 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412606007

Digital Object Identifier
doi:10.1155/2014/835098

Mathematical Reviews number (MathSciNet)
MR3246360

Zentralblatt MATH identifier
07023161

#### Citation

Zhang, Qiang; Li, Shurong; Guo, Jianxin. Minimum Time Trajectory Optimization of CNC Machining with Tracking Error Constraints. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 835098, 15 pages. doi:10.1155/2014/835098. https://projecteuclid.org/euclid.aaa/1412606007

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