When traversing sharp corners, manufacturing machines are forced to tradeoff speed and accuracy. The most common way of reducing this tradeoff is to smooth the sharp corner using a pre-specified curve (e.g., a circular arc or spline). However, pre-specified curves cannot guarantee optimal performance. This paper presents a preliminary investigation into the potential of using methods from optimal control to minimize this tradeoff. First, a useful simplification is made to the exact cornering problem to make it tractable. Dynamic programming is then used to determine the best free-form curve that minimizes corner traversal time while adhering to path tolerance and machine kinematic constraints. Significant improvements in cornering time are demonstrated compared to two methods that use pre-specified curves. However, dynamic programming is found to be too computationally costly, thus impractical. Less computationally intensive techniques in optimal control are considered for future work.
- Dynamic Systems and Control Division
Minimum-Time Cornering for Manufacturing Machines Using Optimal Control
Duan, M, & Okwudire, CE. "Minimum-Time Cornering for Manufacturing Machines Using Optimal Control." Proceedings of the ASME 2014 Dynamic Systems and Control Conference. Volume 1: Active Control of Aerospace Structure; Motion Control; Aerospace Control; Assistive Robotic Systems; Bio-Inspired Systems; Biomedical/Bioengineering Applications; Building Energy Systems; Condition Based Monitoring; Control Design for Drilling Automation; Control of Ground Vehicles, Manipulators, Mechatronic Systems; Controls for Manufacturing; Distributed Control; Dynamic Modeling for Vehicle Systems; Dynamics and Control of Mobile and Locomotion Robots; Electrochemical Energy Systems. San Antonio, Texas, USA. October 22–24, 2014. V001T13A003. ASME. https://doi.org/10.1115/DSCC2014-6143
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