An Embedded System-Based Snap Constrained Trajectory Planning Method for 3D Motion Systems

Abstract

Computer Numerical Control (CNC) is a technology made up of several blocks. Among these, lies the Trajectory Planning block, responsible for reference profile generation that are fed to position control loops. The need for Trajectory Planning arises from the mechanical constraints inherent to every plant to which CNC technology is applied. The machine’s operational limits myst be respected, in order to avoid several issues, such as: loss of precision, early wear of machine’s parts and excessive vibration. This paper proposes a novel smooth real-time trajectory generation setup based on an embedded system platform. A real-time snap and jerk bounded control algorithm is proposed, to achieve continuous and smooth feed motion in traditional Numeric Control code file, dealing both with straight lines and arcs. A local motion blending algorithm, applicable to the proposed method, is also presented. The developed algorithm was deployed to a BeagleBone Black, an embedded System-on-Chip, single board computer and tested in a prototype router machine. A comparison between the proposed method against the seven segments and trapezoidal acceleration methods is presented, both in terms of performance and of real-time computing viability. Simulation and Experimental results demonstrate the effectiveness of the proposed method to generate velocity, acceleration, jerk and snap bounded three dimensional trajectories, reducing the RMS error in up to 8.2% and 22.38% when compared to the Seven Segments and to Trapezoidal Acceleration methods, respectively. Assessing the error area on straight angles, the proposed method produced error areas 24% and 80% smaller when compared to the Seven Segments and to Trapezoidal Acceleration methods, respectively.