FPGA implementation of higher degree polynomial acceleration profiles for peak jerk reduction in servomotors

Acceleration profile generation for jerk limitation is a major issue in automated industrial applications like computer numerical control (CNC) machinery and robotics. The automation machinery dynamics should be kept as smooth as possible with suitable controllers where trajectory precision ensures quality while smoothness decreases machinery stress. During the operation of commercially available CNC and robotics controllers, small discontinuities on the dynamics are generated due to the controller position profiler which is generally based on a trapezoidal velocity profile. These discontinuities can produce undesirable high-frequency harmonics on the position reference which consequentially can excite the natural frequencies of the mechanical structure and servomotors. Previous works have developed jerk limited trajectories with higher degree polynomial-based profiles, but lack one or both of computer efficiency for on-line operation and low-cost hardware implementation. The present work shows a low cost, computationally efficient, on-line hardware implementation of a high-degree polynomial-based profile generator with limited jerk dynamics for CNC machines and robotics applications to improve the machining process. The novelty of the paper is the development of a multiplier-free recursive algorithm for computationally efficient polynomial evaluation in profile generation and a low-cost implementation of the digital structure in field programmable gate array (FPGA). Two experimental setups were prepared in order to test the polynomial profile generator: the first one with the servomotor at no load and the second one for the servomotor driving a CNC milling machine axis. From experimental results it is shown that higher degree polynomial profiles, compared to the standard trapezoidal speed profile improve the system dynamics by reducing peak jerk in more than one order of magnitude while precision is maintained the same and on-line operation is guaranteed.