Convolution-Based Velocity-Smoothing Principle and Its Application to Real-Time Parametric Curve Interpolation

Abstract

Smooth and controlled speed regulation is crucial for multi-axis systems like machine tools and robot arms. Planning the highest possible feedrate within smoothness and axial drive constraints necessitates velocity control methods. However, most methods need repeated calculations or preparation, and the complexity grows quickly with the level of smoothness needed, making it hard to achieve both high smoothness and real-time performance at the same time. This paper proposes a convolution-based velocity-control method. The algorithm is lightweight and straightforward, with complexity independent of the required smoothness order. This is achieved by applying convolution to an original low-order smooth velocity, converting it to arbitrary-order smooth velocity. The smooth order depends solely on the convolution kernel, not the algorithm flow. The method completes smooth velocity control in a single convolution, eliminating the need for iterations. Keys for the method are (1) the design principle of the convolution kernel according to the required smoothness and (2) the control of the trajectory error induced by the convolution. The paper presents the velocity-control scheme and applies it to jounce-bounded feedrate scheduling for parametric curve CNC interpolation. Experimental results confirm high-smoothness and real-time capacity are simultaneously ensured.