B-Spline-Based Curve Fitting to Cam Pitch Curve Using Reinforcement Learning

Abstract

Directly applying the B-spline interpolation function to process plate cams in a computer numerical control (CNC) system may produce verbose tool-path codes and unsmooth trajectories. This paper is devoted to addressing the problem of B-spline fitting for cam pitch curves. Considering that the B-spline curve needs to meet the motion law of the follower to approximate the pitch curve, we use the radial error to quantify the effects of the fitting B-spline curve and the pitch curve. The problem thus boils down to solving a difficult global optimization problem to find the numbers and positions of the control points or data points of the B-spline curve such that the cumulative radial error between the fitting curve and the original curve is minimized, and this problem is attempted in this paper with a double deep Q-network (DDQN) reinforcement learning (RL) algorithm with data points traceability. Specifically, the RL environment, actions set and current states set are designed to facilitate the search of the data points, along with the design of the reward function and the initialization of the neural network. The experimental results show that when the angle division value of the actions set is fixed, the proposed algorithm can maximize the number of data points of the B-spline curve, and accurately place these data points to the right positions, with the minimum average of radial errors. Our work establishes the theoretical foundation for studying spline fitting using the RL method.

Accurate superposition modeling method of grinding-shot peening surfaces

“…Given node sequence E = {a, Ka, e u+1 ,Ke s-u−1 , b, Kb}, the unique B-spline basis function [39], can be obtained directly on the interval [a, b]. Based on the linear combination of basis functions, the formula of the B-spline curve is as follows.…”