An Adaptive Gaussian Integration-Based Real-Time Mapping Method of Spline Length and Parameters

The real-time determination of precise mapping relationship between spline curve length and parameters is essential for efficient spline path planning. This paper proposes a general solution method for the mapping relationship based on the idea of predictor and corrector. The proposed method utilizes first-order derivatives to predict the target parameters. The calibration method employs adaptive Gaussian integration, which avoids uncontrolled errors in traditional Taylor expansion methods. This prediction-correction method ensures real-time performance while guaranteeing mapping accuracy. The correction of the proposed method is verified by simulation result.