Reliability-based G1 continuous arc spline approximation

This paper introduces an algorithm for approximating a set of data points with $G^1$ continuous arcs, leveraging covariance data associated with the points. Prior approaches to arc spline approximation typically assumed equal contribution from all data points, resulting in potential algorithmic instability when outliers are present. To address this challenge, we propose a robust method for arc spline approximation, taking into account the 2D covariance of each data point. Beginning with the definition of models and parameters for single-arc approximation, we extend the framework to support multiple-arc approximation for broader applicability. Finally, we validate the proposed algorithm using both synthetic noisy data and real-world data collected through vehicle experiments conducted in Sejong City, South Korea.