Pure pursuit guidance (PPG) has been used to solve the path following problem for car-like autonomous ground vehicles (CAGV). Most of the PPG guidance laws for CAGV guide the vehicle to follow a circular arc connecting the vehicle with a virtual target point on the path at a specified distance ahead of the vehicle, which could be called ARC PPG. Another type of PPG law for CAGV guides the vehicle by steering its velocity vector to align with the line-of-sight (LOS) connecting the vehicle and the virtual target. While some qualitative stability results exist on ARC PPG for some special types of curves of the path, such as straight and circular, a quantitative stability analysis on general paths is highly desirable but appears missing. Moreover, the existing guidance parameter selection methods depend highly on empirical tuning. In this work, the LOS PPG formulation is used to obtain a rigorous quantitative stability result stated as two theorems for general reference paths by treating the path curvature as a non-vanishing perturbation in a nonlinear context. The result shows that the ARC PPG is a special case of the LOS PPG, whereby establishing the generality of the theorems for PPG of CAGVs. Moreover, a geometric interpretation of the guidance parameters in relation to the path curvature is provided. By using the results of the stability analysis, a practical design guideline for LOS PPG is presented. Simulation results are shown to demonstrate the correctness of the stability analysis and the usefulness of the design guideline.

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