A G2 Continuous Path-smoothing Algorithm Using Modified Quadratic Polynomial Interpolation

Path searching algorithm is one of the main topics in studies on path planning. These algorithms are used to avoiding obstacles and find paths from starting point to target point. There are dynamic problems that must be addressed when these paths are applied in real environments. In order to be applicable in actual situations, the path must be a smooth path. A smooth path is a path that maintains continuity. Continuity is decided by the differential values of the path. In order to be G(2) continuous, the secondary differential values of the path must be connected throughout the path. In this paper, the interpolation method is used to construct continuous paths. The quadratic polynomial interpolation is a simple method for obtaining continuous paths about three points. The proposed algorithm makes a connection of three points with curves and the proposed path is rotated using the parametric method in order to make the path optimal and smooth. The polynomials expand to the next three points and they merge into the entire path using the membership functions with G(2) continuity.