Abstract: A method for path planning for a machine to traverse an area includes calculating a spline trajectory based on a plurality of control points of a first path. A subset of the plurality of control points having an equal step is selected. A direction of the normal to the spline trajectory for each of the selected points is determined. Control points within the subset that are a solution to a second order cone programming class optimization problem along each normal to the spline trajectory are searched for and the spline trajectory is extended to a border of the area to create a second path adjacent to the first path based on the control points. The optimization problem can minimize the weighted sum of the average curvature at junction points of elementary sections of the spline trajectory and/or the average width overlap of adjacent paths.