This research engages in generating trajectories with continuous curvature and applying blending cases. Clothoid spline has an important property that its curvature is linear related to its arclength, this property can provide a curvature (G2) continuity to the interpolation operation. But it is rarely used in the trajectory plan because its shape is hard to control to avoid obstacles. This paper uses a collision-free corridor to limit the trajectory generation to avoid obstacles. In a transformable system, using line segments to connect with Clothoid spiral segments, the computation complexity could be greatly reduced by setting the starting conditions equal to zero. With the computation, a unique solution to the spiral segment is found. The computation process and the corresponding algorithm are elaborated in this paper.