  Trajectory planning is a fundamental task on various autonomous driving
platforms, such as social robotics and self-driving cars. Many trajectory
planning algorithms use a reference curve based Frenet frame with time to
reduce the planning dimension. However, there is a common implicit assumption
in classic trajectory planning approaches, which is that the generated
trajectory should follow the reference curve continuously. This assumption is
not always true in real applications and it might cause some undesired issues
in planning. One issue is that the projection of the planned trajectory onto
the reference curve maybe discontinuous. Then, some segments on the reference
curve are not the image of any part of the planned path. Another issue is that
the planned path might self-intersect when following a simple reference curve
continuously. The generated trajectories are unnatural and suboptimal ones when
these issues happen. In this paper, we firstly demonstrate these issues and
then introduce an efficient trajectory generation method which uses a new
transformation from the Cartesian frame to Frenet frames. Experimental results
on a simulated street scenario demonstrated the effectiveness of the proposed
method.
