Asymptotic Parking of General Two-Trailer Systems Leveraging Singularity

It is challenging to asymptotically stabilize a general two-trailer system consisting of a unicycle car and two identical trailers at a predefined pose efficiently because the system cannot be converted into a chain-form system. In this article, we design a two-phase parking strategy for such a system to park it at the target pose. The proposed strategy is inspired by a new insight on the singularity set of the general two-trailer system, i.e., the singularity set includes a subset that can be asymptotically stabilized directly. In the first phase, a tracking controller is adopted to let the state of the system approach the subset. A parking controller is then developed in the second phase to stabilize the system at the target pose asymptotically. Due to its simplicity and efficiency, the proposed controller has a good potential to be used in practice.