The research interest in mobile robots with independent steering wheels has been increasing over recent years due to their high mobility and better payload capacity over the systems using omnidirectional wheels. However, with more controllable degrees of freedom, almost all of the platforms include redundancy, which are modeled using the instantaneous center of rotation (ICR). This paper deals with a Tetris-inspired floor cleaning robot hTetro which consists of four interconnected differential-drive units. Each module has a differential drive unit which can steer individually. Differing from most other steerable wheeled mobile robots, the wheel arrangement of this robot changes because of its self-reconfigurability. In this paper, we proposed a path tracking controller that can handle discontinuous trajectories and sudden orientation changes for hTetro. Singularity problems are resolved on both the mechanical aspect and the control aspect. The controller is tested experimentally with the self-reconfigurable robotic platform hTetro, and results are discussed.