Multi-robot navigation control in the absence of reference trajectory is rather challenging as it is expected to ensure stability and feasibility while still offer fast computation on control decisions. The intrinsic high complexity of switched linear dynamical robots makes the problem even more challenging. In this paper, we propose a novel HMPC based method to address the navigation problem of multiple robots with switched linear dynamics. We develop a new technique to compute the reachable sets of switched linear systems and use them to enable the parallel computation of control parameters. We present theoretical results on stability, feasibility and complexity of the proposed approach, and demonstrate its empirical advance in performance against other approaches.