Given a group of autonomous vehicles, an initial configuration, a final configuration, a set of inter- and intra-vehicle constraints, and a time for reconfiguration, the Formation Reconfiguration Planning problem is focused on determining a nominal input trajectory for each vehicle such that the group can start from the initial configuration and reach its final configuration at the specified time while satisfying the set of inter-and intra-vehicle constraints. In this paper, we are interested in solving the Formation Reconfiguration Planning problem for a specific class of systems and a particular form of input signals so that the problem can be reformulated as an optimization problem which can be solved more efficiently, especially for a large group of vehicles.