This paper proposes a new navigation approach for two wheeled robots cooperatively carrying an object in unknown environments with concave maps. The navigation approach consists of the three parts of cooperative obstacle boundary following (OBF), cooperative target searching (TS), and a behavior supervisor. The cooperative OBF behavior of the robots is executed by the fuzzy controllers (FCs) learned through a fusion of swarm intelligence algorithms in a convex map. This paper applies the FCs to control the robots in concave maps by incorporating a complementary control rule based on sensor-identified inner corners in an obstacle. To avoid the dead-cycle problem of navigation in concave maps, this paper incorporates the distance information between a target and the leader robot in the behavior supervisor. Simulations and experimental results show the effectiveness of the control and navigation approaches for the two robots in unknown environments with concave maps.