Networked multi-robot systems under the coordinated control can perform tasks more effectively than a group of individually operating robots. This paper studies the group regional consensus of networked multi-robot systems with input disturbances (formulated by second-order Lagrangian dynamics) under directed acyclic topology. An adaptive control protocol is designed to achieve group regional consensus of the networked Lagrangian systems with parametric uncertainties for both leader and leaderless cases. Sufficient conditions are established to guarantee group regional consensus for any prior given desired consensus errors. Compared with the existing work, a distinctive feature of the proposed control algorithm is that the stability analysis indicates the global validity of the obtained consensus results. Numerical examples are provided to demonstrate the effectiveness of the proposed scheme.