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This study addresses the problem of formation control with collision avoidance for networked Lagrangian systems with uncertain parameters interacting on directed network communication topologies. Two adaptive formation control strategies with collision avoidance are proposed by making use of adaptive gain techniques for both cases of with and without a dynamic leader. The main objective of the proposed control strategies is to dispatch a group of agents to maintain a desired geometric pattern, while still guarantee collision avoidance at any time, and eventually to achieve velocity matching. A distinctive feature of the developed adaptive gain is to adapt itself duly based on both the network communication topology and collision avoidance constraints, so it is feasible to be implemented in practice. Some general criteria are derived to guarantee that the desired formation with collision avoidance for the networked Lagrangian systems can be achieved. Finally, numerical simulations are given to show the performance of the proposed control methodologies. [ABSTRACT FROM AUTHOR]