This paper addresses the distributed formation control problem of networked robot manipulators in end-effector coordinates. We propose a distributed bipartite formation controller that guarantees collision avoidance and connectivity maintenance for cooperative and competitive manipulators. In the considered setting, two groups of manipulators are formed and reach bipartite consensus. On the other hand, the end-effectors in the same group achieve formation. We design a gradient-based control law using barrier-Lyapunov functions to ensure that end-effectors do not collide and stay in their sensors' range. Moreover, we establish asymptotic stability of the bipartite formation manifold. Finally, we illustrate our theoretical results via numerical simulations.