A robust distributed adaptive leader-following control for multi-degree-of-freedom (multi-DOF) robot manipulator-type agents is proposed to guarantee finite-time convergence for leader-following tracking and parameter estimation via agent-based estimation and control algorithms. The dynamics of each manipulator agent system of n degrees including the leader agent are assumed unknown. For a specific leader-following network Laplacian, the agents’ position, velocity and some switched control information can be fed back to the communication network. In contrast to the current multi-agent literature for robotic manipulators, the proposed approach does not require a priori information of the leader’s joint velocity and acceleration to be available to all agents due to the use of agent-based robust adaptive control elements. Due to the multi-DOF character of each agent, matrix theoretical results related to M-matrix theory used for multi-agent systems needs to be extended to the multi-degree context in contrast to recent scalar double integrator results. A simulation example of two-degree of freedom manipulators exemplifies the effectiveness of the approach.