One of the main challenges in robotics applications is dealing with inaccurate sensor data. Specifically, for a group of mobile robots the measurement of the exact location of the other robots relative to a particular robot is often inaccurate due to sensor measurement uncertainty or detrimental environmental conditions. In this paper, we address the consensus problem for a group of agent robots with a connected, undirected, and time-invariant communication graph topology in the face of uncertain interagent measurement data. Using agent location uncertainty characterized by norm bounds centered at the neighboring agent’s exact locations, we show that the agents reach an approximate consensus state and converge to a set centered at the centroid of the agents’ initial locations. The diameter of the set is shown to be dependent on the graph Laplacian and the magnitude of the uncertainty norm bound. Furthermore, we show that if the network is all-to-all connected and the measurement uncertainty is characterized by a ball of radius r, then the diameter of the set to which the agents converge is 2r. Finally, we also formulate our problem using set-valued analysis and develop a set-valued invariance principle to obtain set-valued consensus protocols. Two illustrative numerical examples are provided to demonstrate the efficacy of the proposed approximate consensus protocol framework.