In this paper, a consensus algorithm is proposed for interacting multi-agents, which can be modeled as simple Mechanical Control Systems (MCS) evolving on a general compact Lie group. The standard Laplacian flow consensus algorithm for double integrator systems evolving on Euclidean spaces is extended to a general compact Lie group. A tracking error function is defined on a general smooth manifold for measuring the error between the configurations of two interacting agents. The stability of the desired consensus equilibrium is proved using a generalized version of Lyapunov theory and LaSalle’s invariance principle applicable for systems evolving on a smooth manifold. The formulated consensus control law utilizes both the configuration and the velocity information from neighboring agents. The design of tracking error function and consensus control inputs are demonstrated through an application of attitude consensus problem for multiple communicating rigid bodies. The consensus algorithm is numerically validated by demonstrating the attitude consensus problem.