Approximate manipulability of leader-follower networks

We introduce the notion of manipulability to leader-follower networks as a tool to analyze how effective inputs injected at a leader node are in terms of their impact on the movements of the follower nodes, as a function of the interaction topologies and agent configurations. Classic manipulability is an index used in robotics for analyzing the singularity and efficiency of configurations of robot-arm manipulators. To define similar notions for leader-follower networks, we use a rigid-link approximation of the follower dynamics and under this assumption, we prove that the instantaneous follower velocities can be uniquely determined by that of the leader´s, which allows us to define a meaningful manipulability index of the leader-follower networks.