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.