Manipulability of leader–follower networks with the rigid-link approximation

This paper introduces the notion of manipulability to mobile, multi-agent networks as a tool to analyze the instantaneous effectiveness of injecting control inputs at certain, so-called leader nodes in the network. Effectiveness is interpreted to characterize how the movements of the leader nodes translate into responses among the remaining follower nodes. This notion of effectiveness is a function of the interaction topologies, the agent configurations, and the particular choice of inputs used to influence the network. In fact, classic manipulability is an index used in robotics to analyze 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 from that of the leaders’, which allows us to define a meaningful and computable manipulability index for the leader–follower networks. This paper examines the property of the proposed index in simulation and with real mobile robots, and demonstrates how the index can be used to find effective interaction topologies.