Coordinated motions of multiple robotic manipulators with matrix-weighted network

This paper addresses coordinated problem of uncertain robotic manipulators with matrix-weighted network. Given interconnections between agents are weighted by nonnegative definite matrices, we present a sufficient and necessary condition about zero eigenvalues of matrix-weighted Laplacian and types of coordinated behaviors for multiple agents. Based on the condition, two novel control schemes are proposed for the networked robots by introducing matrix-weighted network. We employ the decomposition approach and Lyapunov-like approach to show coordinated motions of the networked system, and demonstrate that the proposed controls are capable of ensuring the robotic agents reach complete/cluster consensus and complete/cluster synchronization. Finally, some numerical examples and simulations demonstrate the obtained theoretical results.