Lag-Bipartite Formation Tracking of Networked Robotic Systems Over Directed Matrix-Weighted Signed Graphs.

ABSTRACT

This article studies the lag-bipartite formation tracking (LBFT) problem of the networked robotic systems (NRSs) with directed matrix-weighted signed graphs. Unlike the traditional formation tracking problems with only cooperative interactions, solving the LBFT problem implies that 1) the robots of the NRS are divided into two complementary subgroups according to the signed graph, describing the coexistence of cooperative and antagonistic interactions; 2) the states of each subgroup form a desired geometric pattern asymptotically in the local coordinate; and 3) the geometric center of each subgroup is forced to track the same leader trajectory with different plus-minus signs and a time lag. A new hierarchical control algorithm is designed to address this challenging problem. Based on the Lyapunov stability argument and the property of the matrix-weighted Laplacian, some sufficient criteria are derived for solving the LBFT problem. Finally, simulation examples are proposed to validate the effectiveness of the main results.