Ding Teng-Fei, Ge Ming-Feng, Liu Zhi-Wei, Wang Yan-Wu, Karimi Hamid Reza
IEEE Trans Cybern. 2022 Jul;52(7):6759-6770. doi: 10.1109/TCYB.2020.3034108. Epub 2022 Jul 4.
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.
