Hierarchical bipartite formation tracking of networked perturbed robotic systems with nonlinear state‐to‐output mappings

This article investigates the hierarchical bipartite formation tracking (HBFT) problem of the networked perturbed robotic system (NPRS) with dynamical uncertainties, actuator faults and nonlinear state‐to‐output mappings. Different from the traditional single‐layer formation tracking problems based on only cooperative interconnections, solving the HBFT problem implies that (a) the robots of the NPRS are divided into two layers of subnetworks, where the ones in subnetwork 1 can directly interconnect with the leader, those in subnetwork 2 can only interconnect with each other or subnetwork 1, and the ones in the different subnetworks form hierarchical formations; (b) each formation is further grouped into two complementary sets according to the cooperative and antagonistic interconnections, where the robots of each formation forms two opposite subformations; (c) for the same subnetwork, the geometric centers of the two subformations track the positive and negative states of the leader respectively. The positive state equals to the leader state, and the negative state has the elements with the same absolute value and opposite sign of the corresponding one in the leader state. Then, a uniform cooperative observer‐based fault‐tolerant control (COFTC) algorithm is designed to solve these challenging problem. By employing the Lyapunov theory, the sufficient conditions are derived for guaranteeing the convergence of the proposed COFTC algorithm. Eventually, simulation results are performed on NPRS to verify the effectiveness of the theoretical results.