Distributed adaptive consensus control for networked robotic manipulators with time-varying delays under directed switching topologies

This work focus on consensus control problem for networked multiple robotic manipulators with and without time-varying delays under directed switching topologies. Two different consensus protocols are proposed with considering dynamic uncertainties in networked robotic manipulators. First, we investigate a distributed adaptive consensus algorithm without communication delays under directed switching topologies in networks. A new analysis method for demonstrating the stability of the designed algorithm is provided by constructing a new matrix and utilizing matrix theory, graph theory, Lyapunov stability and Barbalat's Lemma. Then a consensus controller considering time-varying delays under directed switching topologies is presented. Furthermore, combining with the method for the case without delays, LMI technology is utilized to demonstrate the exponential stability problem. The distributed adaptive consensus control for multiple robotic manipulators with parametric uncertainties, time-varying delays and the directed switching topology is designed and analyzed in a unified framework. Numerical simulations finally prove the validity of the obtained results.