Containment Control of Multirobot Systems With Nonuniform Time-Varying Delays

The containment of multirobot systems (MRSs) has a wide range of applications. However, time delays in communication among robots introduce difficulties to the system to accomplish containment. In addition, the specific dynamics of robot models pose new nonlinear and nonholonomic challenges. To solve these problems, a containment control law is proposed first for double-integrator MRSs subject to nonuniform time-varying delays. In contrast to impractical uniform delays, nonuniform time-varying delays are considered more deeply from the perspective of the Laplacian matrix in this article. The stability is proved by the Lyapunov-Krasovskii function and linear matrix inequalities. The proposed control law is further refined into a dual-loop structure for multi-nonholonomic-mobile-robot systems, addressing the problem of nonholonomic constraints. Specifically, the first loop decouples the control inputs in a finite time, and then the nonholonomic robot models are regarded as linear models, which facilitates the proof of system stability. The effectiveness of the aforementioned two control laws is validated through simulations and experiments. Under these containment control laws, followers in the system reach the convex hull formed by leaders and meet the convergence objective despite the constraint of nonuniform time-varying delays.