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.

Multi-mobile robot systems (MMRSs) show great advantages over one single robot in many applications. However, the robots are required to form desired task-specified formations, making feasible motions decrease significantly. Thus, it is challenging to determine whether the robots can pass through an obstructed environment under formation constraints, especially in an obstacle-rich environment. Furthermore, is there an optimal path for the robots? To deal with the two problems, a novel graph-based motion planner is proposed in this article. Valid configurations of the system are defined to satisfy both formation and obstacle constraints. Then, the whole valid configuration space is identified and mapped to an undirected graph. The breadth-first search (BFS) method is employed on the graph to answer the question of whether there is a feasible path on the graph. Finally, an optimal path will be planned on the updated graph, considering the cost of path length and formation preference. Simulation results show that the planner can be applied to get optimal motions of robots under formation constraints in obstacle-rich environments. In addition, different types of constraints are considered to verify the generality.