Prescribed-Time Containment Control for Multiple Mobile Robot Systems

This article investigates the prescribed-time containment control problem for multiple wheeled mobile robots (MWMRs) with unknown control gains. A novel and generalized prescribed-time stability theorem is established, significantly advancing existing frameworks and facilitating controller design. For each follower, a distributed containment observer is developed to ensure that the observer state converges precisely to the convex hull formed by multiple leaders within a prescribed time. This approach effectively transforms the containment control problem into a more tractable tracking control problem, meanwhile enabling local reconstruction of unmeasured neighbor states using available observer outputs. Then, the type-B Nussbaum function is employed to eliminate the effects of the time-varying unknown control coefficient. Based on the developed prescribed-time theorem and the time-varying parametric Lyapunov equation (PLE), the fully actuated controllers are designed for the MWMRs. It can guarantee that the containment errors converge to zero within the prescribed time. Finally, simulation results validate the effectiveness of the proposed method.