Adaptive Dynamics-Based Prescribed-Time Control for Robots Formation Tracking in Task Space

Abstract

This article investigates the prescribed-time formation control in the task space of multirobot systems (MRSs), which is subject to the uncertain nonlinear dynamics and the position requirements. The strategy constructs a cascade system consisting of control and reference layers by connections of coupled prescribed-time control units, which separately guarantee the convergence of coordination errors, accuracy of states, and synchronization between layers. Meanwhile, the transformation from task space to joint space is built based on the pseudo-inverse of the Jacobi matrix, which avoids the singular value problem brought by computing the inverse kinematics. The adaptive control method utilizes parameter estimation to eliminate the inaccuracy problem brought by the pseudo-inverse of Jacobi matrix transformation. Then, this article provides solutions to the formation control and the formation along the trajectory control. Correspondingly, the Lyapunov analysis process proves the system’s stability and the parameter estimation’s boundedness, which confirms the sufficient conditions for realizing the prescribed-time formation control of the MRSs. Finally, this article presents examples of time-varying formation and along-trajectories formation, thereby demonstrating the effect of the controller.