Novel adaptive robust L1‐based controllers for teleoperation systems with uncertainties and time delays

Despite various proposed control schemes for uncertain bilateral teleoperation systems under time delays, optimally restricting the system's overshoot has remained an overlooked issue in this realm. For this aim, we propose two novel control architectures based on robust L1 theory, entitled position‐based adaptive L1 controller and transparent adaptive L1 controller, with the former focusing on position synchronization and the latter concerning system transparency. Since developing L1‐based controllers for nonlinear telerobotic systems encompassing uncertainty and round‐trip delays puts significant theoretical challenges forward, the main contribution of this paper lies in advancing L1 theory within the field of delayed teleoperation control. To formulate the theories, the asymptotic stability of the closed‐loop system for each controller is first proved utilizing the Lyapunov method, followed by transformation, along with the L1 performance criterion, into linear matrix inequalities. Ultimately, the control gains are attained by solving a convex optimization problem. The superiority of the designed controllers over a benchmark transparent controller for teleoperators is demonstrated via simulation. Furthermore, experimental tests on a two‐degrees‐of‐freedom nonlinear telerobotic system validate the efficient performance of the proposed controllers.