Safe Task Space Synchronization with Time-Delayed Information

Abstract: In this paper, an adaptive controller is designed for the synchronization of the trajectory of a robot with unknown kinematics and dynamics to that of the current human trajectory in the task space using the delayed human trajectory information. The communication time delay may be a result of various factors that arise in human-robot collaboration tasks, such as sensor processing or fusion to estimate trajectory/intent, network delays, or computational limitations. The developed adaptive controller uses Barrier Lyapunov Function (BLF) to constrain the Cartesian coordinates of the robot to ensure safety, an ICL-based adaptive law to account for the unknown kinematics, and a gradient-based adaptive law to estimate unknown dynamics. Barrier Lyapunov-Krasovskii (LK) functionals are used for the stability analysis to show that the synchronization and parameter estimation errors remain semi-globally uniformly ultimately bounded (SGUUB). The simulation results based on a human-robot synchronization scenario with time delay are provided to demonstrate the effectiveness of the designed synchronization controller with safety constraints.