Mapping for stable bilateral teleoperation of manipulators considering time delays

Teleoperation of manipulators has allowed extending the human skills to several areas, where the commands generated by a human operator on the leader robot are followed by a remote robot. For this purpose, position-position tracking requires a mapping given the mismatch between robot workspaces. This paper compares a pair of functions for mapping the haptic device commands to handle a remote robot, considering non-identical workspaces and a classic P+d control scheme. As part of the theoretical analysis, a Lyapunov-Krasovskii-based stability analysis is developed in steps, allowing us for determining the boundedness of velocities and coordination errors. Subsequently, the performance of the teleoperation system is compared using two mapping functions. To achieve a fair comparison of results, a test protocol is developed, where different levels of haptic device damping, time delays, and workspace scales are used to evaluate the time to complete the task and the average coordination errors. Based on the results, the mapping function influences the calculation of force feedback, stability of the system, and performance metrics. During a pick-and-place task, a reduction in coordination error is observed when the linear function is chosen, while the time to complete the task is lower when a non-linear function is considered.