Coordination control for bilateral teleoperation with kinematics and dynamics uncertainties

• Task-space based new controllers are proposed for the different sizes of master and slave.
• Both the dynamics uncertainties and the system kinematics uncertainties are considered.
• The FLs and parameter adaptive method are developed to deal with the uncertainties.
• The delay-dependent stability criterion is derived.

The coordination control design problem for the master–slave system is addressed in this paper. In order to meet the actual work condition, we assume that the master works in a laboratory, the slave works in remote side where the environment is very complex, and the master and slave are in different sizes. Three problems are needed to be solved: system dynamics uncertainties, system kinematics uncertainties, and the asymmetric time-varying delays. The new task-space based Proporation plus damping (P+d) controller and adaptive fuzzy P+d controller are proposed for the master and the slave, respectively. By choosing proper Lyapunov functions, we have proved that the synchronization errors converge to zero asymptotically with the new controllers. The delay-dependent stability criterion is derived. With the given parameters, the proposed allowable maximal transmission delay can be computed. Finally, the simulations are performed to show the effectiveness of the proposed method.