Combined Adaptive-robust and Neural Network Control of Two RLED Cooperating robots using backstepping Design

In this paper, a combined adaptive-robust and neural network control based on backstepping design is proposed for trajectory tracking of two 6-DOF rigid link electrically driven (RLED) elbow robot manipulators moving a rigid object when actuator dynamics is also considered in the system dynamics. First, the authors derive kinematics and dynamics of the mechanical subsystem and the relations among forces/moments acting on the object by the robots, using different Jacobians. Second, the current vector (instead of the torque vector) is regarded as the control input for the mechanical subsystem and, using an adaptive-robust algorithm, an embedded control variable for the desired current vector is designed so that the tracking goal may be achieved. Third, using a neural network controller for DC motor dynamics, the voltage commands are designed such that the joint currents track their desired values. The proposed control algorithm does not require exact knowledge of the mathematical model representing each robot and its actuator dynamics and does not need acceleration measurement. The adaptive-robust control parameters and neural weights are adapted online, and the related Lyapunov function is established and verified. The proposed combined controller guarantees asymptotic tracking of the object desired trajectory. Simulation results show the efficiency and usefulness of the proposed scheme.