Linear/Nonlinear PID Control of Cooperative Multiple Robot Manipulators: A Robust Approach

The issue of position/force control of collaborative robotic systems moving a payload is proposed in this paper. The proposed approach must be able to maintain the orientation/position of the payload on the reference trajectory while applying a limited force to the object through the robot's end-effector. With this in mind, linear/nonlinear PID control schemes have been proposed to achieve accurate and robust tracking performance. Lyapunov's stability analysis is utilized to confirm the stability of the controlled system. It proves that the controlled system is stable, while the object’s orientation/position tracking errors are uniformly ultimately bounded (UUB) in any bounded region of state space. It also presents some conditions for proper selection of the linear/nonlinear PID controllers’ gains in the form of two theorems. The proposed controllers apply to two coordinated 3DOF robotic arms that carry a payload. The simulation results tested two types of trajectories, including simple and complex paths. The results are also compared to those of a strong state-of-the-art approximator, the Chebyshev Neural Network (CNN).