A new learning control scheme for robots

For the trajectory following problem of a robot manipulator, a novel linear learning control law, consisting of the conventional proportional-integral-differential (PID) control law, with respect to position tracking error, and an iterative learning term, is provided. The learning part is a linear feedback control of position, velocity, and acceleration errors. It is shown that this learning control can make the position, velocity, and acceleration tracking errors asymptotically stable in the presence of highly nonlinear dynamics. It is also shown that the proposed control is robust in the sense that no knowledge about nonlinear dynamics is required except for its bounding function. As a consequence, neither linear approximation of nonlinear dynamics nor repeatability of robot motion is required. A constructive algorithm for choosing the control gains is also provided. A simple two-degrees-of-freedom manipulator was simulated to test the proposed learning control law