Linear learning control of robot motion

For the trajectory following problem of a robot manipulator, a new 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 (PDD2). It has been shown that, under the proposed learning control, the position, velocity, and acceleration tracking errors are asymptotically stable in the presence of highly nonlinear dynamics. The proposed control is robust in the sense that exact knowledge about nonlinear dynamics is not required except for the bounding functions on their magnitudes. Further, neither is linear approximation of nonlinear dynamics nor repeatability of robot motion required.