Application of Half-Derivative Damping to Cartesian Space Position Control of a SCARA-like Manipulator

In classical Cartesian space position control, KD, the end-effector follows the set-point trajectory with a stiffness expressed in the directions of the external coordinates through the stiffness matrix, K, and with a damping proportional to the first-order derivatives of errors of the external coordinates through the damping matrix, D. This work deals with a fractional-order extension of the Cartesian space position control, KDHD, which is characterized by an additional damping term, proportional to the half-order derivatives of the errors of the external coordinates through a second damping matrix, HD. The proposed Cartesian position control scheme is applied to a SCARA-like serial manipulator with elastic compensation of gravity. Multibody simulation results show that the proposed scheme was able to reduce the tracking error, in terms of mean absolute value of the end-effector position error and Integral Square Error, with the same amount of Integral Control Effort and comparable maximum actuation torques.