An improved indirect iterative learning control algorithm for high-accuracy trajectory tracking in a planar parallel robot mechanism

To improve trajectory tracking accuracy in parallel mechanisms, an indirect ILC (iterative learning control) algorithm is proposed for a 3-PRR (three degrees of freedom with one prismatic pair and two revolute pairs) planar parallel mechanism. The proposed method maps workspace tracking errors into motor-pulse compensation through inverse kinematics, so that iterative learning is performed in the motor-pulse domain. To avoid repeated learning from cumulative errors during discretized trajectory execution, a cumulative-error model is established, and the effective single-step motion error is extracted as the learning signal. The kinematic model of the 3-PRR mechanism is first developed, followed by the design of indirect open-loop and closed-loop ILC algorithms. Convergence conditions are analyzed, and simulations are conducted to evaluate gain selection and disturbance robustness. Experiments are then performed on a fully closed-loop platform equipped with laser displacement sensors. In the representative experiment, the indirect closed-loop ILC achieves a mean trajectory tracking error of 0.0028 mm, an RMS error of 0.0033 mm, and a maximum error of 0.0115 mm. These results demonstrate that the proposed method improves high-accuracy trajectory tracking and provides an effective learning control strategy for parallel mechanisms.