Fractional-Order Disturbance-Rejection Computed Torque Control for Task-Oriented Robotic Manipulator Tracking

This paper investigates the task-space position tracking problem of a redundant manipulator under multiple disturbances. Different from conventional joint-space tracking schemes, the considered task only constrains the end-effector position, leaving redundant degrees of freedom to be exploited for secondary optimization. However, conventional computed torque control is sensitive to dynamic-model mismatch, while integer-order equivalent input disturbance compensation has limited flexibility in balancing disturbance tracking and noise attenuation. To address these limitations, a composite control framework is proposed by integrating task-space position error regulation, null-space redundancy optimization, and a fractional-order equivalent input disturbance compensation (FEIDC) strategy. The task-space controller generates the desired acceleration, which is mapped to the joint acceleration command through a damped pseudoinverse Jacobian, and a null-space term is incorporated to optimize secondary criteria. For the feedback-linearized joint dynamics, the proposed FEIDC introduces a fractional-order filter into the equivalent input disturbance estimation channel, providing an additional order parameter for shaping disturbance attenuation and noise sensitivity. Simulation validation on a UR5e manipulator compares the effectiveness of the proposed method with sliding mode control (SMC), active disturbance rejection control (ADRC) and integer-order equivalent input disturbance compensation strategy (IEIDC). In comparisons with SMC, ADRC, and IEIDC, the proposed FEIDC achieves the lowest joint and Cartesian RMSEs, namely, 7.2863×10−4 rad and 3.8035×10−4 m, respectively.