Prioritizing multiple tasks has been achieved with null space projection. However, null space projection becomes inaccurate when there are uncertainties in the model, and few studies have addressed this issue. Disturbance observers (DOBs) have been effectively utilized to address disturbances and uncertainties in robot control. However, conventional DOB designs fail to resolve the coupling issue when uncertainties are associated with null space projection. To address this challenge, in this article, we propose a novel hierarchically decoupled disturbance observer (HDDOB) design within a hierarchically decoupled task space (HT space). First, we introduce the concept of hierarchical disturbance to quantify the coupling effect caused by the inaccuracy in the null space projection to highlight the limitations of conventional DOB-based approaches. Second, we propose a novel control framework that utilizes the HT space as the control space. In this framework, the dynamics is reformulated, taking into consideration the task priorities, including the null space projection. Third, we propose the HDDOB to effectively ensure robustness to disturbances and uncertainties without generating hierarchical disturbances between tasks. The effectiveness of the proposed HDDOB is demonstrated through comprehensive validations such as stability analysis and experiments. The results show that the HDDOB effectively maintains robust control performance by preventing hierarchical disturbances.
