Redundant robots are desired to execute multitasks with different priorities simultaneously. The task priorities are necessary to be transitioned for complex task scheduling of whole-body control (WBC). Many methods focused on guaranteeing the control continuity during task priority transition, however either increased the computation consumption or sacrificed the accuracy of tasks inevitably. This work formulates the WBC problem with task priority transition as an Hierarchical Quadratic Programming (HQP) with Recursive Hierarchical Projection (RHP) matrices. The tasks of each level are solved recursively through HQP. We propose the RHP matrix to form the continuously changing projection of each level so that the task priority transition is achieved without increasing computation consumption. Additionally, the recursive approach solves the WBC problem without losing the accuracy of tasks. We verify the effectiveness of this scheme by the comparative simulations of the reactive collision avoidance through multi-tasks priority transitions.
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