  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.
