| Summary: | The task-based control approach with an activation task mechanism endows a robot the possibility to act complex behaviors in an unstructured environment. However, the task-based control approach based on the classical inverse may suffer from discontinuities as tasks switch between inactive and active states. In this paper, an iteratively successive projection method is proposed to construct a null space projection operator by iteratively successive projecting the space between the null space of each task. And the null space projection operator constructed by the iteratively successive projection method should converge to the null space projection operator obtained by the classical inverse, as the iteration time increases to infinity. By introducing activation factors, a continuous projection operator is obtained with a finite-time iteration. Based on the continuous projection operator, a closed-loop control algorithm is presented, which ensures both the continuity of the joint motion and the boundedness of the tracking error. The simulations on a six-link planar manipulator for the trajectory tracking task in the presence of obstacles show the efficacy of the proposed method in continuity, stability, and calculation-time consumption.
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