提出方向约束控制，让机器人在复杂任务中更顺滑地响应人机交互意图。

This paper proposes a control method to address the physical Human-Robot Interaction (pHRI) challenge in the context of hierarchical tasks. A common approach to managing hierarchical tasks is Hierarchical Quadratic Programming (HQP), which, however, cannot be directly applied to human interaction due to its allowance of arbitrary velocity direction adjustments. To resolve this limitation, we introduce the concept of directional constraints and develop a direction-constrained optimization algorithm to handle the nonlinearities induced by these constraints. The algorithm solves two sub-problems, minimizing the error and minimizing the deviation angle, in parallel, and combines the results of the two sub-problems to produce a final optimal outcome. The mutual influence between these two sub-problems is analyzed to determine the best parameter for combination. Additionally, the velocity objective in our control framework is computed using a variable admittance controller. Traditional admittance control does not account for constraints. To address this issue, we propose a variable admittance control method to adjust control objectives dynamically. The method helps reduce the deviation between robot velocity and human intention at the constraint boundaries, thereby enhancing interaction efficiency. We evaluate the proposed method in scenarios where a human operator physically interacts with a 7-degree-of-freedom robotic arm. The results highlight the importance of incorporating directional constraints in pHRI for hierarchical tasks. Compared to existing methods, our approach generates smoother robotic trajectories during interaction while avoiding interaction delays at the constraint boundaries.