--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. T o 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. T o 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. Compared to existing methods, our approach generates smoother robotic trajectories during interaction while avoiding interaction delays at the constraint boundaries. Recent advancements in physical Human-Robot Interaction (pHRI) have significantly improved robots' abilities to support individuals [1] [2]. For example, pHRI has shown promising results in tasks such as load transportation [3], collaborative drawing [4], surface polishing [5], assembly [6], rehabilitation [7], etc. This work was conducted while Mengxin Xu was a visiting researcher at Osaka University, Japan. It was partially supported by the Natural Science Foundation of China under Grant 62225309, 62073222, U21A20480 and U1913204. Mengxin Xu is with the Department of Automation, Shanghai Jiao Tong University, Shanghai 200240, China (e-mail: mengxin xu@sjtu.edu.cn). Weiwei Wan and Kensuke Harada are with the Department of System Innovation, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-0043, Japan (e-mail: wan@sys.es.osaka-u.ac.jp, harada@sys.es.osaka-u.ac.jp). Hesheng Wang is with the Department of Automation, the Key Laboratory of System Control and Information Processing of Ministry of Education and the Shanghai Engineering Research Center of Intelligent Control and Management, Shanghai Jiao Tong University, Shanghai 200240, China (email: wanghesheng@sjtu.edu.cn). In pHRI, the robot can reduce both the physical and cognitive load on humans, while humans contribute valuable guidance based on their experience.