The aging population phenomenon is increasing daily, making the realization of robots to help the elderly via human-robot collaboration an urgent need. However, in terms of the current research, there are many challenges in the realization of collaborative systems applied to help the elderly. The interaction methods used in related studies are single and unfavorable for the elderly, which not only affects the understanding of users' intentions but also brings burdens to the elderly. Moreover, these approaches generally ignore the flexibility of the division of labor and the degree of human need for assistance, which reduces the performance of goal completion and affects the elderly's evaluation of the robot escort. To this end, this paper designs and implements a human-robot collaboration system for helping the elderly (HRCS_EE). A multimodal fusion algorithm based on understanding and supplemented by inquiry is proposed. Additionally, a collaborative division strategy based on a cognitive model is researched, and a decision-making algorithm that aims to achieve the most efficient completion of collaborative tasks and minimize the burden on people is proposed. Finally, the method is verified and applied in a human-robot collaboration system based on repeated interaction. The experimental results show that the system can accurately and reliably obtain users' intentions in complex environments and correctly make division of labor decisions in line with the environment, so that the robot can provide the assistance that is truly needed by the elderly, which is well received by users.