As society continues to age, improving the quality of life for the elderly with the help of intelligent technology has become a research hotspot, and the field of home care robots has attracted significant attention. However, due to physiological and psychological factors, the interaction between the elderly and robots still has great challenges. Based on the theoretical foundation of peripheral interaction, this study focuses on the cognitive burden of elderly users interacting with robots. Through theoretical research and scene simulation experiments, the process of attention changes when the elderly use the robot in different scenarios is systematically analyzed, the theoretical model of peripheral interaction applicable to the home aging scenario is explored. On this basis, the design strategy of the home elderly robot is then proposed to provide theoretical references for the human-robot interaction design of related smart elderly products, to solve the application problems of digital products and services for the elderly.