For successful acceptance and engagement with domestic robots, it is essential to understand individual differences in people’s attitude and preference, and to match appropriate types of robots according to such individual differences. However, in many cases, robot characteristics are described from the viewpoints of engineers and not from those of people who actually use. The purpose of this study was to investigate dimensions of robot characteristics that people perceive important for their engagement with robots. Potential set of elements was extracted from people’s free descriptions and interviews as well as literature review. A questionnaire-based investigation and a factor analysis were conducted to identify dimensional structure of robot characteristics that people perceive as important for their engagement with robots. The extracted factors were compared with variables representing people’s engagements with robots to show its relevance to a variety of engagements. Finally, The Multi-dimensional Perceived Robot Characteristics Scale, a questionnaire-based measurement to assess these dimensions of robots, was proposed based on the extracted factor structure.