Facing the enduring COVID-19 pandemic, Internet of Things and mobile robots have played an important role in the control of the spread of coronavirus in enterprises, campuses, and in the transportation of Fangcang hospitals. However, mainstream mobile robots still have unsatisfactory performance in indoor and outdoor positioning and navigation in terms of the processing environment, overburdened computing power, and insufficient positioning accuracy. This paper proposes a cloud computing framework based on a quadruped robot for indoor and outdoor hybrid positioning. The purpose is to broaden the application of mobile robots in Internet of Things, such as operating in complex terrain with stairs, slopes, indoor, outdoor, and etc.