Human–robot interaction has extended its application horizon to simplify how human beings interact with each other through a remotely controlled telepresence robot. The fast growth of communication technologies such as 4G and 5G has elevated the potential to establish stable audio–video-data transmission. However, human–robot physical interactions are still challenging regarding maneuverability, controllability, stability, drive layout, and autonomy. Hence, this paper presents a systematic design and control approach based on the customer’s needs and expectations of telepresence mobile robots for social interactions. A system model and controller design are developed using the Lagrangian method and linear quadratic regulator, respectively, for different scenarios such as flat surface, inclined surface, and yaw (steering). The robot system is capable of traveling uphill (30\(^{\circ }\)) and has a variable height (600–1200 mm). The robot is advantageous in developing countries to fill the skill gaps as well as for sharing knowledge and expertise using a virtual and mobile physical presence.