Abstract: Currant research on the motion control strategies of the social robots walking side-by-side with a target human body (i.e. human accompanying and obstacle avoidance) is deficient. To improve the accompanying comfort level, and the motion compliance and safe obstacle-avoidance performances of the robot, a human-accompanying and obstacle-avoidance control strategy is proposed based on admittance control. Firstly, an interaction force model is designed based on the theory of human-robot interaction space, which describes the dynamic human-robot interaction relationship to prevent the robot from infringing into the companion's intimate area, thereby enhancing the comfort level of the companion. Secondly, the admittance control model is combined with the interaction force model to improve the motion compliance of the robot through optimal admittance parameters. Finally, a behavioral dynamics model is introduced to simulate the human obstacle-avoidance behavior, thereby ensuring the safety of the human-accompanying task. Additionally, a set of evaluation indexes are proposed for human-accompanying performance. The simulation results show that the robot velocity change under the proposed method is reduced by 69.6% and 67.1% respectively compared with PID (proportional-integral-derivative) and VSM (virtual spring model) methods, demonstrating its advantages in terms of compliance; in terms of comfort, the robot doesn't cause discomfort to humans; in terms of safety, the obstacle-avoidance failure rate of the proposed method is only 10%, better than the 40% and 50% of APF (artificial potential field) and VSM methods. In the physical experiment, the robot exhibits better compliance and comfort performances, and the obstacle-avoidance failure rate is only 5%. Therefore, the proposed method effectively achieves safe and friendly human accompanying and obstacle-avoidance control.