An autonomous mobile robot in a human living space should be able to not only realize collision-free motion but also give way to humans depending on the situation. Although various reactive obstacle avoidance methods have been proposed, it is difficult to achieve such motion. On the other hand, 3D X-Y-T space path planning, which takes into account the motion of both the robot and the human in a look-ahead time horizon, is effective. This paper proposes a real-time obstacle avoidance method for an autonomous mobile robot that considers the robot's dynamic constraints, the personal space, and human directional area based on grid-based 3D X-Y-T space path planning. The proposed method generates collision-free motion in which the robot can yield to humans. To verify the effectiveness of the proposed method, various experiments in which the human's position and velocity were estimated using laser range finders were carried out.