In a trajectory generation apparatus, position coordinates of an obstacle existing in a motion space of a robot arm is acquired. A hand position at a second time, which is a time next to a first time, is estimated by using a learning result of machine learning, based on the position coordinates of the obstacle, a subject joint state of the robot arm at the first time, and a target joint state of the robot arm. A non-interfering joint state of the robot arm at which the obstacle does not interfere with the robot arm at the second time is searched for by using the hand position as a restriction.