To help another person, we need to infer his or her goal and intention and then perform the action that he or she was unable to perform to meet the intended goal. In this study, we investigate a computational mechanism for inferring someone's intention and goal from that person's incomplete action to enable the action to be completed on his or her behalf. As a minimal and idealized motor control task of this type, we analyzed single-link pendulum control tasks by manipulating the underlying goals. By analyzing behaviors generated by multiple types of these tasks, we found that a type of fractal dimension of movements is characteristic of the difference in the underlying motor controllers, which reflect the difference in the underlying goals. To test whether an incomplete action can be completed using this property of the action trajectory, we demonstrated that the simulated pendulum controller can perform an action in the direction of the underlying goal by using the fractal dimension as a criterion for similarity in movements.