In this paper, we propose a long-term motion model for visual object tracking. In crowded street scenes, persistent occlusions are a frequent challenge for tracking algorithm and a robust, long-term motion model could help in these situations. Motivated by progresses in robot motion planning, we propose to construct a set of ‘plausible’ plans for each person, which are composed of multiple long-term motion prediction hypotheses that do not include redundancies, unnecessary loops or collisions with other objects. Constructing plausible plan is the key step in utilizing motion planning in object tracking, which has not been fully investigate in robot motion planning. We propose a novel method of efficiently constructing disjoint plans in different homotopy classes, based on winding numbers and winding angles of planned paths around all obstacles. As the goals can be specified by winding numbers and winding angles, we can avoid redundant plans in the same homotopy class and multiple whirls or loops around a single obstacle. We test our algorithm on a challenging, real-world dataset, and compare our algorithm with Linear Trajectory Avoidance and a simplified linear planning model. We find that our algorithm outperforms both algorithms in most sequences.