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This paper presents a path prediction model for obstacle avoidance. A geodesics model is used to obtain the desired path in Cartesian space. The distance between the start target point (and end target point) and the surface of an obstacle is minimized to determine the boundary points of a geodesic across the surface of the obstacle. The model then numerically solves for a geodesic curve between the two boundary points of the geodesic on the surface of the obstacle. The model offsets the resulting discrete points on the geodesic in the positive normal direction (outside of the obstacle) to form a path of motion around the obstacle.