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In this paper, we propose three types of sensor-based path-planning algorithms and compare them as the image-based path-planning algorithm for a huge search space. In the general image-based path-planning, a camera mounted on a tip of a manipulator is seeking for an objective image while the manipulator is controlled in a joint space. As long as the number of degrees-of-freedom of a manipulator increases, the search space becomes exponentially huge. Though the sensor-based path-planning algorithm is a noncombination search, it sometimes spends much time to escape from a valley minimized by a local minimum. To overcome this problem, we use a modified version of the randomized algorithm as the best image-based path-planning algorithm for a huge search space. This tendency is checked by several simulation results. In addition, the version can be easily applied for a real problem as the classic visual servoing (the steepest descendent method) with memorizing a set of visited points and another set of their neighbor points, as well as generating a sequence of random motions.