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An unmanned forklift requires precise positioning and pallet detection. Therefore, conventional unmanned forklifts use high-cost sensors to find the exact position of the pallet. In this study, a docking algorithm with two cameras is proposed. The proposed method uses vision data to extract the angle difference between the pallet and the forklift. Then the control law is derived from the extracted angle for successful docking. The extracted angle is compared with the actual angle in the real environment. The control law is tested with the Lyapunov stability test and Routh-Hurwitz stability criterion. Through various experiments, the proposed docking algorithm showed the success rate high enough for real-life applications.