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Path planning algorithms applicable to various agricultural operations, such as tillage, planting, and spraying, are needed to generate the guidance lines for auto-guidance tractors. An optimal coverage path algorithm can enable the vehicle to effectively travel the entire field along the path and with parallel paths at a fixed spacing. In addition, it is important to minimize the turning times of the vehicle at headlands to save the working time, especially in relatively small-sized rectangular paddy fields of 100 m x 40 m and 100 m x 100 m. This study reports on the development of path algorithms for an auto-guided Korean tractor with tillage implement to travel in paddy fields. Various turning algorithms, including C-,X-,and R- types, were developed, based on different minimum turn radiuses and other constraints due to a difference in vehicle body and implement dimensions. The direction angles for tractors were generated based on a waypoint tracking technique that uses waypoints and LBOs (Lateral Boundary Offset), which could be employed as an input command in a newly-designed auto-steering control system installed in a Dongyang TX803 tractor. Fundamental test results of using the developed algorithms indicated that the desired path and steering angles were generated with an acceptable level of accuracy.