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A planning method for linear object manipulation including knotting/raveling in the three-dimensional space is proposed. Firstly, topological states of a linear object are represented as finite permutations of crossing points including the crossing type of each crossing point. Secondly, transitions among the topological states are defined. They correspond to operations that change the number of crossing points or crossing point permutation. Then, we can generate possible sequences of crossing state transitions, that is, possible manipulation processes from an initial state to a given objective state. Thirdly, a method for determination of grasping points and their moving direction is proposed in order to realize derived manipulation processes. Furthermore, criteria for evaluation of manipulation processes are introduced in order to reduce the candidates of manipulation plans. Finally, it is demonstrated that our developed system based on the above method can generate manipulation plans for raveling from an overhand knot.