Representation and planning of deformable linear object manipulation including knotting

A qualitative representation method and a rough planning method of linear object manipulation including knotting in the three-dimensional space is proposed. Firstly, states of a linear object are represented as finite permutations of crossing points including the crossing type of each crossing point. Secondly, state transitions among those states are defined. They correspond to operations which change the number of crossing points or permutate their sequence. Then, we can generate possible sequences of crossing state transitions, that is, possible manipulation processes when the initial state and the objective state are given. Thirdly, a method for determination of grasping points and their moving direction in order to realize derived manipulation processes is proposed. Furthermore, some criteria for evaluation of manipulation processes are introduced in order to narrow down candidates for manipulation plans. Finally, that our proposed method can be applied to the rough planning of linear object manipulation is demonstrated.