It needs much computation to develop a contact state graph and find an assembly sequence because polyhedral objects consist of a lot of vertices, edges, and faces. In this paper, we propose a new method to eliminate unnecessary contact states in the contact state graph corresponding to a robotic assembly task. In our method, the faces of polyhedral objects are triangulated, and the adjacency of each vertex, edge, and triangle between an initial contact state and a target contact state is defined. Then, this adjacency is used to create contact state graphs at different priorities. When a contact state graph is finished at a higher priority, a lot of unnecessary contact states can be eliminated because the contact state graph already includes at least one realizable assembly sequence. Our priority-based method is compared with a face-based method through statistically analyzing the contact state graphs obtained from different assembly tasks. Finally, our method results in a significant improvement in the final performance
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