Generating a contact state graph of polyhedral objects for robotic application

Traditional methods require large computation to model a contact state graph of polyhedral objects for robotic application, and moreover they are heuristic. In this paper, we propose a framework to generate the contact state graph automatically. All faces of the polyhedral objects are triangulated. A sub-contact is defined as single contact between two polyhedral objects and a contact state is presented with a set of the sub-contacts. There are two sub-contacts, a vertex-triangle contact and an edge-edge contact. According to convexity or concavity of the edges composing the triangle, the vertex-triangle contact and the edge-edge contact are classified into 10 types and 7 types, respectively. A contact state graph is made by evolutionary transitions of the sub-contacts. This procedure is accomplished only using the topology of the sub-contacts, which is possible in real-time. The proposed framework is evaluated by an example of square peg-in-hole assembly.