This paper addresses the sequence-finding problem for a carton-folding task which requires the possibility that a feasible folding sequence of packaging cartons can be applied to a multi-fingered packaging unit. After reviewing the previous contributions to the related sequence task, this paper presents a solution to the folding sequence of cartons based on robotics and graph theory. Firstly a packaging carton is modelled as a virtual mechanism, whose links represented by panels of carton and joints by folds. Secondly the concept of a hereditary connectivity matrix (HCM) is introduced, which includes both the adjacency and configuration transformation of links of the virtual mechanism. Then a non-searching sequence-finding algorithm is produced to aim at giving a feasible packaging sequence of a foldable carton and giving a folding trajectory for providing the position and even orientation of a multi-fingered packaging unit in carton-folding manipulation. In the end, the simulation result for folding a particular carton is given.

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