## 3 Task-Based Dynamic Disassembly Process Model  
In this section, a task-based dynamic disassembly process model is developed to depict all the potential disassembly sequences of completely separating a product into its components and consider the uncertainty of the disassembly process. Before discussing the model, some related terminologies need to be defined. The basic elements of a product include the components that make up the product and the connections between them. These elements are generally represented using a connection diagram. A disassembly operation is the detachment of a component or a subassembly, represented by a cut-set in the corresponding connection diagram. A disassembly process is a sequence of disassembly operations through which a product is separated into its components. Restricted by topological constraints, geometric constraints, and technical constraints of the product, these operations need to be performed in a specific order. These orderly operations in the disassembly process are also known as disassembly sequences. In general, numerous possible disassembly sequences can be applied to disassemble a product completely. The transformed AND/OR graph (TAOG) [7] is a frequently used disassembly process model representing all these possible disassembly sequences and precedence relationships among all operations in these sequences. In the TAOG representation, nodes are divided into artificial and normal nodes. Artificial nodes represent subassemblies and components, while normal nodes correspond to disassembly operations. The precedence relationships between artificial nodes and normal nodes are represented by the arcs connecting the nodes. Two types of hyperarcs are emphasised to differentiate between AND relationships and OR relationships. An AND-type hyperarc is adjacent to one normal node and two artificial nodes. A disassembly operation can split a product or subassembly into two subassemblies. An OR-type hyperarc is adjacent to one artificial node and adjacent to one or more normal nodes, which indicates that one or more follow-up disassembly operations can be selected, and only one of these operations should be processed. Using a TAOG as the input to the DLB problem implies that the selection of disassembly sequences and the assignment of the selected disassembly sequence are considered simultaneously. However, the TAOG representation ignores the fact that each disassembly operation is complex, requiring multiple humans or robots to work collaboratively in multiple steps. A disassembly operation must be subdivided into multiple elementary tasks to facilitate execution. These tasks involve not only some disassembly tasks, such as disconnecting all connections in the corresponding cut-set, but also some additional tasks, such as component state detection, fixture establishment, robot moving, tool changing, and product transferring. A proper disassembly process model should be able to represent tasks rather than disassembly operations alone, and DLB problems should consider the assignment of tasks rather than the assignment of disassembly operations alone. In addition, used products may contain rusty, deformed, or missing components, together with the variable ability and uncertain behaviour of humans, which determine that the disassembly process is dynamic and uncertain. The TAOG representation cannot model these characteristics of the disassembly process. For the reasons given above, we developed another disassembly process model called a task-based dynamic TAOG (TD-TAOG). It is an extended version of a TAOG containing all possible disassembly operations, and all possible tasks can also consider the dynamics and the uncertainty of the disassembly process. A TD-TAOG contains complete information about the dynamic disassembly process of a product. TD-TAOG is divided into the operation layer and the task layer. The operation layer corresponds to the TAOG of the product.