## 3 Materials and Methods
### The Generic Planning Problem (GPP) for the GIS and Its Instances in PDDL  
To increase the automation degree of industrial processes with robotic mobile manipulators, automated planning methods can be used as a high-level control strategy. As presented in the related work in Section 2, automated planning approaches offer high execution flexibility and autonomy to the system and are already deployed in a large number of real-world applications. Different automated planning approaches exist. Planning problems can be formulated as classical or temporal planning problems [5] in the Planning Domain Definition Language (PDDL) [33], as hierarchical task networks (HTN) [34], or as flexible timelines [35] and solved with corresponding solver. Each planning approach has its advantages and disadvantages. However, their comparison is not the topic of this work and is not discussed further here. In this work, we focus on the formulation of a generic planning problem (GPP) for the generic industrial scenario (GIS). Furthermore, we describe how instances of the generic planning problem (IGPPs) can be derived for IGISs. Both the GPP and the IGPPs are formulated as temporal planning problems in PDDL. The following lines briefly introduce the theoretical aspects of classical and temporal planning problems, as well as the Planning Domain Definition Language that was used for the formulation of these planning problems. **Definition 1**. : _A classical planning problem \(\Pi\) is a 4-tuple \(\Pi=\langle S,A,s_{0},g\rangle\) where \(S\) is a finite set of states \(s\) described with state variables \(x\), \(A\) is a finite set of actions where every action \(a\in A\) has some preconditions \(a_{pre}\) and effects \(a_{off}=\langle a_{add},a_{del}\rangle\), \(s_{0}\in S\) is the initial state, and \(g\) is a set of goals. A solution to the planning problem is a plan \(\pi\) containing a set of grounded actions \(a_{i}\in A\) that bring the system from \(s_{0}\) to a goal state in which the goals from \(g\) hold._  
In PDDL, classical planning problems are described in two different files. The domain file contains the definition of object types, predicates, and actions. PDDL object types are classes (e.g., item) for which instances are defined in the problem file (e.g., corner, tube); PDDL predicates \(p\) correspond to the state variables \(x\) from Definition 1 and have as parameters one or more objects types; PDDL actions correspond to the action \(a\in A\) from Definition 1 and have as parameters zero or more object types. **Definition 2**. : _A predicate \(p\) or an action \(a\) is called grounded if all its parameters are instantiated to objects (e.g., corner) of the corresponding object type (e.g., item)._  
Figure 3: The relations between the process steps on the different items of product \(A\). In this context, a state \(s\in S\) from Definition 1 is described by a list of true grounded predicates. Grounded predicates that do not hold (e.g., are false) are not part of the description. The initial state \(s_{0}\) and the goals \(g\) of the planning problem \(\Pi\) are also formulated as a list of grounded predicates. The initial state and the goals, together with the instantiated object types, form the second PDDL file, i.e., the problem file. A solution to a planning problem \(\Pi=\langle S,A,s_{0},g\rangle\) is the plan \(\pi=[a_{1},\ldots,a_{n}]\), containing grounded actions \(a_{i}\). The actions \(a_{i}\) are selected and grounded in the solving process such that their preconditions \(a_{pre}\) hold in the state \(\tilde{s_{i}}\) to which they are applied (e.g., \(a_{1}\) is applied to \(s_{0}\)). Furthermore, each \(a_{i}\) applies to the state \(\tilde{s_{i}}\)_add_ and _del_ effects. The _add_ effects extend the description of \(\tilde{s_{i}}\) with new grounded predicates, while the _del_ effects remove grounded predicates from the description of \(\tilde{s_{i}}\).