## 3 Materials and Methods
### Validation Methodology for a Main Instance of the Generic Planning Problem (IGPP)  
AI task planning used as a high-level control strategy can deliver the required autonomy and flexibility to an IGIS by generating plans to achieve any set goals. However, automated task planning approaches must cope in most scenarios with two challenges. The first is the large number of situational IGPs that can be derived for an IGIS and for which a plan may be required to be generated. The second challenge is the IGIS-specific planning process constraints. Such a constraint is the planning timeout. This defines the maximal duration during which a planner must generate a plan for a planning problem.  
To ensure that automated task planning can be reliably deployed in an IGIS, an extensive validation of the corresponding main IGPP is required (see Figure 6). The PDDL formulation of the main IGPP and the IGIS requirements are the inputs of our validation approach. These inputs are used to generate a representative set of PDDL planning problems for the situational IGPs, to plan for them under the given requirements, and to analyse the results. The analysis delivers values for defined quantities of interest (QoIs). The QoIs are used to determine the overall characteristics of the main IGPP. One characteristic is the availability of planning solutions (e.g., a plan) for the selected set of situational IGPs.  
In this study, we wished to achieve the availability of planning solutions for at least 90% of the situational IGPs for the custom grippers IGPP, under the constraint of a 10-s planning timeout. Planning in the presence of, or for, humans comes with hard requirements on the available planning time, which should not be longer than a couple of seconds [39].  
Figure 6: Validation methodology for a main IGPP.  
To better comprehend which situational IGPPs can be formulated for a main IGPP, we firstly analysed the task planning degrees of freedom for that IGPP. All possible combinations of the values that these degrees of freedom can take give the set of all possible situational IGPPs. Based on the assessment of these degrees of freedom, we have developed a task planning validation process for any IGPP.  
As presented in Section 3.2.3, the PDDL domain formulation of a main IGPP has a set of fixed predicates and actions, and therefore no degrees of freedom. Furthermore, the PDDL problem formulation of a main IGPP has a set of constants \(s_{0,const}\), the description of the scene \(s_{0,scene}\), and the status of the process steps \(s_{0,ps}\). The constants are the elements of the main IGPP that also reduce the number of degrees of freedom, as they are fixed. For example, each _thingpose_ is attached to one or more _agentposes_ with the _at_ predicate and does not change during the execution of a plan. Other constants are the properties of the _things_ (e.g., _movable_ or _placeable_). Another set of fixed configurations are those of the process steps. These configurations can be defined by the user or derived from a document with instructions. An example of such a document is the manual that describes the assembly steps for a product.  
In this context, the possible configurations of different _agents_, _items_, _tools_, and process steps are limited to only one set \(s_{0,const}\), specific for the main IGPP and all its situational IGPPs. However, other aspects can be varied. These aspects are, for example, the distribution of the _items_ and _tools_ at the _thingposes_ or the distribution of the _agents_ at the _agentposes_. The list of already-executed process steps, as well the list with the process steps to be carried out (e.g., the goals), can also be varied. Therefore, different sets \(s_{0,scene}\), \(s_{0,ps}\), and \(g\) can be formulated for the main IGPP. The scenes, the statuses of the process steps, and the goals are the degrees of freedom of the main IGPP that spawn the set of possible situational IGPPs considered in our validation approach.