## 4 Results  
This section presents the results of the analysis carried out on the custom grippers main IGPP. The inputs of this analysis were the situational IGPs with their variations with respect to the scenes and process steps. For each of these situational IGPs, plans were computed with a timeout of 10 seconds. Four different automated planners were deployed for each situational IGPP: popf [40], optic [41], tflap [42], and tfd [43]. For each obtained plan, three characteristics were derived:  
1. _solvability_: Whether a solution was found in the timeout period of 10 s;
2. _makespan_: If a solution was found, the makespan (latest end time of the actions from a plan) of the plan was determined;
3. _mr_actions_: If a solution was found, the number of actions of that plan was determined. The three characteristics of each plan were analysed in a context (e.g., over all situational IGPs with a specific number of process steps \(n_{ps}\)) and quantities of interest (QoIs) were determined. The QoIs for a set of plans were:  
* QoI 1: Percentage of solved situational IGPs;
* QoI 2: The mean of the plans' makespans;
* QoI 3: The mean of the plans' numbers of actions. For the custom grippers main IGPP, \(n_{scene}=250\) scenes were generated. Corresponding to the DG from Appendix A, \(141+101+55+27+14=338\) pairs of start-process-steps  
Figure 9: The four sub-figures present combinations of start-process-steps sets (blue vertices) and finish-process-steps sets (red vertices): (**a**) is an allowed combination of an \(\hat{st}_{ps,i}\) and an \(\hat{f}_{ip,j}\), where \(n_{ps}=1\); (**b**) is a not-allowed combination of an \(\hat{st}_{ps,i}\) and an \(\hat{f}_{ip,j}\); (**c.d**) are two allowed combinations of an \(\hat{st}_{ps,i}\) and an \(\hat{f}_{ip,j}\), where \(n_{ps}=2\). sets and finish-process-steps sets, for different \(n_{ps}\in\{4,6,8,10,12\}\), were created. By combining all scenes with all process steps configurations, 84,500 situational IGPPs formulated in PDDL were obtained. Each of the obtained situational IGPPs was solved with the four planners, resulting in a total of 338,000 runs. The first computed QoI was the percentage of solved situational IGPPs. The percentage was computed over all scenes and variations in the initial and goal states, for each \(n_{ps}\) value, and for each of the four planners. The results are presented in Table 1.  
The results show that the tfd planner managed to solve more than 90% of the situational IGPPs corresponding to each different number of goals. The optic planner delivered a success rate greater than 84% in finding a plan in all sets of situational IGPPs for different \(n_{ps}\) values. The next two QoIs were the mean of the plans' makespans and the mean of the plans' numbers of actions, over a subset of all situational IGPPs. This subset contained all situational IGPs for all scenes, for a given \(n_{ps}\), and a given planner. The _makespan_ and _nr_actions_ characteristics of the obtained plans were normalized, to enable a comparison of the results of the different subsets (e.g., different \(n_{ps}\) values and planners). For the normalization of the data, the _min-max_ approach was used:  
\[x_{norm}=\frac{x-x_{min}}{x_{max}-x_{min}}. \tag{5}\]  
Here, \(x_{min}\) and \(x_{max}\) are computed for the makespans and numbers of actions of all situational IGPP variations corresponding to one \(n_{ps}\) value but independent of the planner used to solve them. Figure 10 depicts the obtained results. The planners popf and optic computed, in most cases, the plans with the lowest mean makespan. However, the planners tflap and popf generated the plans with the lowest mean numbers of actions for almost all \(n_{ps}\) values. The planner tfd usually generated plans with the highest mean makespans and the highest mean numbers of actions.