# Detecting and Solving Tube Entanglement in Bin Picking Operations
## 4 Experiments
### Results
Table 7 shows how often the entanglement resolution phase was used. Since Set A had a 100% picking success rate with the simulator, this phase was never needed. For Set B, the rate is also quite low since the trajectory simulator had a moderately high success. The usage rate does not seem to vary significantly with the amount of tubes, which is coherent with the previous observation that this solution solves tougher cases of entanglement as late as possible during a round. Table 8 presents the success rate of the entanglement resolution phase. The success rate for Set B was rather low, most likely due to one key observation that was made when the experiments were conducted: most of the time, a rotation of 45\({}^{\circ}\) was not enough to make the other tubes fall because the friction for the rubber material is too high. Higher angles were not attempted as they increased the chances of the tubes falling outside the bin. To increase the likelihood of solving the entanglement, a positive and negative rotation of 45\({}^{\circ}\) (or possibly more, with the appropriate setup) could be \begin{table}
\begin{tabular}{c c c} \hline \hline  & Success rate (upwards trajectories) & 100\% \\  & Success rate (escape trajectories) & 100\% \\
**Set A** & Success rate (total) & 100\% \\  & Number of upward trajectories & 7 \\  & Number of escape trajectories & 3 \\  & Number of uses of simulation & 10 \\ \hline \hline  & Success rate (upwards trajectories) & 63\% \\  & Success rate (escape trajectories) & 78\% \\
**Set B** & Success rate (total) & 68\% \\  & Number of upward trajectories & 16 \\  & Number of escape trajectories & 9 \\  & Number of uses of simulation & 25 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Percentages of picking attempts where trajectory evaluation was performed that resulted in a successful pick. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Number of tubes in the bin** & 7 & 6 & 5 & 4 & 3 & 2 & 1 & Overall \\ \hline
**Set A** & 0\% & 0\% & 0\% & 0\% & 0\% & 0\% & 0\% \\ \hline
**Set B** & 13\% & 5\% & 0\% & 14\% & 14\% & 5\% & 0\% & 8\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Percentages of picking attempts where the entanglement resolution phase was performed. applied according to an axis contained in the xOy plane that is perpendicular to the torque vector \(\overrightarrow{\Delta M}\). Furthermore, negative rotations could be experimented around the axis defined by this vector. In none of the experiments was there a case where all of the tubes had two or more occlusions (strongly-occluded tubes). In these scenarios, one could experiment using the upwards trajectory and, as an alternative, a set of escape trajectories that take into account the properties of each occlusion. Then, the simulator could be used to evaluate the trajectories. Table 9 presents the execution time of different phases of the algorithm considering all of the picking attempts (_all cases_), only the attempts that did not use the simulator (_cases without simulation_), and only the attempts that did use the simulator (_cases with simulation_). _Total processing time_ is the time taken by the solution to perform all of the computations, including those of the tube modeling, motion planning, and grasp planning phases, as well as other operations, including the PCA computations of the tube placement step. _Planning time_ is the combined time taken by the motion and grasp planning phases. Figure 11: Successful escape trajectory example. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Set A**} & \multicolumn{2}{c}{Success rate} & - \\  & Number of uses of entanglement resolution & 0 \\ \hline \multirow{2}{*}{**Set B**} & \multicolumn{2}{c}{Success rate} & 27\% \\  & Number of uses of entanglement resolution & 11 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Percentages of picking attempts where the entanglement resolution step was performed that resulted in a successful pick. As shown in Table 9, using the simulator has a high impact on the total processing time.