# Low-Cost Data-Driven Robot Collision Localization Using a Sparse Modular Point Matrix
## 2 Materials and Methods
### Optimal SMPM Structure
Conversely, \"models without CNN\" correspond to the average collision localization accuracy of models excluding convolutional modules, including ESN-SVM, LSTM-SVM, and GRU-SVM. From the graph, it is evident that fusion models with convolutional modules significantly outperform those relying solely on recursive neural networks for handling collision localization when applied in conjunction with an SMPM. When employing collision localization methods with convolutional modules, the accuracy of SMPMs (Cell 1-1 to Cell 1-8) after removing single points is slightly higher overall than the accuracy achieved by the MPM. In contrast, for collision results obtained using collision localization models without convolutional layers, single-point removal SMPMs are comparatively dis  
Figure 5: Illustration of SMPMs at four corners of the collision point matrix template. Figure 6: Illustration of SMPMs with different distributions. (**a**) Case with horizontal movement; (**b**) case with vertical movement; (**c**) case with movement toward the center. advantaged. This suggests that, when estimating the localization of collisions at zero-shot points, choosing an appropriate model enables the achievement of accuracy levels, even with sample size reduction, equivalent to or higher than those achieved without reducing the sample size. In the case of double-point and quadruple-point removal SMPMs, it is notably observed that when using models with convolutional modules, Cell 2-3, Cell 2-4, and Cell 3-2 achieve significantly higher average collision localization accuracy compared to single-point removal SMPMs. Especially, Cell 3-2 consistently achieves the highest collision accuracy across different sparsification forms. This implies that certain points in the MPM provide redundant or even disruptive information for collision localization. Furthermore, it can be observed that, in the single-point removal SMPM, using models with convolutional modules results in higher collision accuracy for Cell 1-1, Cell 1-3, Cell 1-5, and Cell 1-7 compared to their adjacent counterparts, Cell 1-2, Cell 1-4, Cell 1-6, and Cell 1-8. Similarly, in the double-point removal SMPM, Cell 2-3 and Cell 2-4 achieve significantly higher collision localization accuracy than Cell 2-1 and Cell 2-2, while in the quadruple-point removal SMPM, Cell 3-2 demonstrates markedly higher collision localization accuracy than Cell 3-1. This phenomenon indicates that the sparsification method removing the farthest adjacent points of zero-shot points in the MPM is more effective than removing the nearest adjacent points. Moreover, the standout performance of Cell 3-2 suggests that information from the farthest adjacent points in the MPM may lead to confusion in different regions, resulting in a decrease in collision localization accuracy. Considering the significant advantages of collision localization models with convolutional modules when combined with an SMPM, we focused solely on utilizing collision localization models with convolutional modules when analyzing the zero-shot point localization situation of the SMPM at different positions within the collision point matrix template. In the selection of SMPM structures, we experimentally chose SMPM structures that exhibited clear advantages at the corners of the collision point matrix template, specifically those removing the farthest adjacent points: Cell 1-1, Cell 1-3, Cell 1-5, Cell 1-7, Cell 2-3, Cell 2-4, and Cell 3-2. For the purposes of comparison with cases without any sparsification, Cell 0 was introduced as a control experiment. Figure 8 depicts the collision localization results based on SMPMs positioned at different locations. The best performance in UD1 and UD2 is observed with Cell 1-5 and Cell 2-3, in LR1 and LR2 with Cell 0 and Cell 1-3, and in CT1 and CT2 with Cell 1-7 and Cell 3-2. Comparing the results of SMPMs with those of the MPM, it is evident that the vibration signals acquired at the farthest neighboring points may indeed contain information that could degrade the localization model's performance.