# Low-Cost Data-Driven Robot Collision Localization Using a Sparse Modular Point Matrix
## 2 Materials and Methods
### Collision Localization Results across the Entire Template  
When applying the SMPM with the Cell 3-2 form for collision localization at the charging port, the encountered challenge is not solely limited to accurately identifying collisions occurring at zero-shot points. Rather, it extends to efficiently locating collisions within the entire collision point matrix template. Therefore, it is imperative for the Cell 3-2 SMPM to be comprehensively deployed across the entire collision point matrix template. In order to investigate the feasibility of the proposed sparsification method across the entire domain, a thorough analysis of the complete collision point matrix template area is required under different robot joint angles. The training datasets used for this purpose are D1 and D2, while the testing dataset is D3, isolated from D1 and D2. Additionally, the collisions occurring at the locations of removed fully observable points also need to be addressed. Despite the theoretical capability of SMPMs to effectively locate collisions at both zero-shot and fully observable points, there is currently a lack of adequate information for handling collisions at removed fully observable points. Hence, we introduce the concept of partially observable points, i.e., collision data sampled with a demand lower than that of fully  
Figure 8: Collision localization results using SMPMs with different distributions. (**a**) UD; (**b**) LR; (**c**) CT.  
observable points but greater than zero. In conjunction with training datasets D1 and D2, the specific forms of SMPMs containing locally observable points used in the experiments are illustrated in Figure 9. To ensure the comprehensive deployment of SMPMs across the entire collision point matrix template, a departure from the approach outlined in [7] is taken. Specifically, the outermost points of the collision point matrix template are disregarded, and analysis is conducted only on the inner 15 rows and 15 columns. Building upon the Cell 3-2 form, partially observable points are positioned at the farthest adjacent point of the MPM. The samples include 30 instances of fully observable points, 0 instances of zero-shot points, and N instances of partially observable points. To investigate the impact of different sparsity levels of partially observable points on the collision localization results, five different SMPMs are defined, with N values of 5, 10, 15, 20, and 25, denoted as S1 to S5, respectively. Additionally, for comparison with the case of ample data collection, an MPM (S6) is introduced, and a control experiment (S7) utilizes the collision point matrix template directly without downsampling. In evaluating the effectiveness of applying SMPMs with varying degrees of sparsity to collision localization, we employ assessment criteria that include collision localization accuracy and root mean square error (RMSE). In this study, we treat the SMPM as a unified entity, with its central position representing the estimated positions of individual points within the SMPM. The results of collision localization accuracy are presented in Table 3, where the data scale of S7 is defined as 100%. In S7, the collision localization accuracy of different models exceeded 96%, with the highest reaching 98.67%. As the data scale decreases, the accuracy of collision localization for each method also declines accordingly. At a data scale of 51.85%, the average accuracy of each method only drops by 8.72%. Notably, the CE-SVM method exhibits the smallest decrease, with a reduction of only 7.22%, maintaining an accuracy above 90%. Furthermore, in cases S1 to S6, the CE-SVM method outperforms other methods, especially in situations with higher sparsity, highlighting the pronounced advantage of CE-SVM.