# Low-Cost Data-Driven Robot Collision Localization Using a Sparse Modular Point Matrix
## 1 Introduction
utilized information from multi-core fiber Bragg grating sensors, combined with a k-nearest neighbor (KNN) model to fit a free-space curvature model, successfully estimating collision positions for continuum robots [13]. [PERSON] et al. mounted accelerometers on the joint near the base and end-effector of a robotic arm to capture vibration signals during collisions. They performed reasonable feature extraction on the collision vibration signals and, in conjunction with an artificial neural network (ANN), successfully achieved the localization of the contact points [14]. [PERSON] et al. mounted four accelerometers on a single robotic arm to form an accelerometer array, capturing collision vibration data. They employed a support vector machine (SVM) to learn from the vibration information of different collision positions, thereby achieving collision localization with an error in the centimeter range [15]. In the realm of robot-assisted automatic electric vehicle charging, the end-effector, which is incapable of establishing direct physical contact with the charging port, exclusively interfaces with it through the intermediary of the carried charger. This situation may introduce unknown disturbances in signal measurements within the model-based method, posing challenges for achieving high accuracy in collision localization with model-based methods. Additionally, during the plug-in process, the forces generated during collisions typically act along the robot. As discussed in [5], model-based methods face increased difficulty in handling collision issues when external forces act along the robot. In addition, due to the frequent contacts and substantial contact forces inherent in the plug-in process, this demanding operational environment will significantly diminish the lifespan of artificial skin. Simultaneously, the deployment of artificial skin encounters certain challenges, serving as a constraint that restricts its application in addressing this issue. Considering data-driven collision localization methods, these approaches heavily depend on formulating rules for gathering data tailored to specific scenarios. In our previous research, we introduced a collision point matrix template specifically designed for millimeter-level collision localization in the scenario of automatic charging for electric vehicles [4]. The collision point matrix template consists of collision points spaced at 1 mm intervals on a plane. By pre-setting the collision point matrix template on the surface of the charging port and then colliding with each collision point using the charger carried by the automatic charging robot, we can obtain collision vibration information suitable for collision localization. Utilizing a collision point matrix template composed of densely distributed collision points, the collision localization problem can be transformed into a classification problem, with collision information corresponding to different points in the template. To enhance the generalization ability of the collision localization method, it is necessary to consider the adaptation of the collision localization method to variations in joint configurations during the data collection process. Therefore, it is generally required to collect collision information under as many different joint configurations as possible. As the accuracy of collision localization in this method depends on the dense distribution of collision points in the template, the cost of data collection is typically very high. To alleviate the significant burden of data collection associated with such an approach, we propose a data-driven collision localization method based on a sparse modular point matrix (SMPM). Unlike the earlier collision point matrix template, the SMPM efficiently reduces the density of collision point distribution, thereby reducing the scale and associated costs of building the collision dataset to some extent. The main contributions of this paper are as follows:  
1.