# Low-Cost Data-Driven Robot Collision Localization Using a Sparse Modular Point Matrix
## 1 Introduction  
In the domain of robot-assisted automatic electric vehicle charging, the connection between the charger and the charging port relies on precise visual positioning [1]. However, the visual positioning system may be subject to disturbances in unstructured environments, such as changes in lighting conditions, leading to instances of positioning failure. Visual positioning failure typically results in three scenarios: in cases of minimal localization deviation, the charger carried by the robot's end-effector is able to connect to the charging port, but may experience jamming. In such situations, impedance control implemented on the robot can effectively suppress jamming [2]. When the positioning deviation is substantial, the charger on the robot's end-effector may fail to make contact with the charging port during the connection process, potentially causing contact with other parts of the electric vehicle's body. In this case, implementing a collision classification protection system on the robotic arm ensures the safety of the vehicle and the robot. When the positioning deviation falls between the aforementioned scenarios, meaning that the charger can make contact with the charging port but cannot smoothly insert due to the presence of a visual positioning deviation, imparting a collision localization capability to the robotic arm can effectively correct the deviation caused by the visual positioning failure, serving as a supplementary localization strategy in the event of a visual failure [3, 4]. In the exploration of model-based collision localization methods, [PERSON] et al. achieved collision localization for humanoid robots by constructing a generalized momentum observer to calculate joint torques and estimate joint accelerations [5]. This method enables point estimation in single-contact situations using only onboard sensors. Additional force/torque sensors are introduced only when estimating multi-contact positions. [PERSON] et al. developed a momentum-based external force estimation framework for robot collision localization [6]. This approach includes joint-level residual estimation and uncoupled force-torque estimation in Cartesian space, eliminating the need for acceleration estimation and consequently mitigating the introduction of noise associated with acceleration estimation. [PERSON] et al. addressed the problem of difficulty in achieving high-precision collision localization solely by relying on a generalized momentum observer to a certain extent by combining the generalized momentum observer method with a particle filtering strategy [7]. In the pursuit of achieving high-precision collision localization, artificial-skin-based methods are generally considered a more favorable option. [PERSON] et al. utilized low-cost optical components installed along the edges of the perception region to achieve higher accuracy in contact localization by measuring the impact of touch on the passage of light through elastic material [8]. [PERSON] et al. designed a set of ultrasound sensors deployable on the surface of a robotic arm to achieve high-precision contact localization and analyze contact pressure [9]. [PERSON] et al. achieved interactive touch in different parts of a humanoid robot by employing self-organizing, multimodal artificial skin [10]. [PERSON] et al. developed a tactile sensor composed of overlapping air chambers, leveraging the spatiotemporal continuity of learning contact positions to achieve high-precision and high-resolution collision localization [11]. With the rapid advancement of artificial intelligence technology, supervised learning strategies have become widely utilized to address collision localization problems in robotics. These methods are commonly referred to as data-driven collision localization approaches. [PERSON] et al. employed onboard sensors to collect collision data from robots, utilizing neural network methods to learn from the relevant data, thereby achieving collision localization at the centimeter level [12]. [PERSON] et al.