SPI-BoTER: Error Compensation for Industrial Robots via Sparse Attention Masking and Hybrid Loss with Spatial-Physical Information

The widespread application of industrial robots in fields such as cutting and welding has imposed increasingly stringent requirements on the trajectory accuracy of end-effectors. However, current error compensation methods face several critical challenges, including overly simplified mechanism modeling, a lack of physical consistency in data-driven approaches, and substantial data requirements. These issues make it difficult to achieve both high accuracy and strong generalization simultaneously. To address these challenges, this paper proposes a Spatial-Physical Informed Attention Residual Network (SPI-BoTER). This method integrates the kinematic equations of the robotic manipulator with a Transformer architecture enhanced by sparse self-attention masks. A parameter-adaptive hybrid loss function incorporating spatial and physical information is employed to iteratively optimize the network during training, enabling high-precision error compensation under small-sample conditions. Additionally, inverse joint angle compensation is performed using a gradient descent-based optimization method. Experimental results on a small-sample dataset from a UR5 robotic arm (724 samples, with a train:test:validation split of 8:1:1) demonstrate the superior performance of the proposed method. It achieves a 3D absolute positioning error of 0.2515 mm with a standard deviation of 0.15 mm, representing a 35.16\% reduction in error compared to conventional deep neural network (DNN) methods. Furthermore, the inverse angle compensation algorithm converges to an accuracy of 0.01 mm within an average of 147 iterations. This study presents a solution that combines physical interpretability with data adaptability for high-precision control of industrial robots, offering promising potential for the reliable execution of precision tasks in intelligent manufacturing.