## 1 Introduction  
With the rapid advancement of modern engineering technology, large hydraulic rock drilling robots have found widespread applications in various fields, including mining, tunnel boring, and underground engineering. Drilling and blasting are the most commonly used excavation methods in mining and tunneling [1]. In traditional rock drilling methods, the requirement for positioning accuracy is relatively low, as it primarily serves blasting and rock removal purposes. However, in fully automated rock drilling robots, the drilling task is carried out automatically according to a predefined hole-laying plan, and precise positioning is critical to ensuring the accuracy of the drilling location. This accuracy, in turn, guarantees the successful execution of the drilling and blasting operations. Therefore, high positioning accuracy is essential for fully automated rock drilling robots. The positioning accuracy of the rock drilling robot arm also directly influences both construction efficiency and operational safety. However, due to the influence of mechanical geometry errors, drive system errors, load variations, control system errors, and environmental factors, the actual position of the rock drilling arm's end often deviates from its theoretical position. Therefore, exploring methods to enhance the positioning accuracy of rock drilling robotic arms, particularly in fully automated rock drilling robots, is of substantial practical significance. Common error compensation methods primarily fall into two categories: model-based and non-model-based methods. Model-based methods [2; 3; 4; 5; 6; 7; 8; 9; 10] correct the robot's kinematic model by accounting for kinematic parameter errors, which can yield better results when the system is well-defined and stable. However, these methods involve complex modeling and computational processes [11] and are less effective in compensating for non-geometric errors. Non-model-based methods [12; 13; 14; 15; 16; 17], on the other hand, identify error patterns and trends using real-time feedback or historical data to achieve error compensation without the need for detailed system modeling. This method contributes to enhancing the system's stability and accuracy. However, in the practical application of error compensation for rock drilling robotic arms, traditional non-model-based approaches exhibit certain limitations. Among the non-model-based approaches, neural network-based error compensation algorithms [18; 19] offer advantages such as high efficiency, adaptability, and robustness, enabling them to handle complex nonlinear relationships and improve error correction efficiency. Compared to other traditional non-model-based methods, neural networks possess the ability to adaptively learn error patterns and optimize compensation strategies, thereby addressing the limitations of traditional methods regarding data processing and model complexity. [PERSON] et al. [20] proposed a position error compensation method for rock drilling robots based on LightGBM and RBFN, while ref. [21] employed a genetic algorithm (GA)-optimized deep neural network (DNN) to enhance robot localization accuracy. BP neural networks have been widely applied in the field of robot localization due to their powerful nonlinear mapping capabilities and self-learning properties [22; 23; 24]. However, the BP neural network's training process is prone to falling into local optima, and the training speed is slow, which significantly hinders its application in practical engineering scenarios.To address these challenges, various optimization algorithms have been proposed. [PERSON] et al. [25] optimized the BP neural network using the whale optimization algorithm, significantly enhancing the absolute positioning accuracy of the robotic arm. [PERSON] et al. [26] utilized a particle swarm optimization (PSO) algorithm to enhance the BP neural network's error compensation performance. [PERSON] et al. [27] applied a quantum genetic algorithm to improve the BP neural network for robot localization compensation.