# An Improved NSGA-II-Based Method for Cutting Trajectory Planning of Boom-Type Roadheader
###### Abstract  
This paper proposes a cutting trajectory planning method for boom-type road-headers using an improved Nondominated Sorting Genetic Algorithm II (NSGA-II) with an elitist strategy. Existing methods often overlook constraints related to cutterhead dimensions and target sections, affecting section formation quality. We develop a kinematic model for coordinate transformations and design a simplified cutterhead and constraint model to generate feasible cutting points. Bi-objective functions--minimizing cutting trajectory length and turning angle--are formulated as a bi-objective traveling salesman problem (BO-TSP) withwhile ensuing trajectory smoothness and mining efficiency has become a major challenge in coal mine intelligence research. Unlike manual operations, trajectory planning ensures precise cutting task execution in complex environments, meeting the required roadway formation standards. Existing methods consider various factors such as kinematics, target geometry, and operational conditions. [PERSON] et al. [4] introduced a simplified kinematic model using homogeneous coordinate transformation and robotics theory, achieving effective trajectory planning through simulation [5]. [PERSON] et al. [6] enhanced planning accuracy by incorporating dynamic modeling and path correction. [PERSON] et al. [7] solved the kinematics of the cutterhead using the D-H parameter method and inverse transformation techniques to plan the cutting trajectory. However, these approaches often neglect cutterhead dimensions, leading to suboptimal formation precision [8]. To address this, research has explored cutterhead optimization to improve formation quality. Full-scale simulations of cutterheads at various inclination angles and genetic algorithm optimization of spiral angles demonstrated significant performance improvements in energy consumption, cutting resistance, and vibration control [9; 10]. Despite these advances, conventional methods remain limited in adapting to complex mining conditions. [PERSON] et al. [11] proposed a path correction and scheduling strategy for an underground mining roadheader, integrating BP neural networks and state estimation. By designing a tracking model based on posture deviations and applying SVD-unscented Kalman filtering to estimate the actual posture deviations, they achieved effective path tracking and highly adaptive control of the roadheader. [PERSON] et al. [12] introduced a trajectory planning method for roadheader cutting under uncertainty. By analyzing the cutting mechanism, identifying influencing factors, and using a particle swarm optimization algorithm, they developed an optimal trajectory planning approach that avoids contamination zones and ensures precise roadway formation, laying the foundation for robotic automatic tunneling. Additionally, by analyzing the relationship between coal-rock hardness and the speed of the cutting arm, integrating multi-sensor parameter evaluation, and modeling the environment in a grid format, they proposed a cutting trajectory planning and boundary control method. Experimental results demonstrated that this approach accurately controls the cutterhead to avoid obstacles and completely cut the cross-section [13]. Adaptive algorithms have been proposed to mitigate challenges such as coal-rock variability and obstacles. [PERSON] et al. [5] used ant colony optimization (ACO) with sensor data for obstacle avoidance, enhancing safety and efficiency. [PERSON] et al. [14] integrated machine vision to detect fractures and dynamically adjust cutting paths, demonstrating adaptability to changing environments. However, these approaches often rely on real-time detection methods, which can be ineffective under complex working conditions. Multi-objective optimization has emerged as a critical focus for trajectory planning, addressing conflicting goals such as reducing cutting energy consumption and shortening path length. [PERSON] et al.