# An Improved NSGA-II-Based Method for Cutting Trajectory Planning of Boom-Type Roadheader
###### Abstract
[15] combined particle swarm optimization (PSO) and genetic algorithms to overcome local optima, improving trajectory quality under varying mining conditions. The NSGA-II algorithm has become a standard for solving multi-objective optimization problems in trajectory planning. Its applications include addressing uncertainties in key parameters, such as cutterhead speed, trajectory path, and environmental factors, which can fluctuate during mining operations. Additionally, it facilitates the design of time-optimal trajectories, ensuring that the cutting process is both efficient and precise while minimizing time consumption in complex mining environments [16; 17; 18]. These studies highlight NSGA-II's versatility and effectiveness across diverse scenarios [19; 20; 21]. In a related domain, [PERSON] et al. [22] optimized the flight trajectories of fixed-wing UAVs using a bank-turn mechanism, demonstrating how optimization techniques can handle dynamic constraints in trajectory planning. While UAV trajectory planning differs from mining applications, their approach offers valuable insights into the optimization of constrained trajectories. These methodologies can inform the development of optimized cutting trajectory planning for roadheaders, particularly in addressing dynamic positional changes of the cutterhead and ensuring smooth, efficient cuts in complex environments. To enhance trajectory planning precision and ensure roadway formation quality, this paper proposes an NSGA-II-based method that integrates cutterhead dimensions, target constraints, and machine posture. A bi-objective function is constructed to optimize the cutting trajectory, formalized as a bi-objective traveling salesman problem with adjacency constraints (BOTSP-AC). The NSGA-II algorithm is further improved for this problem, and its effectiveness is validated through numerical simulations and cutting trajectory experiments. The proposed method offers a robust solution for trajectory planning under complex geological conditions, advancing intelligent coal mining technology. The main contributions of this work including the following:  
(1) A cutting path planning method based on an improved NSGA-II is proposed to address the issue of inadequate consideration of cutterhead and target constraints in current underground coal mine trajectory planning, which hinders precise cutting control of the section. This method lays the groundwork for further advancements in autonomous cutting control. (2) A design method for cutting space based on kinematic constraints is introduced, which involves constructing a simplified cutterhead model and establishing a target section constraint model. By taking into account the mechanical characteristics and movement space of the boom-type roadheader, the cutting space driven by the fuselage pose is designed to identify feasible cutting points within the current section. (3) A bi-objective optimization method for cutting trajectories is presented, aiming to minimize both the total length and the total angle. This problem is formulated as a bi-objective traveling salesman problem with adjacency constraints, and an improved NSGA-II algorithm incorporating adjacency constraints is employed to optimize and solve it, generating an executable cutting trajectory.