Multi-Objective Optimal Trajectory Planning for Woodworking Manipulator and Worktable Based on the INSGA-II Algorithm

The manipulator has been widely used in the wood processing industry; the main problem currently faced is optimizing the motion trajectory to enhance the processing efficiency and operational stability of the woodworking manipulator and worktable. A 5-7-5 piecewise polynomial interpolation method is proposed to construct the spatial trajectories of each joint. An improved non-dominated sorting genetic algorithm (INSGA-II) is proposed to achieve a time–jerk multi-objective trajectory planning that can meet the dual requirements of minimal processing time and reduced motion impact. In order to address the limitations of the standard NSGA-II algorithm, which is prone to local optima and exhibits slow convergence, we propose a good point set method for multi-objective optimization population initialization and a linear ranking selection method to refine the parent selection process within the genetic algorithm. The improved NSGA-II algorithm markedly enhanced both the uniformity of the population distribution and convergence speed. In practical applications, selecting suitable weightings to construct a normalized weight function can identify the optimal solution from the Pareto frontier curve. A high-order continuous and smooth optimal trajectory without abrupt changes can be obtained. The simulation results demonstrated that the 5-7-5 piecewise polynomial interpolation curve effectively constructed a high-order smooth processing trajectory with continuous and smooth velocity, acceleration, and jerk, free from discontinuities. Moreover, the INSGA-II algorithm outperforms the original algorithm in terms of convergence and distribution, enabling the optimal time–jerk multi-objective trajectory planning that adheres to constraint conditions. Optimized by the improved NSGA-II algorithm, the optimal total running time is 4.5400 s, and the optimal jerk is 17.934 m(rad)/s3. This provides a novel approach to solving the inefficiencies and operational instability prevalent in traditional woodworking equipment.