Complex Path Planning for Manipulators Based on an Improved NSGA-III Algorithm With Hopfield Network

In various production applications across industries such as manufacturing and agriculture, manipulators often face complex trajectories composed of numerous locally discrete paths during movement. To enhance planning efficiency and convergence accuracy, this paper proposes an improved NSGA-III multi-objective optimization algorithm based on Hopfield neural network. First, we construct an optimization objective function considering three dimensions: the length of the manipulator’s motion path, motion time, and joint impact. We introduce a Hopfield neural network to replace the initial random sampling of the NSGA-III algorithm, allowing for the rapid generation of an initial optimized population. Based on non-dominance relationships, we use reference points for population crossover, mutation, and selection, thereby accelerating convergence to the optimal solution. Additionally, we employ seventh-degree polynomial smooth interpolation to improve the geometric properties of the trajectory. The main contributions include: By utilizing the energy gradient of the Hopfield neural network, we rapidly reduce the random sampling space formed by the multi-objective functions along the gradient direction towards the suboptimal solution set. This approach effectively eliminates a significant number of inferior solutions during the iterations of NSGA-III, leading to a marked improvement in the efficiency of generating the Pareto front. Specifically, the optimization efficiency is enhanced by 45.86%, the length of the robot’s motion path is reduced by 77.9%, motion efficiency is increased by 51.89%, and joint motion stability is improved by 69.45%. The feasibility of the algorithm has been validated through simulations and experiments in complex three-dimensional motion scenarios.