Multi-Objective Trajectory Optimization of a Robotic Manipulator Based on an Improved Dung Beetle Optimizer
Abstract
To address the difficulty of simultaneously optimizing execution time, energy consumption, and motion smoothness for six-degrees-of-freedom (6-DOF) industrial robotic manipulators in continuous operations such as high-speed handling and assembly, this study proposes a multi-objective joint-space trajectory optimization method based on an improved Dung Beetle Optimizer (IDBO). First, to adapt DBO to constrained multi-objective trajectory optimization, an external archive, nondominated sorting, and a crowding distance mechanism were incorporated to construct and maintain the Pareto solution set. Second, Sobol low-discrepancy sequence initialization was used to improve the initial population distribution. Adaptive Lévy flight perturbation and an adaptive random perturbation mutation strategy for non-elite individuals were further combined to enhance global exploration and reduce the risk of premature convergence. Finally, seventh-degree B-spline curves were adopted to construct a continuous joint-space trajectory model. Based on this model, a multi-objective trajectory optimization model was established by considering total execution time, energy consumption, and jerk as the optimization objectives. Furthermore, simulation experiments were conducted using MATLAB R2024a, and the proposed algorithm was compared with multi-objective particle swarm optimization (MOPSO), an improved multi-objective differential evolution algorithm (GMODE), the nondominated sorting genetic algorithm II (NSGA-II), and the multi-objective Dung Beetle Optimizer (MODBO). The results showed that the proposed algorithm obtained a Pareto front with better convergence, wider coverage, and a more uniform distribution. Compared with MOPSO, GMODE, NSGA-II, and MODBO, the mean hypervolume (HV) obtained by IDBO was 13.24%, 8.43%, 2.29%, and 2.34% higher, respectively; the mean inverted generational distance (IGD) was 9.45%, 26.68%, 16.35%, and 11.05% lower, respectively; and the mean Spacing value was 55.09%, 64.81%, 58.95%, and 14.06% lower, respectively. The execution time, energy consumption index, and joint jerk of the selected compromise solution were 5.27 s, 2.48, and 9.79, respectively, which were 29.73%, 43.51%, and 18.14% lower than those of the unoptimized trajectory. Constraint verification showed that the peak joint velocities, accelerations, and jerks remained within their prescribed limits. These results indicate that the proposed method provides a feasible approach for multi-objective joint-space trajectory planning of industrial robotic manipulators.