Planar vector sequential extraction and harvesting optimization for dense quasi-spherical fruits: a low-damage and high-efficiency path balancing strategy based on improved NSGA-II

To address the challenges of excessive fruit damage and low success rates in densely clustered fruit harvesting requiring planar vector sequential extraction (a vector detachment strategy that projects 3D fruit positions onto the optimal operation plane for collision-free path planning, without restricting the end-effector to a fixed height plane), this study proposes a picking sequence optimization method based on multi-objective optimization. First, a geometric constraint model of critical tangent directions is established to determine collision-free detachment orientations for individual fruits. Subsequently, an Improved Non-dominated Sorting Genetic Algorithm II (I-NSGA-II) is developed by integrating multiple mechanisms: PSO-based extremum point injection for initial population generation, elitist selection for solution refinement, two-stage optimization (2-opt) for path smoothing, and cyclic crowding distance sorting for population diversity maintenance. This effectively resolves spatial constraints in dense fruit cluster separation while improving damage-free harvesting success rates. Experimental results demonstrate that compared with standard NSGA-II, our method achieves a significant 2.5% reduction in collision failure rates across various fruit density clusters, with picking path lengths reduced to 55% of those obtained through single-objective optimization. The proposed approach effectively solves low-damage harvesting challenges in densely aggregated fruit regions, demonstrating substantial practical value for advancing robotic harvesting technologies.