Dynamic Trajectory Planning for Atomic Force Microscopy Nanopositioning: An Enhanced A-Star Framework Addressing Displacement Errors in Nonplanar Environments

The use of atomic force microscopy (AFM) for nanoscale surface characterization and mechanical property measurement has attracted considerable interest. At the level of single-molecule mechanical measurement, AFM is a powerful tool for both surface morphology analysis and mechanical assessment. However, its effectiveness is limited by dynamic displacement deviation during precise nanoscale positioning of surface target points, an essential factor in accurately determining surface mechanical properties. This study addresses this limitation by proposing an integrated enhanced A-star (A*) framework for contour-aware motion trajectory planning, ensuring nanometer-level target localization accuracy during AFM measurements on complex surface morphologies. The method employs AFM tip repositioning using prior topographic data and enables trajectory path planning on biological cell surfaces with both high and low topographical undulations. Experimental evaluations using Manhattan, Chebyshev, and Euclidean heuristic metrics in AFM grid modeling demonstrated that the Manhattan approach achieved a heuristic accuracy of 96% ± 4%, significantly outperforming Euclidean (70% ± 4%) and Chebyshev (56% ± 8%) methods ( p < 0.001). In constrained environments, the Manhattan heuristic reduced target localization errors by 30% by alleviating path cost overestimation and resolved the long-standing trade-off between path smoothness (coefficient of variation, CV = 0.28) and positioning precision through adaptive cost-weighting mechanisms. The proposed approach supports precise nanoscale positioning necessary to capture ultramicroscopic topography and physical characteristics, providing a robust framework for quantitative nanomechanical characterization of heterogeneous materials.