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This work presents a motion planning framework for robotic manipulators that computes collision-free paths directly in image space. The generated paths can then be tracked using vision-based control, eliminating the need for an explicit robot model or proprioceptive sensing. At the core of our approach is the construction of a roadmap entirely in image space. To achieve this, we explicitly define sampling, nearest-neighbor selection, and collision checking based on visual features rather than geometric models. We first collect a set of image space samples by moving the robot within its workspace, capturing keypoints along its body at different configurations. These samples serve as nodes in the roadmap, which we construct using either learned or predefined distance metrics. At runtime, the roadmap generates collision-free paths directly in image space, removing the need for a robot model or joint encoders. We validate our approach through an experimental study in which a robotic arm follows planned paths using an adaptive vision-based control scheme to avoid obstacles. The results show that paths generated with the learned-distance roadmap achieved 100% success in control convergence, whereas the predefined image space distance roadmap enabled faster transient responses but had a lower success rate in convergence. 

Abstract Oxide heterostructures exhibit a vast variety of unique physical properties. Examples are unconventional superconductivity in layered nickelates and topological polar order in (PbTiO₃)_n/(SrTiO₃)_nsuperlattices. Although it is clear that variations in oxygen content are crucial for the electronic correlation phenomena in oxides, it remains a major challenge to quantify their impact. Here, we measure the chemical composition in multiferroic (LuFeO₃)₉/(LuFe₂O₄)₁superlattices, mapping correlations between the distribution of oxygen vacancies and the electric and magnetic properties. Using atom probe tomography, we observe oxygen vacancies arranging in a layered three-dimensional structure with a local density on the order of 10¹⁴cm⁻², congruent with the formula-unit-thick ferrimagnetic LuFe₂O₄layers. The vacancy order is promoted by the locally reduced formation energy and plays a key role in stabilizing the ferroelectric domains and ferrimagnetism in the LuFeO₃and LuFe₂O₄layers, respectively. The results demonstrate pronounced interactions between oxygen vacancies and the multiferroic order in this system and establish an approach for quantifying the oxygen defects with atomic-scale precision in 3D, giving new opportunities for deterministic defect-enabled property control in oxide heterostructures.