The Geometry of Interference: Quantifying Spatial Leakage and Biomechanical Adaptation During Human–Robot Collaboration

While industrial safety standards for Human-Robot Collaboration (HRC) prioritize collision avoidance through static distance metrics, they provide limited means to quantify the continuous motor interference imposed on human operators. This study introduces Distractor-Aligned Variance (DAV), a continuous measurement framework designed to characterize how active robotic interference structurally reshapes human motor execution. We analyzed human kinematics (N = 48) in a synchronized pick-and-place task, systematically manipulating trajectory profiles (Rectilinear vs. Curvilinear), spatial layouts, and hardware mounting configurations. To mitigate the sensitivity of static orthogonal metrics to curvature effects, we employ a dynamic 3D-to-2D planar projection that separates variance aligned with the task direction from orthogonal spatial variability. Our results demonstrate that geometric disparity, quantified as the angular incongruency between human and robot velocity vectors, is consistently associated with spatial leakage, particularly under piecewise Rectilinear trajectories. Furthermore, we identify covariation between these geometric patterns and behavioral markers of biomechanical adaptation, specifically arm joint freezing and reduced kinematic smoothness. These findings suggest that trajectory-based interference is a multi-dimensional phenomenon where geometric conflict is linked to motor adaptation patterns. This framework provides metrics that may inform human-aware trajectory planning in shared workspaces, supporting the design of robotic systems that account for the kinematic structure of human movement. This work complements a parallel study that characterizes macroscopic spatial behavior and subjective workload effects in the same experimental dataset (see Related Works). Note: This manuscript is a preprint intended for future journal submission.