Condition-Dependent RGB-D Depth Uncertainty Modeling for Safety-Margin Planning and Empirical Risk Assessment of Robotic Manipulators

RGB-D depth errors vary with observation distance and local geometry, yet robotic-manipulator planning commonly relies on nominal obstacle geometry. This study develops a condition-dependent safety-margin framework using Intel RealSense D435 measurements and an independent physical reacquisition campaign. Three independent physical repetitions were retained for each plane/edge condition-distance cell at 0.4–1.1 m. Because the reacquired data exposed under-coverage of several archived near-distance P95 nodes, conservative P90/P95/P99 envelopes were formed by retaining the larger value between the archived training quantile and the independent-replication quantiles. Six margin strategies (none, fixed_max, fixed_mean, adaptive_P90, adaptive_P95, and adaptive_P99) were evaluated across three static PyBullet scenes, two observation conditions, four distances, and ten planning seeds, yielding 1440 successful frozen-path task records and 144,000 common-random-number empirical-stress evaluations. Observed collision rates were 3.5125% for none, 0.2333% for fixed_mean, 0.0708% for adaptive_P90, 0.0042% for adaptive_P95, and 0% observed for adaptive_P99 and fixed_max. Adaptive_P95 and fixed_mean used the same mean margin (13.3608 mm), yet produced 1 and 56 observed collisions, respectively; however, the 240-case cluster-bootstrap interval for their risk difference slightly included zero, indicating that the advantage was concentrated in a small number of constrained cases. A targeted high-risk resolution study preserved all 360 collision classifications when collision checking was refined from 0.03 to 0.003, 0.0015, and 0.001 rad. These findings characterize an empirical safety–conservatism trade-off for the documented D435 acquisitions and the three tested static scenes; broader probabilistic, continuous-motion, and physical-robot validation remain important next steps.