K-AoI: A Spatio-Temporal Synchronization Metric for Digital Twin-based Teleoperation in Dynamic Network Environments

Synchronization between a digital twin (DT) and its physical robot is critical for effective teleoperation, as mismatches directly degrade operator awareness and task performance. Existing synchronization metrics are predominantly time-based and rarely capture the spatial consequences of delayed information during motion. In this paper, we introduce Kinematic Age of Information (K-AoI), a spatio-temporal metric that weights AoI by instantaneous Cartesian velocity, translating temporal staleness into physically meaningful spatial divergence. We implement and evaluate K-AoI on a DT teleoperation testbed comprising a six-degrees-of-freedom (6-DOF) manipulator, a Unity-based twin, and controlled network impairments using tc netem across seven network conditions. Per-sample analysis shows that K-AoI exhibits rank-correlations with AoI at $ρ\leq 0.65$ across all networks, dropping to $ρ= 0.22$ under satellite connections. This shows that K-AoI is not a simple transformation of AoI, but instead captures velocity-dependent degradation effects that time-only metrics cannot resolve. We further analyze AoI tail behavior using Ultra-Low AoI (ULAoI) and find that the commonly assumed Generalized Pareto Distribution (GPD) model is rejected. This reflects the impact of deterministic forwarding and bounded jitter, which violate standard extreme-value assumptions. Overall, K-AoI provides a complementary and physically grounded synchronization metric, linking network delay to task-relevant spatial error in digital-twin teleoperation systems. The dataset and testbed software are publicly available at: https://github.com/luziyaotian/kaoi-testbed.