Abstract
Physical access to robotic manipulators remains constrained by cost, safety requirements, and limited laboratory availability, creating barriers to both research and education. This paper presents a computational framework that combines stochastic error modeling with Digital Twin technology to characterize positioning uncertainty in a six-degree-of-freedom manipulator without requiring physical hardware. Four independent noise sources—joint encoder noise, thermal drift, elastic link deformation, and geometric parameter tolerances—are modeled as stochastic processes and propagated through the manipulator kinematics using Monte Carlo simulation with N = 10,000 trials across 50 workspace configurations. The results reveal that elastic deformation dominates the combined positioning error by a factor of 45.94 over encoder noise, contributing 99.97% of the total root-mean-square (RMS) uncertainty. A probabilistic workspace map constructed from 3000 sampled configurations quantifies accuracy and manipulability across the reachable space, exposing a counterintuitive trade-off: configurations with higher manipulability indices tend to exhibit larger positioning errors due to gravitational loading on extended links. Two control algorithms—a reverse process-based control law (RPBCL) and sliding mode control (SMC)—are evaluated under stochastic conditions over 200 trials. SMC achieves a mean steady-state error of 0.0029 mm, representing a 48.2% reduction compared to RPBCL (0.0056 mm), with the difference confirmed statistically significant by a two-sample t-test (t = 5.066, p = 0.000002). All results are visualized through a Unity3D Digital Twin interface that renders probabilistic workspace maps, three-dimensional error ellipsoids, and a real-time sliding surface monitor. The proposed framework provides a foundation for safe, hardware-free evaluation of manipulator control strategies in engineering education and research.