  Harmonic drive systems (HDS) are high-precision robotic transmissions
featuring compact size and high gear ratios. However, issues like kinematic
transmission errors hamper their precision performance. This article focuses on
data-driven modeling and analysis of an HDS to improve kinematic error
compensation. The background introduces HDS mechanics, nonlinear attributes,
and modeling approaches from literature. The HDS dynamics are derived using
Lagrange equations. Experiments under aggressive conditions provide training
data exhibiting deterministic patterns. Various linear and nonlinear models
have been developed. The best-performing model, based on a nonlinear neural
network, achieves over 98\% accuracy for one-step predictions on both the
training and validation data sets. A phenomenological model separates the
kinematic error into a periodic pure part and flexible part. Apart from
implementation of estimated transmission error injection compensation, novel
compensation mechanisms policies for the kinematic error are analyzed and
proposed, including nonlinear model predictive control and frequency
loop-shaping. The feedback loop is analyzed to select the controller for
vibration mitigation. Main contributions include the nonlinear dynamics
derivation, data-driven nonlinear modeling of flexible kinematic errors,
repeatable experiment design, and proposed novel compensation mechanism and
policies. Future work involves using physics-informed neural networks,
sensitivity analysis, full life-cycle monitoring, and extracting physical laws
directly from data.
