Extrapolatable analytical functions for tendon excursions and moment arms from sparse datasets.

Computationally efficient modeling of complex neuromuscular systems for dynamics and control simulations often requires accurate analytical expressions for moment arms over the entire range of motion. Conventionally, polynomial expressions are regressed from experimental data. But these polynomial regressions can fail to extrapolate, may require large datasets to train, are not robust to noise, and often have numerous free parameters. We present a novel method that simultaneously estimates both the form and parameter values of arbitrary analytical expressions for tendon excursions and moment arms over the entire range of motion from sparse datasets. This symbolic regression method based on genetic programming has been shown to find the appropriate form of mathematical expressions that capture the physics of mechanical systems. We demonstrate this method by applying it to 1) experimental data from a physical tendon-driven robotic system with arbitrarily routed multiarticular tendons and 2) synthetic data from musculoskeletal models. We show it outperforms polynomial regressions in the amount of training data, ability to extrapolate, robustness to noise, and representation containing fewer parameters--all critical to realistic and efficient computational modeling of complex musculoskeletal systems.