Differentiable Simulation of Inertial Musculotendons

We propose a simple and practical approach for incorporating the effects of muscle inertia, which has been ignored by previous musculoskeletal simulators in both graphics and biomechanics. In our approach, we express the motion of the musculotendons in terms of the motion of the skeletal joints using a chain of Jacobians, so that at the top level, only the reduced degrees of freedom of the skeleton are used to completely drive both bones and musculotendons. Our approach can handle all commonly used musculotendon path types, including those with multiple path points and wrapping surfaces. For muscle paths involving wrapping surfaces, we use neural networks to model the Jacobians, trained using existing wrapping surface libraries, which allows us to effectively handle the discontinuities that occur when musculotendon paths collide with wrapping surfaces. We demonstrate support for higher-order time integrators, complex joints, inverse dynamics, Hill-type muscle models, and differentiability. We also show that in the limit, as the muscle mass is reduced to zero, our approach gracefully degrades to existing simulators in graphics and biomechanics without support for muscle inertia.