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Differentiable Simulation of Inertial Musculotendons
Ying Wang, Jasper Verheul, Sang-Hoon Yeo, Nima Khademi Kalantari, Shinjiro Sueda
Incorporates muscle inertia into musculoskeletal simulation via a chain-of-Jacobians formulation enabling gradient-based optimization.
Abstract
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. We approximate the inertia of the muscle by assuming that muscle mass is distributed along the centerline of the muscle. 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 Jacobian 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. In the limit, as the muscle mass is reduced to zero, our approach gracefully degrades to traditional simulators without support for muscle inertia. Finally, it is possible to mix and match inertial and non-inertial musculotendons, depending on the application.
How to read this
- Category
- Method: a differentiable musculoskeletal simulation technique
- Contributions
- Incorporates muscle inertia (previously ignored) by distributing muscle mass along the musculotendon centerline
- Expresses musculotendon motion from reduced skeletal degrees of freedom via a chain of Jacobians
- Uses neural networks to model Jacobians for wrapping-surface paths, handling discontinuities, and supports higher-order integrators, inverse dynamics, Hill-type muscles, and differentiability
- Context
- Extends reduced-coordinate musculotendon simulation in the lineage of Sueda et al.'s Musculotendon Simulation for Hand Animation, adding inertial effects and gradient-based optimization.Builds on: Musculotendon Simulation for Hand Animation
- Correctness
- Rests on approximating muscle inertia as mass along the centerline and on neural Jacobians trained from existing wrapping-surface libraries, so accuracy near path-collision discontinuities and the validity of the centerline assumption for bulky muscles are the things to watch; the authors note it degrades gracefully to the massless case.
- Clarity
- Moderately technical; a first pass conveys the inertia-plus-Jacobian idea, but a second pass is needed for the chain-of-Jacobians formulation.
- How to read it
- First pass for why muscle inertia matters and the high-level reduced-coordinate framing; do a second pass on the Jacobian chain and the neural wrapping-surface model if you intend to implement or differentiate through it.
Builds on
Built upon by
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Related work
- Generative GaitNet 2022 / SIGGRAPH
- MuscleVAE: Model-Based Controllers of Muscle-Actuated Characters 2023 / SIGGRAPH Asia
- Anatomy Transfer 2013 / SIGGRAPH Asia
- A Neural Network Model for Efficient Musculoskeletal-Driven Skin Deformation 2024 / SIGGRAPH
Keywords
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