PIMBS: Efficient Body Schema Learning

for Musculoskeletal Humanoids

with Physics-Informed Neural Networks

IEEE Robotics and Automation Letters (RA-L)

  • Kento Kawaharazuka
  • Takahiro Hattori
  • Keita Yoneda
  • Kei Okada
  • JSK Robotics Laboratory, The University of Tokyo, Japan

Musculoskeletal humanoids are robots that closely mimic the human musculoskeletal system, offering various advantages such as variable stiffness control, redundancy, and flexibility. However, their body structure is complex, and muscle paths often significantly deviate from geometric models. To address this, numerous studies have been conducted to learn body schema, particularly the relationships among joint angles, muscle tension, and muscle length. These studies typically rely solely on data collected from the actual robot, but this data collection process is labor-intensive, and learning becomes difficult when the amount of data is limited. Therefore, in this study, we propose a method that applies the concept of Physics-Informed Neural Networks (PINNs) to the learning of body schema in musculoskeletal humanoids, enabling high-accuracy learning even with a small amount of data. By utilizing not only data obtained from the actual robot but also the physical laws governing the relationship between torque and muscle tension under the assumption of correct joint structure, more efficient learning becomes possible. We apply the proposed method to both simulation and an actual musculoskeletal humanoid and discuss its effectiveness and characteristics.

The Basic Structure of Musculoskeletal Humanoids

Muscle motors, equipped with incremental encoders, thermal sensors, and tension measurement units, are attached to the skeleton. Muscle wires extend from the muscle motors and are connected to the skeleton via nonlinear elastic elements. The presence of joint encoders depends on the specific robot.

The Basic Body Schema Learning of Musculoskeletal Humanoids

The neural network structures for basic body schema learning: the input consists of joint angles, and in some cases, muscle tension; the output is the muscle length.

This general body schema learning is highly effective, allowing for increasingly accurate learning as more data is collected. However, in practice, it is often difficult to obtain large amounts of data, making it desirable to learn with fewer data points. To address this, we incorporate the concept of Physics-Informed Neural Networks (PINNs), which leverage differential equations expressed through network derivatives. We refer to this network as the Physics-Informed Musculoskeletal Body Schema (PIMBS).

Physics-Informed Body Schema Learning for Musculoskeletal Humanoids

The training scheme of Physics-Informed Musculoskeletal Body Schema, PIMBS. PIMBS leverages not only joint angle, muscle tension, and muscle length data but also the muscle Jacobian obtained through differentiation, as well as the relationship between muscle tension and gravity compensation torque, assuming that the joint structure is correct.

Experimental Setup

The musculoskeletal structures handled in our experiments: 2-DOF 4-muscle musculoskeletal simulation and 5-DOF 10-muscle left arm of the musculoskeletal humanoid.

Body Schema Learning of AL-Map for 2-DOF 4-muscle Musculoskeletal Simulation

The transitions of L_eval when training AL-Map (Angle-Length-Map) with 3 data points in the 2-DOF 4-muscle musculoskeletal simulation.

The transitions of L_eval when training AL-Map (Angle-Length-Map) with 5 data points in the 2-DOF 4-muscle musculoskeletal simulation.

The transitions of L_eval when training AL-Map (Angle-Length-Map) with 10 data points in the 2-DOF 4-muscle musculoskeletal simulation.

Body Schema Learning of ATL-Map for 2-DOF 4-muscle Musculoskeletal Simulation

The transitions of L_eval when training ATL-Map (Angle-Tension-Length-Map) with 5 data points in the 2-DOF 4-muscle musculoskeletal simulation.

The transitions of L_eval when training ATL-Map (Angle-Tension-Length-Map) with 10 data points in the 2-DOF 4-muscle musculoskeletal simulation.

The transitions of L_eval when training ATL-Map (Angle-Tension-Length-Map) with 30 data points in the 2-DOF 4-muscle musculoskeletal simulation.

Body Schema Learning of ATL-Map for 2-DOF 4-muscle Musculoskeletal Simulation

The transitions of L_eval when training ATL-Map with 10 data points in the left arm of the musculoskeletal humanoid.

The transitions of L_eval when training ATL-Map with 30 data points in the left arm of the musculoskeletal humanoid.

Bibtex

@article{kawaharazuka2025pimbs,
  author={K. Kawaharazuka and T. Hattori and K. Yoneda and K. Okada},
  title={{PIMBS: Efficient Body Schema Learning for Musculoskeletal Humanoids with Physics-Informed Neural Networks}},
  journal={IEEE Robotics and Automation Letters},
  year=2025,
  note={presented at ICRA2026},
  doi={10.1109/LRA.2025.3577525},
  robots={musashi},
}

Contact

If you have any questions, please feel free to contact Kento Kawaharazuka.