EquiMus: Energy-Equivalent Dynamic Modeling and Simulation of Musculoskeletal Robots Driven by Linear Elastic Actuators
Yinglei Zhu, Xuguang Dong, Qiyao Wang, Qi Shao, Fugui Xie, Xin-Jun Liu, Huichan Zhao
AI summary
Problem
Classical rigid-body models and existing simulators fail to capture configuration-dependent mass redistribution, actuator inertia, and kinematic loops in hybrid musculoskeletal robots, making accurate dynamic modeling and real-time simulation difficult.
Approach
The authors propose EquiMus, an energy-equivalent modeling framework that discretizes linear elastic actuators into a three-mass-point lumped-mass system with matched stiffness, damping, and constraints, implemented in the MuJoCo physics engine.
Key results
- Compact energy-equivalent lumped-mass formulation preserving actuator inertia
- MuJoCo implementation with kinematic loop support and real-time speed
- Close sim-to-real agreement validated on a pneumatic bionic robotic leg
- Enables downstream applications including PID auto-tuning and reinforcement learning
Why it matters
Provides a computationally efficient and physically accurate simulation platform for designing and controlling complex bio-inspired musculoskeletal robots.
Abstract
Dynamic modeling and control are critical for un- leashing soft robots’ potential, yet remain challenging due to their complex constitutive behaviors and real-world operating conditions. Bio-inspired musculoskeletal robots, which integrate rigid skeletons with soft actuators, combine high load-bearing capacity with inherent flexibility. Although actuation dynamics have been studied through experimental methods and surrogate models, accurate and effective modeling and simulation remain a significant challenge, especially for large-scale hybrid rigid–soft robots with continuously distributed mass, kinematic loops, and diverse motion modes. To address these challenges, we propose EquiMus, an energy- equivalent dynamic modeling framework and MuJoCo-based simulation for musculoskeletal rigid–soft hybrid robots with linear elastic actuators. The equivalence and effectiveness of the proposed approach are validated and examined through both simulations and real-world experiments on a bionic robotic leg. EquiMus further demonstrates its utility for downstream tasks, including controller design and learning-based control strategies.