EquiMus: Energy-Equivalent Dynamic Modeling and Simulation of Musculoskeletal Robots Driven by Linear Elastic Actuators

Abstract: Dynamic modeling and control are critical for unleashing 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.