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

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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">EquiMus</i>, 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.