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

2025-11-11

IEEE Robotics and Automation Letters

AI Summary

Musculoskeletal robots pose significant challenges for dynamic modeling due to the coexistence of linear elastic actuators, continuously distributed mass, kinematic closed loops, and multimodal locomotion. To address this, we propose EquiMus—a novel energy-equivalence-based dynamic modeling framework. EquiMus is the first to systematically integrate the principle of energy equivalence into musculoskeletal robot modeling, enabling unified representation of coupled dynamics between rigid skeletal structures and compliant actuators, and supporting efficient, physically consistent simulation of large-scale rigid–soft hybrid systems. Leveraging MuJoCo, we develop a calibrated simulation platform that fuses experimental data with the equivalent model, establishing a closed loop between numerical simulation and physical validation. Experimental evaluation on a biomimetic leg demonstrates that EquiMus improves dynamic response accuracy by 32% (reduced error) and robustly supports controller design and learning-based control across diverse locomotion modes.

Technology Category

• Intelligent Robots: Multimodal Perception & Sensor Fusion
• Cognitive Modeling & Cognitive Systems: Simulating Human Behavior
• Machine Learning: Imitation Learning & Inverse Reinforcement Learning

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments

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.

Problem

• Modeling musculoskeletal robots with linear elastic actuators
• Simulating hybrid rigid-soft robots with distributed mass
• Addressing dynamic control challenges in bio-inspired robotic systems

Innovation

• Energy-equivalent dynamic modeling for musculoskeletal robots
• MuJoCo-based simulation for rigid-soft hybrid systems
• Framework validated through bionic leg experiments