A Port-Hamiltonian Framework for Passive Analysis and Energy-Safe Control of Coupled Motor-Robot-Environment Systems

Abstract

This paper proposes a unified and rigorously structured energy-based control framework for a coupled motor-robot-environment system grounded in the port-Hamiltonian formalism. The approach aims to simultaneously guarantee stability, robustness, and energetic safety in physical human-robot interaction scenarios, particularly in collaborative and humanoid robotics. Unlike conventional methods primarily focused on kinematic or dynamic performance, the proposed strategy explicitly structures power flows and the global energy balance, while embedding ethical considerations related to human supervision and control. The main contribution introduces a two-layer safety architecture: (i) explicit limitation of the power injected by the electric motor, ensuring bounded torque transmission; and (ii) an Energy Tank di-mensioned from the maximum gravitational torque τgmax = mgℓ, derived from the gradient of the potential energy. This dual constraint enforces a strict bound on the total available mechanical energy, preserving passivity, preventing unsafe energy amplification, and guaranteeing that robotic autonomy remains energetically supervised and physically controllable by humans. By exploiting the symplectic struc-ture of the port-Hamiltonian model, the total energy variation is formally linked to power ports and dissipative effects. Simulation results demon-strate enhanced robustness, intrinsic energetic coherence, and ethically-informed control, representing a significant step toward safe, controlla-ble, energy-responsible, and human-conscious robotic architectures.