Hamiltonian-based energy shaping with attention-augmented fourier neural operators for adaptive torque control in ankle rehabilitation robot

In rehabilitation robotics, control of energy flow is not merely a stability requirement but a therapeutic tool that shapes the quality and safety of human-robot interaction (HRI). The precise modulation of potential and kinetic energy within the coupled human–robot system governs how assistance is provided, how disturbances are rejected, and how patient effort is encouraged. Energy shaping approaches enable the controller to sculpt an artificial energy landscape anchored at a prescribed reference posture, so that restorative torques emerge naturally from the gradient of the shaped potential and disturbance-rich interactions are regulated within bounded, passive operating limits. This study presents a novel deep learning-based energy shaping framework for torque control in a three-degree-of-freedom (DOF) ankle rehabilitation robot. The proposed method is rooted in port-Hamiltonian mechanics. It employs interconnection and damping assignment-passivity-based control (IDA-PBC) to shape the energy landscape of the system, promoting practical stability and safe patient interaction. To address the limitations of static or heuristic energy shaping, we introduce a physics-informed data-driven approach in which the potential energy function is dynamically constructed through an Attention-Augmented Fourier Neural Operator (AFNO). This architecture learns mappings from spatiotemporal sensor data, including joint kinematics and interaction torques, to optimal shaping parameters that define the control energy field. The control strategy was experimentally validated on an ankle rehabilitation robot with ten healthy subjects (eight male, two female, aged 25–43), performing controlled movements across dorsiflexion/plantarflexion, inversion/eversion, and abduction/adduction. Experimental data confirmed that the shaped potential energy fields successfully guided joint trajectories toward the prescribed reference posture under disturbance-rich interaction conditions, while maintaining passivity and minimizing unnecessary energy expenditure.