Minimum-Intervention Hamiltonian-Based Assistance Control for Unicycle Simulator

This paper proposes an energy-based training assistance controller for a unicycle riding simulator inspired by Human Adaptive Mechatronics (HAM). We focus on sagittal plane (pitch) balance for beginners and derive a simplified longitudinal plane unicycle model, where pedaling is represented as an action–reaction torque between the wheel and the rider–saddle body. After time normalization, the saddle dynamics is expressed in a form suitable for energy analysis. Using the natural Hamiltonian of the uncontrolled system, we design a minimum-intervention pumping–damping controller that modifies the energy flow only when necessary. The assistance is smoothly activated outside a training core region defined by a saddle-angle bound: a damping term suppresses excessive motion, and a pumping term prevents trapping in a tilted posture when the energy becomes too small. The proposed framework offers physically interpretable, localized assistance while preserving the natural unicycle dynamics required for skill learning.