Generalized Dynamics of Non-Grounded Systems with Series Elastic Actuators and Effect of Actuator Base Fixation on Force Control Robustness

This paper proposes a generalized dynamics model for a Non-Grounded System (NGS) mounted with a Reaction Force Sensing Series Elastic Actuator (RFSEA), focusing on scenarios where the actuator's base is unfixed and interacts with the ground. In RFSEA-based force control, the actuator base, which provides the necessary reaction force as dictated by Newton's third law, plays a critical role. This study examines how the interaction between the actuator base and the ground it is attached to influences the response of the series elasticity that generates force in the RFSEA. The investigation involves two steps. First, a generalized dynamics model that considers the dynamics between the actuator base and the ground is derived. Second, the Small Gain Theorem (SGT) is applied to evaluate the robustness of force control under load-side model uncertainties when a Force-based Disturbance Observer (FDOB), originally designed for GS, is adapted to NGS. The analysis reveals that force control utilizing FDOB can become unstable when the actuator base is unfixed, and simulations validate these findings.