Velocity field control with energy compensation toward therapeutic exercise

Human-machine systems, such as those used for rehabilitation, must be safe for human use when performing a given operational task. Passivity-based controllers such as the passive velocity field control method helps in realizing safe operation of human-machine systems. However, active behavior toward the external environment, including human bodies, is required to realize a given task. Such active behavior is difficult for passivity-based controllers. This study focuses on ensuring that a manipulator behaves passively toward an external force when the kinetic energy is greater than or equal to a given threshold and actively otherwise. We present a newly developed velocity field control method with an energy compensation mechanism. Theoretical analysis shows the properties of the proposed method: when the passivity toward external forces increases the kinetic energy of the augmented system beyond the required limit, the energy converges to a given range for safety rehabilitation without external forces, and the closed-loop system tracks a given desired velocity field without external forces. As a further theoretical discussion, we show the energy flow between the manipulator and human. Numerical simulations demonstrate that (1) the closed-loop system tracks a given desired velocity field, which describes a rehabilitation task, without external forces, (2) the proposed method inhibits the decrease in the kinetic energy of a closed-loop system, and (3) the closed-loop system behaves passively toward external forces such as an unexpected reaction of a human.