Double inverted pendulum optimal control-basis for unsupported standing in paraplegia

Limited unsupported standing has been restored in a patient with thoracic spinal cord injury through closed loop functional electrical stimulation of paralyzed ankle joint dorsal and plantarflexor muscles and voluntary and reflex activity of intact upper trunk musculature. The paraplegic subject was considered an underactuated double inverted pendulum structure with an active degree of freedom in upper trunk and paralyzed ankle joints. An optimal control system for paralyzed ankle muscles was designed that enables the subject to stand without support in sagittal plane. The control system design was based on minimization of novel cost function that estimates the effort of ankle joint muscles through observation of the ground reaction force position relative to the ankle joint axis. The designed control system integrates voluntary upper trunk activity and artificial control of ankle joint muscles resulting in a robust standing posture, while minimizing stimulated muscles effort. The benefits of the proposed control are the prolonged standing sessions and the fact that the subject maintains voluntary control over the orientation of the upper trunk in space resulting in simple functional standing.