Arm-free paraplegic standing--Part I: Control model synthesis and simulation.

The following paper is the first part of our investigation into the feasibility of arm-free paraplegic standing. A novel control strategy for unsupported paraplegic standing which utilizes the residual sensory and motor abilities of the thoracic spinal cord injured subjects is proposed. The strategy is based on voluntary and reflex activity of the paraplegic person's upper body and artificially controlled stiffness in the ankles. The knees and hips are maintained in an extended position by functional electrical stimulation (FES). The analysis of a linearized double inverted pendulum model revealed that with properly selected ankle stiffness the system can be easily stabilized. We developed a closed-loop double inverted pendulum model including a neural system delay, trunk muscles dynamics, body segmental dynamics and linear quadratic regulator (LQR) optimal controller. Through simulations of the closed-loop model two different strategies for disturbance rejection were explained. We investigated the capability of the closed-loop model to reject disturbances, imposed at the ankle joint (in anterior and posterior directions) for various stiffness levels and neural system delays in the presence of biomechanical constraints. By limiting permissible excursions of the center of pressure, we found out that the length of the foot is the most important constraint, while the strength of the trunk muscles is not of major importance for successful balancing. An ankle stiffness of approximately 10 Nm/degree suffices for arm-free standing of paraplegic subjects.