Matjacić Z, Bajd T
Faculty of Electrical Engineering, University of Ljubljana, Slovenia.
IEEE Trans Rehabil Eng. 1998 Jun;6(2):125-38. doi: 10.1109/86.681178.
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.
以下论文是我们对无臂截瘫患者站立可行性研究的第一部分。提出了一种用于无支撑截瘫患者站立的新型控制策略，该策略利用胸段脊髓损伤患者残留的感觉和运动能力。该策略基于截瘫患者上半身的自主和反射活动以及脚踝处人工控制的刚度。通过功能性电刺激（FES）使膝盖和臀部保持伸展位置。对线性化双倒立摆模型的分析表明，通过适当选择脚踝刚度，系统可以轻松稳定。我们开发了一个包含神经系统延迟、躯干肌肉动力学、身体节段动力学和线性二次调节器（LQR）最优控制器的闭环双倒立摆模型。通过对闭环模型的仿真，解释了两种不同的抗干扰策略。我们研究了闭环模型在存在生物力学约束的情况下，针对各种刚度水平和神经系统延迟，在踝关节处（前后方向）施加干扰时的抗干扰能力。通过限制压力中心的允许偏移，我们发现脚的长度是最重要的约束因素，而躯干肌肉的力量对于成功平衡并非至关重要。对于截瘫患者的无臂站立，大约10 Nm/度的脚踝刚度就足够了。
