In this research, a redundant cable-driven robust rehabilitation robot has been proposed for helping and automating the proper function of the patient’s lower and upper limbs in the presence of uncertainties, disturbances, noise, and time delay using a new control algorithm to derive the best tracking with the least deviations. A new joint limit avoidance path-planning method is exerted while maintaining the bounds of upper and lower angles. Also, a new robust motion controller, namely computed-torque-like controller with a variable-structure compensator was applied to the system and compared with computed-torque controller outputs. Thus, showing the efficiency of the mentioned control algorithm in the presence of uncertainties, disturbances, noise, and time delay and its superior performance and robustness in spatial motions are the goals of this paper as well as taking advantage of a new path-planning approach.

Firstly, the kinematic formulation of the cables is obtained. Then, a joint limit avoidance theory is used to apply upper and lower bounds for the joint angles. In the next step, Lagrangian dynamic equations for the 3D motions are derived. Subsequently, the positive and unilateral tension conditions in cable-driven systems are applied using null-space solutions. To have precise tracking and robustness with the existence of uncertainties, disturbances, noise, and time delay, a computed-torque control and robust computed-torque-like controller with a variable-structure compensator are utilized for the system. Stability analyses of the controllers are presented and the obtained results are compared for tracking a spatial reference trajectory.

Ultimately, this controller witnessed an improvement in the lower limb with the existence of uncertainties and disturbances in terms of the robustness of the given method about 19.5 percent, and in cable forces about 17.1 percent. Improvements for the tracking errors and the control inputs were 10.8 and 7.3 percent in the presence of noise, and 7.3 and 8.6 percent in the presence of the time delay respectively. Similar results were obtained for the upper limb with 21 percent improvement in control inputs and 21.1 percent improvement in tracking performance respectively.

在这项研究中，提出了一种冗余电缆驱动的稳健康复机器人，用于在存在不确定性、干扰、噪声和时间延迟的情况下帮助和自动化患者下肢和上肢的正常功能，并使用新的控制算法推导出偏差最小的最佳跟踪。在保持上下角度范围的情况下，应用了一种新的关节极限规避路径规划方法。此外，将一种新的鲁棒运动控制器，即具有可变结构补偿器的类计算转矩控制器应用于系统，并与计算转矩控制器的输出进行比较。因此，显示了上述控制算法在存在不确定性、干扰、噪声的情况下的效率，

首先，获得了电缆的运动学公式。然后，使用关节极限避免理论来应用关节角度的上限和下限。下一步，导出 3D 运动的拉格朗日动力学方程。随后，使用零空间解决方案应用电缆驱动系统中的正向和单向张力条件。为了在存在不确定性、干扰、噪声和时延的情况下实现精确跟踪和鲁棒性，系统采用了计算转矩控制和具有可变结构补偿器的鲁棒计算转矩控制器。提出了控制器的稳定性分析，并比较了获得的结果以跟踪空间参考轨迹。

最终，该控制器在给定方法的鲁棒性约 19.5% 和电缆力约 17.1% 方面见证了存在不确定性和干扰的下肢的改进。在存在噪声的情况下，跟踪误差和控制输入的改进分别为 10.8% 和 7.3%，在存在时间延迟的情况下分别提高了 7.3% 和 8.6%。上肢也获得了类似的结果，控制输入分别提高了 21%，跟踪性能提高了 21.1%。