Abstract Existing rehabilitation robots focus on mimicking sagittal motion alone; however, sagittal motion is only a subset of actual human motions in three-dimensional space. Thus, the positions and attitudes of limb end-effectors should be controlled. The attitudes are expressed by rotation matrices, which belong to a special orthogonal group SO(3). As they lie in manifold and not in Euclidean space as is the case with the positions, it is difficult to achieve assist-as-needed control. Herein, the moment field control for robotic rehabilitation is studied. First, the error matrix and its exponential coordinate describe the attitude error. Geodesic distance-based Newton method is applied to obtain the closest attitude to the actual attitude in the desired trajectory. Thus, the tangential and normal directions are determined and the moment field is established to generate sufficient torque to adjust the attitude. Using the robotic exoskeleton for hip rehabilitation, the algorithm is simulated, and its effectiveness is verified. The proposed control method achieves adequate attitude control of joints with three degrees of freedom or pose control of limb end-effectors, providing a reference for controlling rehabilitation robots.

中文翻译：

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机器人康复三维空间中的辅助姿态控制

摘要 现有康复机器人只注重模仿矢状运动；然而，矢状运动只是三维空间中实际人体运动的一个子集。因此，应控制肢体末端执行器的位置和姿态。姿态由属于特殊正交群 SO(3) 的旋转矩阵表示。由于它们位于流形中而不是像位置那样位于欧几里得空间中，因此很难实现按需辅助控制。在此，研究了机器人康复的力矩场控制。首先，误差矩阵及其指数坐标描述了姿态误差。应用基于测地距离的牛顿方法来获得期望轨迹中与实际姿态最接近的姿态。因此，确定切线和法线方向并建立力矩场以产生足够的扭矩来调整姿态。使用机器人外骨骼进行髋关节康复，对该算法进行了仿真，验证了其有效性。所提出的控制方法实现了三自由度关节的充分姿态控制或肢体末端执行器的姿态控制，为控制康复机器人提供了参考。