Assist-as-needed attitude control in three-dimensional space for robotic rehabilitation

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.