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This paper describes a supervisory control system for a multi-fingered robotic hand. The proposed method enables a slave robotic hand to grasp an object in a remote environment in several ways, manipulate it, and mimic several non-grasping motions. The key components of the proposed control system are a grasping selector in the master system and motion controllers and a controller selector in the slave system. The grasping selector learns to detect motions commanded by an operator using datagloves. We developed two methods to learn the operator's hand shapes, one that prioritizes the learning time and one that prioritizes the probability of correct detection. The controller selector determines the current command and awaits a transition, while the motion controllers stably realize the currently commanded motion. We have demonstrated the stable operation of a three-fingered robotic hand using the proposed method.