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In this paper, we propose a supervised learning approach based on an Artificial Neural Network (ANN) model for real-time classification of subtasks in a physical human-robot interaction (pHRI) task involving contact with a stiff environment. In this regard, we consider three subtasks for a given pHRI task: Idle, Driving, and Contact. Based on this classification, the parameters of an admittance controller that regulates the interaction between human and robot are adjusted adaptively in real time to make the robot more transparent to the operator (i.e. less resistant) during the Driving phase and more stable during the Contact phase. The Idle phase is primarily used to detect the initiation of task. Experimental results have shown that the ANN model can learn to detect the subtasks under different admittance controller conditions with an accuracy of 98% for 12 participants. Finally, we show that the admittance adaptation based on the proposed subtask classifier leads to 20% lower human effort (i.e. higher transparency) in the Driving phase and 25% lower oscillation amplitude (i.e. higher stability) during drilling in the Contact phase compared to an admittance controller with fixed parameters.