An important direction of human–robot interaction (HRI) is making robots respond to complex and dexterous tasks intelligently. To achieve this, biological signals based on surface electromyography (sEMG) have widely been used to identify human intentions rapidly and effectively. We propose an algorithm that can recognize human intentions conveyed by different hand gestures through analyzing sEMG data. This will facilitate the selection of the most appropriate interaction mode and level during HRI for the robot. We also propose an admittance control framework combining a tan-type barrier Lyapunov function (BLF) and a radial basis function neural network (RBFNN) to ensure the interaction and tracking performance and to guarantee the stability of the system in uncertain environments. Experiments performed on a Baxter robot verify the effectiveness of the proposed framework.