For underwater environments, it is difficult to acquire accurate contact force vectors between the end effecter and the object by multidimensional force sensors. Precise force measurement is the key point for accurate teleoperation tasks. However, existing force estimations are rarely concerned with multidimensional force vector estimations. Therefore, the transparency of the teleoperation system may be attenuated, even resulting in stability or task failure in practical engineering. In this paper, we focus on analyzing the contact force vector in three dimensions. A sliding mode disturbance observer is designed to estimate the contact force. A Q learning process is used to find the optimal multidimensional contact force. Furthermore, a bilateral controller is proposed based on the sliding mode disturbance observer and Q learning-based method for underwater teleoperation systems. The stability is analyzed by Lyapunov functions. Numerical simulations and real robot experiments are performed to verify the effectiveness of the proposed method.
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