Soft robots have attracted much attention for their safe human-robot interaction and flexibility, but the typical continuum structure and nonlinear material behavior make the kinematics modelling complex, especially in non-static motions. In this work, we proposed an LSTM-based pressure predictive control (PPC) for the motion control of a vertebraic soft robotic tail and the coordination with a quadruped robot. The PPC consists of an inverse kinematics (IK) model, a forward kinematics (FK) model and a pressure compensation (P-comp) model, and achieves non-static and quasi-static motion control of the tail. Compared with the IK-only model, the average RMSE of the PPC's simulation trajectories reduces by 69.8%, when executing target trajectories. In the coordinated motions of the soft tail quadruped, using a prediction data set to train the PPC enables next-moment action prediction and reduces computation time by 60.9%, which enhances the real-time response of the tail to match the quadruped torso's moving rate. The PPC provides a simple and effective method to model the soft tail for both non-static and quasi-static motion control, and grants the soft tail quadruped with the functionality of interacting with the environment.

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