Soft robots have the potential to significantly change the way that robots interact with the environment and with humans. However, accurately modeling soft robot and soft actuator dynamics in order to perform model-based control can be extremely difficult. Deep neural networks are a powerful tool for modeling systems with complex dynamics such as the pneumatic, continuum joint, six degree-of-freedom robot shown in this paper. Unfortunately it is also difficult to apply standard model-based control techniques using a neural net. In this work, we show that the gradients used within a neural net to relate system states and inputs to outputs can be used to formulate a linearized discrete state space representation of the system. Using the state space representation, model predictive control (MPC) was developed with a six degree of freedom pneumatic robot with compliant plastic joints and rigid links. Using this neural net model, we were able to achieve an average steady state error across all joints of approximately 1 and 2° with and without integral control respectively. We also implemented a first-principles based model for MPC and the learned model performed better in terms of steady state error, rise time, and overshoot. Overall, our results show the potential of combining empirical modeling approaches with model-based control for soft robots and soft actuators
