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.
Past work has shown model predictive control (MPC) to be an effective strategy for controlling continuum joint soft robots using basic lumped-parameter models. However, the inaccuracies of these models often mean that an integral control scheme must be combined with MPC. In this paper we present a novel dynamic model formulation for continuum joint soft robots that is more accurate than previous models yet remains tractable for fast MPC. This model is based on a piecewise constant curvature (PCC) assumption and a relatively new kinematic representation that allows for computationally efficient state prediction. However, due to the difficulty in determining model parameters (e.g., inertias, damping, and spring effects) as well as effects common in continuum joint soft robots (hysteresis, complex pressure dynamics, etc.), we submit that regardless of the model selected, most model-based controllers of continuum joint soft robots would benefit from online model adaptation. Therefore, in this paper we also present a form of adaptive model predictive control based on model reference adaptive control (MRAC). We show that like MRAC, model reference predictive adaptive control (MRPAC) is able to compensate for “parameter mismatch" such as unknown inertia values. Our experiments also show that like MPC, MRPAC is robust to “structure mismatch” such as unmodeled disturbance forces not represented in the form of the adaptive regressor model. Experiments in simulation and hardware show that MRPAC outperforms individual MPC and MRAC.
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