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Large-scale soft robots have the capability and potential to perform highly dynamic tasks such as hammering a nail into a board, throwing items long distances, or manipulating objects in cluttered environments. This is due to their joints being underdamped and their ability to store potential energy. The soft robots presented in this article are pneumatically actuated and thus have the ability to perform these tasks without the need for large motors or gear trains. However, getting soft robots to perform highly dynamic tasks requires controllers that can track highly dynamic trajectories to complete those tasks. For soft robots, this is a difficult problem to solve due to the uncertainty in their shape and their complicated dynamics and kinematics. This article presents a formulation of a model reference adaptive controller (MRAC) that causes a three-link soft robot arm to behave like a highly dynamic 2nd-order critically damped system. Using the dynamics of a 2nd-order system, we also present a method to generate joint trajectories for throwing a ball to a desired point in Cartesian space. We demonstrate the viability of our joint-level controller in simulation and on hardware with a reported maximum root mean square error of 0.0872 radians between a reference and executed trajectory. We also demonstrate that our combined MRAC controller and trajectory generator can, on average, throw a ball to within 25–28% of a desired landing location for a throwing distance of between 1.5 and 2 m on real hardware. 

Because of the complex nature of soft robots, formulating dynamic models that are simple, efficient, and sufficiently accurate for simulation or control is a difficult task. This paper introduces an algorithm based on a recursive Newton-Euler (RNE) approach that enables an accurate and tractable lumped parameter dynamic model. This model scales linearly in computational complexity with the number of discrete segments. We validate this model by comparing it to actual hardware data from a three-joint continuum soft robot (with six degrees of freedom represented in a constant curvature kinematic model). The results show that this RNE-based model can be computed faster than real-time. We also show that with minimal system identification, a simulation performed using the dynamic model matches the real robot data with a median error of 3.15 degrees. 

Model-based optimal control of soft robots may enable compliant, underdamped platforms to operate in a repeatable fashion and effectively accomplish tasks that are otherwise impossible for soft robots. Unfortunately, developing accurate analytical dynamic models for soft robots is time-consuming, difficult, and error-prone. Deep learning presents an alternative modeling approach that only requires a time history of system inputs and system states, which can be easily measured or estimated. However, fully relying on empirical or learned models involves collecting large amounts of representative data from a soft robot in order to model the complex state space–a task which may not be feasible in many situations. Furthermore, the exclusive use of empirical models for model-based control can be dangerous if the model does not generalize well. To address these challenges, we propose a hybrid modeling approach that combines machine learning methods with an existing first-principles model in order to improve overall performance for a sampling-based non-linear model predictive controller. We validate this approach on a soft robot platform and demonstrate that performance improves by 52% on average when employing the combined model.