Soft robots undergo large nonlinear spatial deformations due to both inherent actuation and external loading. The physics underlying these deformations is complex, and often requires intricate analytical and numerical models. The complexity of these models may render traditional model-based control difficult and unsuitable. Model-free methods offer an alternative for analyzing the behavior of such complex systems without the need for elaborate modeling techniques. In this paper, we present a model-free approach for open loop position control of a soft spatial continuum arm, based on deep reinforcement learning. The continuum arm is pneumatically actuated and attains a spatial work-space by a combination of unidirectional bending and bidirectional torsional deformation. We use Deep-Q Learning with experience replay to train the system in simulation. The efficacy and robustness of the control policy obtained from the system is validated both in simulation and on the continuum arm prototype for varying external loading conditions.

Fiber Reinforced Elastomeric Enclosures (FREEs) are fundamental building blocks of pneumatic soft robots, with McKibben muscles as common examples. When a system of FREEs are arranged in a planar configuration, they undergo large bending deformations due to internal loads and moments. This paper models the bending behavior of FREEs using a modified three-spring Pseudo-Rigid Body (PRB) model, which is commonly used to capture large bending behavior of flexures. The springs of the PRB model are shown to effectively capture the axial and bending stiffness of contracting FREEs, while an internal force accounts for actuation due to internal pressurization. An optimization process is carried out to fit the PRB model parameters with the experimental response curve of different FREEs with varying length to diameter ratio and fiber angles. Unlike conventional models applied to compliant mechanisms, the model parameters are shown to depend on fluid pressure. The PRB model is used to demonstrate and analyze a pennate arrangement of contracting FREEs that exhibit variable gear ratio behavior. The pennate FREEs can serve as building blocks for the design of soft robots.