Ongoing advancements in the design and fabrication of soft robots are creating new challenges in modeling and control. This paper presents a dynamic Cosserat rod model for a single-section 3D-printed pneumatic soft robotic arm capable of combined stretching and bending. The model captures the manufacturing variability of the actuators by tuning the pressure-strain relation for each actuator. Moreover, it includes a simple model of the pneumatic actuation system that incorporates the transient response of proportional pressure-controlled electronic valves. The model was validated experimentally for several quasi-static and dynamic motion patterns with actuation frequencies ranging from 0.2 Hz to 20 Hz. The model reproduced the quasi-static experiments with an average tip error of 4.83% of the arm length. In dynamic conditions, the average tip error was 4.33% for stretching and bending motions, 5.64% for five motor babbling experiments, and 22.53% for three challenging sinusoidal patterns. An ablation study of the model components found that the most influential factors for the average accuracy were gravity and strain gains, followed by damping and pressure transient. This work could assist researchers in focusing on the most significant aspects for closing the real-to-sim gap when modeling pneumatic soft robotic arms.

Ð Recently, learning-based controllers that leverage mechanical models of soft robots have shown promising results. This paper presents a closed-loop controller for dynamic trajectory tracking with a pneumatic soft robotic arm learned via Deep Reinforcement Learning using Proximal Policy Optimization. The control policy was trained in simulation leveraging a dynamic Cosserat rod model of the soft robot. The generalization capabilities of learned controllers are vital for successful deployment in the real world, especially when the encountered scenarios differ from the training environment. We assessed the generalization capabilities of the controller in silico for four tests. The first test involved the dynamic tracking of trajectories that differ significantly in shape and velocity profiles from the training data. Second, we evaluated the robustness of the controller to perpetual external end-point forces for dynamic tracking. For tracking tasks, it was also assessed the generalization to similar materials. Finally, we transferred the control policy without retraining to intercept a moving object with the end-effector. The learned control policy has shown good generalization capabilities in all four tests.