Due to their inherent compliance, soft robots are more versatile than rigid linked robots when they interact with their environment, such as object manipulation or biomimetic motion, and considered the key element in introducing robots to everyday environments. Although various soft robotic actuators exist, past research has focused primarily on designing and analyzing single components. Limited effort has been made to combine each component to create an overall capable, integrated soft robot. Ideally, the behavior of such a robot can be accurately modeled, and its motion within an environment uses its proprioception, without requiring external sensors. This work presents a design and modeling process for a Soft continuum Proprioceptive Arm (SoPrA) actuated by pneumatics. The integrated design is suitable for an analytical model due to its internal capacitive flex sensor for proprioceptive measurements and its fiber-reinforced fluidic elastomer actuators. The proposed analytical dynamical model accounts for the inertial effects of the actuator's mass and the material properties, and predicts in real-time the soft robot's behavior. Our estimation method integrates the analytical model with proprioceptive sensors to calculate external forces, all without relying on an external motion capture system. SoPrA is validated in a series of experiments demonstrating the model's and sensor's accuracy in estimation. SoPrA will enable soft arm manipulation including force sensing while operating in obstructed environments that disallows exteroceptive measurements.
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