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Soft robots promise improved safety and capability over rigid robots when deployed near humans or in complex, delicate, and dynamic environments. However, infinite degrees of freedom and the potential for highly nonlinear dynamics severely complicate their modeling and control. Analytical and machine learning methodologies have been applied to model soft robots but with constraints: quasi-static motions, quasi-linear deflections, or both. Here, we advance the modeling and control of soft robots into the inertial, nonlinear regime. We controlled motions of a soft, continuum arm with velocities 10 times larger and accelerations 40 times larger than those of previous work and did so for high-deflection shapes with more than 110° of curvature. We leveraged a data-driven learning approach for modeling, based on Koopman operator theory, and we introduce the concept of the static Koopman operator as a pregain term in optimal control. Our approach is rapid, requiring less than 5 min of training; is computationally low cost, requiring as little as 0.5 s to build the model; and is design agnostic, learning and accurately controlling two morphologically different soft robots. This work advances rapid modeling and control for soft robots from the realm of quasi-static to inertial, laying the groundwork for the next generation of compliant and highly dynamic robots.

 

Soft, tip-extending "vine" robots offer a unique mode of inspection and manipulation in highly constrained environments. For practicality, it is desirable that the distal end of the robot can be manipulated freely, while the body remains stationary. However, in previous vine robots, either the shape of the body was fixed after growth with no ability to manipulate the distal end, or the whole body moved together with the tip. Here, we present a concept for shape-locking that enables a vine robot to move only its distal tip, while the body is locked in place. This is achieved using two inextensible, pressurized, tip-extending, chambers that "grow" along the sides of the robot body, preserving curvature in the section where they have been deployed. The length of the locked and free sections can be varied by controlling the extension and retraction of these chambers. We present models describing this shape-locking mechanism and workspace of the robot in both free and constrained environments. We experimentally validate these models, showing an increased dexterous workspace compared to previous vine robots. Our shape-locking concept allows improved performance for vine robots, advancing the field of soft robotics for inspection and manipulation in highly constrained environments.