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We review recent advances in algorithmic development and validation for modeling and control of soft robots leveraging the Koopman operator theory.

We identify the following trends in recent research efforts in this area. (1) The design of lifting functions used in the data-driven approximation of the Koopman operator is critical for soft robots. (2) Robustness considerations are emphasized. Works are proposed to reduce the effect of uncertainty and noise during the process of modeling and control. (3) The Koopman operator has been embedded into different model-based control structures to drive the soft robots.

Because of their compliance and nonlinearities, modeling and control of soft robots face key challenges. To resolve these challenges, Koopman operator-based approaches have been proposed, in an effort to express the nonlinear system in a linear manner. The Koopman operator enables global linearization to reduce nonlinearities and/or serves as model constraints in model-based control algorithms for soft robots. Various implementations in soft robotic systems are illustrated and summarized in the review.

 

Soft pneumatic legged robots show promise in their ability to traverse a range of different types of terrain, including natural unstructured terrain met in applications like precision agriculture. They can adapt their body morphology to the intricacies of the terrain at hand, thus enabling robust and resilient locomotion. In this paper we capitalize upon recent developments on soft pneumatic legged robots to introduce a closed-loop trajectory tracking control scheme for operation over flat ground. Closed-loop pneumatic actuation feedback is achieved via a compact and portable pneumatic regulation board. Experimental results reveal that our soft legged robot can precisely control its body height and orientation while in quasi-static operation based on a geometric model. The robot can track both straight line and curved trajectories as well as variable-height trajectories. This work lays the basis to enable autonomous navigation for soft legged robots. 

Pneumatically-actuated soft robots have advantages over traditional rigid robots in many applications. In particular, their flexible bodies and gentle air-powered movements make them more suitable for use around humans and other objects that could be injured or damaged by traditional robots. However, existing systems for controlling soft robots currently require dedicated electromechanical hardware (usually solenoid valves) to maintain the actuation state (expanded or contracted) of each independent actuator. When combined with power, computation, and sensing components, this control hardware adds considerable cost, size, and power demands to the robot, thereby limiting the feasibility of soft robots in many important application areas. In this work, we introduce a pneumatic memory that uses air (not electricity) to set and maintain the states of large numbers of soft robotic actuators without dedicated electromechanical hardware. These pneumatic logic circuits use normally-closed microfluidic valves as transistor-like elements; this enables our circuits to support more complex computational functions than those built from normally-open valves. We demonstrate an eight-bit nonvolatile random-access pneumatic memory (RAM) that can maintain the states of multiple actuators, control both individual actuators and multiple actuators simultaneously using a pneumatic version of time division multiplexing (TDM), and set actuators to any intermediate position using a pneumatic version of analog-to-digital conversion. We perform proof-of-concept experimental testing of our pneumatic RAM by using it to control soft robotic hands playing individual notes, chords, and songs on a piano keyboard. By dramatically reducing the amount of hardware required to control multiple independent actuators in pneumatic soft robots, our pneumatic RAM can accelerate the spread of soft robotic technologies to a wide range of important application areas.