In nature, animals with soft body parts demonstrate remarkable control over their shape, such as an elephant trunk wrapping around a tree branch to pick it up. However, most research on robotic manipulators focuses on controlling the end effector, partly because the manipulator’s arm is rigidly articulated. With recent advances in soft robotics research, controlling a soft manipulator into many different shapes will significantly improve the robot’s functionality, such as medical robots morphing their shape to navigate the digestive system and deliver drugs to specific locations. However, controlling the shape of soft robots is challenging due to their highly nonlinear dynamics that are computationally intensive. In this paper, we leverage a physics-informed, data-driven approach using the Koopman operator to realize the shape control of soft robots. We simulate the dynamics of a soft manipulator using a physics-based simulator (PyElastica) to generate the input-output data, which is then used to identify an approximated linear model based on the Koopman operator. We then formulate the shapecontrol problem as a convex optimization problem that is computationally efficient. Our linear model is over 12 times faster than the physics-based model in simulating the manipulator’s motion. Further, we can control a soft manipulator into different shapes using model predictive control. We envision that the proposed method can be effectively used to control the shapes of soft robots to interact with uncertain environments or enable shape-morphing robots to fulfill diverse tasks.
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This content will become publicly available on August 30, 2024
Control of soft robots with inertial dynamics
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.
more » « less- Award ID(s):
- 1935327
- NSF-PAR ID:
- 10466804
- Publisher / Repository:
- AAAS
- Date Published:
- Journal Name:
- Science Robotics
- Volume:
- 8
- Issue:
- 81
- ISSN:
- 2470-9476
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Purpose of Review We review recent advances in algorithmic development and validation for modeling and control of soft robots leveraging the Koopman operator theory.
Recent Findings 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.
Summary 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.
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