Modeling, simulation, and control of soft robots using Koopman operator theory

Singh, Ajai, author
Chong, Edwin K. P., advisor
Zhao, Jianguo, committee member
Pasricha, Sudeep, committee member
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In nature, animals with soft body parts can control their parts to different shapes, e.g., an elephant trunk can wrap on a tree branch to pick it up. But most research on manipulators only focuses on how to control the end effector, partly because the arm of the manipulator 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 then delivering drugs to the required location. However, controlling the shape of soft robots is challenging since the dynamics of soft robots are highly nonlinear and computationally intensive. In this research, we leverage a data-driven method using the Koopman operator to realize the shape control of soft robots. The dynamics of a soft manipulator are simulated using a physics-based simulator (PyElastica) to generate the input-output data. The data is used to identify an approximated linear model based on the Koopman operator. We then formulate the shape-control problem as a convex optimization problem that is computationally efficient. We demonstrated the 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 (MPC), and then in the subsequent chapters, we build a soft grid consisting of 40 such soft manipulators. We then address the issues related to the Extended Dynamic Mode Decomposition (EDMD) algorithm used for approximating the Koopman operator by developing a deep learning-based framework to learn the Koopman embeddings. On comparing the EDMD and deep learning framework it was found that the deep learning framework was far more accurate than the EDMD framework We then show that the proposed methods can be effectively used to control the shapes of soft robots by having the single soft manipulator morph into "C", "S", and "U" shapes and then extend the shape control method to the soft grid by morphing it into 3 different shapes. We envision that shape control will allow the soft robots to interact with uncertain environments or the shapes of shape-morphing robots to fulfill different tasks.
2023 Spring.
Includes bibliographical references.
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Koopman operator theory
soft robotics
shape control
control systems
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