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IntroductionThis paper addresses the critical need for adaptive formation control in Autonomous Underwater Vehicles (AUVs) without requiring knowledge of system dynamics or environmental data. Current methods, often assuming partial knowledge like known mass matrices, limit adaptability in varied settings. MethodsWe proposed two-layer framework treats all system dynamics, including the mass matrix, as entirely unknown, achieving configuration-agnostic control applicable to multiple underwater scenarios. The first layer features a cooperative estimator for inter-agent communication independent of global data, while the second employs a decentralized deterministic learning (DDL) controller using local feedback for precise trajectory control. The framework's radial basis function neural networks (RBFNN) store dynamic information, eliminating the need for relearning after system restarts. ResultsThis robust approach addresses uncertainties from unknown parametric values and unmodeled interactions internally, as well as external disturbances such as varying water currents and pressures, enhancing adaptability across diverse environments. DiscussionComprehensive and rigorous mathematical proofs are provided to confirm the stability of the proposed controller, while simulation results validate each agent’s control accuracy and signal boundedness, confirming the framework’s stability and resilience in complex scenarios. 

A soft robot is a robot made of soft materials and is capable of doing complex tasks. The soft robot that was created in this experiment is a soft trunk robot actuated by strings. The purpose of this robot is to be able to move around small spaces easily and be able to perform complex tasks. For example, positioning a tip mounted sensor to gather data. From the results in the experiment, the robot can move to a target position when given a set of coordinates by using a P-controller.