Liyao Chang

Conventional aquatic robots are typically constrained by fixed morphology and single-mode locomotion, limiting adaptability to unstructured environments. Inspired by the diverse fin-driven locomotion strategies of natural fish, we present a self-reconfigurable robotic fish swarm system capable of operating across a wide range of aquatic conditions and tasks. Each robotic fish unit features autonomous physical assembly and disassembly capabilities by electropermanent magnets, enabling both connection and intermodule communication, allowing the swarm to dynamically reconfigure its morphology. Systematic evaluation reveals that swarm configurations substantially outperform individual units in various locomotion performance, including stability, maneuverability, swimming speed, energy efficiency, and multimodal locomotion ability. The swarm also demonstrates collaborative capabilities in navigating through complex environments, manipulating obstacles, and transporting objects, both in laboratory and outdoor aquatic settings. This work provides a framework for aquatic robots to adapt to unstructured environments and complex tasks, contributing to the advancement of multifunctional, reconfigurable robotic systems.

The condition number of a network layer, the ratio of its optimal upper and lower Lipschitz constants, measures how severely the layer distorts distances between inputs. Extending the ReLU result of Xia and Zhou, we establish the analogous pair of results for Leaky ReLU with leakage coefficient between 0 and 1. A pointwise algebraic identity decomposes the squared distance between Leaky ReLU images into two standard ReLU terms and one linear term, so existing concentration estimates transfer without modification. The optimal condition number equals sqrt(2(1+alpha^2))/(1+alpha): no choice of weights improves on it, Gaussian weights achieve it asymptotically, and it decreases strictly from sqrt(2) at alpha = 0 to 1 at alpha = 1, quantifying the geometric benefit of leakage.

In integral Lyapunov-Razumikhin conditions, the current value of a Lyapunov function is compared with a weighted integral of its recent history instead of the maximum over the delay window. This paper formulates the comparison with an arbitrary finite positive Borel measure on the delay window and establishes global stability, uniform global asymptotic stability, and input-to-state stability by an elementary record-point argument, recovering the known integral-kernel conditions as the absolutely continuous case. All finite Lp-type formulations are shown to be equivalent to the integral case under an exact reparameterization of the gains, so the exponent carries no structural information; for a scalar linear system with one discrete delay a certificate exists if and only if the measure places positive mass at the delay. The p = infinity endpoint, governed by the support of the measure, connects the framework to the classical maximum-type condition.