Abstract:This paper investigates the robustness of the Lur'e problem under positivity constraints, drawing on results from the positive Aizerman conjecture and the robustness properties of Metzler matrices. Specifically, we consider a control system of Lur'e type in which not only the linear part includes parametric uncertainty but also the nonlinear sector bound is unknown. We investigate tools from positive linear systems to effectively solve the problems in complicated and uncertain nonlinear systems. By leveraging the positivity characteristic of the system, we derive an explicit formula for the stability radius of Lur'e systems. Furthermore, we extend our analysis to systems with neural network (NN) feedback loops. Building on this approach, we also propose a refinement method for sector bounds of feedforward neural networks (FFNNs). This study introduces a scalable and efficient approach for robustness analysis of both Lur'e and NN-controlled systems. Finally, the proposed results are supported by illustrative examples.
Abstract:We propose a novel, heterogeneous multi-agent architecture that miniaturizes rovers by outsourcing power generation to a central hub. By delegating power generation and distribution functions to this hub, the size, weight, power, and cost (SWAP-C) per rover are reduced, enabling efficient fleet scaling. As these rovers conduct mission tasks around the terrain, the hub charges an array of replacement battery modules. When a rover requires charging, it returns to the hub to initiate an autonomous docking sequence and exits with a fully charged battery. This confers an advantage over direct charging methods, such as wireless or wired charging, by replenishing a rover in minutes as opposed to hours, increasing net rover uptime. This work shares an open-source platform developed to demonstrate battery swapping on unknown field terrain. We detail our design methodologies utilized for increasing system reliability, with a focus on optimization, robust mechanical design, and verification. Optimization of the system is discussed, including the design of passive guide rails through simulation-based optimization methods which increase the valid docking configuration space by 258%. The full system was evaluated during integrated testing, where an average servicing time of 98 seconds was achieved on surfaces with a gradient up to 10{\deg}. We conclude by briefly proposing flight considerations for advancing the system toward a space-ready design. In sum, this prototype represents a proof of concept for autonomous docking and battery transfer on field terrain, advancing its Technology Readiness Level (TRL) from 1 to 3.