Three-Dimensional Rendezvous Controls of Multiple Robots with Amplitude-Only Measurements in Cluttered Underwater Environments

Abstract

This study addresses multi-robot distributed rendezvous controls in cluttered underwater environments with many unknown obstacles. In underwater environments, a Unmanned Underwater Vehicle (UUV) cannot localize itself, since a Global Positioning System (GPS) is not available. Assume that each UUV has multiple signal intensity sensors surrounding it. Multiple intensity sensors on a UUV can only measure the amplitude of signals generated from its neighbor UUVs. We prove that multiple UUVs with bounded speed converge to a designated rendezvous point, while maintaining the connectivity of the communication network. This study further discusses a fault detection method, which detects faulty UUVs based on local sensing measurements. In addition, the proposed rendezvous control is adaptive to communication link failure or invisible UUVs. Note that communication link failure or invisible UUVs can happen due to unknown obstacles in the workspace. As far as we know, our study is novel in developing 3D coordinate-free distributed rendezvous control, considering underwater robots that can only measure the amplitude of signals emitted from neighboring robots. The proposed rendezvous algorithms are provably complete, and the effectiveness of the proposed rendezvous algorithms is demonstrated under MATLAB simulations.