<p>This paper presents a novel globally cooperative localization method using a fuzzy broad learning system (FBLS) and a fuzzy distributed and decentralized extended Kalman Filter (FDDEKF) algorithm in order to quickly localize a swarm of cooperative Omnidirectional Mobile Robots (OMRs) with an incompletely connected communication topology. The FBLS is employed to online learn an uncertain dynamic part of each OMR. A new swarm poses initialization method is offered to estimate all the robots’ initial positions and orientations by sharing measurement information among the multi-robots. Once all the initial poses of all the swarmed OMRs have been determined, an FDDEKF method augmented with the FBLS, abbreviated as FBLS-FDDEKF, is proposed to fuse multiple measurements from different sensors to estimate the poses of all the moving OMRs. Comparative simulations are performed to show the superiority of the raised FBLS-FDDEKF method by comparing to existing EKF, Fuzzy EKF, FDDEKF, and BLS-FDDEKF methods. In the experimental validation, each OMR in the swarm uses an RGB-D sensor to recognize nearby landmarks and adopts a LiDAR sensor to perceive the neighboring objects, and the communication topology is incompletely connected. Experimental results are conducted to illustrate that our FBLS-FDDEKF method is more accurate and superior in cooperatively estimating the moving poses of a swarm of three initially unlocalized OMRs. The presented method would provide valuable references for professionals working with mobile multi-robots.</p>