Pattern reconfiguration in swarms-convergence of a distributed asynchronous and bounded iterative algorithm

485 walls to detect multiple echo pulses. The TOF determination as well as the detection of the echo pulses is accomplished by searching the correlation peaks of the matched filter output. The invariant spatial relationship between f he ultrasonic sensor and the reflectors in our method allows simple but robust matching between the echoes obtained at different sensor orientations. The multiple echo pulses are first collected as groups on the basis of their TOF's, then the groups of echo pulses are tested for their physical validity. The distances to the reflectors are estimated from the mean times-of-flight of the groups of echo pulses, and tlhe directions are estimated by fitting the modeled echo amplitude p,attern to the magnitude patterns of the groups of echo pulses in least-square sense. In our method, the specular effect and the wide beam width are exploited positively. The former reduces the number of reflectors to a manageable size in typical indoor environments, and the latter allows large sampling step size in scanning. The validity as well as the performance of the proposed method was shown through the experiments to localize a mobile robot in real environment. We first extracted multiple acoustic landmarks whose positions were known with xespect to the world coordinate frame. Assuming that the spatial relationship between the mobile robot and its ultrasonic sensors was given, the mobile robot was localized to within 2 cm in distance and 0.1 degrees in direction from the true positions. Treatment of systemetic errors in the processing of wide-angle sonar sensor data for robotic navigation, " IEEE Trans. a sonar map in a specular environment using a single mobile sensor, " IEEE Trans. Mobile robot localization by tracking geometric beacons, " IEEE Trans. A high-resolution sensor based on tri-aural perception, " IEEE Trans. Robot. Abstruct-Swarms are physical realizations of self-organizinjg distributed robotic systems (DRS). This paper provides a rigorous anialysis of swarm behavior and introduces a new methodology for using swarms to solve DRS pattern reconfiguration problems. We introduce the linear swarm model and show that it is an iterative method for asynchronously solving linear systems of equations under physically relevant constraints. The main result of tlhe paper is a proof of a sufficient condition for the asynchronous convergence of a linear swarm to a synchronously achievable Configuration. This is important since a large class of DRS self-organizing tasks can be mapped into reconfigurations of patterns in …