Dynamic Cooperative Cleaners — Various Remarks Yaniv Altshuler and Vladimir Yanovski July 10, 2005 Abstract This document contains several corrections and remarks for the Dy- namic Cooperative Cleaners problem and for the CLEAN and SWEEP cleaning protocols, which were presented in previous works [1, 2]. 1 Introduction Several works considered multi agents robotics in static environments. The Dy- namic Cooperative Cleaners problem however, is one of the first problems in which agents are required to work in dynamic environments — an environment in which changes may take place regardless of the agents’ activity. This problem is a dynamic variant of the known Cooperative Cleaners problem, which is de- scribed and analyzed in [1] (including a cleaning protocol called the CLEAN). This problem assumes a grid, part of which is ‘dirty’, where the ‘dirty’ part is a connected region of the grid. On this dirty grid region several agents move, each having the ability to ‘clean’ the place (‘tile’, ‘pixel’ or ‘square’) it is located in. The dynamic variant of the problem involves a deterministic evolution of the environment, simulating a spreading contamination (or spreading fire ). The Dynamic Cooperative Cleaners problem was first introduced in [2], which also included a cleaning protocol for the problem, called the SWEEP protocol, as well as several analytic bounds for the time it takes agents which use this protocol to clean the entire grid. This work contains a discussion concerning several issues regarding the cor- rectness of the SWEEP protocol and its bounds, as well as some clarifications regarding low level details of the SWEEP and CLEAN protocols. The work is organized as follows — section 2 contains a description of the dynamic cooper- ative cleaners problem, while section 3 present the SWEEP cleaning protocol, (as appears in [2]). The following sections contains the various issues to be discussed. Section 5 examines the Danger Zones problem and present a criteria for initial shapes, which must hold for the bounds of the cleaning protocol (de- scribed in [2]) to hold. Sections 7 and 8 discuss delicate issues which concern the low level operation of the agents employing the SWEEP protocol, which 1 Technion - Computer Science Department - Technical Report CS-2005-12 - 2005