  In this report, we try to improve the performance of existing approaches for
search operations in multi-robot context. We propose three novel algorithms
that are using a triangular grid pattern, i.e., robots certainly go through the
vertices of a triangular grid during the search procedure. The main advantage
of using a triangular grid pattern is that it is asymptotically optimal in
terms of the minimum number of robots required for the complete coverage of an
arbitrary bounded area. We use a new topological map which is made and shared
by robots during the search operation. We consider an area that is unknown to
the robots a priori with an arbitrary shape, containing some obstacles. Unlike
many current heuristic algorithms, we give mathematically proofs of convergence
of the algorithms. The computer simulation results for the proposed algorithms
are presented using a simulator of real robots and environment. We evaluate the
performance of the algorithms via experiments with real robots. We compare the
performance of our own algorithms with three existing algorithms from other
researchers. The results demonstrate the merits of our proposed solution. A
further study on formation building with obstacle avoidance for a team of
mobile robots is presented in this report. We propose a decentralized formation
building with obstacle avoidance algorithm for a group of mobile robots to move
in a defined geometric configuration. Furthermore, we consider a more
complicated formation problem with a group of anonymous robots; these robots
are not aware of their position in the final configuration and need to reach a
consensus during the formation process. We propose a randomized algorithm for
the anonymous robots that achieves the convergence to a desired configuration
with probability 1. We also propose a novel obstacle avoidance rule, used in
the formation building algorithm.
