This thesis investigates the cooperative transportation of an object by a group of mobile robots to automate a transportation process. Hence, the objective of this thesis is to develop algorithms for the distributed formation control of a multi-robot system. In addition, a novel approach for transporting a large elastic plate by a swarm of small mobile robots is devised. To overcome the challenges raised by cooperative transportation by a swarm of mobile robots, first, formation control of mobile robots based on the optimization technique is presented. The optimization problem is solved by the augmented Lagrangian particle swarm optimization method. Then, we develop a novel approach for transporting a plate using mobile robots through an unknown environment using only the friction and normal forces between the plate and the robots. The scheme includes calculating the normal forces by solving a linear complementarity problem and formation control of the swarm of robots while they keep the plate stable. The possible stability conditions of the transportation mechanism are investigated and used to formulate an optimization problem describing the control task. The approach makes use of a repeated Voronoi decomposition. The robots are controlled distributedly using augmented Lagrangian particle swarm optimization to solve the formulated optimization problem that makes it possible to enforce constraints on the movements of the robots to allow for successful transportation of the plate. In this thesis, all the proposed schemes are extensively tested in various simulations and experiments, and the results show that the localization, mapping, path planning, transportation mechanism, and following a dynamic object work successfully.