It has many challenges to assign a group of mobile robots to individual targets according to the specific constraints. In addition to the group behavior constraints (one-toone or one-to-many) of the task assignment, some of the performance constraints include (1) proximity from robot to target (2) suitability of robot in performing a task and (3) quality of connectivity among the robots. Due to the computational complexities and the nature of the dynamical systems, the task assignment approaches have been developed as distributed and dynamical systems approaches with various simplified assumptions. In this thesis, first, I investigate one of the most recently proposed distributed task assignment approaches (Peter Molnar's approach) that combines target assignment and motion planning in order to minimize the robots travelling distance and overhead cost for its one-to-one target assignment. Second, I find that the approach does not provide an efficient path finding algorithm in the environment with obstacles. It simply uses proximity sensors to direct the robots away from obstacles. Based upon the observation, third, I propose efficient task assignment approaches to minimize the robot's travel distance and overhead cost in an environment with one immobile obstacle of any shape and size. In detail, the thesis addresses 1) obstacle modeling and simplification: Initially the vertices of an obstacle were provided to the robots. The robots reconstruct the obstacle to a rectangle shape that encircles the original obstacle, 2) obstacle decomposition for an adjustment: The reconstructed obstacle is further decomposed in case if there was a robot or target object present within the reconstructed area, and 3) optimal target path calculation: Two approaches are designed for calculating distance from robot to target by taking the reconstructed obstacle into account. Approach 1 calculates the shortest distance from robot to target along the perimeter of the obstacle. Approach 2 further optimizes the path by connecting the robot and target to the shortest distance vertices of the obstacle. The computational overhead and task assignment efficiency of the proposed approaches are compared via MATLAB simulations.