This paper aims at proposing an algorithm for collision-free motion planning of two wheeled mobile robots. The proposed approach relies on discrete motion planning, convex optimization and receding horizon control (RHC) concepts. The proposed algorithm is employed for motion planning and control of a mobile robot in order to pass through an unknown environment both in simulation and practical implementation. In this regard, CVX package benefited from the Gurobi solver is employed to solve the optimization problem in the simulation. Moreover, in order to perform a collision-free motion planning, corresponding Robot Operating System (ROS) package with the intended mobile robot is employed to cooperate with the provided motion planner package. The provided package utilizes educational license of Gurobi optimizer solely to speed up solving proposed optimization problem and its built in branch and bound for Mixed Linear Integer Programming (MLIP). In order to keep the linear form of the constraints, a combination of the Velocity Obstacle (VO) in the first horizon and Bug method concept for the rest of the horizons is used. Obtained results show the reliability of this algorithm for safe collision avoidance. The reported results reveal this fact that by considering the maximum velocity of the E-puck, obtained computational time is less than 0.004 sec. in each stage which is fast enough for robot motion planning tasks.