This paper deals with avoidance constraints while following an optimal trajectory for a group of agents operating in open space. The basic idea is to use the Model Predictive Control (MPC) technique to solve a real time optimization problem over a finite time horizon. Following a specified trajectory, the agents move in the same direction and eventually they end up in a particular formation. Combining the optimization-based control study with the ability of MPC to handle convex and non-convex constraints allows a thorough analysis of the motion control of a group of agents with linear dynamics subject to state constraints. Avoidance constraints are also added to the optimization problem when the agents are operating in an environment with obstacles. A flat trajectory is planned in the physical open space allowing the agents to maneuver successfully in such a dynamic environment and to reach a common objective.