In this paper, a novel Formation Potential Field method is proposed for the multi-agent formation control. The objective is to control a group of agents to automatically generate and maintain a specific formation while avoiding internal collisions and collisions with spatial constraints. A Formation Potential Field is designed combining multiple local attractive potential fields with multiple local repulsive potential fields. To further relax requirements of agents' initial positions and enhance the robustness, a global attractive potential field is added outside the influence range of the local Formation Potential Field. The optimality of the proposed scheme in formation time is analysed as well as illustrated by contrast simulation results. Following the design of the Formation Potential Field, two controllers are proposed accordingly to achieve a stable dynamic formation during the process of trajectory tracking, while the saturation effect of input is taken into account. Furthermore, a collision avoidance strategy based on artificial potential field and Dirac delta function is applied to locally modify the original trajectory of the virtual leader such that agents can avoid collisions with unexpected spatial constraints while maintaining the given formation. Simulation results are presented to illustrate the performance of proposed approaches.