In this paper, relation-invariable persistent formation (RIPF) control with collision avoidance and connectivity preservation is presented. RIPF can construct an optimal formation of least edges when agents in formation can only receive range information. And this formation requires less communication and computation. It has not been studied how to drive the agents to their desired position in RIPF control while avoid collision and preserve connectivity. Three goals for RIPF are as follows: formation shape maintenances, collision avoidance (obstacle-collision avoidance, and interagent-collision avoidance), and connectivity preservation. To realize the control goals, a novel potential function is designed. The simulation results show that our control law is efficient.