This paper proposes a control strategy to autonomously deploy optimal placements of range-only mobile sensors in 2D and 3D spaces. Based on artificial potential approaches, the control strategy is designed to minimize the intersensor and external potentials. The inter-sensor potential is the objective function for optimal sensor placements. A placement is optimal when the inter-sensor potential is minimized. The external potential is introduced to fulfill constraints on sensor trajectories. Since artificial potential approaches can handle various issues such as obstacle avoidance and collision avoidance among sensors, the proposed control strategy provides a flexible solution to practical autonomous optimal sensor deployment. The control strategy is applied to several optimal sensor deployment problems in 2D and 3D spaces. Simulation results illustrate how the proposed control strategy can improve target tracking performance.