The notion of safety in multi-agent systems assumes great significance in many emerging collaborative multi-robot applications. In this paper, we present a multi-UAV collaborative target-tracking application by defining bounded inter-UAV distances in the formation in order to ensure safe operation. In doing so, we address the problem of prioritizing specific objectives over others in a multi-objective control framework. We propose a barrier Lyapunov function-based distributed control law to enforce the bounds on the distances and assess its Lyapunov stability using a kinematic model. The theoretical analysis is supported by numerical results, which account for measurement noise and moving targets. Straight-line and circular motion of the target are considered, and results for quadratic Lyapunov function-based control, often used in multi-agent multi-objective problems, are also presented. A comparison of the two control approaches elucidates the advantages of our proposed safe-control in bounding the inter-agent distances in a formation. A concluding evaluation using ROS simulations illustrates the practical applicability of the proposed control to a pair of multi-rotors visually estimating and maintaining their mutual separation within specified bounds, as they track a moving target.