Robotic sensor network (RSN) contains mobile sensors and robots providing feasible solution for many multi-agent applications. One of the most critical issues in RSN and its application is how to effectively assign tasks. This paper presents a novel connectivity preserving hybrid task allocation strategy to answer the question particularly for RSN. Firstly, we model the task allocation in RSN to distinguish the discovering and allocating processes. Secondly, a fully distributed simple Task-oriented Unoccupied Neighbor Algorithm, named TUNA, is developed to allocate tasks with only partial view of the network topology. A connectivity controller is finally developed and integrated into the strategy to guarantee the global connectivity of entire RSN, which is critical to most RSN applications. The correctness, efficiency and scalability of TUNA are proved with both theoretical analysis and experimental simulations. The evaluation results show that TUNA can effectively assign tasks to mobile robots with the requirements of only a few messages and small movements of mobile agents.