Robotic sensor networks (RSNs) can be described as networks of devices equipped with communication, sensing and actuation capabilities. Successful implementations of RSNs require tackling challenging problems lying at the intersection of robotics, communication and perception. In addition, RSNs resemble human societies and emerging intelligent multi-agent systems in some respects. In these collaborative distributed systems, each node decides which to interact with and forms a network with other nodes in order to improve the quality of the decisions. In order to achieve this goal, trust and reputation models are of practical use. In this paper, a trust and reputation model for RNSs is proposed. Also, performance evaluations of the model in comparison with well-known models in the literature are given to prove its effectiveness. The results of the performance evaluations prove that the proposed model is successful in RSNs comprising of a large number of sensor nodes. In addition, the processing and memory requirements of the proposed model are moderate and the system runs effectively in systems with low processing power and limited main memory.