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In this paper we introduce a novel mechanism for controlling autonomous mobile robots that is based on using spiking neural networks (SNNs). The SNNs are inspired by biological neurons that communicate using pulses or spikes. As SNNs have shown to be excellent control systems for biological organisms, they have the potential to produce good control systems for autonomous robots. In this paper we present the use and benefits of SNNs for mobile robot control. We also present an adaptive genetic algorithm (GA) to evolve the weights of the SNNs online using real robots. The adaptive GA using adaptive crossover and mutation converge in a small number of generations to solutions that allow the robots to complete the desired tasks. We have performed many experiments using real mobile robots to test the evolved SNNs in which the SNNs provided a good response.