Neuromorphic computing --- brainlike computing in hardware --- typically requires myriad CMOS spiking neurons interconnected by a dense mesh of nanoscale plastic synapses. Memristors are frequently citepd as strong synapse candidates due to their statefulness and potential for low-power implementations. To date, plentiful research has focused on the bipolar memristor synapse, which is capable of incremental weight alterations and can provide adaptive self-organisation under a Hebbian learning scheme. In this paper we consider the Unipolar memristor synapse --- a device capable of non-Hebbian switching between only two states (conductive and resistive) through application of a suitable input voltage --- and discuss its suitability for neuromorphic systems. A self-adaptive evolutionary process is used to autonomously find highly fit network configurations. Experimentation on a two robotics tasks shows that unipolar memristor networks evolve task-solving controllers faster than both bipolar memristor networks and networks containing constant nonplastic connections whilst performing at least comparably.