In this paper we introduce the concept of Adaptive Traversability (AT), which we define as means of autonomous motion control adapting the robot morphology — configuration of articulated parts and their compliance — to traverse unknown complex terrain with obstacles in an optimal way. We verify this concept by proposing a reinforcement learning based AT algorithm for mobile robots operating in such conditions. We demonstrate the functionality by training the AT algorithm under lab conditions on simple EUR-pallet obstacles and then testing it successfully on natural obstacles in a forest. For quantitative evaluation we define a metrics based on comparison with expert operator. Exploiting the proposed AT algorithm significantly decreases the cognitive load of the operator.