It is known that tension in the track of a tracked vehicle has a large effect on its driving properties. Simple track tensioning solutions, like track adjusting link assembly, use a one-road wheel motion to govern the motion of a track tensioning element. Thus the track tensioning force is a function of a terrain micro-profile. A logical improvement of this approach is to use all of the road wheels to govern the motion of the track tensioning element. This can be achieved by an auxiliary track tensioning system. This paper analyzes the conceptual track tensioning system governed by a terrain micro-profile. The motion of the track tensioning element is designed as a function of all of the road wheels' motions. A genetic algorithm method, implemented in Java language, is used to find the optimal parameters of the tensioning system and the results are verified via multibody dynamics simulation using the MSC.ADAMS/View system. The paper answers the question of whether the use of all of the road wheels' motions to govern the motion of the track tensioning element can be useful or not. The results indicate that the use of the auxiliary system can decrease the variance of the track tensioning force, in comparison with the track tensioning system without auxiliary tensioning. This means that the value of the track tensioning force is closer to its desired, predefined, and constant value during the whole simulation. The tracked vehicle model that is used is a simplified one and it is intended as a base for specific designs of track tensioning systems with auxiliary tensioning. The results suggest that the system can be used to improve the driving properties of tracked vehicles or robots.