His leading foot, in frame 2 and frame 6, isn't swung far enough forward, so that when (in frame 3 and frame 7) it hits the ground to take the weight, it's completely flat and the heel is behind the knee instead of under it to firmly take the weight (usually the heel touches down first, not the whole foot). So if you shift the foot forward in all four frames, it should look more natural. (the brain will perceive the action of his foot moving further in the transition from frames 5 to 6, and frames 1 to 2, than it does in the other frames, as the foot swinging out to quickly take the weight -- just like in real running -- this variation in timing makes it look less robotic. I notice you have already done something similar in your
walk animation, which looks great!)
Also, I used to mistakenly use the head as a reference, and the body would animate underneath it, but having a non-moving point in a run animation just didn't look good, so I had to learn to 'bob' the head naturally. But I notice that the hips of your soldier are similarly stable in space, so maybe you might want them to shift up as he kicks off the ground, and then come back down?
Otherwise, I just want to say that your project looks terrific, and there's a lot of impressive work on display!
