Kant appears to view things a bit differently than Hobbes. Kant talks about a free will but believes that free will is doing what ought to do rather than act from a selfish standpoint. Hobbes believes man does what he does for no other reason than personal gain. Man does things because the thing is good. We desire good and we have contempt of evil. Kant does not view things as cut and dried as Hobbes. While happiness is desirable, it is not the immediate object of men.
Perhaps Kant's view is more in line with Hobbs who believes we need to have civil authority as the foundation for morality. In a way, that is what we have in our country today. We have laws, rules and regulations that govern how we act, what we do, and when we do it. For instance traffic signals. They tell us when to stop, or go. If we do not follow that rule, we get a ticket. If tickets were not issue, how many folks would stop at a red light?
It seems to me that all of these men are saying the same thing, but using different concepts to explain their position. They all believe in good and bad, but they view the reasons for obtaining good and bad results is driven by different desires or needs. When Kant speaks of duty, it sounds like Hobbs who talks about civil authority. Kant says, "Duty is the necessity of acting from respect for the law."
This group of philosophers seems to share each other's view to a certain extent in believing that morality is achieved for reasons of pleasure. We do what we do to be happy or because it is pleasurable, or we do what we do because we are governed to do it that way or suffer consequences. Perhaps they share common view because they seemed to be from similar eras.