One is a very well known controller called a proportional plus derivative control scheme in which the torque or the forces which are acting at the robot joints are proportional to the error, proportional to the derivative of the error and maybe some feed-forward term. Often an integral term is also added. Another common controller which is used in robots is called as a model based controller in which the torque is proportional not only to the previous proportional plus derivative controller but it is also multiplied by the mass matrix of the robot and there is a bias which consists of the estimated non-linear terms. It has been known in literature that a proportional plus derivative controller is asymptotically stable. We can show that the error between what we want, how the robot should move and how the robot is behaving will always tend to zero, which is what is expected of any controller. We try to do the same thing for various robots.

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