In the linear control of a manipulator, we make several approximations to allow a linear analysis of the manipulator-control problem. Most important among these approximations was that each joint could be considered independent and that the inertia "seen" by each joint actuator was constant. This approximation results in nonuniform damping throughout the workspace and other undesirable effects.

In order to avoid these undesirable effects, we consider a more complicated control law as it is introduced in [1], in which the gains are time-varying (actually, varying as a function of the block's position) in such a manner that the system is always critically damped. Essentially, this would be done by computing the gains such that the combination of the nonlinear effect of the system would be exactly canceled by a nonlinear term in the control law so that the overall stiffness would stay a constant at all times. Such a control scheme might be called a linearizing control law because it uses a nonlinear control term to "cancel" a nonlinearity in the controlled system so that the overall closed-loop system is linear.

The presented control system is a case study of the described linearized control system on manipulator KUKA KR6 R900.

[1] John J. Craig, Nonlinear control of a manipulator, introduction to robotics, Pearson Education, 2005