Shadmehr R (1990), Learning virtual equilibrium trajectories for control of a robot arm. Neural Computation 2(4):446-456.

Abstract The cerebellar model articulation controller (CMAC) (Albus 1975) is applied for learning the inverse dynamics of a simulated two joint, planar arm. The actuators were antagonistic muscles, which acted as feedback controller for each joint. We use this example to demonstrate some limitations of the control paradigm used in earlier applications of the CMAC (e.g., Miller et al. 1987, 1990): the CMAC learns dynamics of the arm and not those of the feedback system. We suggest an alternate approach, one in which the CMAC learns to manipulate the feedback controller's input, producing a virtual trajectory, rather than the controller's output, which is torque. Several experiments are performed that suggest that the CMAC learns to
compensate for the dynamics of the plant, as well as the controller.