  This paper focuses on the construction of differential-cascaded structures
for control of nonlinear robot manipulators subjected to disturbances and
unavailability of partial information of the desired trajectory. The proposed
differential-cascaded structures rely on infinite differential series to handle
the robustness with respect to time-varying disturbances and the partial
knowledge of the desired trajectories for nonlinear robot manipulators. The
long-standing problem of reliable adaptation in the presence of sustaining
disturbances is solved by the proposed forwardstepping control with
forwardstepping adaptation, and stacked reference dynamics yielding adaptive
differential-cascaded structures have been proposed to facilitate the
forwardstepping adaptation to both the uncertainty of robot dynamics and that
of the frequencies of disturbances. A distinctive point of the proposed
differential-cascaded approach is that the reference dynamics for design and
analysis involve high-order quantities, but via degree-reduction implementation
of the reference dynamics, the control typically involves only the low-order
quantities, thus facilitating its applications to control of most physical
systems. Our result relies on neither the explicit estimation of the
disturbances or derivative and second derivative of the desired position nor
the solutions to linear/nonlinear regulator equations, and the employed
essential element is a differential-cascaded structure governing robot
dynamics.
