The tracking control of underactuated systems is a challenging problem due to the
structural differences compared to fully actuated systems. Contrarily to fully actuated
systems, resolving the inverse kinematics problem of underactuated systems is not
possible independently from the dynamic equations. Instead, the inverse dynamics must
be addressed. It is common to extend the computed torque control (CTC) technique with
servoconstraints. Besides the CTC's clearness, the stability of the system cannot
be always guaranteed. A novel predictive controller (PC) is presented in this paper.
Our PC applies the variational principle to design the motion of the system in order
to achieve a stable motion with the lowest possible tracking error. To demonstrate
the applicability and the performance of the PC method, a numerical study is presented
for a planar manipulator resulting in about 20% RMS error compared to the CTC method
from the literature.
