  This paper proposes a novel control approach composed of sinusoidal reference
trajectories and trajectory tracking controller for the second-order chained
form system. The system is well-known as a canonical form for a class of
second-order nonholonomic systems obtained by appropriate transformation of the
generalized coordinates and control inputs. The system is decomposed into three
subsystems, two of them are the so-called double integrators and the other
subsystem is a nonlinear system depending on one of the double integrators. The
double integrators are linearly controllable, which enables to transit the
value of the position state in order to modify the nature of the nonlinear
system that depends on them. Transiting the value to "one" corresponds to
modifying the nonlinear subsystem into the double integrator; transiting the
value to "zero" corresponds to modifying the nonlinear subsystem into an
uncontrollable linear autonomous system. Focusing on this nature, this paper
proposes a feedforward control strategy. Furthermore, from the perspective of
practical usefulness, the control strategy is extended into trajectory tracking
control by using proportional-derivative feedback. The effectiveness of the
proposed method is demonstrated through several numerical experiments including
an application to an underactuated manipulator.
