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This paper proposes a novel control approach composed of sinusoidal referencetrajectories and trajectory tracking controller for the second-order chainedform system. The system is well-known as a canonical form for a class ofsecond-order nonholonomic systems obtained by appropriate transformation of thegeneralized coordinates and control inputs. The system is decomposed into threesubsystems, two of them are the so-called double integrators and the othersubsystem is a nonlinear system depending on one of the double integrators. Thedouble integrators are linearly controllable, which enables to transit thevalue of the position state in order to modify the nature of the nonlinearsystem that depends on them. Transiting the value to "one" corresponds tomodifying the nonlinear subsystem into the double integrator; transiting thevalue to "zero" corresponds to modifying the nonlinear subsystem into anuncontrollable linear autonomous system. Focusing on this nature, this paperproposes a feedforward control strategy. Furthermore, from the perspective ofpractical usefulness, the control strategy is extended into trajectory trackingcontrol by using proportional-derivative feedback. The effectiveness of theproposed method is demonstrated through several numerical experiments includingan application to an underactuated manipulator.

Trajectory tracking control of the second-order chained form system by using state transitions