Sliding Mode Control of a Class of Underactuated System With Non-integrable Momentum

In this paper, a sliding mode control scheme is developed to stabilise a class of nonlinear perturbed underactuated
system with a non-integral momentum. In this scheme, by initially maintaining a subset of actuated variables on
sliding manifolds, the underactuated system with the non-integrable momentum can be approximated by one with
the integrable momentum in finite time. During sliding, a subset of the actuated variables converge to zero and a
physically meaningful diffeomorphism is systematically calculated to transform the reduced order sliding motion into
one in a strict feedback normal form in which the control signals are decoupled from the underactuated subsystem.
Furthermore, based on the perturbed strict feedback form, it is possible to find a sliding mode control law to ensure
the asymptotic stability of the remaining actuated and unactuated variables. The design efficacy is verified via a
multi-link planar robot case study.