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

Mien Van, Lejun Chen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)
312 Downloads (Pure)


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.
Original languageEnglish
Pages (from-to)9484-9504
JournalJournal of the Franklin Institute
Early online date20 Jul 2020
Publication statusEarly online date - 20 Jul 2020


  • Sliding mode control, Underactuated System, Robotics.


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