Stabilization of a mobile inverted pendulum with IDA-PBC and experimental verification

Kazuto Yokoyama, Masaki Takahashi

Research output: Contribution to journalArticlepeer-review


Mobile inverted pendulums are expected to be applied to personal mobility and robots which areused in human living space. Although this mobility always needsto be stabilized, previous approacheswerebased on a linearizedmodel or feedback linearization. In this study, interconnection and damping assignment passivity-based control (IDA-PBC) is applied. The IDA-PBC is a nonlinear control method which hasbeen shown to be powerful to stabilize underactuated mechanical systems. Although partial differential equation (PDE) must be solved to derive the IDA-PBCcontroller and it is a difficult taskin general, we show that the controllerfor the mobile inverted pendulum can be constructed. Asystematicgraphical methodto select controller parameters which guarantee asymptotic stability and estimate the domain of attractionisalso proposed. Simulation results show that the IDA-PBC controller performs fast responses theoretically ensuring sufficient domain of attraction.The effectiveness of the IDA-PBC controller is also verified inexperiments.Especially control performanceunder an impulsive disturbance on the mobile inverted pendulum isverified. The IDA-PBC achievesas fast transient performance as a linear-quadratic regulator (LQR). In addition, we show that when the pendulum inclines quickly and largely due to the disturbance, the IDA-PBC controller can stabilize itwhereasthe LQRcan not.

Original languageEnglish
Pages (from-to)1850-1865
Number of pages16
JournalNihon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C
Issue number777
Publication statusPublished - 2011


  • Energy shaping
  • Mobile inverted pendulum
  • Moving robot
  • Nonlinear control
  • Passivity-based control

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering


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