Real-time estimation of rollover index for tripped rollovers with a novel unknown input nonlinear observer

Gridsada Phanomchoeng, Rajesh Rajamani

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


Accurate detection of the danger of an impending rollover is necessary for active vehicle rollover prevention systems. A real-time rollover index is an indicator used for this purpose. A traditional rollover index detects only untripped rollovers that happen due to high lateral acceleration from a sharp turn. It fails to detect tripped rollovers that happen due to tripping from external inputs such as forces when a vehicle strikes a curb or a road bump. Therefore, this paper develops a novel new rollover index that can detect both tripped and untripped rollovers. A methodology is developed for estimation of unknown inputs in a class of nonlinear systems. The methodology is based on the nonlinear observer design and dynamic model inversion to compute the unknown inputs from output measurements. The observer design utilizes the mean value theorem to express the nonlinear estimation error dynamics as a convex combination of known matrices with time-varying coefficients. The observer gains are then obtained by solving linear matrix inequalities. The developed approach can enable observer design for a large class of differentiable nonlinear systems with a globally (or locally) bounded Jacobian. The developed nonlinear observer is then applied for rollover index estimation. The developed rollover index is also evaluated through simulations with an industry standard software, CARSIM, and with experimental tests on a 1/8th scaled vehicle. In order to verify that the scaled vehicle experiments can represent a full-sized vehicle, the Buckingham π theorem is used to show dynamic similarity. The simulation and experimental results show that the developed nonlinear observer can reliably estimate vehicle states, unknown normal tire forces, and rollover index for predicting both untripped and tripped rollovers.

Original languageEnglish (US)
Article number6509941
Pages (from-to)743-754
Number of pages12
JournalIEEE/ASME Transactions on Mechatronics
Issue number2
StatePublished - Apr 2014


  • Rollover
  • Rollover prevention
  • Tripped rollover
  • Unknown input estimation
  • Vehicle dynamics
  • Vehicle state estimation

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