Nonlinear Observer Design for Vehicle Lateral Load Transfer Ratio Estimation

This paper proposes a nonlinear observer design for estimating the lateral load transfer ratio (LTR), a type of rollover index for vehicle safety, with a reduced reliance on measurable signals, applicable to both untripped and tripped rollovers. The dynamics of the four-degree-of-freedom vehicle are modeled to include tripped rollover, treating tire forces as unknown inputs. To address output nonlinearity, the observer employs a generalized inverse, offering an innovative solution. Benefiting from the unique structure of the state-space equations of the vehicle model, only three measurable signals are required for state and unknown input estimation. An algorithm for the observer is presented, ensuring the asymptotic stability of error through parametric solutions for matrix equations and the Lyapunov stability theorem. Validation conducted via Car-Sim simulations demonstrates the effectiveness of the proposed nonlinear observer in accurately estimating the vehicle states and tire forces. This accuracy positions it as a valuable tool for rollover prediction in vehicle safety applications.