### LANS Publications

# "A Gaussian Process-Based Approach for Handling Uncertainty in Vehicle Dynamics Simulation"

K. Schmitt, J. Madsen, M. Anitescu, and D. Negrut

Preprint ANL/MCS-P1505-0608

Preprint Version: [pdf]

Advances in vehicle modeling and simulation in recent years have led to designs that are safer, easier to handle, and less sensitive to external factors. Yet, the potential of simulation is adversely impacted by its limited ability to predict vehicle dynamics in the presence of uncertainty. A commonly occurring source of uncertainty in vehicle dynamics is the road-tire friction interaction, typically represented through a spatially distributed stochastic friction coefficient. The importance of its variation becomes apparent on roads with ice patches, where if the stochastic attributes of the friction coefficient are correctly factored into real time dynamics simulation, robust control strategies could be designed to improve transportation safety. This work concentrates on correctly accounting in the nonlinear dynamics of a car model for the inherent uncertainty in

friction coefficient distribution at the road/tire interface. The outcome of this effort is the ability to quantify the effect of input

uncertainty on a vehicle’s trajectory and the associated escalation

of risk in driving. By using a space-dependent Gaussian process, the statistical representation of the friction coefficient allows for consistent space dependence of randomness. The approach proposed allows for the incorporation of noise in the observed data and a nonzero mean for inhomogeneous distribution of the friction coefficient. Based on the statistical model considered, consistent friction coefficient sample distributions are generated over large spatial domains of interest. These samples are subsequently used to compute and characterize the statistics associated with the dynamics of a nonlinear vehicle model. The information concerning the state of the road and thus the friction coefficient is assumed available (measured) at a limited number of points by some sensing device that has a relatively homogeneous noise field (satellite picture or ground sensors, for instance). The methodology proposed can be modified to incorporate information that is sensed by each individual car as it

advances along its trajectory.