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Accurate terrain models provide the chassis designer with a powerful tool to make informed design decisions early in the design process. It is beneficial to characterize the terrain as a stochastic process, allowing limitless amounts of synthetic terrain to be created from a small number of parameters. A continuous-state Markov chain is proposed as an alternative to the traditional discrete-state chain currently used in terrain modeling practice. For discrete-state chains, the profile transitions are quantized then characterized by a transition matrix (with many values). In contrast, the transition function of a continuous-state chain represents the probability density of transitioning between any two states in the continuum of terrain heights. The transition function developed in this work uses a location-scale distribution with polynomials modeling the parameters as functions of the current state.

The vertical force generated from terrain-tire interaction has long been of interest for vehicle dynamic simulations and chassis development. To improve simulation efficiency while still providing reliable load prediction, a terrain pre-filtering technique using a constraint mode tire model is developed. The wheel is assumed to convey one quarter of the vehicle load constantly. At each location along the tire's path, the wheel center height is adjusted until the spindle load reaches the pre-designated load. The resultant vertical trajectory of the wheel center can be used as an equivalent terrain profile input to a simplified tire model. During iterative simulations, the filtered terrain profile, coupled with a simple point follower tire model is used to predict the spindle force. The same vehicle dynamic simulation system coupled with constraint mode tire model is built to generate reference forces.