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This paper revisits the fundamental mathematics of Taylor series toapproximate curves with function representation and arc-length-based parametricrepresentation. Parametric representation is shown to preserve its form incoordinate transformation and parameter shifting. These preservations cansignificantly facilitate lane estimation in vehicle control since lanesperceived by cameras are typically represented in vehicle body-fixed frameswhich are translating and rotating. Then we derived the transformation fromfunction representation to arc-length-based parametric representation and itsinverse. We applied the transformation to lane estimation in vehicle controlproblem, and derived the evolution of coefficients for parametricrepresentation that can be used for prediction. We come up with a procedure tosimulate the whole process with perception, lane estimation and control for thepath-following problem. Simulations are performed to demonstrate the efficacyof the proposed lane estimation algorithm using parametric representation. Theresults indicate that the proposed technique ensures that vehicle control canachieve reasonably good performance at very low perception updating rate.

Representing Lanes as Arc-length-based Parametric Curves to Facilitate Estimation in Vehicle Control