Minimization of curvature with cubic spline interpolation for optimal racing line - Chen, Chuei Yee; Kai, Zen Cheong (Universiti Putra Malaysia, 2024)
In motor sports, racing line optimization is important since different race line can result in different speed and time taken to complete a race track. In competitive motor sport events such as NASCAR cup, Formula 1 and WRC, the lap time of top racers can differ in mere milliseconds. Hence, it is important to formulate a racing strategy to achieve the best possible lap time. Optimizing the lap time requires one to minimize the curvature around the corner, and this in turn can be formulated as a variational problem. This study proposes cubic spline interpolation as a strategy to find the curvature and time taken for a race car to complete a corner at the race track, bounded by physical limits of the race car and the radius of turn of the race track. The strategy, which allows one to explore different points on the Cartesian plane, is illustrated through an example on a simple corner.