Determination of the optimal trajectories on race tracks with dynamic and geometric constraints

Vivian S. Medeiros¹; Ivan F. M. Menezes¹; Mauro Speranza Neto¹

¹ Pontifical Catholic University of Rio de Janeiro

doi:10.20906/CPS/COB-2015-0614

Resumo

This work proposes a new procedure to determine the optimal trajectory on race tracks based on constrained optimization techniques, where the constraints are defined by means of the dynamic characteristics of the vehicle and the geometrical limits of the track. The vehicle is represented by an oriented particle with the capabilities of traction, braking and lateral acceleration, which are typical in a competition vehicle. First, the minimum-time trajectory for a 90-degree curve is obtained through a geometrical analysis of the problem. The solution is then expanded to be applied to all angles. Starting from the individual minimum-time trajectory for each curve of the track, a constrained optimization technique is employed in order to obtain a shorter curve that concatenates these optimal trajectories. The optimization model consists in determining the coefficients of a well-known Hermite cubic polynomial curve that better concatenates the individual trajectories without violating any of the constraints. The results of the concatenation procedure are presented and the advantages and disadvantages of the proposed method are discussed.

Palavras-chave: constrained optimization; optimal trajectory; race tracks; Hermite curve