Semi-analytical minimum time solutions for a vehicle following clothoid-based trajectory subject to velocity constraints

A possible strategy for finding the optimal path that connects two different configurations of a car-like vehicle can be addressed by solving two different sub-problems: 1. identifying a curve that connects the two points respecting the geometric constraints, 2. finding an optimal control strategy that drives the vehicle along the trajectory accounting for its dynamic constraints. In this paper, we focus on the second problem. Assuming that the vehicle moves along a specified clothoid, we find a semi-analytical solution for the optimal profile of the longitudinal acceleration (the control variable). Our technique explicitly considers non-linear dynamics, aerodynamic drag effect and bounds on the longitudinal and on the lateral acceleration.