Consumption minimisation for a car-like robot: Case study for a non-flat road profile

This article presents the study of an optimal control problem having a non-smooth cost function and nonlinear constraints. This problem consist in the minimisation of the energy expended by a car-like vehicle or robot along a road having a known profile. The contraints are given by means of a simple model of the longitudinal dynamics. In this paper, we're interested in a particular road profile. The optimal trajectories are made of bang, inactivated, singular and backward arcs.