Optimal trajectory planning combining model-based and data-driven hybrid approaches

Trajectory planning aims at computing an optimal trajectory through the minimization of a cost function. This paper considers four different scenarios: (i) the first concerns a given trajectory on which a cost function is minimized by a acting on the velocity along it; (ii) the second considers trajectories expressed parametrically, from which an optimal path and the velocity along it are computed; (iii), the case in which only the departure and arrival points of the trajectory are known, and the optimal path must be determined; and finally, (iv) the case involving uncertainty in the environment in which the trajectory operates. When the considered cost functions are expressed analytically, the application of Euler–Lagrange equations constitutes an appealing option. However, in many applications, complex cost functions are learned by using black-box machine learning techniques, for instance deep neural networks. In such cases, a neural approach of the trajectory planning becomes an appealing alternative. Different numerical experiments will serve to illustrate the potential of the proposed methodologies on some selected use cases.