Just-in-Time Optimal Routing in the Presence of Non-Uniform and Time-Evolving Uncertainty

Trajectory planning aims to compute an optimal path and velocity of an agent through the minimization of a cost function. This paper proposes a just-in-time routing method, incorporating the stochastic minimization of a cost function, which ingests the effect of the agent’s environment evolving in space and time. The environment is considered known at present, but the uncertainty increases when advancing in time. To compute the optimal routing in such an uncertain environment, Euler–Lagrange equations will be formulated in a stochastic setting, to obtain a probabilistic optimal planning. With the cost function approximated by using a surrogate modeling based on deep neural networks, a neural formulation of the stochastic Euler–Lagrange equations is proposed and employed.