Trajectory optimization

Summary

Trajectory optimization is the computation of a state trajectory and an open-loop control that minimise a cost for a control system, subject to constraints. It is the numerical side of optimal control: one wants one good trajectory from a given initial state, not a feedback law for every state. Indirect methods solve the necessary conditions, as in shooting, while direct methods discretise the problem into a nonlinear program, as in direct collocation. It is used to plan rocket ascents, satellite transfers, walking robots and vehicle manoeuvres.