Robust near time-optimal trajectory planning by intermediate targets assignment

Robustified time-optimal trajectories are constructed by concatenation of arcs connecting appropriately selected intermediate targets. Stochastic methods are used for the examination of the vicinity of the time-optimal trajectory to find a set of displacement points such that: (i) time T necessary to reach the final target along the concatenated trajectory is close to the original optimal control time, and (ii) global sensitivity of T with respect to state disturbances with given stochastic properties is sufficiently small. This is obtained by backward tracking admissible and inadmissible terminal states of randomly generated trajectories. Geometric properties are discussed. The method of robustification is illustrated by an example of a nonlinear fourth-order cart-pendulum system.