In this article, we present an optimization-based framework for multicopter trajectory planning subject to geometrical configuration constraints and user-defined dynamic constraints. The basis of the is a novel representation built upon our optimality conditions unconstrained control effort minimization. We design linear-complexity operations on conduct spatial–temporal deformation under variou...

Some traffic monitoring systems have been proposed for predicting behaviors of vehicles. However, a few attempts have been made at estimating how vehicles influence each other at some time point in the near future. In order to estimate such interactions, we introduce a concept of Attainable Region to predict future behaviors of vehicles. Attainable Region is efficient to estimate interactions b...

Nowadays, the ubiquity of various sensors enables the collection of voluminous datasets of car trajectories. Such datasets enable analysts to make sense of driving patterns and behaviors: in order to understand the behavior of drivers, one approach is to break a trajectory into its underlying patterns and then analyze that trajectory in terms of derived patterns. The process of trajectory segme...

This paper presents the time optimal trajectories for differential drive vehicles in the unobstructed plane. The wheel angular velocities are bounded, but may be discontinuous. The paper proves the existence of optimal controls, derives the structure of optimal trajectories, and develops an algorithm for producing a time optimal trajectory between any two configurations. Every nontrivial optima...

By taking the high-energy limit of the two-loop amplitudes for parton-parton scattering, we have tested the validity of the loop expansion of the high-energy amplitude, arising from a reggeized gluon passed in the crossed channel. As expected, we have found that it holds at LL and NLL accuracy, and hence we have independently re-evaluated the two-loop Regge trajectory, finding full agreement wi...