This paper is an introductory tutorial for numerical trajectory optimization with a focus on direct collocation methods. These methods are relatively simple to understand and effectively solve a wide variety of trajectory optimization problems. Throughout the paper we illustrate each new set of concepts by working through a sequence of four example problems. We start by using trapezoidal colloc...

In this paper, we introduce a trajectory-based nonadiabatic dynamics algorithm which aims to correct the well-known overcoherence problem in Tully's popular fewest-switches surface hopping algorithm. Our simultaneous-trajectory surface hopping algorithm propagates a separate classical trajectory on each energetically accessible adiabatic surface. The divergence of these trajectories generates d...

Phase-Doppler interferometry in which a probe volume that is much smaller than the droplets being measured has been shown to work well when coupled with a phase-ratio and intensity-validation scheme that is capable of eliminating trajectory-dependent scattering errors. With ray-tracing and geometric-optics models, the type and magnitude of trajectory errors were demonstrated quantitatively thro...

We have previously proposed a trajectory model which is based on a mixture density network (MDN) trained with target variables augmented with dynamic features together with an algorithm for estimating maximum likelihood trajectories which respects the constraints between those features. In this paper, we have extended that model to allow diagonal covariance matrices and multiple mixture compone...

Introduction: Sparse MRI [1] is able to reduce the acquisition time and raw data size by significantly undersampling the k-space. However, the issue on how to design an optimal k-space trajectory on sparse k-space is technically challenging and has not been addressed. In this work, we use graphic theory to design an optimized non-Cartesian k-trajectory which can further decrease the acquisition...

The design of movement trajectories for mobile sink plays an important role in data gathering for Wireless Sensor Networks (WSNs), as it affects the network coverage, and packet delivery ratio, as well as the network lifetime. In some scenarios, the whole network can be divided into subareas where the nodes are randomly deployed. The node densities of these subareas are quite different, which m...

A major objective of next generation reusable launch vehicle (RLV) programs includes significant improvements in vehicle safety, reliability, and operational costs. In this paper, trajectory generation on approach/landing (A&L) for RLVs using motion primitives (MPs) and neighboring optimal control (NOC) is discussed. The proposed trajectory generation approach at A&L phase is based on an MP sch...

We aim at building a joint space trajectory generation system. Connected to a xed manipulator with sensory feedback, neural networks are expected to move the end-eeector from any start to any goal connguration without colliding with obstacles. The output of our system is a series of consecutive conngurations yielding a joint-space trajectory. Sensory information serves as the only source of kno...