This survey paper presents a holistic perspective on the state-of-the-art in the design of
guidance, navigation, and control systems for autonomous multi-rotor small unmanned …

Accurate numerical simulation of dynamical systems is essential in applications ranging
from particle physics to geophysical fluid flow to space hazard analysis. However, most …

A fundamental aspect of autonomous vehicle guidance is planning trajectories. Historically,
two fields have contributed to trajectory or motion planning methods: robotics and dynamics …

In recent years, the success of the Koopman operator in dynamical systems analysis has
also fueled the development of Koopman operator-based control frameworks. In order to …

The optimal control of a mechanical system is of crucial importance in many application
areas. Typical examples are the determination of a time-minimal path in vehicle dynamics, a …

The equations of motion of a controlled mechanical system subject to holonomic constraints
may be formulated in terms of the states and controls by applying a constrained version of …

Geometric integration is the numerical integration of a differential equation, while preserving
one or more of its' geometric'properties exactly, ie to within round-off error. Many of these …

Contact constraints arise naturally in many robot planning problems. In recent years, a
variety of contact-implicit trajectory optimization algorithms have been developed that avoid …

We present a general-purpose numerical scheme for time integration of Lagrangian
dynamical systems—an important computational tool at the core of most physics-based …

We consider the optimal control of mechanical systems on Lie groups and develop
numerical methods that exploit the structure of the state space and preserve the system …