Autonomous suspended load operations via trajectory optimization and variational integrators

Advances in machine autonomy hold great promise in advancing technology, economic markets, and general societal well-being. For example, the progression of unmanned air systems (UAS) research has demonstrated the effectiveness and reliability of these autonomous systems in performing complex tasks. UAS have shown to not only outperformed human pilots in some tasks, but have also made novel applications not possible for human pilots practical. Nevertheless, human pilots are still favored when performing specific challenging tasks. For example, transportation of suspended (sometimes called slung or sling) loads requires highly skilled pilots and has only been performed by UAS in highly controlled environments. The presented work begins to bridge this autonomy gap by proposing a trajectory optimization framework for operations involving autonomous rotorcraft with suspended loads. The framework generates optimized vehicle trajectories that are used by existing guidance, navigation, and control systems and estimates the state of the non-instrumented load using a downward facing camera. Data collected from several simulation studies and a flight test demonstrates the proposed framework is able to produce effective guidance during autonomous suspended load operations. In addition, variational integrators are extensively studied in this dissertation. The derivation of a stochastic variational integrator is presented. It is shown that the presented stochastic variational integrator significantly improves the performance of the stochastic differential dynamical programming and the extended Kalman filter algorithms. A variational integrator for the propagation of polynomial chaos expansion coefficients is also presented. As a result, the expectation and variance of the trajectory of an uncertain system can be accurately predicted.Ph.D

Geometric Numerical Integration (hybrid meeting)

The topics of the workshop included interactions between geometric numerical integration and numerical partial differential equations; geometric aspects of stochastic differential equations; interaction with optimisation and machine learning; new applications of geometric integration in physics; problems of discrete geometry, integrability, and algebraic aspects

Automating the Analysis of Uncertainties in Multi-Body Dynamic Systems Using Polynomial Chaos Theory

Variation occurs in many multi-body dynamic (MBD) systems in the geometry, mass, or forces. This variation creates uncertainty in the responses of an MBD system. Understanding how MBD systems respond to the variation is imperative for the design of a robust system. However, the simulation of how variation propagates into the solution is complicated as most MBD systems cannot be simplified into to a system of ordinary differential equations (ODE). This presentation shows the automation of an uncertainty analysis of an MBD system with variation. The first step to automating the solution is to create a robust algorithm based on the Constrained Lagrangian formulation for deriving the equations of motion. Using the Constrained Lagrangian algorithm as a starting point, the new process presented uses polynomial chaos theory (PCT) to embed the stochastic parameters into the equations of motion. To accomplish this, the concept of Variational Work is derived and implemented in the solution. Variational Work applies PCT to the energy terms and Principle of Virtual Work of the Constrained Lagrangian rather than applying PCT on the equations of motion. Using an automated process for applying PCT to an MBD system, some example problems are solved. Each of these problems is compared to a Monte Carlo analysis using the deterministic automation process. Some of the examples are non-textbook based problems, which show limitations in the application of PCT to an MBD system. The limitations and the possible solutions to overcoming them are discussed

Geometric Numerical Integration

The subject of this workshop was numerical methods that preserve geometric properties of the flow of an ordinary or partial differential equation. This was complemented by the question as to how structure preservation affects the long-time behaviour of numerical methods

Applied Dynamics and Geometric Mechanics

This one week workshop was organized around several central subjects in applied dynamics and geometric mechanics. The specific organization with afternoons free for discussion led to intense exchanges of ideas. Bridges were forged between researchers representing different fields. Links were established between pure mathematical ideas and applications. The meeting was not restricted to any particular application area. One of the main goals of the meeting, like most others in this series for the past twenty years, has been to facilitate cross fertilization between various areas of mathematics, physics, and engineering. New collaborative projects emerged due to this meeting. The workshop was well attended with participants from Europe, North America, and Asia. Young researchers (doctoral students, postdocs, junior faculty) formed about 30% of the participants

Nonlinear Evolution Equations: Analysis and Numerics

The workshop was devoted to the analytical and numerical investigation of nonlinear evolution equations. The main aim was to stimulate a closer interaction between experts in analytical and numerical methods for areas such as wave and Schrödinger equations or the Navier–Stokes equations and fluid dynamics