We provide a tutorial and review of the state-of-the-art in robot dynamics algorithms that rely
on methods from differential geometry, particularly the theory of Lie groups. After reviewing …

The areas of mechanics and control theory have a rich and productive history of interaction
with the broad mathematical subject of differential geometry. This article provides an …

In this paper, we investigate the task of approaching a rigid tumbling satellite (Target) with a
fully-actuated manipulator-equipped spacecraft (Servicer). We consider a Servicer with an …

We address the problem of encoding and executing skills, ie motion tasks involving a
combination of specifications regarding constraints and variability. We take an approach that …

This article is concerned with the geometric tracking control of a free-flying space robot with
predefined-time stability. To overcome the singularity and nonuniqueness issues in attitude …

The present work revolves around employing the benefits of neighboring extremal approach
in the nonlinear model predictive control of mechanical systems evolving on SE (3). In the …

The main focus of this article is the motion planning problem for a deeply submerged rigid
body. The equations of motion are formulated and presented by use of the framework of …

This text tells a story. A story written in the language of mathematics. A story of a journey,
driven by passion for engineering and programming. A journey embarked on in the pursuit …

This paper considers the problem of path following control of a planar snake robot without
sideslip constraints. We use Lagrangian mechanics to derive the dynamical equations of …

In this paper, nonlinear model predictive control of mechanical systems evolving on Lie
group SE (3) is studied. Discrete-time equations of motion referred to as LGVI are used in …