Related papers: Coordinated motion design on Lie groups
The use of double groupoids and their associated double Lie algebroids and characteristic distributions is proposed for the description and analysis of continuous media that carry two different constitutive or geometric structures. Various…
In this paper we study, from a variational and geometrical point of view, second-order variational problems on Lie groupoids and the construction of variational integrators for optimal control problems. First, we develop variational…
Many robotic systems allow independent control of position and orientation (pose), including omnidirectional aerial vehicles, underwater robots, and manipulator end-effectors. In many applications, these systems must follow a continuous…
This paper studies the reduction by symmetry of variational problems on Lie groups and Riemannian homogeneous spaces. We derive the reduced equations of motion in the case of Lie groups endowed with a left-invariant metric, and on Lie…
This letter studies a distributed collision avoidance control problem for a group of rigid bodies on a sphere. A rigid body network, consisting of multiple rigid bodies constrained to a spherical surface and an interconnection topology, is…
We develop a Lie group geometric framework for the motion of fluids with permeable boundaries that extends Arnold's geometric description of fluid in closed domains. Our setting is based on the classical Hamilton principle applied to fluid…
Let H denote the 3-dimensional Heisenberg Lie group. The present paper classify all possible linear control systems on the homogeneous spaces of H through its closed subgroups and expose a detailed study on the control behavior…
We develop a discrete-time optimal control framework for systems evolving on Lie groups. Our work generalizes the original Differential Dynamic Programming method, by employing a coordinate-free, Lie-theoretic approach for its derivation. A…
In this work, we propose a distributed hierarchical locomotion control strategy for whole-body cooperation and demonstrate the potential for migration into large numbers of agents. Our method utilizes a hierarchical structure to break down…
In this paper, we propose a whole-body planning framework that unifies dynamic locomotion and manipulation tasks by formulating a single multi-contact optimal control problem. We model the hybrid nature of a generic multi-limbed mobile…
Adaptive tracking control for rigid body dynamics is of critical importance in control and robotics, particularly for addressing uncertainties or variations in system model parameters. However, most existing adaptive control methods are…
We introduce a compactification of the group of rigid motions in 3-space derived from the Study model for this group. We use this compactifi-cation in robot kinematics, by considering the boundary of the configuration space of a robot. We…
Handling orientations of robots and objects is a crucial aspect of many applications. Yet, ever so often, there is a lack of mathematical correctness when dealing with orientations, especially in learning pipelines involving, for example,…
Recent experimental studies have shown that confinement can profoundly affect self-organization in semi-dilute active suspensions, leading to striking features such as the formation of steady and spontaneous vortices in circular domains and…
We propose a sliding surface for systems on the Lie group $SO(3)\times \mathbb{R}^3$ . The sliding surface is shown to be a Lie subgroup. The reduced-order dynamics along the sliding subgroup have an almost globally asymptotically stable…
Bilinear systems emerge in a wide variety of fields as natural models for dynamical systems ranging from robotics to quantum dots. Analyzing controllability of such systems is of fundamental and practical importance, for example, for the…
We consider the problem of feasible coordination control for multiple homogeneous or heterogeneous mobile vehicles subject to various constraints (nonholonomic motion constraints, holonomic coordination constraints, equality/inequality…
We introduce the use of hierarchical clustering for relaxed, deterministic coordination and control of multiple robots. Traditionally an unsupervised learning method, hierarchical clustering offers a formalism for identifying and…
We develop a new framework for the study of complex continuous time dynamical systems based on viewing them as collections of interacting control modules. This framework is inspired by and builds upon the groupoid formalism of Golubitsky,…
This paper addresses the path following control problem for scale-model fixed-wing aircraft. Kinematic guidance and dynamic control laws are developed within a single coherent framework that exploits a simple generic model of aerodynamics…