Related papers: Coordinated motion design on Lie groups
Robots exhibit a rich variety of symmetries arising from their mechanical structure and the properties of their tasks. Although many robotics problems exhibit several symmetries simultaneously, existing approaches typically treat them in…
A fundamental problem in traffic networks is driving under safety and limited physical space constraints. In this paper, we design longitudinal vehicle controllers and study the dynamics of a system of homogeneous vehicles on a single-lane…
We use group theoretic methods to obtain the extended Lie point symmetries of the equations of motion for a charged particle in the field of a monopole. Cases with certain model magnetic fields and potentials are also studied. Our analysis…
In this paper, two cooperative guidance laws based on two-point boundary value are designed to deal with the problem of cooperative encirclement and simultaneous attack under condition of both known target acceleration and unknown target…
We propose a geometric integrator to numerically approximate the flow of Lie systems. The key is a novel procedure that integrates the Lie system on a Lie group intrinsically associated with a Lie system on a general manifold via a Lie…
This paper discusses dynamical systems for disk-covering and sphere-packing problems. We present facility location functions from geometric optimization and characterize their differentiable properties. We design and analyze a collection of…
This paper formulates an optimal control problem for a system of rigid bodies that are connected by ball joints and immersed in an irrotational and incompressible fluid. The rigid bodies can translate and rotate in three-dimensional space,…
Some positive answers to the problem of endowing a dynamical system with a Hamiltonian formulation are presented within the class of Poisson structures in a geometric framework. We address this problem on orientable manifolds and by using…
For over fifty years, the dynamical systems perspective has had a prominent role in evolutionary biology and economics, through the lens of game theory. In particular, the study of replicator differential equations on the standard…
We propose a unified framework in which the different constructions of cohomology groups for topological and Lie groups can all be treated on equal footings. In particular, we show that the cohomology of "locally continuous" cochains…
This paper studies the problem of stabilizing a leader-follower formation specified by a set of bearing constraints and being disturbed by some unknown uniformly bounded disturbance{s}. A set of leaders are positioned at their desired…
Dynamical systems can be coupled in a manner that is designed to drive the resulting dynamics onto a specified lower dimensional submanifold in the phase space of the combined system. On the submanifold, the variables of the two systems…
In this paper, the problem of reaching formation for a network of rigid agents over a special orthogonal group is investigated by considering bearing-only constraints as the desired formation. Each agent is able to gather the measurements…
This work explores the geometrical/algebraic framework of Lie algebroids, with a specific focus on the decoupling and coupling phenomena within the bicocycle double cross product realization. The bicocycle double cross product theory serves…
Motivated by applications in intelligent highway systems, the paper studies the problem of guiding mobile agents in a one-dimensional formation to their desired relative positions. Only coarse information is used which is communicated from…
When a team of agents, such as unmanned aerial/underwater vehicles, are operating in $3$-dimensional space, their coordinated action in pursuit of a cooperative task generally requires all agents to either share a common coordinate system…
Symmetry is fundamental to understanding physical systems and can improve performance and sample efficiency in machine learning. Both pursuits require knowledge of the underlying symmetries in data, yet discovering these symmetries…
Mobile manipulators are finding use in numerous practical applications. The current issues with mobile manipulation are the large state space owing to the mobile base and the challenge of modeling high degree of freedom systems. It is…
Lie symmetry group method is applied to study the boundary-layer equations for two-dimensional steady flow of an incompressible, viscous fluid near a stagnation point at a heated stretching sheet placed in a porous medium equation. The…
This paper presents a unified approach for inverse and direct dynamics of constrained multibody systems that can serve as a basis for analysis, simulation, and control. The main advantage of the formulation of the dynamic is that it does…